Template:Incident potential for two dimensions - Revision history

Tertius: /* Incident potential */

2012-03-21T21:24:10Z

Incident potential

← Older revision		Revision as of 21:24, 21 March 2012
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	which represents the reflected wave.		which represents the reflected wave.

	In any scattering problem <math>\|R\|^2 + \|T\|^2 = 1</math> where <math>R</math> and <math>T</math> are the reflection and transmission coefficients respectively. In our case of the semi-infinite dock <math>\|a_{0}\| = \|R\| = 1</math> and <math>\|T\| = 0</math> as there are no transmitted waves in the region of the dock.		In any scattering problem <math>\|R\|^2 + \|T\|^2 = 1</math> where <math>R</math> and <math>T</math> are the reflection and transmission coefficients respectively. In our case of the semi-infinite dock <math>\|a_{0}\| = \|R\| = 1</math> and <math>\|T\| = 0</math> as there are no transmitted waves in the region under the dock.

2012-03-14T00:57:43Z

Incident potential

← Older revision		Revision as of 00:57, 14 March 2012
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	which represents the reflected wave.		which represents the reflected wave.

	In any scattering problem <math>\|R\|^2 + \|T\|^2 = 1</math> where <math>R</math> and <math>T</math> are the reflection and transmission coefficients respectively. In our case of the semi-infinite dock ~~the~~ <math>\|a_{0}\| = \|R\| = 1</math> and <math>\|T\| = 0</math> as there are no transmitted waves in the region of the dock.		In any scattering problem <math>\|R\|^2 + \|T\|^2 = 1</math> where <math>R</math> and <math>T</math> are the reflection and transmission coefficients respectively. In our case of the semi-infinite dock <math>\|a_{0}\| = \|R\| = 1</math> and <math>\|T\| = 0</math> as there are no transmitted waves in the region of the dock.

2012-03-14T00:56:23Z

Incident potential

← Older revision		Revision as of 00:56, 14 March 2012
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	which represents the reflected wave.		which represents the reflected wave.

	In any scattering problem <math>\|R\|^2 + \|T\|^2 = 1</math> where <math>R</math> and <math>T</math> are the reflection and transmission coefficients respectively. In our case of the semi-infinite dock		In any scattering problem <math>\|R\|^2 + \|T\|^2 = 1</math> where <math>R</math> and <math>T</math> are the reflection and transmission coefficients respectively. In our case of the semi-infinite dock the <math>\|a_{0}\| = \|R\| = 1</math> and <math>\|T\| = 0</math> as there are no transmitted waves in the region of the dock.

2012-03-14T00:47:46Z

Incident potential

← Older revision		Revision as of 00:47, 14 March 2012
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	which represents the reflected wave.		which represents the reflected wave.

	In any scattering problem <math>\|R\|^2 + \|T\|^2 = 1</math> where <math>R</math> and <math>T</math> are the reflection and transmission coefficients respectively.		In any scattering problem <math>\|R\|^2 + \|T\|^2 = 1</math> where <math>R</math> and <math>T</math> are the reflection and transmission coefficients respectively. In our case of the semi-infinite dock

2012-03-14T00:36:35Z

Incident potential

← Older revision		Revision as of 00:36, 14 March 2012
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	To create meaningful solutions of the velocity potential <math>\phi</math> in the specified domains we add an incident wave term to the expansion for the domain of <math>x < 0</math> above. The incident potential is a wave of amplitude <math>A</math>		To create meaningful solutions of the velocity potential <math>\phi</math> in the specified domains we add an incident wave term to the expansion for the domain of <math>x < 0</math> above. The incident potential is a wave of amplitude <math>A</math>
	in displacement travelling in the positive <math>x</math>-direction. We would only see this in the time domain <math>\Phi(x,z,t)</math> however, in the frequency domain the incident potential can ~~therefore~~ be written as		in displacement travelling in the positive <math>x</math>-direction. We would only see this in the time domain <math>\Phi(x,z,t)</math> however, in the frequency domain the incident potential can be written as
	<center>		<center>
	<math>		<math>

2012-03-13T03:19:08Z

Incident potential

← Older revision		Revision as of 03:19, 13 March 2012
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	</math>		</math>
	</center>		</center>
	The total velocity (scattered) potential now becomes <math>\phi = \~~phi^~~{\mathrm{I}} + \~~phi^~~{\mathrm{D}}</math> for the domain of <math>x < 0</math>.		The total velocity (scattered) potential now becomes <math>\phi = \phi_{\mathrm{I}} + \phi_{\mathrm{D}}</math> for the domain of <math>x < 0</math>.

	The first term in the expansion of the diffracted potential for the domain <math>x < 0</math> is given by		The first term in the expansion of the diffracted potential for the domain <math>x < 0</math> is given by

2012-03-13T03:18:34Z

Incident potential

2012-03-06T06:36:11Z

Incident potential

← Older revision		Revision as of 06:36, 6 March 2012
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	</math>		</math>
	</center>		</center>
	which represents the reflected wave. In any scattering problem <math>\|R\|^2 + \|T\|^2 = 1</math> where <math>R</math> and <math>T</math> are the reflection and transmission coefficients respectively.		which represents the reflected wave.

			In any scattering problem <math>\|R\|^2 + \|T\|^2 = 1</math> where <math>R</math> and <math>T</math> are the reflection and transmission coefficients respectively.

2012-03-06T06:35:47Z

Incident potential

← Older revision		Revision as of 06:35, 6 March 2012
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	</math>		</math>
	</center>		</center>
	which represents the reflected wave. In any scattering problem <math>\|R\|^2~~\rightarrow\infty~~</math>		which represents the reflected wave. In any scattering problem <math>\|R\|^2 + \|T\|^2 = 1</math> where <math>R</math> and <math>T</math> are the reflection and transmission coefficients respectively.

2012-03-06T06:31:44Z

Incident potential

← Older revision		Revision as of 06:31, 6 March 2012
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	</math>		</math>
	</center>		</center>
	which represents the reflected wave. In any scattering problem,		which represents the reflected wave. In any scattering problem <math>\|R\|^2\rightarrow\infty</math>