Template:Standard linear wave scattering equations - Revision history

Meylan at 04:20, 20 August 2009

2009-08-20T04:20:43Z

← Older revision		Revision as of 04:20, 20 August 2009
Line 1:		Line 1:
	The equations are the following		The equations are the following
	{{standard linear wave scattering equations without body condition}}		{{standard linear wave scattering equations without body condition}}
	~~<center><math>~~		{{general body boundary condition}}
	~~\partial_n\phi = \mathcal~~{L}~~\phi, \, z\in\partial\Omega,~~
	~~</math></center>~~
	~~where <math>\alpha</math> is the wavenumber in [[Infinite Depth]] which is given by~~
	~~<math>\alpha=\omega^2/g</math> where <math>g</math> is gravity. <math>\mathcal{L~~}~~</math> is a linear~~
	~~operator which relates the normal and potential on the body surface through the physics~~
	~~of the body.~~

Meylan at 04:09, 20 August 2009

2009-08-20T04:09:25Z

← Older revision		Revision as of 04:09, 20 August 2009
Line 1:		Line 1:
	The equations are the following		The equations are the following

	{{standard linear wave scattering equations without body condition}}		{{standard linear wave scattering equations without body condition}}

	<center><math>		<center><math>
	\partial_n\phi = \mathcal{L}\phi, \, z\in\partial\Omega,		\partial_n\phi = \mathcal{L}\phi, \, z\in\partial\Omega,

Meylan at 04:08, 20 August 2009

2009-08-20T04:08:41Z

← Older revision		Revision as of 04:08, 20 August 2009
Line 1:		Line 1:
	The equations are the following		The equations are the following
	~~<center><math>~~
	~~\Delta\phi=0, \, -h<z<0,\,\,\,\mathbf~~{~~x} \in \Omega~~		{{standard linear wave scattering equations without body condition}}
	~~</math></center>~~
	~~<center><math>~~
	~~\frac{\partial\phi}~~{~~\partial z~~}~~=0, \, z=-h,~~
	~~</math></center>~~
	~~<center><math>~~
	~~\partial_n \phi = \alpha \phi,\,z=0,\,\,\mathbf{x~~} ~~\in F,~~
	~~</math></center>~~
	<center><math>		<center><math>
	\partial_n\phi = \mathcal{L}\phi, \, z\in\partial\Omega,		\partial_n\phi = \mathcal{L}\phi, \, z\in\partial\Omega,

Meylan at 01:42, 18 August 2009

2009-08-18T01:42:38Z

← Older revision		Revision as of 01:42, 18 August 2009
Line 1:		Line 1:
	The equations are the following		The equations are the following
	<center><math>		<center><math>
	\~~nabla^{2}~~\phi=0, \, -h<z<0,\,\,\,\mathbf{x}\~~notin~~ \Omega		\Delta\phi=0, \, -h<z<0,\,\,\,\mathbf{x} \in \Omega
	</math></center>		</math></center>
	<center><math>		<center><math>
Line 7:		Line 7:
	</math></center>		</math></center>
	<center><math>		<center><math>
	\~~frac{\partial~~\phi~~}{\partial z}~~ = \alpha \phi,\,z=0,\,\,\mathbf{x}\~~notin\Omega~~,		\partial_n \phi = \alpha \phi,\,z=0,\,\,\mathbf{x} \in F,
	</math></center>		</math></center>
	<center><math>		<center><math>
	~~\frac{~~\~~partial~~\phi~~}{\partial z}~~ = \mathcal{L}\phi, \, z\in\partial\Omega,		\partial_n\phi = \mathcal{L}\phi, \, z\in\partial\Omega,
	</math></center>		</math></center>

	where <math>\alpha</math> is the wavenumber in [[Infinite Depth]] which is given by		where <math>\alpha</math> is the wavenumber in [[Infinite Depth]] which is given by
	<math>\alpha=\omega^2/g</math> where <math>g</math> is gravity. <math>\mathcal{L}</math> is a linear		<math>\alpha=\omega^2/g</math> where <math>g</math> is gravity. <math>\mathcal{L}</math> is a linear
	operator which relates the normal and potential on the body surface through the physics		operator which relates the normal and potential on the body surface through the physics
	of the body.		of the body.

Meylan at 22:52, 22 March 2009

2009-03-22T22:52:22Z

← Older revision		Revision as of 22:52, 22 March 2009
Line 10:		Line 10:
	</math></center>		</math></center>
	<center><math>		<center><math>
	\frac{\partial\phi}{\partial z} = L\phi, \, z\in\partial\Omega,		\frac{\partial\phi}{\partial z} = \mathcal{L}\phi, \, z\in\partial\Omega,
	</math></center>		</math></center>

	where <math>\alpha</math> is the wavenumber in [[Infinite Depth]] which is given by		where <math>\alpha</math> is the wavenumber in [[Infinite Depth]] which is given by
	<math>\alpha=\omega^2/g</math> where <math>g</math> is gravity. <math>L</math> is a linear		<math>\alpha=\omega^2/g</math> where <math>g</math> is gravity. <math>\mathcal{L}</math> is a linear
	operator which relates the normal and potential on the body surface through the physics		operator which relates the normal and potential on the body surface through the physics
	of the body.		of the body.

Meylan at 21:44, 18 August 2008

2008-08-18T21:44:12Z

New page

The equations are the following
<center><math>
\nabla^{2}\phi=0, \, -h<z<0,\,\,\,\mathbf{x}\notin \Omega
</math></center>
<center><math>
\frac{\partial\phi}{\partial z}=0, \, z=-h,
</math></center>
<center><math>
\frac{\partial\phi}{\partial z} = \alpha \phi,\,z=0,\,\,\mathbf{x}\notin\Omega,
</math></center>
<center><math>
\frac{\partial\phi}{\partial z} = L\phi, \, z\in\partial\Omega,
</math></center>

where <math>\alpha</math> is the wavenumber in [[Infinite Depth]] which is given by
<math>\alpha=\omega^2/g</math> where <math>g</math> is gravity. <math>L</math> is a linear
operator which relates the normal and potential on the body surface through the physics
of the body.