On toroidal Green{close_quote}s functions
- Department of Physics and Astronomy, Dartmouth College, Hanover, New Hampshire 03755-3528 (United States)
Green{close_quote}s functions are valuable analytical tools for solving a myriad of boundary-value problems in mathematical physics. Here, Green{close_quote}s functions of the Laplacian and biharmonic operators are derived for a three-dimensional toroidal domain. In some sense, the former result may be regarded as {open_quotes}standard,{close_quotes} but the latter is most certainly not. It is shown that both functions can be constructed to have zero value on a specified toroidal surface with a circular cross section. Additionally, the Green{close_quote}s function of the biharmonic operator may be chosen to have the property that its normal derivative also vanishes there. A {open_quotes}torsional{close_quotes} Green{close_quote}s function is derived for each operator which is useful in solving some boundary-value problems involving axisymmetric vector equations. Using this approach, the magnetic vector potential of a wire loop is computed as a simple example. {copyright} {ital 1997 American Institute of Physics.}
- DOE Contract Number:
- FG02-85ER53194
- OSTI ID:
- 530083
- Journal Information:
- Journal of Mathematical Physics, Vol. 38, Issue 7; Other Information: PBD: Jul 1997
- Country of Publication:
- United States
- Language:
- English
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