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Copy file name to clipboardExpand all lines: documentation/chapters/emissions.tex
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@@ -10,7 +10,7 @@ \chapter{Acoustic emissions}
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\vspace{1mm} \\ \hline
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{\tt BUBBLE} & {\tt Emissions IC <float>} & Computes the acoustic emissions using the standard incompressible model, Section \ref{sec:emissionsic}.\\
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& {\tt Emissions FSIC <float>} & Computes the acoustic emissions using the finite-speed incompressible model, Section \ref{sec:emissionsfsic}.\\
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& {\tt Emissions QA <float>} & Computes the acoustic emissions using the quasi-acoustic model, Section \ref{sec:emissionsqa}.\\
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& {\tt Emissions QA <float>} & Computes the acoustic emissions using the quasi-acoustic model\citep{Coulombel2024}, Section \ref{sec:emissionsqa}.\\
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& {\tt Emissions EV <float>} & Computes the acoustic emissions based on the Kirkwood-Bethe hypothesis, Section \ref{sec:emissionskb}, with the explicit expression for velocity, see Eq.~\eqref{eq:u_rt}.\\
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& {\tt Emissions TIV <float>} & Computes the acoustic emissions using the model of \citet{Hickling1963} based on the Kirkwood-Bethe hypothesis, Section \ref{sec:emissionskb}, with the temporally-integrated velocity, see Eq.~\eqref{eq:dudt_rt}.\\
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& {\tt EmissionIntegration Euler} & Integrates the radial position and, if applicable, the velocity using an Euler scheme.\\
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\end{align}
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and $\tau$ is the time at which the acoustic information is emitted at the bubble wall. For $t=\tau$ with $r(t)=R(\tau)$, Eq.~(\ref{eq:u_rt_qa}) reduces to $u(R,\tau)=\dot{R}(\tau)$ and Eq.~(\ref{eq:p_rt_qa}) reduces to $p(R,\tau)=p_\mathrm{L}(\tau)$, thus satisfying the boundary conditions at the bubble wall.
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The quasi-acoustic model is consistent in its modelling assumptions with the Keller-Miksis model, Eq.~\eqref{eq:keller}. The applicability of the quasi-acoustic model is limited to small Mach numbers, $(\dot{R}/c_0)^2\ll1$, as it incorporates a finite propagation speed of the acoustic emissions and the nonlinear pressure contributions resulting from the flow, but since all parts of the wave propagate with speed $c_0$, the quasi-acoustic model can neither describe the nonlinear distortion of acoustic waves nor the formation of shock fronts.
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The quasi-acoustic model is consistent in its modelling assumptions with the Keller-Miksis model, Eq.~\eqref{eq:keller}\citep{Coulombel2024}. The applicability of the quasi-acoustic model is limited to small Mach numbers, $(\dot{R}/c_0)^2\ll1$, as it incorporates a finite propagation speed of the acoustic emissions and the nonlinear pressure contributions resulting from the flow, but since all parts of the wave propagate with speed $c_0$, the quasi-acoustic model can neither describe the nonlinear distortion of acoustic waves nor the formation of shock fronts.
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