Potential Methods for Anisotropic Pseudo-Maxwell Equations in Screen Type Problems

For the symmetry group of internal-wave equations, the mechanical content of invariants and symmetry transformations is determined. The performed comparison makes it possible to construct expressions for analogs of momentum, angular momentum, energy, Lorentz transformations, and other characteristics of special relativity and electro-dynamics. The expressions for the Lagrange function are defined, and the conservation laws are derived. An analogy is drawn both in the case of the absence of sources and currents in the Maxwell equations and in their presence.

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New Approach to the Theory of Circular Dichroism

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc19981187 ◽

1998 ◽

Vol 63 (8) ◽

pp. 1187-1201 ◽

Cited By ~ 1

Author(s):

Jaroslav Zamastil ◽

Lubomír Skála ◽

Petr Pančoška ◽

Oldřich Bílek

Keyword(s):

Electromagnetic Wave ◽

Circular Dichroism ◽

Electromagnetic Waves ◽

Maxwell Equations ◽

Optically Active ◽

Semiclassical Approach ◽

New Approach ◽

Isotropic Media ◽

New Formula ◽

Circular Dichroïsm

Using the semiclassical approach for the description of the propagation of the electromagnetic waves in optically active isotropic media we derive a new formula for the circular dichroism parameter. The theory is based on the idea of the time damped electromagnetic wave interacting with the molecules of the sample. In this theory, the Lambert-Beer law need not be taken as an empirical law, however, it follows naturally from the requirement that the electromagnetic wave obeys the Maxwell equations.

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Electromagnetic waves

10.1093/oso/9780198786399.003.0033 ◽

2018 ◽

Author(s):

Nathalie Deruelle ◽

Jean-Philippe Uzan

Keyword(s):

Plane Wave ◽

Electromagnetic Waves ◽

Maxwell Equations ◽

Plane Waves ◽

Geometrical Optics ◽

Particle Detection ◽

Spatial Coordinates ◽

A Charge

This chapter examines solutions to the Maxwell equations in a vacuum: monochromatic plane waves and their polarizations, plane waves, and the motion of a charge in the field of a wave (which is the principle upon which particle detection is based). A plane wave is a solution of the vacuum Maxwell equations which depends on only one of the Cartesian spatial coordinates. The monochromatic plane waves form a basis (in the sense of distributions, because they are not square-integrable) in which any solution of the vacuum Maxwell equations can be expanded. The chapter concludes by giving the conditions for the geometrical optics limit. It also establishes the connection between electromagnetic waves and the kinematic description of light discussed in Book 1.

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Time-Stepping and Convergence Characteristics of the Discontinuous Galerkin Time-Domain Approach for the Maxwell Equations

10.1063/1.3183437 ◽

2009 ◽

Cited By ~ 2

Author(s):

Jens Niegemann ◽

Kurt Busch ◽

M. R. Singh ◽

R. H. Lipson

Keyword(s):

Discontinuous Galerkin ◽

Time Domain ◽

Maxwell Equations ◽

Time Stepping

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Multi-domain spectral approach with Sommerfeld condition for the Maxwell equations

Journal of Computational Physics ◽

10.1016/j.jcp.2021.110149 ◽

2021 ◽

pp. 110149

Author(s):

Christian Klein ◽

Nikola Stoilov

Keyword(s):

Maxwell Equations ◽

Spectral Approach

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Geometric particle-in-cell methods for the Vlasov–Maxwell equations with spin effects

Journal of Plasma Physics ◽

10.1017/s0022377821000532 ◽

2021 ◽

Vol 87 (3) ◽

Author(s):

Nicolas Crouseilles ◽

Paul-Antoine Hervieux ◽

Yingzhe Li ◽

Giovanni Manfredi ◽

Yajuan Sun

Keyword(s):

Phase Space ◽

Maxwell Equations ◽

Stimulated Raman Scattering ◽

Extended Phase ◽

Five Dimensions ◽

Particle In Cell ◽

Spin Effects ◽

Dimensional Phase Space ◽

Spin Polarized ◽

Underdense Plasma

We propose a numerical scheme to solve the semiclassical Vlasov–Maxwell equations for electrons with spin. The electron gas is described by a distribution function $f(t,{\boldsymbol x},{{{\boldsymbol p}}}, {\boldsymbol s})$ that evolves in an extended 9-dimensional phase space $({\boldsymbol x},{{{\boldsymbol p}}}, {\boldsymbol s})$ , where $\boldsymbol s$ represents the spin vector. Using suitable approximations and symmetries, the extended phase space can be reduced to five dimensions: $(x,{{p_x}}, {\boldsymbol s})$ . It can be shown that the spin Vlasov–Maxwell equations enjoy a Hamiltonian structure that motivates the use of the recently developed geometric particle-in-cell (PIC) methods. Here, the geometric PIC approach is generalized to the case of electrons with spin. Total energy conservation is very well satisfied, with a relative error below $0.05\,\%$ . As a relevant example, we study the stimulated Raman scattering of an electromagnetic wave interacting with an underdense plasma, where the electrons are partially or fully spin polarized. It is shown that the Raman instability is very effective in destroying the electron polarization.

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Designing of Green Plasticizers and Assessment of the Effectiveness of Their Use

Polymers ◽

10.3390/polym13111761 ◽

2021 ◽

Vol 13 (11) ◽

pp. 1761

Author(s):

Aliya K. Mazitova ◽

Guliya K. Aminova ◽

Irina N. Vikhareva

Keyword(s):

Adipic Acid ◽

Polymer Materials ◽

Operational Parameters ◽

Solid Domestic Waste ◽

Polymer Waste ◽

Synthetic Materials ◽

Environmental Requirements ◽

Potential Methods ◽

High Set ◽

Acid Esters

The growing anthropogenic load on the lithosphere is currently characterized by the alienation of huge areas for solid domestic waste. One of the most common pollutants is traditional plastics with a degradation period of over 100 years. In connection with the increasing environmental requirements, polymer materials, along with a high set of technological and operational parameters, must be environmentally friendly and biodegradable. The development of polymer composite materials that undergo accelerated physicochemical and biological changes in the natural environment due to the introduction of biodegradable additives is one of the potential methods for processing synthetic materials and ensures the release of significant areas of fertile soils and lands from the steadily increasing amount of polymer waste. The use of adipic acid esters as PVC plasticizers contributes to the production of biodegradable composites. The article describes a method for obtaining new esters of adipic acid, presents the results of studying their properties for practical use in PVC composites, and assesses the economic efficiency of preventing damage to the environment when using them.

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