Template:Standard linear wave scattering equations without body condition: Difference between revisions
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<center><math> | <center><math> | ||
\Delta\phi=0, | \begin{align} | ||
\Delta\phi &=0, &-h<z<0,\,\,\mathbf{x} \in \Omega \\ | |||
\partial_z\phi &= 0, &z=-h, \\ | |||
\partial_z\phi = 0, | \partial_z \phi &= \alpha \phi, &z=0,\,\,\mathbf{x} \in \partial \Omega_{\mathrm{F}}, | ||
\end{align} | |||
\partial_z \phi = \alpha \phi, | |||
</math></center> | </math></center> | ||
| Line 12: | Line 10: | ||
(note that the last expression can be obtained from combining the expressions: | (note that the last expression can be obtained from combining the expressions: | ||
<center><math> | <center><math> | ||
\partial_z \phi = -\mathrm{i} \omega \zeta, | \begin{align} | ||
\partial_z \phi &= -\mathrm{i} \omega \zeta, &z=0,\,\,\mathbf{x} \in \partial \Omega_{\mathrm{F}}, \\ | |||
\mathrm{i} \omega \phi &= g\zeta, &z=0,\,\,\mathbf{x} \in \partial \Omega_{\mathrm{F}}, | |||
\mathrm{i} \omega \phi = g\zeta, | \end{align} | ||
</math></center> | </math></center> | ||
where <math>\alpha = \omega^2/g </math>) | where <math>\alpha = \omega^2/g \,</math>) | ||
Latest revision as of 10:40, 6 November 2010
(note that the last expression can be obtained from combining the expressions:
where [math]\displaystyle{ \alpha = \omega^2/g \, }[/math])
