Eigenvalues for a uniform fluid waveguide with an eccentric-annulus cross-section

Hine, Michael J.

doi:10.1016/0022-460x(71)90426-3

Cited by 26 publications

(2 citation statements)

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“…The eigenvalues have been computed using different approaches, as for instance conformal transformations that map the eccentric annulus onto a concentric one. As the two dimensional Helmholtz equation is not conformally invariant, the transformed equation has coordinate dependent coefficients and has to be solved numerically [22]. As is well known, it is very difficult to compute the Casimir energy from the numerical eigenfrequencies.…”

Section: The Classical Eigenvaluesmentioning

confidence: 99%

Exact zero-point interaction energy between cylinders

2006

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We calculate the exact Casimir interaction energy between two perfectly conducting, very long, eccentric cylindrical shells using a mode summation technique. Several limiting cases of the exact formula for the Casimir energy corresponding to this configuration are studied both analytically and numerically. These include concentric cylinders, cylinder-plane, and eccentric cylinders, for small and large separations between the surfaces. For small separations we recover the proximity approximation, while for large separations we find a weak logarithmic decay of the Casimir interaction energy, typical of cylindrical geometries.

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Section: The Classical Eigenvaluesmentioning

confidence: 99%

Exact zero-point interaction energy between cylinders

2006

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“…Davies and Muilwyk [7] and Steele [8] used the finite difference method to compute eigenvalues of waveguides with arbitrary cross-section. The Helmholtz equation, which describes the dynamics of waveguides, was solved by Arlett et al [9] and Gass [10] using finite element methods, by Laura [11] and Hine [12] using the Galerkin method, and by Bulley and Davies [13] using the Rayleigh-Ritz method.…”

Section: Introductionmentioning

confidence: 99%