Random walk approach to wave radiation in cylindrical and spherical domains

Budaev, Bair V.; Bogy, David B.

doi:10.1016/j.probengmech.2003.07.002

Cited by 7 publications

(5 citation statements)

References 11 publications

(20 reference statements)

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“…So for plasmonic materials the stochastic representation (3) remains valid for any domain size. It is important to realize that the spacetime trajectory for Helmholtz equation here is governed by the Brownian motion in real space even for lossy media, a distinct advantage over the eikonal/transport equation procedure of [12], which requires trajectories in complex space.…”

Section: Stochastic Representationmentioning

confidence: 99%

“…However, its utility was limited to sizes below the first resonance [9], [10], [11]. Even the eikonal/transport approach of [12] it requires analytical continuation of trajectories traversing a complex space. The approach presented here is free from such limitations and has the advantage of being directly amenable to integration with traditional numerical methods such as the integral equation methods or finite element methods for exterior regions in domains containing arbitrary plasmonic geometric shapes.…”

Section: Introductionmentioning

confidence: 99%

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Field Determination Near Plasmonic Structures by the Feynman–Kac Stochastic Representation

Janaswamy

2017

Antennas Wirel. Propag. Lett.

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Abstract-Feynman-Kac stochastic representation for elliptic equations is used to construct the solution of Helmholtz equation in domains containing plasmonic structures. The method involves initiation of Brownian motion at an interior point in the plasmonic structure and relating the field there to that on the structure boundary (equivalent surface) through the FeynmanKac formula. The field exterior to the plasmonic structure can be related to the field on the equivalent surface through a variety of numerical methods depending on the complexity of the exterior domain. Finally, the field on the equivalent surface is determined by the imposition of boundary conditions. Comparison is shown here with the exact solution for the total field on the surface of a circular nano-cylinder and a nano-sphere driven by localized sources and where the permittivity is described by the Drude model.

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Section: Stochastic Representationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Field Determination Near Plasmonic Structures by the Feynman–Kac Stochastic Representation

Janaswamy

2017

Antennas Wirel. Propag. Lett.

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“…Equations of the type (3.16) were discussed in [3][4][5] where it was shown that the solution of the Dirichlet problem (3.16), (3.17) can be represented by either of two equivalent formulas…”

Section: Probabilistic Solution Of the Scattering Problemmentioning

confidence: 99%

Wave scattering by surface-breaking cracks and cavities

Budaev

Bogy

2004

Wave Motion

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“…These results were used in Budaev & Bogy (2004c) for the analysis of two-dimensional problems of wave scattering by surface breaking cavities and cracks of virtually arbitrary shape. In Budaev & Bogy (2003b), the method was adapted to problems of wave propagation in exterior cylindrical and spherical domains.…”

Section: Introductionmentioning

confidence: 99%

Diffraction by a plane sector

Budaev

Bogy

2004

Proc. R. Soc. Lond. A

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The problem of diffraction by a perfectly reflecting screen occupying an infinite sector of the equatorial plane is addressed by the random-walk method. The solution is represented as a superposition of the wave field completely determined by an elementary ray analysis and of the field formed by the waves diffracted by the tip of the screen. The diffracted field is explicitly represented as the mathematical expectation of a specified functional on trajectories of the random motion, the radial component of which runs in a complex space while the two-dimensional angular component remains real valued. The numerical results confirm the efficiency of the random-walk approach to the analysis of diffraction by wedge-shaped screens of arbitrary angles.

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Random walk approach to wave radiation in cylindrical and spherical domains

Cited by 7 publications

References 11 publications

Field Determination Near Plasmonic Structures by the Feynman–Kac Stochastic Representation

Field Determination Near Plasmonic Structures by the Feynman–Kac Stochastic Representation

Wave scattering by surface-breaking cracks and cavities

Diffraction by a plane sector

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