Template:Standard linear wave scattering equations without body condition: Difference between revisions

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Mike smith (talk | contribs)
186 edits
standard notation fix
Line 6: Line 6:
</math></center>
</math></center>
<center><math>
<center><math>
  \partial_n \phi  =\mathrm{i} \omega \zeta,\,z=0,\,\,\mathbf{x} \in F,
  \partial_n \phi  = \alpha \phi,\,z=0,\,\,\mathbf{x} \in \partial \Omega_{\mathrm{F}},
</math></center>
</math></center>
(note that the last expression can be obtained from combining the expressions:
<center><math>
<center><math>
\mathrm{i} \omega \phi  = -g\zeta,\,z=0,\,\,\mathbf{x} \in F,
\partial_n \phi  =\mathrm{i} \omega \zeta,\,z=0,\,\,\mathbf{x} \in \partial \Omega_{\mathrm{F}},
</math></center>
</math></center>
(note that the latter two can be combined as
<center><math>
<center><math>
\partial_n \phi  = \alpha \phi,\,z=0,\,\,\mathbf{x} \in F,
\mathrm{i} \omega \phi  = -g\zeta,\,z=0,\,\,\mathbf{x} \in \partial \Omega_{\mathrm{F}},
</math></center>
</math></center>
where <math>\alpha = \omega^2/g </math>)
where <math>\alpha = \omega^2/g </math>)

Revision as of 21:37, 3 September 2009

[math]\displaystyle{ \Delta\phi=0, \, -h\lt z\lt 0,\,\,\,\mathbf{x} \in \Omega }[/math]
[math]\displaystyle{ \partial_n\phi = 0, \, z=-h, }[/math]
[math]\displaystyle{ \partial_n \phi = \alpha \phi,\,z=0,\,\,\mathbf{x} \in \partial \Omega_{\mathrm{F}}, }[/math]


(note that the last expression can be obtained from combining the expressions:

[math]\displaystyle{ \partial_n \phi =\mathrm{i} \omega \zeta,\,z=0,\,\,\mathbf{x} \in \partial \Omega_{\mathrm{F}}, }[/math]
[math]\displaystyle{ \mathrm{i} \omega \phi = -g\zeta,\,z=0,\,\,\mathbf{x} \in \partial \Omega_{\mathrm{F}}, }[/math]

where [math]\displaystyle{ \alpha = \omega^2/g }[/math])

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