Related papers: A k-space method for nonlinear wave propagation
We propose a self-adaptive absorbing technique for quasilinear ultrasound waves in two- and three-dimensional computational domains. As a model for the nonlinear ultrasound propagation in thermoviscous fluids, we employ Westervelt's wave…
The Westervelt equation describes the propagation of pressure waves in continuous nonlinear and, eventually, diffusive media. The classical framework of this equation corresponds to fluid dynamics theory. This work seeks to connect this…
High-frequency wave propagation is often modelled by nonlinear Friedrichs systems where both the differential equation and the initial data contain the inverse of a small parameter $\varepsilon$, which causes oscillations with wavelengths…
This paper provides a theoretical foundation for some common formulations of inverse problems in wave propagation, based on hyperbolic systems of linear integro-differential equations with bounded and measurable coefficients. The…
Numerical methods are developed to simulate the wave propagation in heterogeneous 2D fluid / poroelastic media. Wave propagation is described by the usual acoustics equations (in the fluid medium) and by the low-frequency Biot's equations…
It is demonstrated that current theoretical models utilize equations for description of laser beam propagation in nonlinear media that were deduced under the assumption of homogeneity of dielectric constant of the media and for the case of…
The paper describes a formulation of discrete scalar wave propagation in an inhomogeneous medium by the use of elementary processes obeying a discrete Huygens' principle and satisfying fundamental symmetries such as time-reversal,…
We present preliminary results on a novel numerical method describing wave propagation in non-uniform media. Following Huygens-Fresnel' principle, we model the wavefront as an array of point sources that emit wavelets, which interfere. We…
We present a new methodology, based on the WKB approximation and Fast Fourier Transforms, for the evaluation of wave propagation through inhomogeneous media. This method can accurately resolve fields containing caustics, while still…
An electromagnetic wave-packet propagating in a linear, homogeneous, and isotropic medium changes shape while its envelope travels with different velocities at different points in spacetime. In general, a wave-packet can be described as a…
With the increasing use of ultrashort laser pulses and nanoscale-materials, one is regularly confronted to situations in which the properties of the media supporting propagation are not varying slowly with time (or space). Hence, the usual…
We present an explicit finite difference time domain method to solve the lossless Westervelt equation for a moving wave emitting boundary in one dimension and in spherical symmetry. The approach is based on a coordinate transformation…
The vector electric-field Helmholtz equation, containing cross-polarization terms, is factored to produce both pseudo-differential and exponential operator forms of a three-dimensional, one-way, vector, wave equation for propagation through…
Characterizing electromagnetic wave propagation in nonlinear and inhomogeneous media is of great interest from both theoretical and practical perspectives, even though it is extremely complicated. In fact, it is still an unresolved issue to…
In geophysics, wave propagation in elastic media is a crucial subject. In this context, seismology has made significant progress as a result of numerous advances, among these stands out the advancement of numerical methods such as the…
The effects of the non-extensive statistics on the nonlinear propagation of perturbations have been studied within the scope of relativistic second order dissipative hydrodynamics with the non-extensive equation of state. We have shown that…
The time-dependent Maxwell system describing electromagnetic wave propagation in inhomogeneous isotropic media in the one-dimensional case reduces to a Vekua-type equation for bicomplex-valued functions of a hyperbolic variable, see…
Multi-scale wave propagation problems are computationally costly to solve by traditional techniques because the smallest scales must be represented over a domain determined by the largest scales of the problem. We have developed and…
We study the diffusion equation with a position-dependent, power-law diffusion coefficient. The equation possesses the Riesz-Weyl fractional operator and includes a memory kernel. It is solved in the diffusion limit of small wave numbers.…
A novel statistical approach based on the Wigner transform is proposed for the description of partially incoherent optical wave dynamics in nonlinear media. An evolution equation for the Wigner transform is derived from a nonlinear…