Non-Relativistic Scattering: Pulsating Interfaces

Censor, D.

doi:10.2528/pier05011801

Cited by 5 publications

(12 citation statements)

References 13 publications

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“…We now focus on the term v ν f appearing in the expansion (14). A similar approach can be adapted to the other terms v νm , for m ∈ N. Based on the method of separation of variables, we define…”

Section: The Specific Case Of a Boundary With Sine Motion 31 Analysis For The Case Of A Small Amplitude Boundary Motionmentioning

confidence: 99%

“…where the Fourier coefficients of w I − are the complex conjugates of the Fourier coefficients of w I + . Let us remark that the expression (14) of v also involves the functions v νm . However, their contribution to v is less significant than v ν f .…”

Section: The Specific Case Of a Boundary With Sine Motion 31 Analysis For The Case Of A Small Amplitude Boundary Motionmentioning

confidence: 99%

“…Analytical approaches for solving wave-like problems with simple motions have been developed e.g. for rotating obstacles [12,17,21,45] or vibrating objects [14,17,34,40]. In addition, numerical schemes based e.g.…”

Section: Introductionmentioning

confidence: 99%

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A frequency domain method for scattering problems with moving boundaries

Gasperini

Beise²,

Schroeder³

et al. 2021

Wave Motion

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We propose a multi-harmonic numerical method for solving wave scattering problems with moving boundaries, where the scatterer is assumed to move smoothly around an equilibrium position. We first develop an analysis to justify the method and its validity in the one-dimensional case with small-amplitude sinusoidal motions of the scatterer, before extending it to large-amplitude, arbitrary motions in oneand two-dimensional settings. We compare the numerical results of the proposed approach to standard space-time resolution schemes, which illustrates the efficiency of the new method.

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Section: The Specific Case Of a Boundary With Sine Motion 31 Analysis For The Case Of A Small Amplitude Boundary Motionmentioning

confidence: 99%

Section: The Specific Case Of a Boundary With Sine Motion 31 Analysis For The Case Of A Small Amplitude Boundary Motionmentioning

confidence: 99%

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A frequency domain method for scattering problems with moving boundaries

Gasperini

Beise²,

Schroeder³

et al. 2021

Wave Motion

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“…Heuristic models that in the case of constant v merge into exact SR are not unique. Presently the Quasi Lorentz Transformation (Censor, 2005(Censor, , 2010 9is employed. Subject to the constraint of MM and EM space and time scaling, the FO ME and FT (1), (2), (6), apply to varying ( , ) t v r .…”

Section: Summary and Concluding Remarksmentioning

confidence: 99%

EM WAVE PROPAGATION AND SCATTERING IN SPATIOTEMPORALLY VARYING MOVING MEDIAThe Exponential Model

Censor

2013

Proceedings of the 2nd International Conference on Telecommunications and Remote Sensing

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An approximate method for analyzing EM wave propagation and scattering in the presence of temporally and spatially varying media is investigated. The method is quasi-relativistic in the sense that for constant velocity it reduces to Einstein's Special Relativity theory to the first order in the normalized speed / v c. The present exponential model was previously used for temporally invariant velocity only. The motion must be irrotational and the characteristic wavelength and period scales of the mechanical motion must be much larger compared to those of the EM field ones. For simple periodic motion it is shown that the EM field is modulated by the motion, and a spectrum of discrete sidebands is created, with frequencies separated by the mechanical frequencies. The results suggest new approaches to the celebrated Fizeau experiment. Rather than using an interferometer setup as in the traditional experiment, the equivalent phase velocity in a periodically moving medium can be deduced from the measured. Simple examples are computed: the effect of the motion on an initially plane harmonic wave, and scattering by perfectly conducting and refractive planes and cylinders. Scattering of EM waves in the presence of moving media and scatterers is of interest for theoretical and engineering applications, see (Van Bladel, 1984) for a comprehensive introduction to the relevant literature. Einstein's SR; Minkowski, 1908; Sommerfeld, 1964; Pauli, 1958) facilitates the analysis for problems involving constant velocities. Historically this is related to the FE and the associated Fresnel drag phenomenon (Einstein, 1905; Pauli, 1958). Heuristic approximations are required for varying velocities, and it stands to reason that they will adequately apply to cases involving the normalized speed / v c to the FO only. Historically, the present exponential model seems to have originated with Collier and Tai (1965), and later considered for general temporally invariant velocities (Nathan and Censor, 1968; Censor, 1969a, 1972).

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“…It was exploited for analyzing scattering by harmonically moving mirrors [3]. Other attempts of incorporating varying velocities, based on different modeling, have been made too, e.g., see [4] and references mentioned therein.…”

Section: Introduction and Rationalementioning

confidence: 99%

The Need for a First-order Quasi Lorentz Transformation

Censor¹,

Todorov²,

Christov³

2010

AIP Conference Proceedings

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Solving electromagnetic scattering problems involving non-uniformly moving objects or media requires an approximate but consistent extension of Einstein's Special Relativity theory, originally valid for constant velocities only. For moderately varying velocities a quasi Lorentz transformation is presented. The conditions for form-invariance of the Maxwell equations, the so-called "principle of relativity", are shown to hold for a broad class of motional modes and time scales. A simple example of scattering by a harmonically oscillating mirror is analyzed in detail. Application to generally orbiting objects is mentioned.

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Non-Relativistic Scattering: Pulsating Interfaces

Cited by 5 publications

References 13 publications

A frequency domain method for scattering problems with moving boundaries

A frequency domain method for scattering problems with moving boundaries

EM WAVE PROPAGATION AND SCATTERING IN SPATIOTEMPORALLY VARYING MOVING MEDIAThe Exponential Model

The Need for a First-order Quasi Lorentz Transformation

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