On toroidal Green{close_quote}s functions

Journal Article · Tue Jul 01 04:00:00 EDT 1997 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.532061· OSTI ID:530083

Bates, J W ^[1]

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1. 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, Journal Name: Journal of Mathematical Physics Journal Issue: 7 Vol. 38; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
BOUNDARY-VALUE PROBLEMS
CROSS SECTIONS
GREEN FUNCTION
HARMONIC OSCILLATORS
LAPLACE EQUATION
MAGNETIC FIELDS
TOROIDAL CONFIGURATION
VECTORS