Category:Interaction Theory - Revision history

Meylan at 08:16, 19 October 2009

2009-10-19T08:16:08Z

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			{{complete pages}}

	Interaction theory is based on calculating a solution for a number of individual scatterers		Interaction theory is based on calculating a solution for a number of individual scatterers
	without simply discretising the total problem. The theory is generally applied in		without simply discretising the total problem. The theory is generally applied in

2008-01-10T01:19:22Z

Reverted edits by TaalcAlibo (TaalcAlibo); changed back to last version by Meylan

← Older revision		Revision as of 01:19, 10 January 2008
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	~~delliracva~~
	Interaction theory is based on calculating a solution for a number of individual scatterers		Interaction theory is based on calculating a solution for a number of individual scatterers
	without simply discretising the total problem. The theory is generally applied in		without simply discretising the total problem. The theory is generally applied in

2007-12-30T22:30:57Z

lalichiorror

← Older revision		Revision as of 22:30, 30 December 2007
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			delliracva
	Interaction theory is based on calculating a solution for a number of individual scatterers		Interaction theory is based on calculating a solution for a number of individual scatterers
	without simply discretising the total problem. The theory is generally applied in		without simply discretising the total problem. The theory is generally applied in

2006-07-09T10:55:56Z

← Older revision		Revision as of 10:55, 9 July 2006
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	We present an illustrative example of an interaction theory for the case of <math>n</math>		We present an illustrative example of an interaction theory for the case of <math>n</math>
	[[Linton and Evans 1990]] presented an [[Interaction Theory for Cylinders]]		[[Linton and Evans 1990]] presented an [[Interaction Theory for Cylinders]]
	which was [[Kagemoto and Yue Interaction Theory]] by ~~simply~~ assuming that each		which was [[Kagemoto and Yue Interaction Theory]] simplified by assuming that each
	body is a [[Bottom Mounted Cylinder~~\|Bottom Mounted Cylinders~~]].		body is a [[Bottom Mounted Cylinder]].


	[[Category:Linear Water-Wave Theory]]		[[Category:Linear Water-Wave Theory]]

2006-06-21T01:29:24Z

2006-06-21T01:20:15Z

← Older revision		Revision as of 01:20, 21 June 2006
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	Interaction theory is based on calculating a solution for a number of individual scatterers		Interaction theory is based on calculating a solution for a number of individual scatterers
	without simply discretising the total problem. ~~THe~~ theory is generally applied in		without simply discretising the total problem. The theory is generally applied in
	three dimensions.		three dimensions.
	Essentially the [[Cylindrical Eigenfunction Expansion]]		Essentially the [[Cylindrical Eigenfunction Expansion]]
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	a solution without any approximation. This solution method is valid, provided only that		a solution without any approximation. This solution method is valid, provided only that
	an escribed circle can be drawn around each body.		an escribed circle can be drawn around each body.
			We present an illustrative example of an interaction theory for the case of <math>n</math>
			[[Linton and Evans 1990]] presented an [[Interaction Theory for Cylinders]]
			which was [[Kagemoto and Yue Interaction Theory]] by simply assuming that each
			body is a [[Bottom Mounted Cylinder\|Bottom Mounted Cylinders]].

	= Illustrative Example =		= Illustrative Example =

2006-06-20T16:11:16Z

Final Equations

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	R_{jl}) \mathrm{e}^{\mathrm{i}(\tau -\nu) \varphi_{jl}} \Big],		R_{jl}) \mathrm{e}^{\mathrm{i}(\tau -\nu) \varphi_{jl}} \Big],
	</math></center>		</math></center>
	~~<math>m \in \mathbb{N}</math>,~~ <math>\mu \in \mathbb{Z}</math>, <math>l=1,\dots,n</math>.		<math>\mu \in \mathbb{Z}</math>, <math>l=1,\dots,n</math>.


	[[Category:Linear Water-Wave Theory]]		[[Category:Linear Water-Wave Theory]]

2006-06-20T16:10:50Z

Final Equations

← Older revision		Revision as of 16:10, 20 June 2006
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	Therefore, the diffraction transfer matrix of the <math>l</math>th cylinder (having radius <math>a_l</math>) is diagonal and defined as		Therefore, the diffraction transfer matrix of the <math>l</math>th cylinder (having radius <math>a_l</math>) is diagonal and defined as
	<center><math> (diff_op)		<center><math> (diff_op)
	(B^l)_{\mu\mu} = J'_\mu(k a_j)/H^{(1)}_\mu{}'(k a_j).		(B^l)_{\mu\mu} = J'_\mu(k a_j)/H^{(1)}_\mu{}'(k a_j) = B_{\mu}^l.
	</math></center>		</math></center>

2006-06-20T16:10:13Z

Final Equations

← Older revision		Revision as of 16:10, 20 June 2006
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	[[Diffraction Transfer Matrix]] for a [[Bottom Mounted Cylinder]] acting in the following way,		[[Diffraction Transfer Matrix]] for a [[Bottom Mounted Cylinder]] acting in the following way,
	<center><math> (diff_op)		<center><math> (diff_op)
	A_{\mu}^l = J'_\mu(k a_j)/H^{(1)}_\mu~~\prime~~(k a_j)D_{\mu}^l.		A_{\mu}^l = J'_\mu(k a_j)/H^{(1)}_\mu{}'(k a_j)D_{\mu}^l.
	</math></center>		</math></center>
	Therefore, the diffraction transfer matrix of the <math>l</math>th cylinder (having radius <math>a_l</math>) is diagonal and defined as		Therefore, the diffraction transfer matrix of the <math>l</math>th cylinder (having radius <math>a_l</math>) is diagonal and defined as
	<center><math> (diff_op)		<center><math> (diff_op)
	(B^l)_{\mu\mu} = J'_\mu(k a_j)/H^{(1)}_\mu~~\prime~~(k a_j).		(B^l)_{\mu\mu} = J'_\mu(k a_j)/H^{(1)}_\mu{}'(k a_j).
	</math></center>		</math></center>

2006-06-20T16:09:40Z

Final Equations

← Older revision		Revision as of 16:09, 20 June 2006
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	[[Diffraction Transfer Matrix]] for a [[Bottom Mounted Cylinder]] acting in the following way,		[[Diffraction Transfer Matrix]] for a [[Bottom Mounted Cylinder]] acting in the following way,
	<center><math> (diff_op)		<center><math> (diff_op)
	A_{\mu}^l = J'_\mu(k a_j)/H^{(1)}_\mu'(k a_j)D_{\mu}^l.		A_{\mu}^l = J'_\mu(k a_j)/H^{(1)}_\mu\prime(k a_j)D_{\mu}^l.
	</math></center>		</math></center>
	Therefore, the diffraction transfer matrix of the <math>l</math>th cylinder (having radius <math>a_l</math>) is diagonal and defined as		Therefore, the diffraction transfer matrix of the <math>l</math>th cylinder (having radius <math>a_l</math>) is diagonal and defined as
	<center><math> (diff_op)		<center><math> (diff_op)
	(B^l)_{\mu\mu} = J'_\mu(k a_j)/H^{(1)}_\mu'(k a_j).		(B^l)_{\mu\mu} = J'_\mu(k a_j)/H^{(1)}_\mu\prime(k a_j).
	</math></center>		</math></center>