Template:Standard linear wave scattering equations without body condition - Revision history

Adi Kurniawan at 10:40, 6 November 2010

2010-11-06T10:40:05Z

← Older revision		Revision as of 10:40, 6 November 2010
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	<center><math>		<center><math>
	\Delta\phi=0, \, -h<z<0,\,\,\,\mathbf{x} \in \Omega		\begin{align}
	~~</math></center>~~		\Delta\phi &=0, &-h<z<0,\,\,\mathbf{x} \in \Omega \\
	~~<center><math>~~		\partial_z\phi &= 0, &z=-h, \\
	\partial_z\phi = 0, \, z=-h,		\partial_z \phi &= \alpha \phi, &z=0,\,\,\mathbf{x} \in \partial \Omega_{\mathrm{F}},
	~~</math></center>~~		\end{align}
	~~<center><math>~~
	\partial_z \phi = \alpha \phi,\,z=0,\,\,\mathbf{x} \in \partial \Omega_{\mathrm{F}},
	</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,\,z=0,\,\,\mathbf{x} \in \partial \Omega_{\mathrm{F}},		\begin{align}
	~~</math></center>~~		\partial_z \phi &= -\mathrm{i} \omega \zeta, &z=0,\,\,\mathbf{x} \in \partial \Omega_{\mathrm{F}}, \\
	~~<center><math>~~		\mathrm{i} \omega \phi &= g\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}},		\end{align}
	</math></center>		</math></center>

	where <math>\alpha = \omega^2/g </math>)		where <math>\alpha = \omega^2/g \,</math>)

2010-04-28T09:39:19Z

← Older revision		Revision as of 09:39, 28 April 2010
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	</math></center>		</math></center>
	<center><math>		<center><math>
	-\mathrm{i} \omega \phi = -g\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}},
	</math></center>		</math></center>

	where <math>\alpha = \omega^2/g </math>)		where <math>\alpha = \omega^2/g </math>)

2010-04-28T09:32:24Z

← Older revision		Revision as of 09:32, 28 April 2010
Line 12:		Line 12:
	(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,\,z=0,\,\,\mathbf{x} \in \partial \Omega_{\mathrm{F}},		\partial_z \phi = -\mathrm{i} \omega \zeta,\,z=0,\,\,\mathbf{x} \in \partial \Omega_{\mathrm{F}},
	</math></center>		</math></center>
	<center><math>		<center><math>
	\mathrm{i} \omega \phi = -g\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}},
	</math></center>		</math></center>

	where <math>\alpha = \omega^2/g </math>)		where <math>\alpha = \omega^2/g </math>)

2009-11-07T09:30:01Z

← Older revision		Revision as of 09:30, 7 November 2009
Line 3:		Line 3:
	</math></center>		</math></center>
	<center><math>		<center><math>
	\~~partial_n~~\phi = 0, \, z=-h,		\partial_z\phi = 0, \, z=-h,
	</math></center>		</math></center>
	<center><math>		<center><math>
	\~~partial_n~~ \phi = \alpha \phi,\,z=0,\,\,\mathbf{x} \in \partial \Omega_{\mathrm{F}},		\partial_z \phi = \alpha \phi,\,z=0,\,\,\mathbf{x} \in \partial \Omega_{\mathrm{F}},
	</math></center>		</math></center>

Line 12:		Line 12:
	(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_n~~ \phi =\mathrm{i} \omega \zeta,\,z=0,\,\,\mathbf{x} \in \partial \Omega_{\mathrm{F}},		\partial_z \phi =\mathrm{i} \omega \zeta,\,z=0,\,\,\mathbf{x} \in \partial \Omega_{\mathrm{F}},
	</math></center>		</math></center>
	<center><math>		<center><math>

2009-09-03T21:37:53Z

standard notation fix

← Older revision		Revision as of 21:37, 3 September 2009
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>)

2009-09-01T10:08:01Z

← Older revision		Revision as of 10:08, 1 September 2009
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 =\mathrm{i} \omega \zeta,\,z=0,\,\,\mathbf{x} \in F,
	</math></center>		</math></center>
	<center><math>		<center><math>

2009-08-22T05:47:06Z

← Older revision		Revision as of 05:47, 22 August 2009
Line 15:		Line 15:
	\partial_n \phi = \alpha \phi,\,z=0,\,\,\mathbf{x} \in F,		\partial_n \phi = \alpha \phi,\,z=0,\,\,\mathbf{x} \in F,
	</math></center>		</math></center>
	where <math>\alpha = g\omega^2 </math>)		where <math>\alpha = \omega^2/g </math>)

2009-08-22T05:46:32Z

← Older revision		Revision as of 05:46, 22 August 2009
Line 9:		Line 9:
	</math></center>		</math></center>
	<center><math>		<center><math>
	\mathrm{i} \omega \phi = -\zeta,\,z=0,\,\,\mathbf{x} \in F,		\mathrm{i} \omega \phi = -g\zeta,\,z=0,\,\,\mathbf{x} \in F,
	</math></center>		</math></center>
	(note that the latter two can be combined as		(note that the latter two can be combined as
Line 15:		Line 15:
	\partial_n \phi = \alpha \phi,\,z=0,\,\,\mathbf{x} \in F,		\partial_n \phi = \alpha \phi,\,z=0,\,\,\mathbf{x} \in F,
	</math></center>		</math></center>
	where <math>\alpha = \omega^2 </math>)		where <math>\alpha = g\omega^2 </math>)

2009-08-21T11:44:05Z

← Older revision		Revision as of 11:44, 21 August 2009
Line 11:		Line 11:
	\mathrm{i} \omega \phi = -\zeta,\,z=0,\,\,\mathbf{x} \in F,		\mathrm{i} \omega \phi = -\zeta,\,z=0,\,\,\mathbf{x} \in F,
	</math></center>		</math></center>
	(note that ~~The~~ latter two can be combined as		(note that the latter two can be combined as
	<center><math>		<center><math>
	\partial_n \phi = \alpha \phi,\,z=0,\,\,\mathbf{x} \in F,		\partial_n \phi = \alpha \phi,\,z=0,\,\,\mathbf{x} \in F,
	</math></center>		</math></center>
	where <math>\alpha = \omega^2 </math>)		where <math>\alpha = \omega^2 </math>)

2009-08-21T01:44:30Z

← Older revision		Revision as of 01:44, 21 August 2009
Line 13:		Line 13:
	(note that The latter two can be combined as		(note that The latter two can be combined as
	<center><math>		<center><math>
	\partial_n \phi = \~~omega^2~~ \phi,\,z=0,\,\,\mathbf{x} \in F,		\partial_n \phi = \alpha \phi,\,z=0,\,\,\mathbf{x} \in F,
	</math></center>		</math></center>
	where <math>\alpha = \omega^2 </math>)		where <math>\alpha = \omega^2 </math>)