Linear peridynamics for triclinic materials

2020 ◽  
pp. 108128652096988
Author(s):  
Yozo Mikata
Keyword(s):  
Constitutive Equation ◽  
Plane Wave ◽  
Governing Equation ◽  
Wave Solution ◽  
Anisotropic Materials ◽  
Dispersion Curves ◽  
Plane Wave Solution ◽  
Peridynamic Theory

The governing equation of linear peridynamics is developed for the most general anisotropic materials (triclinic materials). As a departure from the standard peridynamic theory, the linear constitutive equation in the form of a micromodulus is determined by directly requiring the resulting peridynamic equation to converge to a comparable classical elastodynamic equation for a triclinic material as the generalized material horizon approaches zero. As a result, a new peridynamic governing equation is obtained for triclinic peridynamic materials. As an application of the newly obtained peridynamic equation, a plane wave solution is analytically obtained and discussed, and dispersion curves are plotted for triclinic peridynamic materials.

Polarization

Optics f2f ◽  
2018 ◽  
pp. 51-70
Author(s):  
Charles S. Adams ◽  
Ifan G. Hughes
Keyword(s):  
Plane Wave ◽  
Wave Solution ◽  
Polarized Light ◽  
Plane Wave Solution ◽  
Polarization Of Light

This chapter discusses the polarization of light, including the transverse nature of the plane-wave solution; the linear and circular bases are introduced, and the propagation of polarized light in media is analysed.

Plane-wave solution of systems of einstein-weyl equations

1996 ◽  
Vol 39 (2) ◽  
pp. 121-124
Author(s):  
V. G. Bagrov ◽  
V. V. Obukhov ◽  
A. G. Sakhapov
Keyword(s):  
Plane Wave ◽  
Wave Solution ◽  
Plane Wave Solution

Exact plane-wave solution of equations of gravitation theory with massive graviton

2021 ◽  
Vol 64 (1) ◽  
pp. 10-15
Author(s):  
A.A. Baiderin ◽  
◽  
I.P. Denisova ◽  
V.S. Rostovsky ◽  
◽  
...  
Keyword(s):  
Exact Solution ◽  
Gravitational Field ◽  
Plane Wave ◽  
Wave Solution ◽  
Jacobi Method ◽  
Scalar Wave ◽  
Massive Graviton ◽  
Plane Wave Solution ◽  
Solution Of Equations ◽  
Theory Of Gravitation

The theory of gravitation with a massive graviton, which was proposed by Visser, is considered. The exact solution of this theory is found when the source of the gravitational field is plane scalar wave. The Hamilton-Jacobi method obtained the laws of motion of massive and massless particles in this gravitational field.

scholarly journals Stability of the NLS Equation with Viscosity Effect

2011 ◽  
Vol 2011 ◽  
pp. 1-11
Author(s):  
N. Karjanto ◽  
K. M. Tiong
Keyword(s):  
Plane Wave ◽  
Wave Solution ◽  
Kdv Equation ◽  
Modulational Instability ◽  
Quadratic Equation ◽  
Multiple Time ◽  
Nls Equation ◽  
Plane Wave Solution ◽  
Viscosity Effect ◽  
Complex Valued

A nonlinear Schrödinger (NLS) equation with an effect of viscosity is derived from a Korteweg-de Vries (KdV) equation modified with viscosity using the method of multiple time scale. It is well known that the plane-wave solution of the NLS equation exhibits modulational instability phenomenon. In this paper, the modulational instability of the plane-wave solution of the NLS equation modified with viscosity is investigated. The corresponding modulational dispersion relation is expressed as a quadratic equation with complex-valued coefficients. By restricting the modulational wavenumber into the case of narrow-banded spectra, it is observed that a type of dissipation, in this case the effect of viscosity, stabilizes the modulational instability, as confirmed by earlier findings.

Analytical Solitons for Langmuir Waves in Plasma Physics with Cubic Nonlinearity and Perturbations

2016 ◽  
Vol 71 (9) ◽  
pp. 807-815 ◽  
Author(s):  
Qin Zhou ◽  
M. Mirzazadeh
Keyword(s):  
Plane Wave ◽  
Plasma Physics ◽  
Soliton Solution ◽  
Wave Solution ◽  
Soliton Solutions ◽  
Travelling Wave ◽  
Hyperbolic Function ◽  
Travelling Wave Solution ◽  
Langmuir Waves ◽  
Plane Wave Solution

AbstractWe presented an analytical study on dynamics of solitons for Langmuir waves in plasma physics. The mathematical model is given by the perturbed nonlinear Schrödinger equation with full nonlinearity and Kerr law nonlinearity. There are three techniques of integrability were employed to extract exact solutions along with the integrability conditions. The topological 1-soliton solutions, singular 1-soliton solutions, and plane wave solution were reported by Ricatti equation expansion approach and then the bright 1-soliton solution, singular 1-soliton solution, periodic singular solutions, and plane wave solution were derived with the help of trial solution method. Finally, based on theG′/G-expansion scheme, we obtained the hyperbolic function travelling wave solution, trigonometric function travelling wave solution, and plane wave solution.

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