Template:Sommerfeld radiation condition three dimensions - Revision history

Meylan at 22:27, 29 April 2010

2010-04-29T22:27:59Z

← Older revision		Revision as of 22:27, 29 April 2010
Line 1:		Line 1:
	In three-dimensions the [[Sommerfeld Radiation Condition]] is		In three-dimensions the [[Sommerfeld Radiation Condition]] is
	<center><math>		<center><math>
	\sqrt{\|\mathbf{r}\|}\left( \frac{\partial}{\partial\|\mathbf{r}\|} + \mathrm{i} k \right)		\sqrt{\|\mathbf{r}\|}\left( \frac{\partial}{\partial\|\mathbf{r}\|} - \mathrm{i} k \right)
	(\phi-\phi^{\mathrm{{I}}})=0,\;\mathrm{{as\;}}\|\mathbf{r}\|\rightarrow\infty\mathrm{.}		(\phi-\phi^{\mathrm{{I}}})=0,\;\mathrm{{as\;}}\|\mathbf{r}\|\rightarrow\infty\mathrm{.}
	</math></center>		</math></center>
	where <math>\phi^{\mathrm{{I}}}</math> is the incident potential.		where <math>\phi^{\mathrm{{I}}}</math> is the incident potential.

Meylan at 22:26, 29 April 2010

2010-04-29T22:26:25Z

← Older revision		Revision as of 22:26, 29 April 2010
Line 1:		Line 1:
	In three-dimensions the [[Sommerfeld Radiation Condition]] is		In three-dimensions the [[Sommerfeld Radiation Condition]] is
	<center><math>		<center><math>
	\sqrt{\|\mathbf{r}\|}\left( \frac{\partial}{\partial\|\mathbf{r}\|}~~-k_0~~\right)		\sqrt{\|\mathbf{r}\|}\left( \frac{\partial}{\partial\|\mathbf{r}\|} + \mathrm{i} k \right)
	(\phi-\phi^{\mathrm{{I}}})=0,\;\mathrm{{as\;}}\|\mathbf{r}\|\rightarrow\infty\mathrm{.}		(\phi-\phi^{\mathrm{{I}}})=0,\;\mathrm{{as\;}}\|\mathbf{r}\|\rightarrow\infty\mathrm{.}
	</math></center>		</math></center>
	where <math>\phi^{\mathrm{{I}}}</math> is the incident potential.		where <math>\phi^{\mathrm{{I}}}</math> is the incident potential.

Adi Kurniawan at 09:06, 13 April 2009

2009-04-13T09:06:45Z

← Older revision		Revision as of 09:06, 13 April 2009
Line 2:		Line 2:
	<center><math>		<center><math>
	\sqrt{\|\mathbf{r}\|}\left( \frac{\partial}{\partial\|\mathbf{r}\|}-k_0\right)		\sqrt{\|\mathbf{r}\|}\left( \frac{\partial}{\partial\|\mathbf{r}\|}-k_0\right)
	(\phi-\phi^{\mathrm{{In}}})=0,\;\mathrm{{as\;}}\|\mathbf{r}\|\rightarrow\infty\mathrm{.}		(\phi-\phi^{\mathrm{{I}}})=0,\;\mathrm{{as\;}}\|\mathbf{r}\|\rightarrow\infty\mathrm{.}
	</math></center>		</math></center>
	where <math>\phi^{\mathrm{{In}}}</math> is the incident potential.		where <math>\phi^{\mathrm{{I}}}</math> is the incident potential.

Meylan at 07:57, 25 August 2008

2008-08-25T07:57:05Z

← Older revision		Revision as of 07:57, 25 August 2008
Line 4:		Line 4:
	(\phi-\phi^{\mathrm{{In}}})=0,\;\mathrm{{as\;}}\|\mathbf{r}\|\rightarrow\infty\mathrm{.}		(\phi-\phi^{\mathrm{{In}}})=0,\;\mathrm{{as\;}}\|\mathbf{r}\|\rightarrow\infty\mathrm{.}
	</math></center>		</math></center>
			where <math>\phi^{\mathrm{{In}}}</math> is the incident potential.

Meylan at 07:38, 24 August 2008

2008-08-24T07:38:17Z

← Older revision		Revision as of 07:38, 24 August 2008
Line 1:		Line 1:
	In three-dimensions the [[Sommerfeld Radiation Condition]] is		In three-dimensions the [[Sommerfeld Radiation Condition]] is
	<center><math>		<center><math>
	\sqrt{\|\mathbf{r}\|}\left( \frac{\partial}{\partial\|\mathbf{r}\|}-~~{i}k~~\right)		\sqrt{\|\mathbf{r}\|}\left( \frac{\partial}{\partial\|\mathbf{r}\|}-k_0\right)
	(\phi-\phi^{\mathrm{{In}}})=0,\;\mathrm{{as\;}}\|\mathbf{r}\|\rightarrow\infty\mathrm{.}		(\phi-\phi^{\mathrm{{In}}})=0,\;\mathrm{{as\;}}\|\mathbf{r}\|\rightarrow\infty\mathrm{.}
	</math></center>		</math></center>

Meylan at 06:23, 24 August 2008

2008-08-24T06:23:38Z

New page

In three-dimensions the [[Sommerfeld Radiation Condition]] is
<center><math>
\sqrt{|\mathbf{r}|}\left( \frac{\partial}{\partial|\mathbf{r}|}-{i}k\right)
(\phi-\phi^{\mathrm{{In}}})=0,\;\mathrm{{as\;}}|\mathbf{r}|\rightarrow\infty\mathrm{.}
</math></center>