Difference between revisions of "Kagemoto and Yue Interaction Theory"
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| − | This is an interaction theory | + | This is an interaction theory which provides the exact solution (i.e. it is not based on a [[Wide Spacing Approximation]]). |
The theory uses the [[Cylindrical Eigenfunction Expansion]] and [[Graf's Addition Theorem]] to represent the potential in local coordinates. The incident and scattered potential of each body are then related by the associated [[Diffraction Transfer Matrix]]. | The theory uses the [[Cylindrical Eigenfunction Expansion]] and [[Graf's Addition Theorem]] to represent the potential in local coordinates. The incident and scattered potential of each body are then related by the associated [[Diffraction Transfer Matrix]]. | ||
| − | The basic idea is as follows: The scattered potential of each body is represented in the [Cylindrical Eigenfunction Expansion]] associated with the local coordinates centred at the mean centre position of the body. Using [[Graf's Addition Theorem]], the scattered potential of all | + | The basic idea is as follows: The scattered potential of each body is represented in the [[Cylindrical Eigenfunction Expansion]] associated with the local coordinates centred at the mean centre position of the body. Using [[Graf's Addition Theorem]], the scattered potential of all bodies (given in their local coordinates) can be mapped to an incident potential associated with the coordiates of all other bodies. Doing this, the incident potential of each body (which is given by the ambient incident potential plus the scattered potentials of all other bodies) is given in its [[Cylindrical Eigenfunction Expansion]] associated with its local coordinates. Using the [[Diffraction Transfer Matrix]], which relates the incident and scattered potential of each body in isolation, a system of equations for the coefficients of the scattered potential is obtained. |
The theory is described in [[Kagemoto_Yue_1986a|Kagemoto and Yue 1986]] and in | The theory is described in [[Kagemoto_Yue_1986a|Kagemoto and Yue 1986]] and in | ||
[[Peter_Meylan_2004a|Peter and Meylan 2004]] | [[Peter_Meylan_2004a|Peter and Meylan 2004]] | ||
Revision as of 08:38, 17 May 2006
This is an interaction theory which provides the exact solution (i.e. it is not based on a Wide Spacing Approximation). The theory uses the Cylindrical Eigenfunction Expansion and Graf's Addition Theorem to represent the potential in local coordinates. The incident and scattered potential of each body are then related by the associated Diffraction Transfer Matrix.
The basic idea is as follows: The scattered potential of each body is represented in the Cylindrical Eigenfunction Expansion associated with the local coordinates centred at the mean centre position of the body. Using Graf's Addition Theorem, the scattered potential of all bodies (given in their local coordinates) can be mapped to an incident potential associated with the coordiates of all other bodies. Doing this, the incident potential of each body (which is given by the ambient incident potential plus the scattered potentials of all other bodies) is given in its Cylindrical Eigenfunction Expansion associated with its local coordinates. Using the Diffraction Transfer Matrix, which relates the incident and scattered potential of each body in isolation, a system of equations for the coefficients of the scattered potential is obtained.
The theory is described in Kagemoto and Yue 1986 and in Peter and Meylan 2004
