Wave Propagation in Materials for Modern Applications

Petrin, A. B.

doi:10.5772/113

2010

DOI: 10.5772/113

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Wave Propagation in Materials for Modern Applications

A. B. Petrin¹

Abstract: as a Lecturer of General Physics. Since 1996, he has been with the Joint Institute for High Temperatures of Russian Academy of Sciences, Moscow, as a Leading Scientific Researcher of Theoretical Department. His scientific interests include propagation of electromagnetic waves, electrodynamics of plasma, gasdynamics, ECR microwave gas discharges, electrowetting phenomena, electric field singularities on geometric singularities such as microtips and microwedges, electric field induced instabilities of free fluid… Show more

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Cited by 10 publications

References 208 publications

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Higher order mixture nonlocal gradient theory of wave propagation

Faghidian

2020

Math Methods in App Sciences

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The higher order mixture nonlocal gradient theory of elasticity is conceived via consistent unification of the higher order stress‐ and strain‐driven mixture nonlocal elasticity and the higher order strain gradient theory. The integro‐differential constitutive law is established applying an abstract variational approach and appropriately replaced with the equivalent differential condition subject to nonclassical boundary conditions. The introduced higher order elasticity theory provides, as special cases, a variety of generalized elasticity theories adopted in nanomechanics to assess size effects in continua with nanostructural features. The well‐posed higher order mixture nonlocal gradient theory is elucidated and invoked to examine the flexural wave propagation. The closed‐form wave propagation relation between the phase velocity and the wave number is analytically derived. The determined wave propagation response and ensuing results are compared and calibrated with the pertinent molecular dynamic simulations. The demonstrated results of the phase velocity of the flexural wave propagation detect new benchmarks for numerical analyses. The proposed higher order size‐dependent elasticity approach can be profitably employed in rigorous analysis of pioneering nanotechnological devices.

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Higher order mixture nonlocal gradient theory of wave propagation

Faghidian

2020

Math Methods in App Sciences

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General properties of small-amplitude fluctuations in magnetized and unmagnetized collision poor plasmas. I. The dielectric tensor

Schlickeiser

2010

Physics of Plasmas

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The dielectric tensor of a collision poor plasma determines all the physical properties of small-amplitude fluctuations for given initial plasma particle distribution functions, as it enters the Maxwell operator as the only plasma-specific quantity. For the important class of gyrotropic initial particle distribution functions fa(0)(p∥,p⊥) in a uniform magnetic field, we rigorously investigate the general properties of the plasma fluctuations without specifying the explicit momentum dependence of the gyrotropic distribution function. Two alternative forms of the relativistically correct dielectric tensor are derived which differ from nonrelativistic expressions in the literature. The first standard form is expressed in terms of infinite series of Bessel functions, whereas in the second form these infinite series are calculated with the Lerche–Newberger sum rules, yielding products of Bessel functions with complex indices for the individual elements of the Maxwell operator. The second form of the dielectric tensor is well suited to simplify the tensor in the special cases of parallel wave vectors and unmagnetized plasmas. For unmagnetized plasmas it is shown that aperiodic electrostatic and transverse fluctuations can only exist in symmetric distribution functions with f(−p∥,p⊥)=f(p∥,p⊥). Because this includes isotropic distribution functions, the more thorough investigation of this special case reveals that no electrostatic and fluctuations with positive growth rates γ=kcS>0 exist in an isotropic unmagnetized plasma, excluding both aperiodic (with R=0) and wave-like (with R≠0) instabilities, where R=ωR/(kc) denotes the real part of the phase speed. The second form of the dielectric tensor is also most appropriate to investigate fluctuations in magnetized equal mass plasmas, such as electron-positron-pair and/or proton-antiproton plasmas. Here for arbitrary wave vector orientation the dispersion relation factorizes into three separate modes. For fluctuations with parallel wave vectors in isotropic plasmas of arbitrary composition, the electromagnetic stability of such isotropic plasma populations is proven, relativistically generalizing the known corresponding nonrelativistic theorem.

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On the resolution of lenses made of a negative-index material

Petrin¹

2013

Quantum Electron.

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Wave Propagation in Materials for Modern Applications

Cited by 10 publications

References 208 publications

Higher order mixture nonlocal gradient theory of wave propagation

Higher order mixture nonlocal gradient theory of wave propagation

General properties of small-amplitude fluctuations in magnetized and unmagnetized collision poor plasmas. I. The dielectric tensor

On the resolution of lenses made of a negative-index material

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