Related papers: Causality Analysis of Frequency Dependent Wave Att…
This study explores the use of fractional calculus as a possible tool to model wave propagation in complex, heterogeneous media. We illustrate the methodology by focusing on elastic wave propagation in a one-dimensional periodic rod. The…
The present study investigates novelties brought about into the classic Biot's theory of propagation of elastic waves in a fluid-saturated porous solid by inclusion of non-Newtonian effects that are important, for example, for hydrocarbons.…
The dissipation of acoustic wave propagation has long been found to obey an empirical power function of frequency, whose exponent parameter varies through different media. This note aims to unveil the inherent relationship between this…
For any kind of wave phenomenon one can find ways to derive the respective dispersion relation from experimental observations and measurements. This dispersion relation determines the structure of the wave equation and thus characterizes…
The concept of causality has a controversial history. The question of whether it is possible to represent and address causal problems with probability theory, or if fundamentally new mathematics such as the do-calculus is required has been…
We consider an undetermined coefficient inverse problem for a nonlinear partial differential equation describing high intensity ultrasound propagation as widely used in medical imaging and therapy. The usual nonlinear term in the standard…
We investigate the causality and stability of relativistic dissipative fluid dynamics in the absence of conserved charges. We perform a linear stability analysis in the rest frame of the fluid and find that the equations of relativistic…
The problem of attenuation and sound speed of bubbly media has remained partially unsolved. Comprehensive data regarding pressure-dependent changes of the attenuation and sound speed of a bubbly medium are not available. Our theoretical…
The irreducible representations of the extended Galilean group are used to derive the symmetric and asymmetric wave equations. It is shown that among these equations only a new asymmetric wave equation is fundamental. By being fundamental…
We consider a system of two reaction-diffusion-advection equations describing the one dimensional directed motion of particles with superimposed diffusion and mutual alignment. For this system we show the existence of traveling wave…
We demonstrate the existence of a frequency band exhibiting acoustic transparency in 2D and 3D dense granular suspensions, enabling the transmission of a low-frequency ballistic wave excited by a high-frequency broadband ultrasound pulse.…
The propagation of an acoustic wave through two-phase porous media with spatial variation in porosity is studied. The evolutionary wave equation is derived, and the propagation of an acoustic wave is numerically analyzed in application to…
We develop a diagrammatic theory for transport of waves in disordered media with weak nonlinearity. We first represent the solution of the nonlinear wave equation as a nonlinear Born series. From this, we construct nonlinear ladder and…
Sound attenuation in low temperature amorphous solids originates from their disordered structure. However, its detailed mechanism is still being debated. Here we analyze sound attenuation starting directly from the microscopic equations of…
A modification of the Drude dispersive model based on fractional time derivative is presented. The dielectric susceptibility is calculated analytically and simulated numerically, showing a good agreement between theoretical description and…
Effects of spatially varying interfacial parameters on the propagation of surface waves are studied. These variations can arise from inhomogeneities in coverage of surface active substances such as amphiphillic molecules at the fluid/gas…
A one-dimensional wave propagation through elastically asymmetric media is investigated. A class of metamaterials possessing an arbitrary elastic asymmetry is proposed. This asymmetry results in different wave speeds of tensile and…
This work is concerned with the study of fundamental models from nonlinear acoustics. In Part~I, a hierarchy of nonlinear damped wave equations arising in the description of sound propagation in thermoviscous fluids is deduced. In…
Nonlinear stochastic differential equations generating signals with 1/f spectrum have been used so far to describe socio-economical systems. In this paper we consider the motion of a Brownian particle in an inhomogeneous environment such…
Over the past two decades, the rapid surge in data-intensive computational techniques for statistical modeling may have had the effect of diminishing the use of applied mathematics in causal scientific inquiry. In this paper, co-authored by…