From be2b340a0a2a509f16af283c554dbf3959bbddac Mon Sep 17 00:00:00 2001
From: Ben Mackay <jbmackay@caltech.edu>
Date: Tue, 5 Oct 2021 17:00:09 -0700
Subject: [PATCH 01/12] Initial aoutline of spontaneous breakup.

---
 PySDM/dynamics/__init__.py            |   3 +-
 PySDM/dynamics/spontaneous_breakup.py | 183 ++++++++++++++++++++++++++
 2 files changed, 185 insertions(+), 1 deletion(-)
 create mode 100644 PySDM/dynamics/spontaneous_breakup.py

diff --git a/PySDM/dynamics/__init__.py b/PySDM/dynamics/__init__.py
index c4652229e0..956212e77f 100644
--- a/PySDM/dynamics/__init__.py
+++ b/PySDM/dynamics/__init__.py
@@ -9,4 +9,5 @@
 from .eulerian_advection import EulerianAdvection
 from .ambient_thermodynamics import AmbientThermodynamics
 from .aqueous_chemistry import AqueousChemistry
-from .breakup import Breakup
\ No newline at end of file
+from .breakup import Breakup
+from .spontaneous_breakup import SpontaneousBreakup
\ No newline at end of file
diff --git a/PySDM/dynamics/spontaneous_breakup.py b/PySDM/dynamics/spontaneous_breakup.py
new file mode 100644
index 0000000000..bb9cbe17ea
--- /dev/null
+++ b/PySDM/dynamics/spontaneous_breakup.py
@@ -0,0 +1,183 @@
+"""
+Created at 05.13.21 by jb-mackay
+"""
+
+import numpy as np
+from PySDM.physics import si
+from PySDM.dynamics.impl.random_generator_optimizer import RandomGeneratorOptimizer
+from PySDM.dynamics.impl.random_generator_optimizer_nopair import RandomGeneratorOptimizerNoPair
+import warnings
+
+# checks that timestep is within this range
+default_dt_coal_range = (.1 * si.second, 100 * si.second)
+
+
+class SpontaneousBreakup:
+
+    def __init__(self,
+                 breakup_rate, # rate function
+                 fragmentation, # frag function 
+                 seed=None, # rng seed
+                 croupier=None,
+                 optimized_random=False,
+                 substeps: int = 1,
+                 adaptive: bool = False,
+                 dt_coal_range=default_dt_coal_range
+                 ):
+        assert substeps == 1 or adaptive is False
+
+        self.core = None # .core is the parent for all attributes, dynamics, etc
+        self.enable = True # on/off for the dynamic
+
+        self.breakup_rate = breakup_rate
+        self.fragmentation = fragmentation
+        self.seed = seed
+
+        assert dt_coal_range[0] > 0
+        self.croupier = croupier
+        self.optimized_random = optimized_random
+        self.__substeps = substeps
+        self.adaptive = adaptive
+        self.stats_n_substep = None
+        self.stats_dt_min = None
+        self.dt_coal_range = tuple(dt_coal_range)
+
+        # temporary storage for outputs (may need add some (and remove))
+        self.n_fragment = None
+        self.breakup_rate_temp = None
+        self.norm_factor_temp = None # renormalizes the system
+        self.prob = None
+        self.dt_left = None
+
+        # simulation diagnositcs (TODO)
+       
+
+    # registering the process with the builder (initialization)
+    def register(self, builder):
+        self.core = builder.core
+
+        # outputs a random number (will need one for IF breakup? and for fragmentation number)
+        self.rnd_opt = RandomGeneratorOptimizerNoPair(optimized_random=self.optimized_random,
+                                                dt_min=self.dt_coal_range[0],
+                                                seed=self.seed) #self.core.formulae.seed+1)
+        self.rnd_opt_frag = RandomGeneratorOptimizerNoPair(optimized_random=self.optimized_random,
+                                                dt_min=self.dt_coal_range[0],
+                                                seed=self.seed) #self.core.formulae.seed+1)
+        
+        self.optimised_random = None
+
+        if self.dt_coal_range[1] > self.core.dt:
+            self.dt_coal_range = (self.dt_coal_range[0], self.core.dt)
+        assert self.dt_coal_range[0] <= self.dt_coal_range[1]
+
+        # init temporary storage; swap to Storage (see Condensation)
+        self.n_fragment = self.core.Storage.empty(self.core.n_sd, dtype=int)
+        self.breakup_rate_temp = self.core.Storage.empty(self.core.n_sd, dtype=float)
+        self.norm_factor_temp = self.core.Storage.empty(self.core.mesh.n_cell, dtype=float)
+        self.prob = self.core.Storage.empty(self.core.n_sd, dtype=float) # does the event happen?
+        self.dt_left = self.core.Storage.empty(self.core.mesh.n_cell, dtype=float)
+
+        self.stats_n_substep = self.core.Storage.empty(self.core.mesh.n_cell, dtype=int)
+        self.stats_n_substep[:] = 0 if self.adaptive else self.__substeps
+        self.stats_dt_min = self.core.Storage.empty(self.core.mesh.n_cell, dtype=float)
+        self.stats_dt_min[:] = np.nan
+
+        # registering helper processes
+        self.rnd_opt.register(builder)
+        self.rnd_opt_frag.register(builder)
+        self.breakup_rate.register(builder)
+        self.fragmentation.register(builder)
+
+        if self.croupier is None:
+            self.croupier = self.core.backend.default_croupier
+        
+        # Diagnostics
+        # self.collision_rate = self.core.Storage.from_ndarray(np.zeros(self.core.mesh.n_cell, dtype=int))
+        # self.collision_rate_deficit = self.core.Storage.from_ndarray(np.zeros(self.core.mesh.n_cell, dtype=int))
+
+    def __call__(self):
+        if self.enable:
+            if not self.adaptive:
+                for _ in range(self.__substeps):
+                    self.step()
+            else:
+                self.dt_left[:] = self.core.dt
+
+                # work on all particles
+                while self.core.particles.get_working_length() != 0:
+                    self.core.particles.cell_idx.sort_by_key(self.dt_left)
+                    self.step() # do breakup
+
+                self.core.particles.reset_working_length()
+                self.core.particles.reset_cell_idx()
+            self.rnd_opt.reset()
+            self.rnd_opt_frag.reset()
+
+    def step(self):
+        # (1) Make the superdroplet list and random numbers for fragmentation
+        rand = self.rnd_opt.get_random_arrays() # does event occur
+        rand_frag = self.rnd_opt_frag.get_random_arrays() # for # fragments
+        
+        # (3a) Compute the probability of spontaneous breakup
+        self.compute_probability(self.prob, self.is_first_in_pair)
+        
+        # (3b) Compute the number of fragments
+        self.compute_n_fragment(self.n_fragment, rand_frag, self.is_first_in_pair)
+        
+        # (4) Compute gamma...
+        self.compute_gamma(self.prob, rand, self.is_first_in_pair)
+        
+        # (5) Perform the collisional-breakup step: 
+        self.core.particles.breakup(gamma=self.prob, n_fragment=self.n_fragment, is_first_in_pair=self.is_first_in_pair)
+        
+        if self.adaptive:
+            self.core.particles.cut_working_length(self.core.particles.adaptive_sdm_end(self.dt_left))
+
+    # (3) TODO: Does spont breakup occur?
+    def compute_probability(self, prob, is_first_in_pair):
+        self.kernel(self.kernel_temp, is_first_in_pair) # args: 1: where to put output (hint: temp storage), other args
+        self.coal_eff(self.coal_eff_temp, is_first_in_pair)
+        self.coal_eff_temp *= self.neg_ones
+        self.coal_eff_temp -= self.neg_ones
+        # P_jk = max(xi_j, xi_k)*P_jk*E_c
+        prob.max(self.core.particles['n'], is_first_in_pair)
+        prob *= self.kernel_temp
+        prob *= self.coal_eff_temp
+
+        self.core.normalize(prob, self.norm_factor_temp)
+        
+    # (4a) Compute n_fragment
+    def compute_n_fragment(self, n_fragment, u01, is_first_in_pair):
+        self.fragmentation(n_fragment, u01, is_first_in_pair)
+
+    # (4) Compute gamma, i.e. whether the collision leads to breakup
+    def compute_gamma(self, prob, rand, is_first_in_pair):
+        if self.adaptive:
+            self.core.backend.adaptive_sdm_gamma(
+                prob,
+                self.core.particles['n'],
+                self.core.particles["cell id"],
+                self.dt_left,
+                self.core.dt,
+                self.dt_coal_range,
+                is_first_in_pair,
+                self.stats_n_substep,
+                self.stats_dt_min
+            )
+            if self.stats_dt_min.amin() == self.dt_coal_range[0]:
+                warnings.warn("breakup adaptive time-step reached dt_min")
+        else:
+            prob /= self.__substeps
+            
+        # src is ../backends/numba/impl/_algorithmic_methods.py, line 149
+        self.core.backend.compute_gamma(
+            prob,
+            rand,
+            self.core.particles['n'],
+            self.core.particles["cell id"],
+            self.collision_rate_deficit,
+            self.collision_rate,
+            is_first_in_pair
+        )
+        
+

From 9358d47c1235c93c32bd188ab74b95a369155feb Mon Sep 17 00:00:00 2001
From: Ben Mackay <jbmackay@caltech.edu>
Date: Wed, 6 Oct 2021 18:15:08 -0700
Subject: [PATCH 02/12] Add spontaneous breakup mechanism

---
 .../numba/impl/_algorithmic_methods.py        | 22 ++++++
 PySDM/dynamics/spontaneous_breakup.py         | 78 ++++++-------------
 PySDM/state/particles.py                      | 17 ++++
 3 files changed, 62 insertions(+), 55 deletions(-)

diff --git a/PySDM/backends/numba/impl/_algorithmic_methods.py b/PySDM/backends/numba/impl/_algorithmic_methods.py
index f6cbdf583f..98f86faf0e 100644
--- a/PySDM/backends/numba/impl/_algorithmic_methods.py
+++ b/PySDM/backends/numba/impl/_algorithmic_methods.py
@@ -173,6 +173,28 @@ def breakup(n, idx, length, attributes, gamma, n_fragment, healthy, is_first_in_
                                             attributes.data, gamma.data, n_fragment.data, healthy.data,
                                             is_first_in_pair.indicator.data)
         
+    ## TODO: Ben implement spontaneous breakup
+    @staticmethod
+    @numba.njit(**conf.JIT_FLAGS)
+    def spontaneous_breakup_body(n, idx, length, attributes, gamma, n_fragment, healthy):
+        for i in numba.prange(length):
+            # no spontaneous breakup occurs
+            if gamma[i] == 0:
+                continue
+            # breakup does occur
+            if n_fragment > 0:
+                n[i] = n[i] * int(n_fragment[i])
+                # what is this?
+                # for a in range(0, len(attributes)):
+                #     attributes[a, k] += gamma[i] * attributes[a, j]
+                #     attributes[a, k] /= n_fragment[i]
+
+    @staticmethod
+    def spontaneous_breakup(n, idx, length, attributes, gamma, n_fragment, healthy):
+        AlgorithmicMethods.breakup_body(n.data, idx.data, length,
+                                            attributes.data, gamma.data, n_fragment.data, healthy.data,
+                                            )
+    
     # Emily: SLAMS fragmentation function
     @numba.njit(**{**conf.JIT_FLAGS})
     def slams_fragmentation_body(n_fragment, probs, rand):
diff --git a/PySDM/dynamics/spontaneous_breakup.py b/PySDM/dynamics/spontaneous_breakup.py
index bb9cbe17ea..3fad693ab3 100644
--- a/PySDM/dynamics/spontaneous_breakup.py
+++ b/PySDM/dynamics/spontaneous_breakup.py
@@ -1,5 +1,5 @@
 """
-Created at 05.13.21 by jb-mackay
+Created at 10.05.21 by jb-mackay
 """
 
 import numpy as np
@@ -11,13 +11,13 @@
 # checks that timestep is within this range
 default_dt_coal_range = (.1 * si.second, 100 * si.second)
 
-
+# TODO: define some a rate function
 class SpontaneousBreakup:
 
     def __init__(self,
                  breakup_rate, # rate function
                  fragmentation, # frag function 
-                 seed=None, # rng seed
+                 seed=None,
                  croupier=None,
                  optimized_random=False,
                  substeps: int = 1,
@@ -118,66 +118,34 @@ def step(self):
         rand = self.rnd_opt.get_random_arrays() # does event occur
         rand_frag = self.rnd_opt_frag.get_random_arrays() # for # fragments
         
-        # (3a) Compute the probability of spontaneous breakup
-        self.compute_probability(self.prob, self.is_first_in_pair)
-        
-        # (3b) Compute the number of fragments
-        self.compute_n_fragment(self.n_fragment, rand_frag, self.is_first_in_pair)
+        # (2) Compute the probability of spontaneous breakup
+        self.compute_probability(self.prob)
         
-        # (4) Compute gamma...
-        self.compute_gamma(self.prob, rand, self.is_first_in_pair)
+        # (3) Compute the number of fragments
+        self.compute_n_fragment(self.n_fragment, rand_frag)
+
+        # (4) Compute gamma
+        self.compute_gamma(self.prob, rand)
         
         # (5) Perform the collisional-breakup step: 
-        self.core.particles.breakup(gamma=self.prob, n_fragment=self.n_fragment, is_first_in_pair=self.is_first_in_pair)
+        self.core.particles.spontaneous_breakup(gamma=self.prob, n_fragment=self.n_fragment)
         
         if self.adaptive:
             self.core.particles.cut_working_length(self.core.particles.adaptive_sdm_end(self.dt_left))
 
-    # (3) TODO: Does spont breakup occur?
-    def compute_probability(self, prob, is_first_in_pair):
-        self.kernel(self.kernel_temp, is_first_in_pair) # args: 1: where to put output (hint: temp storage), other args
-        self.coal_eff(self.coal_eff_temp, is_first_in_pair)
-        self.coal_eff_temp *= self.neg_ones
-        self.coal_eff_temp -= self.neg_ones
-        # P_jk = max(xi_j, xi_k)*P_jk*E_c
-        prob.max(self.core.particles['n'], is_first_in_pair)
-        prob *= self.kernel_temp
-        prob *= self.coal_eff_temp
+    # (2) TODO: Does spont breakup occur?
+    def compute_probability(self, prob):
+        self.breakup_rate(self.breakup_rate_temp)
+        # P_j = xi_j*P_j
+        prob = self.core.particles['n']
+        prob *= self.breakup_rate_temp
 
         self.core.normalize(prob, self.norm_factor_temp)
         
-    # (4a) Compute n_fragment
-    def compute_n_fragment(self, n_fragment, u01, is_first_in_pair):
-        self.fragmentation(n_fragment, u01, is_first_in_pair)
-
-    # (4) Compute gamma, i.e. whether the collision leads to breakup
-    def compute_gamma(self, prob, rand, is_first_in_pair):
-        if self.adaptive:
-            self.core.backend.adaptive_sdm_gamma(
-                prob,
-                self.core.particles['n'],
-                self.core.particles["cell id"],
-                self.dt_left,
-                self.core.dt,
-                self.dt_coal_range,
-                is_first_in_pair,
-                self.stats_n_substep,
-                self.stats_dt_min
-            )
-            if self.stats_dt_min.amin() == self.dt_coal_range[0]:
-                warnings.warn("breakup adaptive time-step reached dt_min")
-        else:
-            prob /= self.__substeps
-            
-        # src is ../backends/numba/impl/_algorithmic_methods.py, line 149
-        self.core.backend.compute_gamma(
-            prob,
-            rand,
-            self.core.particles['n'],
-            self.core.particles["cell id"],
-            self.collision_rate_deficit,
-            self.collision_rate,
-            is_first_in_pair
-        )
-        
+    # (3) Compute n_fragment
+    def compute_n_fragment(self, n_fragment, u01):
+        self.fragmentation(n_fragment, u01)
 
+# Compute gamma, i.e. whether the collision leads to breakup
+def compute_gamma(self, prob, rand):
+    
\ No newline at end of file
diff --git a/PySDM/state/particles.py b/PySDM/state/particles.py
index 911c054889..f3a3d2f96e 100644
--- a/PySDM/state/particles.py
+++ b/PySDM/state/particles.py
@@ -164,6 +164,23 @@ def breakup(self, gamma, n_fragment, is_first_in_pair):
             if isinstance(attr, ExtensiveAttribute):
                 attr.mark_updated()
 
+    ## TODO Ben: def spontaneous_breakup(self, gamma=prob, n_fragment) gamma = prob of breakup occuring
+    def spontaneous_breakup(self, gamma, n_fragment, is_first_in_pair):
+        self.core.bck.spontaneous_breakup(n=self['n'],
+                              idx=self.__idx,
+                              length=self.SD_num,
+                              attributes=self.get_extensive_attrs(),
+                              gamma=gamma,
+                              n_fragment=n_fragment,
+                              healthy=self.__healthy_memory,
+                             )
+        self.healthy = bool(self.__healthy_memory)
+        self.core.particles.sanitize()
+        self.attributes['n'].mark_updated()
+        for attr in self.attributes.values():
+            if isinstance(attr, ExtensiveAttribute):
+                attr.mark_updated()
+
     def adaptive_sdm_end(self, dt_left):
         return self.core.bck.adaptive_sdm_end(dt_left, self.core.particles.cell_start)
 

From e961da720dae0b0f755e1291a8648c1f6310f0c8 Mon Sep 17 00:00:00 2001
From: Ben Mackay <jbmackay@caltech.edu>
Date: Thu, 7 Oct 2021 11:09:16 -0700
Subject: [PATCH 03/12] Add spontaneous breakup functions to physics

---
 PySDM/physics/__init__.py                     |  1 +
 .../__init__.py                               |  1 +
 .../always_n.py                               | 23 +++++++++++++++++++
 3 files changed, 25 insertions(+)
 create mode 100644 PySDM/physics/spontaneous_breakup_fragmentations/__init__.py
 create mode 100644 PySDM/physics/spontaneous_breakup_fragmentations/always_n.py

diff --git a/PySDM/physics/__init__.py b/PySDM/physics/__init__.py
index 078bd7eccb..61143b1f31 100644
--- a/PySDM/physics/__init__.py
+++ b/PySDM/physics/__init__.py
@@ -18,3 +18,4 @@
 import PySDM.physics.hydrostatics
 import PySDM.physics.breakup_fragmentations
 import PySDM.physics.coalescence_efficiencies
+import PySDM.physics.spontaneous_breakup_fragmentations
diff --git a/PySDM/physics/spontaneous_breakup_fragmentations/__init__.py b/PySDM/physics/spontaneous_breakup_fragmentations/__init__.py
new file mode 100644
index 0000000000..ded13056cc
--- /dev/null
+++ b/PySDM/physics/spontaneous_breakup_fragmentations/__init__.py
@@ -0,0 +1 @@
+from .always_n import SpontaneousAlwaysN
\ No newline at end of file
diff --git a/PySDM/physics/spontaneous_breakup_fragmentations/always_n.py b/PySDM/physics/spontaneous_breakup_fragmentations/always_n.py
new file mode 100644
index 0000000000..0bd0bab8d9
--- /dev/null
+++ b/PySDM/physics/spontaneous_breakup_fragmentations/always_n.py
@@ -0,0 +1,23 @@
+import numpy as np
+
+
+class SpontaneousAlwaysN:
+
+    def __init__(self, n):
+        self.core = None
+        self.N = n
+        self.N_vec = None
+        self.zeros = None
+        
+
+    def __call__(self, output):
+        output *= self.zeros
+        output += self.N_vec
+        
+    def register(self, builder):
+        self.core = builder.core
+        N_vec_tmp = np.tile([self.N], self.core.n_sd)
+        zeros_tmp = np.tile([0], self.core.n_sd)
+        self.N_vec = self.core.PairwiseStorage.from_ndarray(N_vec_tmp)
+        self.zeros = self.core.PairwiseStorage.from_ndarray(zeros_tmp)
+        
\ No newline at end of file

From e4b04047ee30db4aa6a6b0deb12b65f77cca7869 Mon Sep 17 00:00:00 2001
From: Ben Mackay <jbmackay@caltech.edu>
Date: Thu, 7 Oct 2021 14:05:45 -0700
Subject: [PATCH 04/12] Add spont breakup rates to physics.

---
 PySDM/physics/__init__.py                           |  1 +
 PySDM/physics/spontaneous_breakup_rates/__init__.py |  1 +
 PySDM/physics/spontaneous_breakup_rates/constant.py | 12 ++++++++++++
 3 files changed, 14 insertions(+)
 create mode 100644 PySDM/physics/spontaneous_breakup_rates/__init__.py
 create mode 100644 PySDM/physics/spontaneous_breakup_rates/constant.py

diff --git a/PySDM/physics/__init__.py b/PySDM/physics/__init__.py
index 61143b1f31..69b351cb97 100644
--- a/PySDM/physics/__init__.py
+++ b/PySDM/physics/__init__.py
@@ -19,3 +19,4 @@
 import PySDM.physics.breakup_fragmentations
 import PySDM.physics.coalescence_efficiencies
 import PySDM.physics.spontaneous_breakup_fragmentations
+import PySDM.physics.spontaneous_breakup_rates
\ No newline at end of file
diff --git a/PySDM/physics/spontaneous_breakup_rates/__init__.py b/PySDM/physics/spontaneous_breakup_rates/__init__.py
new file mode 100644
index 0000000000..3553d38e34
--- /dev/null
+++ b/PySDM/physics/spontaneous_breakup_rates/__init__.py
@@ -0,0 +1 @@
+from .constant import Constant
\ No newline at end of file
diff --git a/PySDM/physics/spontaneous_breakup_rates/constant.py b/PySDM/physics/spontaneous_breakup_rates/constant.py
new file mode 100644
index 0000000000..20b4be3ea4
--- /dev/null
+++ b/PySDM/physics/spontaneous_breakup_rates/constant.py
@@ -0,0 +1,12 @@
+class Constant:
+
+    def __init__(self, a):
+        self.a = a
+        self.core = None
+
+    def __call__(self, output):
+        output *= 0
+        output += self.a
+
+    def register(self, builder):
+        self.core = builder.core
\ No newline at end of file

From 0dba5540233effa4ebab9adcd79a1dff10cc46aa Mon Sep 17 00:00:00 2001
From: Ben Mackay <jbmackay@caltech.edu>
Date: Thu, 7 Oct 2021 14:06:21 -0700
Subject: [PATCH 05/12] Create compuute_gamma stub.

---
 PySDM/dynamics/spontaneous_breakup.py | 7 ++++---
 1 file changed, 4 insertions(+), 3 deletions(-)

diff --git a/PySDM/dynamics/spontaneous_breakup.py b/PySDM/dynamics/spontaneous_breakup.py
index 3fad693ab3..4f68854956 100644
--- a/PySDM/dynamics/spontaneous_breakup.py
+++ b/PySDM/dynamics/spontaneous_breakup.py
@@ -146,6 +146,7 @@ def compute_probability(self, prob):
     def compute_n_fragment(self, n_fragment, u01):
         self.fragmentation(n_fragment, u01)
 
-# Compute gamma, i.e. whether the collision leads to breakup
-def compute_gamma(self, prob, rand):
-    
\ No newline at end of file
+    # Compute gamma, i.e. whether the collision leads to breakup
+    # TODO: move to backend?
+    def compute_gamma(self, prob, rand):
+        return
\ No newline at end of file

From b1cce540a91ab3680bb3113a4c6aea6292099027 Mon Sep 17 00:00:00 2001
From: Ben Mackay <jbmackay@caltech.edu>
Date: Thu, 7 Oct 2021 14:06:50 -0700
Subject: [PATCH 06/12] Add broken spontaneous breakup test.

---
 .../spontaneous_breakup_test.ipynb            | 197 ++++++++++++++++++
 1 file changed, 197 insertions(+)
 create mode 100644 PySDM_tests/breakup_tests/spontaneous_breakup_test.ipynb

diff --git a/PySDM_tests/breakup_tests/spontaneous_breakup_test.ipynb b/PySDM_tests/breakup_tests/spontaneous_breakup_test.ipynb
new file mode 100644
index 0000000000..e7180d650e
--- /dev/null
+++ b/PySDM_tests/breakup_tests/spontaneous_breakup_test.ipynb
@@ -0,0 +1,197 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "source": [
+    "import sys\n",
+    "import numpy as np\n",
+    "\n",
+    "from PySDM.backends import CPU, GPU\n",
+    "from PySDM.builder import Builder\n",
+    "from PySDM.environments import Box\n",
+    "from PySDM.dynamics import Coalescence\n",
+    "from PySDM.dynamics import SpontaneousBreakup\n",
+    "from PySDM.initialisation.spectral_sampling import ConstantMultiplicity\n",
+    "\n",
+    "from PySDM.products.state import ParticlesVolumeSpectrum, ParticlesConcentration, ParticleMeanRadius\n",
+    "from PySDM.products.stats.timers import WallTime\n",
+    "\n",
+    "from matplotlib import pyplot"
+   ],
+   "outputs": [],
+   "metadata": {}
+  },
+  {
+   "cell_type": "markdown",
+   "source": [
+    "## AlwaysN fragments, Golovin kernel"
+   ],
+   "metadata": {}
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "source": [
+    "from PySDM.initialisation.spectra import Exponential\n",
+    "from PySDM.physics.spontaneous_breakup_rates import Constant\n",
+    "from PySDM.physics.spontaneous_breakup_fragmentations import SpontaneousAlwaysN\n",
+    "from PySDM.physics.constants import si\n",
+    "from PySDM.physics.formulae import Formulae\n",
+    "#from pystrict import strict\n",
+    "\n",
+    "#@strict\n",
+    "class Settings:\n",
+    "\n",
+    "    def __init__(self):\n",
+    "        self.formulae = Formulae()\n",
+    "        self.n_sd = 2**10\n",
+    "        self.n_part = 100 / si.cm**3\n",
+    "        self.X0 = self.formulae.trivia.volume(radius=30.531 * si.micrometres)\n",
+    "        self.dv = 1 * si.m**3\n",
+    "        self.norm_factor = self.n_part * self.dv\n",
+    "        self.rho = 1000 * si.kilogram / si.metre**3\n",
+    "        self.dt = 1 * si.seconds\n",
+    "        self.adaptive = False\n",
+    "        self.seed = 44\n",
+    "        self._steps = [0, 100, 200]\n",
+    "        self.breakup_rate = Constant(100. / si.second)\n",
+    "        self.fragmentation = SpontaneousAlwaysN(n=3)\n",
+    "        self.spectrum = Exponential(norm_factor=self.norm_factor, scale=self.X0)\n",
+    "        self.radius_bins_edges = np.logspace(np.log10(10 * si.um), np.log10(100 * si.um), num=128, endpoint=True)\n",
+    "        self.radius_range = [0 * si.um, 1e6 * si.um]\n",
+    "\n",
+    "    @property\n",
+    "    def output_steps(self):\n",
+    "        return [int(step/self.dt) for step in self._steps]"
+   ],
+   "outputs": [],
+   "metadata": {}
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "source": [
+    "settings = Settings()\n",
+    "backend = CPU\n",
+    "\n",
+    "builder = Builder(n_sd=settings.n_sd, backend=backend, formulae=settings.formulae)\n",
+    "builder.set_environment(Box(dv=settings.dv, dt=settings.dt))\n",
+    "attributes = {}\n",
+    "attributes['volume'], attributes['n'] = ConstantMultiplicity(settings.spectrum).sample(settings.n_sd)\n",
+    "breakup = SpontaneousBreakup(settings.breakup_rate, settings.fragmentation, adaptive=settings.adaptive)\n",
+    "builder.add_dynamic(breakup)\n"
+   ],
+   "outputs": [],
+   "metadata": {}
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "source": [
+    "#coalescence = Coalescence(settings.kernel, settings.coal_eff adaptive=settings.adaptive)\n",
+    "#builder.add_dynamic(coalescence)\n",
+    "products = [ParticlesVolumeSpectrum(), WallTime(), ParticleMeanRadius(), ParticlesConcentration(radius_range = settings.radius_range)]\n",
+    "core = builder.build(attributes, products)\n",
+    "\n",
+    "for step in settings.output_steps:\n",
+    "    print(step, flush=True)\n",
+    "    core.run(step - core.n_steps)\n",
+    "    pyplot.step(x=settings.radius_bins_edges[:-1] / si.micrometres, \n",
+    "                y=core.products['dv/dlnr'].get(settings.radius_bins_edges) * settings.rho,\n",
+    "                where='post', label=\"t = {step*settings.dt}s\")\n",
+    "    print(core.products['radius_m1'].get(), core.products['n_a_cm3'].get())\n",
+    "    \n",
+    "pyplot.xscale(\"log\")\n",
+    "pyplot.xlabel(\"radius (um)\")\n",
+    "pyplot.ylabel(\"dm/dlnr\")\n",
+    "pyplot.legend()"
+   ],
+   "outputs": [
+    {
+     "output_type": "stream",
+     "name": "stdout",
+     "text": [
+      "0\n"
+     ]
+    },
+    {
+     "output_type": "stream",
+     "name": "stderr",
+     "text": [
+      "OMP: Info #271: omp_set_nested routine deprecated, please use omp_set_max_active_levels instead.\n"
+     ]
+    },
+    {
+     "output_type": "stream",
+     "name": "stdout",
+     "text": [
+      "[27.26283229] [99.997696]\n",
+      "100\n",
+      "<PySDM.storages.indexed_storage.make_IndexedStorage.<locals>.IndexedStorage object at 0x7f96aaf8fdc0>\n",
+      "<PySDM.backends.numba.storage.Storage object at 0x7f96989d0130>\n"
+     ]
+    },
+    {
+     "output_type": "error",
+     "ename": "TypeError",
+     "evalue": "Use *=",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
+      "\u001b[0;32m/var/folders/zf/r2fhb0614kd1820s6vy114fh0000gn/T/ipykernel_52894/2050934313.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      6\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mstep\u001b[0m \u001b[0;32min\u001b[0m \u001b[0msettings\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0moutput_steps\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      7\u001b[0m     \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstep\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mflush\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 8\u001b[0;31m     \u001b[0mcore\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstep\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mcore\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mn_steps\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      9\u001b[0m     pyplot.step(x=settings.radius_bins_edges[:-1] / si.micrometres, \n\u001b[1;32m     10\u001b[0m                 \u001b[0my\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mcore\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mproducts\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'dv/dlnr'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msettings\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mradius_bins_edges\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0msettings\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrho\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m~/opt/anaconda3/envs/pysdm/lib/python3.8/site-packages/PySDM-0.1.dev1908+ge961da7.d20211007-py3.8.egg/PySDM/core.py\u001b[0m in \u001b[0;36mrun\u001b[0;34m(self, steps)\u001b[0m\n\u001b[1;32m    116\u001b[0m             \u001b[0;32mfor\u001b[0m \u001b[0mkey\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdynamic\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdynamics\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mitems\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    117\u001b[0m                 \u001b[0;32mwith\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtimers\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 118\u001b[0;31m                     \u001b[0mdynamic\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    119\u001b[0m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mn_steps\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    120\u001b[0m             \u001b[0mreversed_order_so_that_environment_is_last\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mreversed\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mobservers\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m~/opt/anaconda3/envs/pysdm/lib/python3.8/site-packages/PySDM-0.1.dev1908+ge961da7.d20211007-py3.8.egg/PySDM/dynamics/spontaneous_breakup.py\u001b[0m in \u001b[0;36m__call__\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    100\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madaptive\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    101\u001b[0m                 \u001b[0;32mfor\u001b[0m \u001b[0m_\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__substeps\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 102\u001b[0;31m                     \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstep\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    103\u001b[0m             \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    104\u001b[0m                 \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdt_left\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcore\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdt\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m~/opt/anaconda3/envs/pysdm/lib/python3.8/site-packages/PySDM-0.1.dev1908+ge961da7.d20211007-py3.8.egg/PySDM/dynamics/spontaneous_breakup.py\u001b[0m in \u001b[0;36mstep\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    120\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    121\u001b[0m         \u001b[0;31m# (2) Compute the probability of spontaneous breakup\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 122\u001b[0;31m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcompute_probability\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mprob\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    123\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    124\u001b[0m         \u001b[0;31m# (3) Compute the number of fragments\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m~/opt/anaconda3/envs/pysdm/lib/python3.8/site-packages/PySDM-0.1.dev1908+ge961da7.d20211007-py3.8.egg/PySDM/dynamics/spontaneous_breakup.py\u001b[0m in \u001b[0;36mcompute_probability\u001b[0;34m(self, prob)\u001b[0m\n\u001b[1;32m    141\u001b[0m         \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mprob\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    142\u001b[0m         \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbreakup_rate_temp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 143\u001b[0;31m         \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mprob\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbreakup_rate_temp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    144\u001b[0m         \u001b[0mprob\u001b[0m \u001b[0;34m*=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbreakup_rate_temp\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    145\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m~/opt/anaconda3/envs/pysdm/lib/python3.8/site-packages/PySDM-0.1.dev1908+ge961da7.d20211007-py3.8.egg/PySDM/backends/numba/storage.py\u001b[0m in \u001b[0;36m__mul__\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m     65\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     66\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0m__mul__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 67\u001b[0;31m         \u001b[0;32mraise\u001b[0m \u001b[0mTypeError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Use *=\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     68\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     69\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0m__imul__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;31mTypeError\u001b[0m: Use *="
+     ]
+    },
+    {
+     "output_type": "display_data",
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     }
+    }
+   ],
+   "metadata": {}
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "source": [],
+   "outputs": [],
+   "metadata": {}
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "name": "python3",
+   "display_name": "Python 3.8.11 64-bit ('pysdm': conda)"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.8.11"
+  },
+  "interpreter": {
+   "hash": "edf7e9822b7c1e609a65d73347baf735d21a74e379f9d1f2c2648473c494d495"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
\ No newline at end of file

From 286b50d6a680e7b9989d680e906ad84c34eb9d25 Mon Sep 17 00:00:00 2001
From: Ben Mackay <jbmackay@caltech.edu>
Date: Thu, 7 Oct 2021 18:02:45 -0700
Subject: [PATCH 07/12] Debugging with edejong

---
 .../numba/impl/_algorithmic_methods.py        |  2 +-
 PySDM/dynamics/spontaneous_breakup.py         |  2 +-
 .../always_n.py                               |  2 +-
 PySDM/state/particles.py                      |  2 +-
 .../spontaneous_breakup_test.ipynb            | 36 ++++++++++---------
 5 files changed, 23 insertions(+), 21 deletions(-)

diff --git a/PySDM/backends/numba/impl/_algorithmic_methods.py b/PySDM/backends/numba/impl/_algorithmic_methods.py
index 98f86faf0e..c63a4f54a3 100644
--- a/PySDM/backends/numba/impl/_algorithmic_methods.py
+++ b/PySDM/backends/numba/impl/_algorithmic_methods.py
@@ -191,7 +191,7 @@ def spontaneous_breakup_body(n, idx, length, attributes, gamma, n_fragment, heal
 
     @staticmethod
     def spontaneous_breakup(n, idx, length, attributes, gamma, n_fragment, healthy):
-        AlgorithmicMethods.breakup_body(n.data, idx.data, length,
+        AlgorithmicMethods.spontaneous_breakup_body(n.data, idx.data, length,
                                             attributes.data, gamma.data, n_fragment.data, healthy.data,
                                             )
     
diff --git a/PySDM/dynamics/spontaneous_breakup.py b/PySDM/dynamics/spontaneous_breakup.py
index 4f68854956..dbd5b47ce0 100644
--- a/PySDM/dynamics/spontaneous_breakup.py
+++ b/PySDM/dynamics/spontaneous_breakup.py
@@ -137,7 +137,7 @@ def step(self):
     def compute_probability(self, prob):
         self.breakup_rate(self.breakup_rate_temp)
         # P_j = xi_j*P_j
-        prob = self.core.particles['n']
+        prob[:] = self.core.particles['n'] # in other version, not using prob =; 
         prob *= self.breakup_rate_temp
 
         self.core.normalize(prob, self.norm_factor_temp)
diff --git a/PySDM/physics/spontaneous_breakup_fragmentations/always_n.py b/PySDM/physics/spontaneous_breakup_fragmentations/always_n.py
index 0bd0bab8d9..a024c11a89 100644
--- a/PySDM/physics/spontaneous_breakup_fragmentations/always_n.py
+++ b/PySDM/physics/spontaneous_breakup_fragmentations/always_n.py
@@ -10,7 +10,7 @@ def __init__(self, n):
         self.zeros = None
         
 
-    def __call__(self, output):
+    def __call__(self, output, u01):
         output *= self.zeros
         output += self.N_vec
         
diff --git a/PySDM/state/particles.py b/PySDM/state/particles.py
index f3a3d2f96e..0dbc48ca10 100644
--- a/PySDM/state/particles.py
+++ b/PySDM/state/particles.py
@@ -165,7 +165,7 @@ def breakup(self, gamma, n_fragment, is_first_in_pair):
                 attr.mark_updated()
 
     ## TODO Ben: def spontaneous_breakup(self, gamma=prob, n_fragment) gamma = prob of breakup occuring
-    def spontaneous_breakup(self, gamma, n_fragment, is_first_in_pair):
+    def spontaneous_breakup(self, gamma, n_fragment):
         self.core.bck.spontaneous_breakup(n=self['n'],
                               idx=self.__idx,
                               length=self.SD_num,
diff --git a/PySDM_tests/breakup_tests/spontaneous_breakup_test.ipynb b/PySDM_tests/breakup_tests/spontaneous_breakup_test.ipynb
index e7180d650e..372273bc59 100644
--- a/PySDM_tests/breakup_tests/spontaneous_breakup_test.ipynb
+++ b/PySDM_tests/breakup_tests/spontaneous_breakup_test.ipynb
@@ -45,7 +45,7 @@
     "\n",
     "    def __init__(self):\n",
     "        self.formulae = Formulae()\n",
-    "        self.n_sd = 2**10\n",
+    "        self.n_sd = 3\n",
     "        self.n_part = 100 / si.cm**3\n",
     "        self.X0 = self.formulae.trivia.volume(radius=30.531 * si.micrometres)\n",
     "        self.dv = 1 * si.m**3\n",
@@ -55,7 +55,7 @@
     "        self.adaptive = False\n",
     "        self.seed = 44\n",
     "        self._steps = [0, 100, 200]\n",
-    "        self.breakup_rate = Constant(100. / si.second)\n",
+    "        self.breakup_rate = Constant(100 / si.second)\n",
     "        self.fragmentation = SpontaneousAlwaysN(n=3)\n",
     "        self.spectrum = Exponential(norm_factor=self.norm_factor, scale=self.X0)\n",
     "        self.radius_bins_edges = np.logspace(np.log10(10 * si.um), np.log10(100 * si.um), num=128, endpoint=True)\n",
@@ -126,32 +126,34 @@
      "output_type": "stream",
      "name": "stdout",
      "text": [
-      "[27.26283229] [99.997696]\n",
-      "100\n",
-      "<PySDM.storages.indexed_storage.make_IndexedStorage.<locals>.IndexedStorage object at 0x7f96aaf8fdc0>\n",
-      "<PySDM.backends.numba.storage.Storage object at 0x7f96989d0130>\n"
+      "[27.13815313] [99.998001]\n",
+      "100\n"
      ]
     },
     {
      "output_type": "error",
-     "ename": "TypeError",
-     "evalue": "Use *=",
+     "ename": "SystemError",
+     "evalue": "CPUDispatcher(<function AlgorithmicMethods.spontaneous_breakup_body at 0x7fb169ada790>) returned a result with an error set",
      "traceback": [
       "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
-      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
-      "\u001b[0;32m/var/folders/zf/r2fhb0614kd1820s6vy114fh0000gn/T/ipykernel_52894/2050934313.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      6\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mstep\u001b[0m \u001b[0;32min\u001b[0m \u001b[0msettings\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0moutput_steps\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      7\u001b[0m     \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstep\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mflush\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 8\u001b[0;31m     \u001b[0mcore\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstep\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mcore\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mn_steps\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      9\u001b[0m     pyplot.step(x=settings.radius_bins_edges[:-1] / si.micrometres, \n\u001b[1;32m     10\u001b[0m                 \u001b[0my\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mcore\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mproducts\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'dv/dlnr'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msettings\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mradius_bins_edges\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0msettings\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrho\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m~/opt/anaconda3/envs/pysdm/lib/python3.8/site-packages/PySDM-0.1.dev1908+ge961da7.d20211007-py3.8.egg/PySDM/core.py\u001b[0m in \u001b[0;36mrun\u001b[0;34m(self, steps)\u001b[0m\n\u001b[1;32m    116\u001b[0m             \u001b[0;32mfor\u001b[0m \u001b[0mkey\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdynamic\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdynamics\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mitems\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    117\u001b[0m                 \u001b[0;32mwith\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtimers\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 118\u001b[0;31m                     \u001b[0mdynamic\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    119\u001b[0m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mn_steps\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    120\u001b[0m             \u001b[0mreversed_order_so_that_environment_is_last\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mreversed\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mobservers\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m~/opt/anaconda3/envs/pysdm/lib/python3.8/site-packages/PySDM-0.1.dev1908+ge961da7.d20211007-py3.8.egg/PySDM/dynamics/spontaneous_breakup.py\u001b[0m in \u001b[0;36m__call__\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    100\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madaptive\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    101\u001b[0m                 \u001b[0;32mfor\u001b[0m \u001b[0m_\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__substeps\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 102\u001b[0;31m                     \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstep\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    103\u001b[0m             \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    104\u001b[0m                 \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdt_left\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcore\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdt\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m~/opt/anaconda3/envs/pysdm/lib/python3.8/site-packages/PySDM-0.1.dev1908+ge961da7.d20211007-py3.8.egg/PySDM/dynamics/spontaneous_breakup.py\u001b[0m in \u001b[0;36mstep\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    120\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    121\u001b[0m         \u001b[0;31m# (2) Compute the probability of spontaneous breakup\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 122\u001b[0;31m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcompute_probability\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mprob\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    123\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    124\u001b[0m         \u001b[0;31m# (3) Compute the number of fragments\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m~/opt/anaconda3/envs/pysdm/lib/python3.8/site-packages/PySDM-0.1.dev1908+ge961da7.d20211007-py3.8.egg/PySDM/dynamics/spontaneous_breakup.py\u001b[0m in \u001b[0;36mcompute_probability\u001b[0;34m(self, prob)\u001b[0m\n\u001b[1;32m    141\u001b[0m         \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mprob\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    142\u001b[0m         \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbreakup_rate_temp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 143\u001b[0;31m         \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mprob\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbreakup_rate_temp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    144\u001b[0m         \u001b[0mprob\u001b[0m \u001b[0;34m*=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbreakup_rate_temp\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    145\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m~/opt/anaconda3/envs/pysdm/lib/python3.8/site-packages/PySDM-0.1.dev1908+ge961da7.d20211007-py3.8.egg/PySDM/backends/numba/storage.py\u001b[0m in \u001b[0;36m__mul__\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m     65\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     66\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0m__mul__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 67\u001b[0;31m         \u001b[0;32mraise\u001b[0m \u001b[0mTypeError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Use *=\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     68\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     69\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0m__imul__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;31mTypeError\u001b[0m: Use *="
+      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
+      "\u001b[0;32m~/opt/anaconda3/envs/pysdm/lib/python3.8/site-packages/numba-0.54.1rc1-py3.8-macosx-10.9-x86_64.egg/numba/np/arrayobj.py\u001b[0m in \u001b[0;36mimpl\u001b[0;34m()\u001b[0m\n\u001b[1;32m   5403\u001b[0m                        \"is ambiguous. Use a.any() or a.all()\")\n\u001b[0;32m-> 5404\u001b[0;31m                 \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmsg\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   5405\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mimpl\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;31mValueError\u001b[0m: The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()",
+      "\nThe above exception was the direct cause of the following exception:\n",
+      "\u001b[0;31mSystemError\u001b[0m                               Traceback (most recent call last)",
+      "\u001b[0;32m/var/folders/zf/r2fhb0614kd1820s6vy114fh0000gn/T/ipykernel_56212/2050934313.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      6\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mstep\u001b[0m \u001b[0;32min\u001b[0m \u001b[0msettings\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0moutput_steps\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      7\u001b[0m     \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstep\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mflush\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 8\u001b[0;31m     \u001b[0mcore\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstep\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mcore\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mn_steps\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      9\u001b[0m     pyplot.step(x=settings.radius_bins_edges[:-1] / si.micrometres, \n\u001b[1;32m     10\u001b[0m                 \u001b[0my\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mcore\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mproducts\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'dv/dlnr'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msettings\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mradius_bins_edges\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0msettings\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrho\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m~/opt/anaconda3/envs/pysdm/lib/python3.8/site-packages/PySDM-0.1.dev1911+gb1cce54.d20211008-py3.8.egg/PySDM/core.py\u001b[0m in \u001b[0;36mrun\u001b[0;34m(self, steps)\u001b[0m\n\u001b[1;32m    116\u001b[0m             \u001b[0;32mfor\u001b[0m \u001b[0mkey\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdynamic\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdynamics\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mitems\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    117\u001b[0m                 \u001b[0;32mwith\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtimers\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 118\u001b[0;31m                     \u001b[0mdynamic\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    119\u001b[0m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mn_steps\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    120\u001b[0m             \u001b[0mreversed_order_so_that_environment_is_last\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mreversed\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mobservers\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m~/opt/anaconda3/envs/pysdm/lib/python3.8/site-packages/PySDM-0.1.dev1911+gb1cce54.d20211008-py3.8.egg/PySDM/dynamics/spontaneous_breakup.py\u001b[0m in \u001b[0;36m__call__\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    100\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madaptive\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    101\u001b[0m                 \u001b[0;32mfor\u001b[0m \u001b[0m_\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__substeps\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 102\u001b[0;31m                     \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstep\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    103\u001b[0m             \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    104\u001b[0m                 \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdt_left\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcore\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdt\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m~/opt/anaconda3/envs/pysdm/lib/python3.8/site-packages/PySDM-0.1.dev1911+gb1cce54.d20211008-py3.8.egg/PySDM/dynamics/spontaneous_breakup.py\u001b[0m in \u001b[0;36mstep\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    129\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    130\u001b[0m         \u001b[0;31m# (5) Perform the collisional-breakup step:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 131\u001b[0;31m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcore\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mparticles\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mspontaneous_breakup\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgamma\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mprob\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mn_fragment\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mn_fragment\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    132\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    133\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madaptive\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m~/opt/anaconda3/envs/pysdm/lib/python3.8/site-packages/PySDM-0.1.dev1911+gb1cce54.d20211008-py3.8.egg/PySDM/state/particles.py\u001b[0m in \u001b[0;36mspontaneous_breakup\u001b[0;34m(self, gamma, n_fragment)\u001b[0m\n\u001b[1;32m    167\u001b[0m     \u001b[0;31m## TODO Ben: def spontaneous_breakup(self, gamma=prob, n_fragment) gamma = prob of breakup occuring\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    168\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mspontaneous_breakup\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgamma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mn_fragment\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 169\u001b[0;31m         self.core.bck.spontaneous_breakup(n=self['n'],\n\u001b[0m\u001b[1;32m    170\u001b[0m                               \u001b[0midx\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__idx\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    171\u001b[0m                               \u001b[0mlength\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mSD_num\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m~/opt/anaconda3/envs/pysdm/lib/python3.8/site-packages/PySDM-0.1.dev1911+gb1cce54.d20211008-py3.8.egg/PySDM/backends/numba/impl/_algorithmic_methods.py\u001b[0m in \u001b[0;36mspontaneous_breakup\u001b[0;34m(n, idx, length, attributes, gamma, n_fragment, healthy)\u001b[0m\n\u001b[1;32m    194\u001b[0m     \u001b[0;34m@\u001b[0m\u001b[0mstaticmethod\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    195\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mspontaneous_breakup\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0midx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlength\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mattributes\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgamma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mn_fragment\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mhealthy\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 196\u001b[0;31m         AlgorithmicMethods.spontaneous_breakup_body(n.data, idx.data, length,\n\u001b[0m\u001b[1;32m    197\u001b[0m                                             \u001b[0mattributes\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgamma\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mn_fragment\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mhealthy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    198\u001b[0m                                             )\n",
+      "\u001b[0;31mSystemError\u001b[0m: CPUDispatcher(<function AlgorithmicMethods.spontaneous_breakup_body at 0x7fb169ada790>) returned a result with an error set"
      ]
     },
     {
      "output_type": "display_data",
      "data": {
-      "image/png": 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",
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",
       "text/plain": [
        "<Figure size 432x288 with 1 Axes>"
       ]

From 84bb721c37ce78f0aac28ee0af4cde50d1d8091a Mon Sep 17 00:00:00 2001
From: Emily de Jong <edejong@caltech.edu>
Date: Fri, 8 Oct 2021 11:09:20 -0700
Subject: [PATCH 08/12] EJ: Reformulated spont_break rate as a probability with
 dt, and rand num to determine whether it occurs

---
 .../numba/impl/_algorithmic_methods.py        | 21 +++--
 PySDM/dynamics/spontaneous_breakup.py         | 23 ++---
 PySDM/state/particles.py                      |  6 +-
 .../spontaneous_breakup_test.ipynb            | 87 ++++++++-----------
 4 files changed, 58 insertions(+), 79 deletions(-)

diff --git a/PySDM/backends/numba/impl/_algorithmic_methods.py b/PySDM/backends/numba/impl/_algorithmic_methods.py
index c63a4f54a3..c9e67ab02c 100644
--- a/PySDM/backends/numba/impl/_algorithmic_methods.py
+++ b/PySDM/backends/numba/impl/_algorithmic_methods.py
@@ -176,23 +176,29 @@ def breakup(n, idx, length, attributes, gamma, n_fragment, healthy, is_first_in_
     ## TODO: Ben implement spontaneous breakup
     @staticmethod
     @numba.njit(**conf.JIT_FLAGS)
-    def spontaneous_breakup_body(n, idx, length, attributes, gamma, n_fragment, healthy):
+    def spontaneous_breakup_body(n, length, attributes, gamma, rand, n_fragment, healthy):
         for i in numba.prange(length):
+            gamma[i] = np.ceil(gamma[i] - rand[i])
             # no spontaneous breakup occurs
             if gamma[i] == 0:
                 continue
             # breakup does occur
-            if n_fragment > 0:
+            if n_fragment[i] > 0:
                 n[i] = n[i] * int(n_fragment[i])
                 # what is this?
-                # for a in range(0, len(attributes)):
+                # EJ: this changes the attributes and multiplicities when a coalescence occurs
+                for a in range(0, len(attributes)):
                 #     attributes[a, k] += gamma[i] * attributes[a, j]
-                #     attributes[a, k] /= n_fragment[i]
+                     attributes[a, i] /= n_fragment[i]
+            # should not be an issue unless n_frag < 1
+            if n[i] == 0:
+                healthy[0] = 0
 
     @staticmethod
-    def spontaneous_breakup(n, idx, length, attributes, gamma, n_fragment, healthy):
-        AlgorithmicMethods.spontaneous_breakup_body(n.data, idx.data, length,
-                                            attributes.data, gamma.data, n_fragment.data, healthy.data,
+    def spontaneous_breakup(n, length, attributes, gamma, u01, n_fragment, healthy):
+        AlgorithmicMethods.spontaneous_breakup_body(n.data, length,
+                                            attributes.data, gamma.data, u01.data, 
+                                            n_fragment.data, healthy.data,
                                             )
     
     # Emily: SLAMS fragmentation function
@@ -350,7 +356,6 @@ def normalize(prob, cell_id, cell_idx, cell_start, norm_factor, dt, dv):
         return AlgorithmicMethods.normalize_body(
             prob.data, cell_id.data, cell_idx.data, cell_start.data, norm_factor.data, dt, dv)
 
-
     @staticmethod
     @numba.njit(**{**conf.JIT_FLAGS, **{'parallel': False}})
     def remove_zero_n_or_flagged(multiplicity, idx, length) -> int:
diff --git a/PySDM/dynamics/spontaneous_breakup.py b/PySDM/dynamics/spontaneous_breakup.py
index dbd5b47ce0..523ef65724 100644
--- a/PySDM/dynamics/spontaneous_breakup.py
+++ b/PySDM/dynamics/spontaneous_breakup.py
@@ -123,30 +123,19 @@ def step(self):
         
         # (3) Compute the number of fragments
         self.compute_n_fragment(self.n_fragment, rand_frag)
-
-        # (4) Compute gamma
-        self.compute_gamma(self.prob, rand)
-        
-        # (5) Perform the collisional-breakup step: 
-        self.core.particles.spontaneous_breakup(gamma=self.prob, n_fragment=self.n_fragment)
         
+        # (4) Perform the collisional-breakup step: 
+        self.core.particles.spontaneous_breakup(gamma=self.prob, u01=rand, n_fragment=self.n_fragment)
         if self.adaptive:
             self.core.particles.cut_working_length(self.core.particles.adaptive_sdm_end(self.dt_left))
 
     # (2) TODO: Does spont breakup occur?
     def compute_probability(self, prob):
         self.breakup_rate(self.breakup_rate_temp)
-        # P_j = xi_j*P_j
-        prob[:] = self.core.particles['n'] # in other version, not using prob =; 
-        prob *= self.breakup_rate_temp
-
-        self.core.normalize(prob, self.norm_factor_temp)
+        prob[:] = self.breakup_rate_temp
+        # breakup_rate * dt = expected number of breakups in time dt
+        prob[:] *= self.core.dt
         
     # (3) Compute n_fragment
     def compute_n_fragment(self, n_fragment, u01):
-        self.fragmentation(n_fragment, u01)
-
-    # Compute gamma, i.e. whether the collision leads to breakup
-    # TODO: move to backend?
-    def compute_gamma(self, prob, rand):
-        return
\ No newline at end of file
+        self.fragmentation(n_fragment, u01)
\ No newline at end of file
diff --git a/PySDM/state/particles.py b/PySDM/state/particles.py
index 0dbc48ca10..0439b4e8cf 100644
--- a/PySDM/state/particles.py
+++ b/PySDM/state/particles.py
@@ -164,13 +164,13 @@ def breakup(self, gamma, n_fragment, is_first_in_pair):
             if isinstance(attr, ExtensiveAttribute):
                 attr.mark_updated()
 
-    ## TODO Ben: def spontaneous_breakup(self, gamma=prob, n_fragment) gamma = prob of breakup occuring
-    def spontaneous_breakup(self, gamma, n_fragment):
+    ## TODO Ben: def spontaneous_breakup(self, gamma=prob, u01, n_fragment) gamma = prob of breakup occuring
+    def spontaneous_breakup(self, gamma, u01, n_fragment):
         self.core.bck.spontaneous_breakup(n=self['n'],
-                              idx=self.__idx,
                               length=self.SD_num,
                               attributes=self.get_extensive_attrs(),
                               gamma=gamma,
+                              u01=u01,
                               n_fragment=n_fragment,
                               healthy=self.__healthy_memory,
                              )
diff --git a/PySDM_tests/breakup_tests/spontaneous_breakup_test.ipynb b/PySDM_tests/breakup_tests/spontaneous_breakup_test.ipynb
index 372273bc59..08704649f9 100644
--- a/PySDM_tests/breakup_tests/spontaneous_breakup_test.ipynb
+++ b/PySDM_tests/breakup_tests/spontaneous_breakup_test.ipynb
@@ -3,6 +3,16 @@
   {
    "cell_type": "code",
    "execution_count": 1,
+   "source": [
+    "%load_ext autoreload\n",
+    "%autoreload 2"
+   ],
+   "outputs": [],
+   "metadata": {}
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
    "source": [
     "import sys\n",
     "import numpy as np\n",
@@ -31,7 +41,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 81,
    "source": [
     "from PySDM.initialisation.spectra import Exponential\n",
     "from PySDM.physics.spontaneous_breakup_rates import Constant\n",
@@ -45,7 +55,7 @@
     "\n",
     "    def __init__(self):\n",
     "        self.formulae = Formulae()\n",
-    "        self.n_sd = 3\n",
+    "        self.n_sd = 2**8\n",
     "        self.n_part = 100 / si.cm**3\n",
     "        self.X0 = self.formulae.trivia.volume(radius=30.531 * si.micrometres)\n",
     "        self.dv = 1 * si.m**3\n",
@@ -54,8 +64,8 @@
     "        self.dt = 1 * si.seconds\n",
     "        self.adaptive = False\n",
     "        self.seed = 44\n",
-    "        self._steps = [0, 100, 200]\n",
-    "        self.breakup_rate = Constant(100 / si.second)\n",
+    "        self._steps = [0, 1, 2]\n",
+    "        self.breakup_rate = Constant(1 / si.second)\n",
     "        self.fragmentation = SpontaneousAlwaysN(n=3)\n",
     "        self.spectrum = Exponential(norm_factor=self.norm_factor, scale=self.X0)\n",
     "        self.radius_bins_edges = np.logspace(np.log10(10 * si.um), np.log10(100 * si.um), num=128, endpoint=True)\n",
@@ -70,7 +80,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 82,
    "source": [
     "settings = Settings()\n",
     "backend = CPU\n",
@@ -80,22 +90,20 @@
     "attributes = {}\n",
     "attributes['volume'], attributes['n'] = ConstantMultiplicity(settings.spectrum).sample(settings.n_sd)\n",
     "breakup = SpontaneousBreakup(settings.breakup_rate, settings.fragmentation, adaptive=settings.adaptive)\n",
-    "builder.add_dynamic(breakup)\n"
+    "builder.add_dynamic(breakup)\n",
+    "\n",
+    "products = [ParticlesVolumeSpectrum(), WallTime(), ParticleMeanRadius(), ParticlesConcentration(radius_range = settings.radius_range)]\n",
+    "core = builder.build(attributes, products)"
    ],
    "outputs": [],
    "metadata": {}
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 83,
    "source": [
-    "#coalescence = Coalescence(settings.kernel, settings.coal_eff adaptive=settings.adaptive)\n",
-    "#builder.add_dynamic(coalescence)\n",
-    "products = [ParticlesVolumeSpectrum(), WallTime(), ParticleMeanRadius(), ParticlesConcentration(radius_range = settings.radius_range)]\n",
-    "core = builder.build(attributes, products)\n",
-    "\n",
     "for step in settings.output_steps:\n",
-    "    print(step, flush=True)\n",
+    "    #print(step, flush=True)\n",
     "    core.run(step - core.n_steps)\n",
     "    pyplot.step(x=settings.radius_bins_edges[:-1] / si.micrometres, \n",
     "                y=core.products['dv/dlnr'].get(settings.radius_bins_edges) * settings.rho,\n",
@@ -112,48 +120,25 @@
      "output_type": "stream",
      "name": "stdout",
      "text": [
-      "0\n"
+      "[27.26101585] [99.997952]\n",
+      "[18.97043708] [294.525218]\n",
+      "[13.14061108] [878.107016]\n"
      ]
     },
     {
-     "output_type": "stream",
-     "name": "stderr",
-     "text": [
-      "OMP: Info #271: omp_set_nested routine deprecated, please use omp_set_max_active_levels instead.\n"
-     ]
-    },
-    {
-     "output_type": "stream",
-     "name": "stdout",
-     "text": [
-      "[27.13815313] [99.998001]\n",
-      "100\n"
-     ]
-    },
-    {
-     "output_type": "error",
-     "ename": "SystemError",
-     "evalue": "CPUDispatcher(<function AlgorithmicMethods.spontaneous_breakup_body at 0x7fb169ada790>) returned a result with an error set",
-     "traceback": [
-      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
-      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
-      "\u001b[0;32m~/opt/anaconda3/envs/pysdm/lib/python3.8/site-packages/numba-0.54.1rc1-py3.8-macosx-10.9-x86_64.egg/numba/np/arrayobj.py\u001b[0m in \u001b[0;36mimpl\u001b[0;34m()\u001b[0m\n\u001b[1;32m   5403\u001b[0m                        \"is ambiguous. Use a.any() or a.all()\")\n\u001b[0;32m-> 5404\u001b[0;31m                 \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmsg\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   5405\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mimpl\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;31mValueError\u001b[0m: The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()",
-      "\nThe above exception was the direct cause of the following exception:\n",
-      "\u001b[0;31mSystemError\u001b[0m                               Traceback (most recent call last)",
-      "\u001b[0;32m/var/folders/zf/r2fhb0614kd1820s6vy114fh0000gn/T/ipykernel_56212/2050934313.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      6\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mstep\u001b[0m \u001b[0;32min\u001b[0m \u001b[0msettings\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0moutput_steps\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      7\u001b[0m     \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstep\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mflush\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 8\u001b[0;31m     \u001b[0mcore\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstep\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mcore\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mn_steps\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      9\u001b[0m     pyplot.step(x=settings.radius_bins_edges[:-1] / si.micrometres, \n\u001b[1;32m     10\u001b[0m                 \u001b[0my\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mcore\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mproducts\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'dv/dlnr'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msettings\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mradius_bins_edges\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0msettings\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrho\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m~/opt/anaconda3/envs/pysdm/lib/python3.8/site-packages/PySDM-0.1.dev1911+gb1cce54.d20211008-py3.8.egg/PySDM/core.py\u001b[0m in \u001b[0;36mrun\u001b[0;34m(self, steps)\u001b[0m\n\u001b[1;32m    116\u001b[0m             \u001b[0;32mfor\u001b[0m \u001b[0mkey\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdynamic\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdynamics\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mitems\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    117\u001b[0m                 \u001b[0;32mwith\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtimers\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 118\u001b[0;31m                     \u001b[0mdynamic\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    119\u001b[0m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mn_steps\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    120\u001b[0m             \u001b[0mreversed_order_so_that_environment_is_last\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mreversed\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mobservers\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m~/opt/anaconda3/envs/pysdm/lib/python3.8/site-packages/PySDM-0.1.dev1911+gb1cce54.d20211008-py3.8.egg/PySDM/dynamics/spontaneous_breakup.py\u001b[0m in \u001b[0;36m__call__\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    100\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madaptive\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    101\u001b[0m                 \u001b[0;32mfor\u001b[0m \u001b[0m_\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__substeps\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 102\u001b[0;31m                     \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstep\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    103\u001b[0m             \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    104\u001b[0m                 \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdt_left\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcore\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdt\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m~/opt/anaconda3/envs/pysdm/lib/python3.8/site-packages/PySDM-0.1.dev1911+gb1cce54.d20211008-py3.8.egg/PySDM/dynamics/spontaneous_breakup.py\u001b[0m in \u001b[0;36mstep\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    129\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    130\u001b[0m         \u001b[0;31m# (5) Perform the collisional-breakup step:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 131\u001b[0;31m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcore\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mparticles\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mspontaneous_breakup\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgamma\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mprob\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mn_fragment\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mn_fragment\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    132\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    133\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madaptive\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m~/opt/anaconda3/envs/pysdm/lib/python3.8/site-packages/PySDM-0.1.dev1911+gb1cce54.d20211008-py3.8.egg/PySDM/state/particles.py\u001b[0m in \u001b[0;36mspontaneous_breakup\u001b[0;34m(self, gamma, n_fragment)\u001b[0m\n\u001b[1;32m    167\u001b[0m     \u001b[0;31m## TODO Ben: def spontaneous_breakup(self, gamma=prob, n_fragment) gamma = prob of breakup occuring\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    168\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mspontaneous_breakup\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgamma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mn_fragment\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 169\u001b[0;31m         self.core.bck.spontaneous_breakup(n=self['n'],\n\u001b[0m\u001b[1;32m    170\u001b[0m                               \u001b[0midx\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__idx\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    171\u001b[0m                               \u001b[0mlength\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mSD_num\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m~/opt/anaconda3/envs/pysdm/lib/python3.8/site-packages/PySDM-0.1.dev1911+gb1cce54.d20211008-py3.8.egg/PySDM/backends/numba/impl/_algorithmic_methods.py\u001b[0m in \u001b[0;36mspontaneous_breakup\u001b[0;34m(n, idx, length, attributes, gamma, n_fragment, healthy)\u001b[0m\n\u001b[1;32m    194\u001b[0m     \u001b[0;34m@\u001b[0m\u001b[0mstaticmethod\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    195\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mspontaneous_breakup\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0midx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlength\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mattributes\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgamma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mn_fragment\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mhealthy\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 196\u001b[0;31m         AlgorithmicMethods.spontaneous_breakup_body(n.data, idx.data, length,\n\u001b[0m\u001b[1;32m    197\u001b[0m                                             \u001b[0mattributes\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgamma\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mn_fragment\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mhealthy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    198\u001b[0m                                             )\n",
-      "\u001b[0;31mSystemError\u001b[0m: CPUDispatcher(<function AlgorithmicMethods.spontaneous_breakup_body at 0x7fb169ada790>) returned a result with an error set"
-     ]
+     "output_type": "execute_result",
+     "data": {
+      "text/plain": [
+       "<matplotlib.legend.Legend at 0x7fd32de53880>"
+      ]
+     },
+     "metadata": {},
+     "execution_count": 83
     },
     {
      "output_type": "display_data",
      "data": {
-      "image/png": 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",
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",
       "text/plain": [
        "<Figure size 432x288 with 1 Axes>"
       ]
@@ -176,7 +161,7 @@
  "metadata": {
   "kernelspec": {
    "name": "python3",
-   "display_name": "Python 3.8.11 64-bit ('pysdm': conda)"
+   "display_name": "Python 3.9.4 64-bit ('edjPySDM': conda)"
   },
   "language_info": {
    "codemirror_mode": {
@@ -188,10 +173,10 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.8.11"
+   "version": "3.9.4"
   },
   "interpreter": {
-   "hash": "edf7e9822b7c1e609a65d73347baf735d21a74e379f9d1f2c2648473c494d495"
+   "hash": "a75ec040163759486af1b34912b938f3bf396ad0d146e1bd1595d18e46184c90"
   }
  },
  "nbformat": 4,

From e79b475bd3e5a87c5d4df9421b61eea943572e94 Mon Sep 17 00:00:00 2001
From: Emily de Jong <edejong@caltech.edu>
Date: Wed, 13 Oct 2021 11:46:00 -0700
Subject: [PATCH 09/12] Add exponential fragmentation rate, as in Kamra 1991

---
 .../numba/impl/_algorithmic_methods.py        |  12 ++
 .../spontaneous_breakup_rates/__init__.py     |   3 +-
 .../spontaneous_breakup_rates/exponential.py  |  16 +++
 .../spontaneous_breakup_test.ipynb            | 134 ++++++++++++++++--
 4 files changed, 156 insertions(+), 9 deletions(-)
 create mode 100644 PySDM/physics/spontaneous_breakup_rates/exponential.py

diff --git a/PySDM/backends/numba/impl/_algorithmic_methods.py b/PySDM/backends/numba/impl/_algorithmic_methods.py
index c9e67ab02c..9c53c6f875 100644
--- a/PySDM/backends/numba/impl/_algorithmic_methods.py
+++ b/PySDM/backends/numba/impl/_algorithmic_methods.py
@@ -298,6 +298,18 @@ def linear_collection_efficiency(params, output, radii, is_first_in_pair, unit):
         return AlgorithmicMethods.linear_collection_efficiency_body(
             params, output.data, radii.data, is_first_in_pair.indicator.data, radii.idx.data, len(is_first_in_pair), unit)
 
+    @staticmethod
+    @numba.njit(**conf.JIT_FLAGS)
+    def exponential_body(output, scaling, radii, idx, length, unit):
+        output[:] = 0
+        for i in numba.prange(length):
+            output[i] = np.exp(scaling * radii[idx[i]] / unit)
+
+    @staticmethod
+    def exponential(output, scaling, radii, unit):
+        return AlgorithmicMethods.exponential_body(
+            output.data, scaling, radii.data, radii.idx.data, len(radii), unit)
+
     @staticmethod
     @numba.njit(**conf.JIT_FLAGS)
     def interpolation_body(output, radius, factor, b, c):
diff --git a/PySDM/physics/spontaneous_breakup_rates/__init__.py b/PySDM/physics/spontaneous_breakup_rates/__init__.py
index 3553d38e34..c2076fb6f5 100644
--- a/PySDM/physics/spontaneous_breakup_rates/__init__.py
+++ b/PySDM/physics/spontaneous_breakup_rates/__init__.py
@@ -1 +1,2 @@
-from .constant import Constant
\ No newline at end of file
+from .constant import Constant
+from .exponential import Expon
\ No newline at end of file
diff --git a/PySDM/physics/spontaneous_breakup_rates/exponential.py b/PySDM/physics/spontaneous_breakup_rates/exponential.py
new file mode 100644
index 0000000000..876eba7610
--- /dev/null
+++ b/PySDM/physics/spontaneous_breakup_rates/exponential.py
@@ -0,0 +1,16 @@
+from PySDM.physics import constants as const
+
+class Expon:
+
+    def __init__(self, a, b):
+        self.a = a
+        self.b = b
+        self.core = None
+
+    def __call__(self, output):
+        self.core.backend.exponential(output, self.b, self.core.particles['radius'], const.si.um)
+        output *= self.a
+
+    def register(self, builder):
+        self.core = builder.core
+        builder.request_attribute('radius')
\ No newline at end of file
diff --git a/PySDM_tests/breakup_tests/spontaneous_breakup_test.ipynb b/PySDM_tests/breakup_tests/spontaneous_breakup_test.ipynb
index 08704649f9..cd547e3a9c 100644
--- a/PySDM_tests/breakup_tests/spontaneous_breakup_test.ipynb
+++ b/PySDM_tests/breakup_tests/spontaneous_breakup_test.ipynb
@@ -12,7 +12,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 4,
    "source": [
     "import sys\n",
     "import numpy as np\n",
@@ -80,7 +80,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 82,
+   "execution_count": 85,
    "source": [
     "settings = Settings()\n",
     "backend = CPU\n",
@@ -100,7 +100,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 83,
+   "execution_count": 86,
    "source": [
     "for step in settings.output_steps:\n",
     "    #print(step, flush=True)\n",
@@ -121,24 +121,142 @@
      "name": "stdout",
      "text": [
       "[27.26101585] [99.997952]\n",
-      "[18.97043708] [294.525218]\n",
-      "[13.14061108] [878.107016]\n"
+      "[18.95139778] [296.087686]\n",
+      "[13.13134485] [884.356888]\n"
      ]
     },
     {
      "output_type": "execute_result",
      "data": {
       "text/plain": [
-       "<matplotlib.legend.Legend at 0x7fd32de53880>"
+       "<matplotlib.legend.Legend at 0x7fd32db22430>"
       ]
      },
      "metadata": {},
-     "execution_count": 83
+     "execution_count": 86
     },
     {
      "output_type": "display_data",
      "data": {
-      "image/png": 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",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     }
+    }
+   ],
+   "metadata": {}
+  },
+  {
+   "cell_type": "markdown",
+   "source": [
+    "## Exponential rate, AlwaysN fragments"
+   ],
+   "metadata": {}
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "source": [
+    "from PySDM.initialisation.spectra import Exponential\n",
+    "from PySDM.physics.spontaneous_breakup_rates import Expon\n",
+    "from PySDM.physics.spontaneous_breakup_fragmentations import SpontaneousAlwaysN\n",
+    "from PySDM.physics.constants import si\n",
+    "from PySDM.physics.formulae import Formulae\n",
+    "#from pystrict import strict\n",
+    "\n",
+    "#@strict\n",
+    "class Settings:\n",
+    "\n",
+    "    def __init__(self):\n",
+    "        self.formulae = Formulae()\n",
+    "        self.n_sd = 2**8\n",
+    "        self.n_part = 100 / si.cm**3\n",
+    "        self.X0 = self.formulae.trivia.volume(radius=30.531 * si.micrometres)\n",
+    "        self.dv = 1 * si.m**3\n",
+    "        self.norm_factor = self.n_part * self.dv\n",
+    "        self.rho = 1000 * si.kilogram / si.metre**3\n",
+    "        self.dt = 1 * si.seconds\n",
+    "        self.adaptive = False\n",
+    "        self.seed = 44\n",
+    "        self._steps = [0, 1, 2]\n",
+    "        self.breakup_rate = Expon(1.58e-4 / si.s, 0.773 * si.mm)\n",
+    "        self.fragmentation = SpontaneousAlwaysN(n=3)\n",
+    "        self.spectrum = Exponential(norm_factor=self.norm_factor, scale=self.X0)\n",
+    "        self.radius_bins_edges = np.logspace(np.log10(10 * si.um), np.log10(100 * si.um), num=128, endpoint=True)\n",
+    "        self.radius_range = [0 * si.um, 1e6 * si.um]\n",
+    "\n",
+    "    @property\n",
+    "    def output_steps(self):\n",
+    "        return [int(step/self.dt) for step in self._steps]"
+   ],
+   "outputs": [],
+   "metadata": {}
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "source": [
+    "settings = Settings()\n",
+    "backend = CPU\n",
+    "\n",
+    "builder = Builder(n_sd=settings.n_sd, backend=backend, formulae=settings.formulae)\n",
+    "builder.set_environment(Box(dv=settings.dv, dt=settings.dt))\n",
+    "attributes = {}\n",
+    "attributes['volume'], attributes['n'] = ConstantMultiplicity(settings.spectrum).sample(settings.n_sd)\n",
+    "breakup = SpontaneousBreakup(settings.breakup_rate, settings.fragmentation, adaptive=settings.adaptive)\n",
+    "builder.add_dynamic(breakup)\n",
+    "\n",
+    "products = [ParticlesVolumeSpectrum(), WallTime(), ParticleMeanRadius(), ParticlesConcentration(radius_range = settings.radius_range)]\n",
+    "core = builder.build(attributes, products)"
+   ],
+   "outputs": [],
+   "metadata": {}
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "source": [
+    "for step in settings.output_steps:\n",
+    "    #print(step, flush=True)\n",
+    "    core.run(step - core.n_steps)\n",
+    "    pyplot.step(x=settings.radius_bins_edges[:-1] / si.micrometres, \n",
+    "                y=core.products['dv/dlnr'].get(settings.radius_bins_edges) * settings.rho,\n",
+    "                where='post', label=\"t = {step*settings.dt}s\")\n",
+    "    print(core.products['radius_m1'].get(), core.products['n_a_cm3'].get())\n",
+    "    \n",
+    "pyplot.xscale(\"log\")\n",
+    "pyplot.xlabel(\"radius (um)\")\n",
+    "pyplot.ylabel(\"dm/dlnr\")\n",
+    "pyplot.legend()"
+   ],
+   "outputs": [
+    {
+     "output_type": "stream",
+     "name": "stdout",
+     "text": [
+      "[27.26101585] [99.997952]\n",
+      "[23.15512423] [199.995904]\n",
+      "[17.18684981] [499.98976]\n"
+     ]
+    },
+    {
+     "output_type": "execute_result",
+     "data": {
+      "text/plain": [
+       "<matplotlib.legend.Legend at 0x7f95c2558520>"
+      ]
+     },
+     "metadata": {},
+     "execution_count": 7
+    },
+    {
+     "output_type": "display_data",
+     "data": {
+      "image/png": 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",
       "text/plain": [
        "<Figure size 432x288 with 1 Axes>"
       ]

From 8d211cd3371c56dda8bcaf40b122d7e8a1021ad9 Mon Sep 17 00:00:00 2001
From: Emily de Jong <edejong@caltech.edu>
Date: Wed, 13 Oct 2021 13:50:27 -0700
Subject: [PATCH 10/12] Added exponential-cubic fragmentation function, as in
 Kamra 1991. Change n_fragment to float type.

---
 PySDM/dynamics/spontaneous_breakup.py         |   2 +-
 .../__init__.py                               |   3 +-
 .../expo_cube.py                              |  27 +++
 .../spontaneous_breakup_test.ipynb            | 215 +++++++++++++++++-
 4 files changed, 244 insertions(+), 3 deletions(-)
 create mode 100644 PySDM/physics/spontaneous_breakup_fragmentations/expo_cube.py

diff --git a/PySDM/dynamics/spontaneous_breakup.py b/PySDM/dynamics/spontaneous_breakup.py
index 523ef65724..e44cc07bb1 100644
--- a/PySDM/dynamics/spontaneous_breakup.py
+++ b/PySDM/dynamics/spontaneous_breakup.py
@@ -71,7 +71,7 @@ def register(self, builder):
         assert self.dt_coal_range[0] <= self.dt_coal_range[1]
 
         # init temporary storage; swap to Storage (see Condensation)
-        self.n_fragment = self.core.Storage.empty(self.core.n_sd, dtype=int)
+        self.n_fragment = self.core.Storage.empty(self.core.n_sd, dtype=float)
         self.breakup_rate_temp = self.core.Storage.empty(self.core.n_sd, dtype=float)
         self.norm_factor_temp = self.core.Storage.empty(self.core.mesh.n_cell, dtype=float)
         self.prob = self.core.Storage.empty(self.core.n_sd, dtype=float) # does the event happen?
diff --git a/PySDM/physics/spontaneous_breakup_fragmentations/__init__.py b/PySDM/physics/spontaneous_breakup_fragmentations/__init__.py
index ded13056cc..4421292b04 100644
--- a/PySDM/physics/spontaneous_breakup_fragmentations/__init__.py
+++ b/PySDM/physics/spontaneous_breakup_fragmentations/__init__.py
@@ -1 +1,2 @@
-from .always_n import SpontaneousAlwaysN
\ No newline at end of file
+from .always_n import SpontaneousAlwaysN
+from .expo_cube import SpontaneousExpoCube
\ No newline at end of file
diff --git a/PySDM/physics/spontaneous_breakup_fragmentations/expo_cube.py b/PySDM/physics/spontaneous_breakup_fragmentations/expo_cube.py
new file mode 100644
index 0000000000..42eecb235e
--- /dev/null
+++ b/PySDM/physics/spontaneous_breakup_fragmentations/expo_cube.py
@@ -0,0 +1,27 @@
+'''
+For a fragmentation function of the form:
+    Q(D0, D) dD = A * (D0)**3 * exp(-B * D) dD
+where D0 is the parent droplet size, Q(D) dD is the number of drops of size D
+formed from the breakup. Then it can be shown that:
+    N_frag = int (Q(D0, D) dD) = A * (D0)**3 / B
+and furthermore for consistency with mass conservation,
+    6*A = B**3
+
+Therefore this function takes a single argument C = A/B = 1/6 * B**2, and 
+translates to a fragmentation function which is cubic in the parent size D0.
+    N_frag = C * (D0)**3
+'''
+class SpontaneousExpoCube:
+
+    def __init__(self, C):
+        self.core = None
+        self.C = C  
+
+    def __call__(self, output, u01):
+        output[:] = self.core.particles['volume']
+        output *= self.C
+        
+    def register(self, builder):
+        self.core = builder.core
+        builder.request_attribute('volume')
+        
\ No newline at end of file
diff --git a/PySDM_tests/breakup_tests/spontaneous_breakup_test.ipynb b/PySDM_tests/breakup_tests/spontaneous_breakup_test.ipynb
index cd547e3a9c..1dbde9d58a 100644
--- a/PySDM_tests/breakup_tests/spontaneous_breakup_test.ipynb
+++ b/PySDM_tests/breakup_tests/spontaneous_breakup_test.ipynb
@@ -12,7 +12,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 2,
    "source": [
     "import sys\n",
     "import numpy as np\n",
@@ -268,6 +268,219 @@
    ],
    "metadata": {}
   },
+  {
+   "cell_type": "markdown",
+   "source": [
+    "## Exponential rate, cubic fragmentation function"
+   ],
+   "metadata": {}
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "source": [
+    "from PySDM.initialisation.spectra import Exponential\n",
+    "from PySDM.physics.spontaneous_breakup_rates import Expon\n",
+    "from PySDM.physics.spontaneous_breakup_fragmentations import SpontaneousExpoCube\n",
+    "from PySDM.physics.constants import si\n",
+    "from PySDM.physics.formulae import Formulae\n",
+    "#from pystrict import strict\n",
+    "\n",
+    "#@strict\n",
+    "class Settings:\n",
+    "\n",
+    "    def __init__(self):\n",
+    "        self.formulae = Formulae()\n",
+    "        self.n_sd = 12\n",
+    "        self.n_part = 100 / si.cm**3\n",
+    "        self.X0 = self.formulae.trivia.volume(radius=30.531 * si.micrometres)\n",
+    "        self.dv = 1 * si.m**3\n",
+    "        self.norm_factor = self.n_part * self.dv\n",
+    "        self.rho = 1000 * si.kilogram / si.metre**3\n",
+    "        self.dt = 1 * si.seconds\n",
+    "        self.adaptive = False\n",
+    "        self.seed = 44\n",
+    "        self._steps = [0, 1, 2]\n",
+    "        self.breakup_rate = Expon(1.58e-4 / si.s, 0.773 * si.mm)\n",
+    "        self.fragmentation = SpontaneousExpoCube(C = 0.034 / si.mm**3)\n",
+    "        self.spectrum = Exponential(norm_factor=self.norm_factor, scale=self.X0)\n",
+    "        self.radius_bins_edges = np.logspace(np.log10(10 * si.um), np.log10(100 * si.um), num=128, endpoint=True)\n",
+    "        self.radius_range = [0 * si.um, 1e6 * si.um]\n",
+    "\n",
+    "    @property\n",
+    "    def output_steps(self):\n",
+    "        return [int(step/self.dt) for step in self._steps]"
+   ],
+   "outputs": [],
+   "metadata": {}
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "source": [
+    "settings = Settings()\n",
+    "backend = CPU\n",
+    "\n",
+    "builder = Builder(n_sd=settings.n_sd, backend=backend, formulae=settings.formulae)\n",
+    "builder.set_environment(Box(dv=settings.dv, dt=settings.dt))\n",
+    "attributes = {}\n",
+    "attributes['volume'], attributes['n'] = ConstantMultiplicity(settings.spectrum).sample(settings.n_sd)\n",
+    "breakup = SpontaneousBreakup(settings.breakup_rate, settings.fragmentation, adaptive=settings.adaptive)\n",
+    "builder.add_dynamic(breakup)\n",
+    "\n",
+    "products = [ParticlesVolumeSpectrum(), WallTime(), ParticleMeanRadius(), ParticlesConcentration(radius_range = settings.radius_range)]\n",
+    "core = builder.build(attributes, products)"
+   ],
+   "outputs": [],
+   "metadata": {}
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "source": [
+    "for step in settings.output_steps:\n",
+    "    #print(step, flush=True)\n",
+    "    core.run(step - core.n_steps)\n",
+    "    pyplot.step(x=settings.radius_bins_edges[:-1] / si.micrometres, \n",
+    "                y=core.products['dv/dlnr'].get(settings.radius_bins_edges) * settings.rho,\n",
+    "                where='post', label=\"t = {step*settings.dt}s\")\n",
+    "    print(core.products['radius_m1'].get(), core.products['n_a_cm3'].get())\n",
+    "    \n",
+    "pyplot.xscale(\"log\")\n",
+    "pyplot.xlabel(\"radius (um)\")\n",
+    "pyplot.ylabel(\"dm/dlnr\")\n",
+    "pyplot.legend()"
+   ],
+   "outputs": [
+    {
+     "output_type": "stream",
+     "name": "stdout",
+     "text": [
+      "[27.26101585] [99.997952]\n",
+      "<PySDM.backends.numba.storage.Storage object at 0x7fc34d40b5b0> 0.000158\n",
+      "[1.00296041 1.00427038 1.00506727 1.00567359 1.00617463 1.00660734\n",
+      " 1.00699151 1.00733912 1.00765802 1.00795369 1.0082301  1.00849026\n",
+      " 1.00873648 1.0089706  1.00919409 1.00940817 1.00961384 1.00981196\n",
+      " 1.01000324 1.01018831 1.01036769 1.01054186 1.01071122 1.01087614\n",
+      " 1.01103693 1.01119388 1.01134726 1.01149728 1.01164416 1.0117881\n",
+      " 1.01192925 1.01206778 1.01220384 1.01233756 1.01246906 1.01259845\n",
+      " 1.01272584 1.01285132 1.01297499 1.01309693 1.01321722 1.01333593\n",
+      " 1.01345313 1.01356888 1.01368325 1.0137963  1.01390807 1.01401862\n",
+      " 1.014128   1.01423625 1.01434341 1.01444953 1.01455464 1.01465878\n",
+      " 1.014762   1.01486431 1.01496575 1.01506636 1.01516615 1.01526517\n",
+      " 1.01536343 1.01546097 1.0155578  1.01565395 1.01574945 1.01584431\n",
+      " 1.01593855 1.01603221 1.01612528 1.0162178  1.01630978 1.01640124\n",
+      " 1.0164922  1.01658267 1.01667267 1.01676221 1.01685131 1.01693998\n",
+      " 1.01702824 1.01711611 1.01720358 1.01729068 1.01737742 1.01746381\n",
+      " 1.01754987 1.0176356  1.01772101 1.01780613 1.01789095 1.01797548\n",
+      " 1.01805975 1.01814376 1.01822751 1.01831102 1.0183943  1.01847735\n",
+      " 1.01856019 1.01864283 1.01872526 1.01880751 1.01888958 1.01897148\n",
+      " 1.01905322 1.0191348  1.01921623 1.01929753 1.01937869 1.01945973\n",
+      " 1.01954066 1.01962148 1.01970219 1.01978281 1.01986335 1.01994381\n",
+      " 1.02002419 1.02010452 1.02018478 1.020265   1.02034517 1.0204253\n",
+      " 1.02050541 1.02058549 1.02066556 1.02074562 1.02082568 1.02090575\n",
+      " 1.02098583 1.02106593 1.02114605 1.02122621 1.02130641 1.02138666\n",
+      " 1.02146696 1.02154732 1.02162776 1.02170827 1.02178886 1.02186954\n",
+      " 1.02195032 1.02203121 1.02211221 1.02219333 1.02227458 1.02235596\n",
+      " 1.02243749 1.02251917 1.02260101 1.02268301 1.02276519 1.02284756\n",
+      " 1.02293011 1.02301287 1.02309584 1.02317903 1.02326244 1.02334609\n",
+      " 1.02342999 1.02351414 1.02359856 1.02368325 1.02376823 1.0238535\n",
+      " 1.02393908 1.02402498 1.02411121 1.02419777 1.02428469 1.02437197\n",
+      " 1.02445963 1.02454767 1.02463612 1.02472497 1.02481426 1.02490399\n",
+      " 1.02499418 1.02508483 1.02517598 1.02526762 1.02535978 1.02545248\n",
+      " 1.02554574 1.02563956 1.02573397 1.025829   1.02592465 1.02602095\n",
+      " 1.02611792 1.02621559 1.02631397 1.02641309 1.02651298 1.02661366\n",
+      " 1.02671516 1.02681751 1.02692074 1.02702487 1.02712995 1.027236\n",
+      " 1.02734306 1.02745116 1.02756035 1.02767067 1.02778216 1.02789487\n",
+      " 1.02800883 1.02812411 1.02824076 1.02835883 1.02847838 1.02859948\n",
+      " 1.02872219 1.02884657 1.02897272 1.02910071 1.02923062 1.02936254\n",
+      " 1.02949658 1.02963284 1.02977143 1.02991247 1.0300561  1.03020246\n",
+      " 1.03035169 1.03050397 1.03065949 1.03081842 1.03098101 1.03114748\n",
+      " 1.03131809 1.03149314 1.03167295 1.03185788 1.03204832 1.03224474\n",
+      " 1.03244764 1.0326576  1.03287529 1.03310146 1.033337   1.03358293\n",
+      " 1.03384049 1.0341111  1.03439653 1.03469889 1.03502083 1.03536566\n",
+      " 1.03573767 1.0361425  1.03658782 1.03708446 1.03764843 1.038305\n",
+      " 1.03909776 1.04011279 1.04156481 1.04439057] 0.000158\n",
+      "[0.00015847 0.00015867 0.0001588  0.0001589  0.00015898 0.00015904\n",
+      " 0.0001591  0.00015916 0.00015921 0.00015926 0.0001593  0.00015934\n",
+      " 0.00015938 0.00015942 0.00015945 0.00015949 0.00015952 0.00015955\n",
+      " 0.00015958 0.00015961 0.00015964 0.00015967 0.00015969 0.00015972\n",
+      " 0.00015974 0.00015977 0.00015979 0.00015982 0.00015984 0.00015986\n",
+      " 0.00015988 0.00015991 0.00015993 0.00015995 0.00015997 0.00015999\n",
+      " 0.00016001 0.00016003 0.00016005 0.00016007 0.00016009 0.00016011\n",
+      " 0.00016013 0.00016014 0.00016016 0.00016018 0.0001602  0.00016021\n",
+      " 0.00016023 0.00016025 0.00016027 0.00016028 0.0001603  0.00016032\n",
+      " 0.00016033 0.00016035 0.00016036 0.00016038 0.0001604  0.00016041\n",
+      " 0.00016043 0.00016044 0.00016046 0.00016047 0.00016049 0.0001605\n",
+      " 0.00016052 0.00016053 0.00016055 0.00016056 0.00016058 0.00016059\n",
+      " 0.00016061 0.00016062 0.00016063 0.00016065 0.00016066 0.00016068\n",
+      " 0.00016069 0.0001607  0.00016072 0.00016073 0.00016075 0.00016076\n",
+      " 0.00016077 0.00016079 0.0001608  0.00016081 0.00016083 0.00016084\n",
+      " 0.00016085 0.00016087 0.00016088 0.00016089 0.00016091 0.00016092\n",
+      " 0.00016093 0.00016095 0.00016096 0.00016097 0.00016098 0.000161\n",
+      " 0.00016101 0.00016102 0.00016104 0.00016105 0.00016106 0.00016107\n",
+      " 0.00016109 0.0001611  0.00016111 0.00016113 0.00016114 0.00016115\n",
+      " 0.00016116 0.00016118 0.00016119 0.0001612  0.00016121 0.00016123\n",
+      " 0.00016124 0.00016125 0.00016127 0.00016128 0.00016129 0.0001613\n",
+      " 0.00016132 0.00016133 0.00016134 0.00016135 0.00016137 0.00016138\n",
+      " 0.00016139 0.0001614  0.00016142 0.00016143 0.00016144 0.00016146\n",
+      " 0.00016147 0.00016148 0.00016149 0.00016151 0.00016152 0.00016153\n",
+      " 0.00016155 0.00016156 0.00016157 0.00016158 0.0001616  0.00016161\n",
+      " 0.00016162 0.00016164 0.00016165 0.00016166 0.00016168 0.00016169\n",
+      " 0.0001617  0.00016172 0.00016173 0.00016174 0.00016176 0.00016177\n",
+      " 0.00016178 0.0001618  0.00016181 0.00016182 0.00016184 0.00016185\n",
+      " 0.00016186 0.00016188 0.00016189 0.00016191 0.00016192 0.00016193\n",
+      " 0.00016195 0.00016196 0.00016198 0.00016199 0.00016201 0.00016202\n",
+      " 0.00016204 0.00016205 0.00016207 0.00016208 0.0001621  0.00016211\n",
+      " 0.00016213 0.00016214 0.00016216 0.00016217 0.00016219 0.0001622\n",
+      " 0.00016222 0.00016224 0.00016225 0.00016227 0.00016229 0.0001623\n",
+      " 0.00016232 0.00016234 0.00016235 0.00016237 0.00016239 0.00016241\n",
+      " 0.00016243 0.00016244 0.00016246 0.00016248 0.0001625  0.00016252\n",
+      " 0.00016254 0.00016256 0.00016258 0.0001626  0.00016262 0.00016264\n",
+      " 0.00016266 0.00016268 0.0001627  0.00016273 0.00016275 0.00016277\n",
+      " 0.0001628  0.00016282 0.00016284 0.00016287 0.00016289 0.00016292\n",
+      " 0.00016295 0.00016298 0.000163   0.00016303 0.00016306 0.00016309\n",
+      " 0.00016313 0.00016316 0.00016319 0.00016323 0.00016327 0.00016331\n",
+      " 0.00016335 0.00016339 0.00016343 0.00016348 0.00016353 0.00016359\n",
+      " 0.00016365 0.00016371 0.00016378 0.00016386 0.00016395 0.00016405\n",
+      " 0.00016418 0.00016434 0.00016457 0.00016501] 1.0\n",
+      "<PySDM.backends.numba.storage.Storage object at 0x7fc34d3f8970> 34000000.0\n"
+     ]
+    },
+    {
+     "output_type": "error",
+     "ename": "TypingError",
+     "evalue": "Failed in nopython mode pipeline (step: nopython frontend)\nNo implementation of function Function(<built-in function imul>) found for signature:\n \n >>> imul(array(int64, 1d, C), float64)\n \nThere are 8 candidate implementations:\n      - Of which 4 did not match due to:\n      Overload of function 'imul': File: <numerous>: Line N/A.\n        With argument(s): '(array(int64, 1d, C), float64)':\n       No match.\n      - Of which 2 did not match due to:\n      Overload in function 'NumpyRulesInplaceArrayOperator.generic': File: numba/core/typing/npydecl.py: Line 213.\n        With argument(s): '(array(int64, 1d, C), float64)':\n       Rejected as the implementation raised a specific error:\n         AttributeError: 'NoneType' object has no attribute 'args'\n  raised from /Users/emilydejong/opt/anaconda3/envs/edjPySDM/lib/python3.9/site-packages/numba/core/typing/npydecl.py:224\n      - Of which 2 did not match due to:\n      Operator Overload in function 'imul': File: unknown: Line unknown.\n        With argument(s): '(array(int64, 1d, C), float64)':\n       No match for registered cases:\n        * (int64, int64) -> int64\n        * (int64, uint64) -> int64\n        * (uint64, int64) -> int64\n        * (uint64, uint64) -> uint64\n        * (float32, float32) -> float32\n        * (float64, float64) -> float64\n        * (complex64, complex64) -> complex64\n        * (complex128, complex128) -> complex128\n\nDuring: typing of intrinsic-call at /Users/emilydejong/Documents/PySDM/PySDM/backends/numba/impl/storage_impl.py (36)\n\nFile \"../../PySDM/backends/numba/impl/storage_impl.py\", line 36:\ndef multiply(output, multiplier):\n    <source elided>\n    output *= multiplier\n\n ^\n",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mTypingError\u001b[0m                               Traceback (most recent call last)",
+      "\u001b[0;32m<ipython-input-7-d4ce0bf34c72>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mstep\u001b[0m \u001b[0;32min\u001b[0m \u001b[0msettings\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0moutput_steps\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m     \u001b[0;31m#print(step, flush=True)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m     \u001b[0mcore\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstep\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mcore\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mn_steps\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      4\u001b[0m     pyplot.step(x=settings.radius_bins_edges[:-1] / si.micrometres, \n\u001b[1;32m      5\u001b[0m                 \u001b[0my\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mcore\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mproducts\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'dv/dlnr'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msettings\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mradius_bins_edges\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0msettings\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrho\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m~/Documents/PySDM/PySDM/core.py\u001b[0m in \u001b[0;36mrun\u001b[0;34m(self, steps)\u001b[0m\n\u001b[1;32m    116\u001b[0m             \u001b[0;32mfor\u001b[0m \u001b[0mkey\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdynamic\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdynamics\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mitems\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    117\u001b[0m                 \u001b[0;32mwith\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtimers\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 118\u001b[0;31m                     \u001b[0mdynamic\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    119\u001b[0m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mn_steps\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    120\u001b[0m             \u001b[0mreversed_order_so_that_environment_is_last\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mreversed\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mobservers\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m~/Documents/PySDM/PySDM/dynamics/spontaneous_breakup.py\u001b[0m in \u001b[0;36m__call__\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    100\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madaptive\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    101\u001b[0m                 \u001b[0;32mfor\u001b[0m \u001b[0m_\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__substeps\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 102\u001b[0;31m                     \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstep\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    103\u001b[0m             \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    104\u001b[0m                 \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdt_left\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcore\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdt\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m~/Documents/PySDM/PySDM/dynamics/spontaneous_breakup.py\u001b[0m in \u001b[0;36mstep\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    123\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    124\u001b[0m         \u001b[0;31m# (3) Compute the number of fragments\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 125\u001b[0;31m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcompute_n_fragment\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mn_fragment\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrand_frag\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    126\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    127\u001b[0m         \u001b[0;31m# (4) Perform the collisional-breakup step:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m~/Documents/PySDM/PySDM/dynamics/spontaneous_breakup.py\u001b[0m in \u001b[0;36mcompute_n_fragment\u001b[0;34m(self, n_fragment, u01)\u001b[0m\n\u001b[1;32m    139\u001b[0m     \u001b[0;31m# (3) Compute n_fragment\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    140\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mcompute_n_fragment\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mn_fragment\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mu01\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 141\u001b[0;31m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfragmentation\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn_fragment\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mu01\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
+      "\u001b[0;32m~/Documents/PySDM/PySDM/physics/spontaneous_breakup_fragmentations/expo_cube.py\u001b[0m in \u001b[0;36m__call__\u001b[0;34m(self, output, u01)\u001b[0m\n\u001b[1;32m     21\u001b[0m         \u001b[0moutput\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcore\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mparticles\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'volume'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     22\u001b[0m         \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0moutput\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mC\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 23\u001b[0;31m         \u001b[0moutput\u001b[0m \u001b[0;34m*=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mC\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     24\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     25\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mregister\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbuilder\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m~/Documents/PySDM/PySDM/backends/numba/storage.py\u001b[0m in \u001b[0;36m__imul__\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m     71\u001b[0m             \u001b[0mimpl\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmultiply\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     72\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 73\u001b[0;31m             \u001b[0mimpl\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmultiply\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     74\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     75\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m~/opt/anaconda3/envs/edjPySDM/lib/python3.9/site-packages/numba/core/dispatcher.py\u001b[0m in \u001b[0;36m_compile_for_args\u001b[0;34m(self, *args, **kws)\u001b[0m\n\u001b[1;32m    418\u001b[0m                 \u001b[0me\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpatch_message\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmsg\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    419\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 420\u001b[0;31m             \u001b[0merror_rewrite\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0me\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'typing'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    421\u001b[0m         \u001b[0;32mexcept\u001b[0m \u001b[0merrors\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mUnsupportedError\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0me\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    422\u001b[0m             \u001b[0;31m# Something unsupported is present in the user code, add help info\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m~/opt/anaconda3/envs/edjPySDM/lib/python3.9/site-packages/numba/core/dispatcher.py\u001b[0m in \u001b[0;36merror_rewrite\u001b[0;34m(e, issue_type)\u001b[0m\n\u001b[1;32m    359\u001b[0m                 \u001b[0;32mraise\u001b[0m \u001b[0me\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    360\u001b[0m             \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 361\u001b[0;31m                 \u001b[0;32mraise\u001b[0m \u001b[0me\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mwith_traceback\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    362\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    363\u001b[0m         \u001b[0margtypes\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;31mTypingError\u001b[0m: Failed in nopython mode pipeline (step: nopython frontend)\nNo implementation of function Function(<built-in function imul>) found for signature:\n \n >>> imul(array(int64, 1d, C), float64)\n \nThere are 8 candidate implementations:\n      - Of which 4 did not match due to:\n      Overload of function 'imul': File: <numerous>: Line N/A.\n        With argument(s): '(array(int64, 1d, C), float64)':\n       No match.\n      - Of which 2 did not match due to:\n      Overload in function 'NumpyRulesInplaceArrayOperator.generic': File: numba/core/typing/npydecl.py: Line 213.\n        With argument(s): '(array(int64, 1d, C), float64)':\n       Rejected as the implementation raised a specific error:\n         AttributeError: 'NoneType' object has no attribute 'args'\n  raised from /Users/emilydejong/opt/anaconda3/envs/edjPySDM/lib/python3.9/site-packages/numba/core/typing/npydecl.py:224\n      - Of which 2 did not match due to:\n      Operator Overload in function 'imul': File: unknown: Line unknown.\n        With argument(s): '(array(int64, 1d, C), float64)':\n       No match for registered cases:\n        * (int64, int64) -> int64\n        * (int64, uint64) -> int64\n        * (uint64, int64) -> int64\n        * (uint64, uint64) -> uint64\n        * (float32, float32) -> float32\n        * (float64, float64) -> float64\n        * (complex64, complex64) -> complex64\n        * (complex128, complex128) -> complex128\n\nDuring: typing of intrinsic-call at /Users/emilydejong/Documents/PySDM/PySDM/backends/numba/impl/storage_impl.py (36)\n\nFile \"../../PySDM/backends/numba/impl/storage_impl.py\", line 36:\ndef multiply(output, multiplier):\n    <source elided>\n    output *= multiplier\n\n ^\n"
+     ]
+    },
+    {
+     "output_type": "display_data",
+     "data": {
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYEAAAD4CAYAAAAKA1qZAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8rg+JYAAAACXBIWXMAAAsTAAALEwEAmpwYAAAUL0lEQVR4nO3df4xl5X3f8fenu4HYrhdngVjrXbY7FZtGg62QeMRiNarSuLhEtbNExd0NTo0iGizFKGnVqsKRjBOUVEWqmtoFWd4YYkDdgEXiMm1JaBwcJa7wZIcYFTMO6hQw7HYTlh9hE0eYLv32j3vu5u7dO8ydnR/33jnvlzSae859ztlzj87ezzw/znNSVUiS2ulvjPoAJEmjYwhIUosZApLUYoaAJLWYISBJLbZ11AewEhdddFHt2bNn1IchSRPlsccee7GqLh703kSFwJ49e5ifnx/1YUjSREnyraXeszlIklrMEJCkFjMEJKnFDAFJajFDQJJazBCQpBYzBCSpxSbqPgFtLofnnuPBx4+dXt5/+U6u27d7hEcktY81AY3Mg48fY+H4SQAWjp88IxAkbQxDQCM1vWMb93/sfUzv2DbqQ5FayRCQpBYzBCSpxQwBSWoxQ0CSWswQkKQWMwQkqcUMAUlqMUNAklrMEJCkFjMEJKnFnEBOE6F3sjknmpPWjiGgidA72RxgCEhrxBDQxHCSOWnt2ScgSS1mCEhSixkCktRihoAktZgdw1o1h29Kk8sQ0KoNM3xz0EPlJY2eIaA1sdzwzW5QTO/YdkZgSBot+wS0YXyovDR+DAFJarGhQiDJ1UmeSrKY5OYB75+f5P7m/bkke5r1VyV5LMkTze8f7dnmvc36xSSfSZI1+1SSpKEsGwJJtgB3AD8GTAM/mWS6r9gNwCtVdSnwq8BtzfoXgQ9V1XuA64F7e7b5LPAzwN7m5+pVfA5J0jkYpiZwBbBYVU9X1evAfcD+vjL7gbub1w8A70+Sqvp6Vf2fZv2TwFuaWsMOYFtVfa2qCrgHuGa1H0aStDLDhMBO4Pme5aPNuoFlquoU8CpwYV+Zfwz8cVV9pyl/dJl9ApDkxiTzSeZPnDgxxOFKkoa1IR3DSS6j00T0sZVuW1WHqmqmqmYuvvjitT84SWqxYULgGHBJz/KuZt3AMkm2AhcALzXLu4AvAR+tqv/dU37XMvvUJnB47jkOfO5R7w2QxtQwIXAE2JtkKsl5wEFgtq/MLJ2OX4BrgUeqqpK8A/hvwM1V9T+6havqOHAyyZXNqKCPAg+u7qNoHPXeJOZdwtL4WfaO4ao6leQm4GFgC3BXVT2Z5FZgvqpmgTuBe5MsAi/TCQqAm4BLgVuS3NKs+0BVvQD8LPAF4C3Abzc/2oS6N4kNY9D0Es5FJK2foaaNqKqHgIf61t3S8/o14MMDtvtl4JeX2Oc88O6VHKw2v0HTSxgC0vrxjmGNHaeXkDaOISBJLWYISFKLGQKS1GI+T0Ar1v8kMUmTyxDQivU/SWyQblB0R/pIGk+GgM7JSp4kZm1BGl+GgNbNSm4SA07XLqw5SBvHENBY6K0tWHOQNo4hoLFw3b7d3hksjYBDRCWpxQwBSWoxm4O06TgTqTQ8awIa2jAPiFk4fnLkD5HpvY9h4fjJMwJB0pkMAQ1tubH/+y/feXp456jvD3AmUmk4NgdpRXrH/vf/he0IH2nyWBOQpBYzBCSpxQwBSWoxQ0CSWswQkKQWc3SQluWzAaTNy5qAluWzAaTNy5qAhrLSZwNImgzWBDQSC8dPjnRqCUkd1gS04XyAjDQ+DAFtuLWaXsLZQqXVMwQ0sXo7rLtNS+MWAgaVxp19AlrSMFNHj9q4zxbqtNYad4aAljTM0FA7eJc37kGldrM5SG/qzYaG2sErTT5DQOfM5wdIk8/mIElqsaFCIMnVSZ5Kspjk5gHvn5/k/ub9uSR7mvUXJvlKkr9McnvfNr/f7PPx5ud71+QTadMbh+cYS5vFss1BSbYAdwBXAUeBI0lmq2qhp9gNwCtVdWmSg8BtwAHgNeCTwLubn34fqar5VX4GtUhv34NzGUmrN0yfwBXAYlU9DZDkPmA/0BsC+4FfbF4/ANyeJFX1beCrSS5du0PWehvnWUPth5DW1jDNQTuB53uWjzbrBpapqlPAq8CFQ+z715umoE8myRDltQGcNVRqj1GODvpIVR1L8nbgN4F/CtzTXyjJjcCNALt3+xfgRnHWUKkdhqkJHAMu6Vne1awbWCbJVuAC4KU322lVHWt+/wVwmE6z06Byh6pqpqpmLr744iEOV5I0rGFC4AiwN8lUkvOAg8BsX5lZ4Prm9bXAI1VVS+0wydYkFzWvvwv4IPCNlR68JGl1lm0OqqpTSW4CHga2AHdV1ZNJbgXmq2oWuBO4N8ki8DKdoAAgybPANuC8JNcAHwC+BTzcBMAW4MvAr63lB5MkLW+oPoGqegh4qG/dLT2vXwM+vMS2e5bY7XuHO0RJ0npx2gidNs5DQyWtD6eN0GkODZXax5qAzuDQUKldrAlIUosZApLUYoaAxpozhkrryz4Bje2oIGcMldafIaCxHRXkjKHS+jMEBDgqSGorQ0AaQrfJrGv/5TutpWhTsGNYGkK3yQw6ndW9gSBNMkNAGlK3yWycOs+l1bI5qMXGdVSQpI1jTaDFxnVUkKSNY02g5RwVJLWbNQFJajFDQJJazBCQpBazT6CFHBUkqcuaQAs5KkhSlzWBlnJU0GBOD6G2sSYg9XB6CLWNISD1cXoItYkhIEktZp9AizgqSFI/awIt4qggSf2sCbSMo4Ik9bImIEktZk1Ardd7b4D9JWobawItcHjuOQ587tHT4991pt57A+wvUdtYE2gBO4SXZ1+J2soQaAm/5CQNYnOQJLWYNQG1Tv8kcXYGq82GqgkkuTrJU0kWk9w84P3zk9zfvD+XZE+z/sIkX0nyl0lu79vmvUmeaLb5TJKsySfSaXYID9bbEQx2Bqvdlq0JJNkC3AFcBRwFjiSZraqFnmI3AK9U1aVJDgK3AQeA14BPAu9ufnp9FvgZYA54CLga+O3VfRz1skN4afaRSB3D1ASuABar6umqeh24D9jfV2Y/cHfz+gHg/UlSVd+uqq/SCYPTkuwAtlXV16qqgHuAa1bxObSE7pedc+JLGmSYENgJPN+zfLRZN7BMVZ0CXgUuXGafR5fZJwBJbkwyn2T+xIkTQxyuJGlYY98xXFWHgEMAMzMzNeLDmRiH555j7pmX2Te1fdSHMha8K1gabJiawDHgkp7lXc26gWWSbAUuAF5aZp+7ltmnVqH7hWdfQId3BUuDDVMTOALsTTJF54v6IHBdX5lZ4HrgUeBa4JGmrX+gqjqe5GSSK+l0DH8U+I/ncPx6E/umttsX0MPOYOlsy4ZAVZ1KchPwMLAFuKuqnkxyKzBfVbPAncC9SRaBl+kEBQBJngW2AecluQb4QDOy6GeBLwBvoTMqyJFBWhe9NQBJZxqqT6CqHqIzjLN33S09r18DPrzEtnuWWD/P2cNGpTXV2+xjE5B0trHvGNbK+AjJM123b7dNYtKbcO6gTcYbxCSthDWBTcgOUEnDsiYgSS1mTWCTsC9A0rmwJrBJ2Bcg6VxYE9hE7AuQtFLWBLRpLBw/6fMTpBUyBDaB7mRxbbb/8p2n+0JsEpOGZ3PQJuBkcd4UJp0rawKbhJPFSToXhoAktZghIEktZghIUosZApLUYo4OmkC9z8tt84ggSatnCEyg3uflStJqGAITykniJK0F+wQkqcUMAUlqMUNAklrMEJCkFrNjeEL0Dgude+Zl9k1tH/ERSdoMDIEJ4bBQSevB5qAJMr1jm0NDJa0pQ2DCLRw/aQ1B0jmzOWiC9U4Z4fQRks6FITDBfJqWpNWyOUiSWswQkKQWMwQkqcUMAUlqMTuGJ0x3FJCjgSStBUNgwjgiSNJaGqo5KMnVSZ5Kspjk5gHvn5/k/ub9uSR7et77RLP+qST/sGf9s0meSPJ4kvk1+TSSpBVZtiaQZAtwB3AVcBQ4kmS2qhZ6it0AvFJVlyY5CNwGHEgyDRwELgPeBXw5yfdV1RvNdn+/ql5cw88jSVqBYWoCVwCLVfV0Vb0O3Afs7yuzH7i7ef0A8P4kadbfV1XfqapngMVmf1qBw3PPMffMy6M+DEmb0DAhsBN4vmf5aLNuYJmqOgW8Cly4zLYF/PckjyW5cal/PMmNSeaTzJ84cWKIw918ulNI2xksaa2NsmP4h6vqWJLvBX43yZ9U1R/0F6qqQ8AhgJmZmdrogxyl7jMEFo6fZN/UdjuEJa25YWoCx4BLepZ3NesGlkmyFbgAeOnNtq2q7u8XgC9hM9FZugEwvWObtQBJ62KYEDgC7E0yleQ8Oh29s31lZoHrm9fXAo9UVTXrDzajh6aAvcAfJXlbkrcDJHkb8AHgG6v/OJtHtx9gesc27v/Y+6wFSFoXyzYHVdWpJDcBDwNbgLuq6skktwLzVTUL3Ancm2QReJlOUNCU+yKwAJwCPl5VbyR5J/ClTt8xW4HDVfU76/D5Jpb9AJI2wlB9AlX1EPBQ37pbel6/Bnx4iW1/BfiVvnVPAz+w0oNtA/sBJG0k5w4aM/YDSNpIThsxhrr9AJK03qwJSFKLGQJj4vDccxz43KPeGSxpQxkCY+LBx48ZAJI2nCEgSS1mx/AIdYeDOgpI0qgYAiNkE5CkUbM5SJJazBCQpBYzBCSpxQyBMbNvarsdxZI2jB3DY2Tf1Hani5C0oawJjIGF4ydZOH5y1IchqYWsCYyB6R3bAJ8dIGnjGQIj0n1ymE1AkkbJENhg3buEuzeJ+de/pFEyBDbQ4bnn+IUvPQH89SggnxwmaZQMgQ3SGwD/5ife45e/pLHg6KANYABIGleGwAZ48PFjgAEgafzYHLRO+qeJ3je13QCQNHYMgTXWP/pHksaZzUFrzACQNEkMAUlqMUNgnTkvkKRxZp/AOnNeIEnjzBBYQ935gMA7giVNBkNgDfSPCPJ+AEmTwhA4R90vfsC//iVNLENghXr/6n/7d29lesc2v/wlTSxDYBndL/2/ev0N3nreljPuAZjesc1nAUiaaIbAMrz5S9Jm5n0CktRiQ9UEklwNfBrYAny+qv5t3/vnA/cA7wVeAg5U1bPNe58AbgDeAH6uqh4eZp8bqbeTt1/3Rq99U9tPNwl1fzv2X9KkWzYEkmwB7gCuAo4CR5LMVtVCT7EbgFeq6tIkB4HbgANJpoGDwGXAu4AvJ/m+Zpvl9rmmfurzc3x18cWBX+a9o3v6Te/YZqevpE1rmJrAFcBiVT0NkOQ+YD/Q+4W9H/jF5vUDwO1J0qy/r6q+AzyTZLHZH0Psc8380n95kq8uvggwsH3f0T1aysLxkxz43KMsHD95+u7v3vXDbH8u20m9pt+1jU996LJ12fcwIbATeL5n+Siwb6kyVXUqyavAhc36r/Vt221DWW6fACS5EbgRYPfu1X9Jv2fnBWc16fjlr0F6m/u6NcL+9cs51+2kjTL2o4Oq6hBwCGBmZqbOZR+f+tBl65ai2ryu27d74B8IS60/1/1JozTM6KBjwCU9y7uadQPLJNkKXECng3ipbYfZpyRpnQ0TAkeAvUmmkpxHp6N3tq/MLHB98/pa4JGqqmb9wSTnJ5kC9gJ/NOQ+JUnrbNnmoKaN/ybgYTrDOe+qqieT3ArMV9UscCdwb9Px+zKdL3Wacl+k0+F7Cvh4Vb0BMGifa//xJElvJp0/2CfDzMxMzc/Pj/owJGmiJHmsqmYGvecdw5LUYoaAJLWYISBJLWYISFKLTVTHcJITwLdGfRyrdBHw4qgPYsx4Ts7mOTmb5+Rsw56Tv1VVFw96Y6JCYDNIMr9UL31beU7O5jk5m+fkbGtxTmwOkqQWMwQkqcUMgY13aNQHMIY8J2fznJzNc3K2VZ8T+wQkqcWsCUhSixkCktRihsA6SnJJkq8kWUjyZJKfb9ZvT/K7Sf5X8/t7Rn2sGy3JliRfT/Jfm+WpJHNJFpPc30wx3hpJ3pHkgSR/kuSbSd7X9uskyb9o/t98I8lvJPnutl0nSe5K8kKSb/SsG3hdpOMzzbn5n0l+aJh/wxBYX6eAf1lV08CVwMeTTAM3A79XVXuB32uW2+bngW/2LN8G/GpVXQq8AtwwkqManU8Dv1NV3w/8AJ1z09rrJMlO4OeAmap6N50p5w/SvuvkC8DVfeuWui5+jM4zW/bSeSTvZ4f5BwyBdVRVx6vqj5vXf0HnP/ZOYD9wd1PsbuCakRzgiCTZBfwj4PPNcoAfBR5oirTqnCS5APh7dJ7LQVW9XlV/TsuvEzrPO3lL87TCtwLHadl1UlV/QOcZLb2Wui72A/dUx9eAdyTZsdy/YQhskCR7gB8E5oB3VtXx5q0/Bd45quMakf8A/Gvg/zXLFwJ/XlWnmuWjdMKyLaaAE8CvN01kn0/yNlp8nVTVMeDfAc/R+fJ/FXiMdl8nXUtdFzuB53vKDXV+DIENkORvAr8J/POqOtn7XvMYztaM003yQeCFqnps1McyRrYCPwR8tqp+EPg2fU0/LbxOvofOX7ZTwLuAt3F2s0jrrcV1YQissyTfRScA/lNV/Vaz+s+61bTm9wujOr4R+LvAjyd5FriPTvX+03Sqrt3Hne4Cjo3m8EbiKHC0quaa5QfohEKbr5N/ADxTVSeq6v8Cv0Xn2mnzddK11HVxDLikp9xQ58cQWEdNW/edwDer6t/3vDULXN+8vh54cKOPbVSq6hNVtauq9tDp6Hukqj4CfAW4tinWtnPyp8DzSf5Os+r9dJ7L3drrhE4z0JVJ3tr8P+qek9ZeJz2Wui5mgY82o4SuBF7taTZakncMr6MkPwz8IfAEf93+/Qt0+gW+COymMzX2P6mq/s6fTS/JjwD/qqo+mORv06kZbAe+DvxUVX1nhIe3oZJcTqej/DzgaeCn6fyR1trrJMkvAQfojLL7OvDP6LRxt+Y6SfIbwI/QmTL6z4BPAf+ZAddFE5a302k2+yvgp6tq2YeyGwKS1GI2B0lSixkCktRihoAktZghIEktZghIUosZApLUYoaAJLXY/wfYOr5kES7VVwAAAABJRU5ErkJggg==",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     }
+    }
+   ],
+   "metadata": {}
+  },
   {
    "cell_type": "code",
    "execution_count": null,

From afcb1835235ca7619d3728452cc1b641ca01a954 Mon Sep 17 00:00:00 2001
From: Ben Mackay <jbmackay@caltech.edu>
Date: Fri, 15 Oct 2021 10:55:02 -0400
Subject: [PATCH 11/12] Minor documentation additions

---
 .../physics/spontaneous_breakup_fragmentations/expo_cube.py | 6 +++---
 PySDM/physics/spontaneous_breakup_rates/constant.py         | 3 +++
 PySDM/physics/spontaneous_breakup_rates/exponential.py      | 3 +++
 3 files changed, 9 insertions(+), 3 deletions(-)

diff --git a/PySDM/physics/spontaneous_breakup_fragmentations/expo_cube.py b/PySDM/physics/spontaneous_breakup_fragmentations/expo_cube.py
index 42eecb235e..92071b74c6 100644
--- a/PySDM/physics/spontaneous_breakup_fragmentations/expo_cube.py
+++ b/PySDM/physics/spontaneous_breakup_fragmentations/expo_cube.py
@@ -4,10 +4,10 @@
 where D0 is the parent droplet size, Q(D) dD is the number of drops of size D
 formed from the breakup. Then it can be shown that:
     N_frag = int (Q(D0, D) dD) = A * (D0)**3 / B
-and furthermore for consistency with mass conservation,
-    6*A = B**3
+and furthermore for consistency with mass conservation:
+    D0**3 = int(D**3 Q(D0, D) dD) => 6*A = B**4
 
-Therefore this function takes a single argument C = A/B = 1/6 * B**2, and 
+Therefore this function takes a single argument C = A/B = 1/6 * B**3, and 
 translates to a fragmentation function which is cubic in the parent size D0.
     N_frag = C * (D0)**3
 '''
diff --git a/PySDM/physics/spontaneous_breakup_rates/constant.py b/PySDM/physics/spontaneous_breakup_rates/constant.py
index 20b4be3ea4..8e44696a8e 100644
--- a/PySDM/physics/spontaneous_breakup_rates/constant.py
+++ b/PySDM/physics/spontaneous_breakup_rates/constant.py
@@ -1,3 +1,6 @@
+'''
+Constant rate of breakup for particles of any size
+'''
 class Constant:
 
     def __init__(self, a):
diff --git a/PySDM/physics/spontaneous_breakup_rates/exponential.py b/PySDM/physics/spontaneous_breakup_rates/exponential.py
index 876eba7610..fbc045c113 100644
--- a/PySDM/physics/spontaneous_breakup_rates/exponential.py
+++ b/PySDM/physics/spontaneous_breakup_rates/exponential.py
@@ -1,5 +1,8 @@
 from PySDM.physics import constants as const
 
+''' 
+Exponential breakup rate by particle diameter: a * r**b
+'''
 class Expon:
 
     def __init__(self, a, b):

From fe091cb823e1ff084d5f672329b67790e1006de1 Mon Sep 17 00:00:00 2001
From: Ben Mackay <jbmackay@caltech.edu>
Date: Fri, 22 Oct 2021 15:07:32 -0700
Subject: [PATCH 12/12] Add basic docstrings to modules and classes.

---
 PySDM/dynamics/spontaneous_breakup.py                     | 8 +++++---
 .../spontaneous_breakup_fragmentations/__init__.py        | 3 +++
 .../spontaneous_breakup_fragmentations/always_n.py        | 1 +
 .../spontaneous_breakup_fragmentations/expo_cube.py       | 2 ++
 PySDM/physics/spontaneous_breakup_rates/__init__.py       | 3 +++
 PySDM/physics/spontaneous_breakup_rates/constant.py       | 5 +----
 PySDM/physics/spontaneous_breakup_rates/exponential.py    | 5 +----
 7 files changed, 16 insertions(+), 11 deletions(-)

diff --git a/PySDM/dynamics/spontaneous_breakup.py b/PySDM/dynamics/spontaneous_breakup.py
index e44cc07bb1..1115ba8e08 100644
--- a/PySDM/dynamics/spontaneous_breakup.py
+++ b/PySDM/dynamics/spontaneous_breakup.py
@@ -1,5 +1,7 @@
 """
-Created at 10.05.21 by jb-mackay
+Single particle spontaneous breakup into uniformly sized fragments.
+
+Created at 10.05.21 by jb-mackay & edejong
 """
 
 import numpy as np
@@ -114,7 +116,7 @@ def __call__(self):
             self.rnd_opt_frag.reset()
 
     def step(self):
-        # (1) Make the superdroplet list and random numbers for fragmentation
+        # (1) Make the random numbers for fragmentation
         rand = self.rnd_opt.get_random_arrays() # does event occur
         rand_frag = self.rnd_opt_frag.get_random_arrays() # for # fragments
         
@@ -129,7 +131,7 @@ def step(self):
         if self.adaptive:
             self.core.particles.cut_working_length(self.core.particles.adaptive_sdm_end(self.dt_left))
 
-    # (2) TODO: Does spont breakup occur?
+    # (2) Does spont breakup occur?
     def compute_probability(self, prob):
         self.breakup_rate(self.breakup_rate_temp)
         prob[:] = self.breakup_rate_temp
diff --git a/PySDM/physics/spontaneous_breakup_fragmentations/__init__.py b/PySDM/physics/spontaneous_breakup_fragmentations/__init__.py
index 4421292b04..47ab773f12 100644
--- a/PySDM/physics/spontaneous_breakup_fragmentations/__init__.py
+++ b/PySDM/physics/spontaneous_breakup_fragmentations/__init__.py
@@ -1,2 +1,5 @@
+"""
+Single droplet breakup fragmentation functions.
+"""
 from .always_n import SpontaneousAlwaysN
 from .expo_cube import SpontaneousExpoCube
\ No newline at end of file
diff --git a/PySDM/physics/spontaneous_breakup_fragmentations/always_n.py b/PySDM/physics/spontaneous_breakup_fragmentations/always_n.py
index a024c11a89..7808a31f2d 100644
--- a/PySDM/physics/spontaneous_breakup_fragmentations/always_n.py
+++ b/PySDM/physics/spontaneous_breakup_fragmentations/always_n.py
@@ -2,6 +2,7 @@
 
 
 class SpontaneousAlwaysN:
+    """Breakup into `n` droplets"""
 
     def __init__(self, n):
         self.core = None
diff --git a/PySDM/physics/spontaneous_breakup_fragmentations/expo_cube.py b/PySDM/physics/spontaneous_breakup_fragmentations/expo_cube.py
index 92071b74c6..7b906c616c 100644
--- a/PySDM/physics/spontaneous_breakup_fragmentations/expo_cube.py
+++ b/PySDM/physics/spontaneous_breakup_fragmentations/expo_cube.py
@@ -1,4 +1,6 @@
 '''
+Linear fragmentation function in volume.
+
 For a fragmentation function of the form:
     Q(D0, D) dD = A * (D0)**3 * exp(-B * D) dD
 where D0 is the parent droplet size, Q(D) dD is the number of drops of size D
diff --git a/PySDM/physics/spontaneous_breakup_rates/__init__.py b/PySDM/physics/spontaneous_breakup_rates/__init__.py
index c2076fb6f5..7581bd755d 100644
--- a/PySDM/physics/spontaneous_breakup_rates/__init__.py
+++ b/PySDM/physics/spontaneous_breakup_rates/__init__.py
@@ -1,2 +1,5 @@
+"""
+Single droplet spontaneous breakup rates.
+"""
 from .constant import Constant
 from .exponential import Expon
\ No newline at end of file
diff --git a/PySDM/physics/spontaneous_breakup_rates/constant.py b/PySDM/physics/spontaneous_breakup_rates/constant.py
index 8e44696a8e..95cf959dc1 100644
--- a/PySDM/physics/spontaneous_breakup_rates/constant.py
+++ b/PySDM/physics/spontaneous_breakup_rates/constant.py
@@ -1,8 +1,5 @@
-'''
-Constant rate of breakup for particles of any size
-'''
 class Constant:
-
+    '''Constant rate of breakup for particles of any size'''
     def __init__(self, a):
         self.a = a
         self.core = None
diff --git a/PySDM/physics/spontaneous_breakup_rates/exponential.py b/PySDM/physics/spontaneous_breakup_rates/exponential.py
index fbc045c113..300abc91ec 100644
--- a/PySDM/physics/spontaneous_breakup_rates/exponential.py
+++ b/PySDM/physics/spontaneous_breakup_rates/exponential.py
@@ -1,10 +1,7 @@
 from PySDM.physics import constants as const
 
-''' 
-Exponential breakup rate by particle diameter: a * r**b
-'''
 class Expon:
-
+    '''Exponential breakup rate by particle diameter: a * r**b'''
     def __init__(self, a, b):
         self.a = a
         self.b = b