Related papers: Shock and Rarefaction Waves in Generalized Hertzia…
It is shown that the tight-binding approximation of the nonlinear Schr\"odinger equation with a periodic linear potential and periodic in space nonlinearity coefficient gives rise to a number of nonlinear lattices with complex, both linear…
We analyze rarefaction wave interactions of self-similar transonic irrotational flow in gas dynamics for the two dimensional Riemann problems. We establish the existence result of the supersonic solution to the prototype nonlinear wave…
A simple exactly solvable kinetic model for the non-linear inelastic hard sphere Boltzmann equation is used to explore the relevance of hydrodynamics for a granular gas. The equation predicts a non-trivial homogeneous cooling state (HCS),…
We study the interaction of highly nonlinear solitary waves in granular crystals, with an adjacent linear elastic medium. We investigate the effects of interface dynamics on the reflection of incident waves and on the formation of primary…
In granular media, the characterization of the behavior of solitary waves around interfaces is of importance in order to look for more applications of these systems. We study the behavior of solitary waves at both interfaces of a symmetric…
Here we theoretically and computationally study the frequency dependence of phase speed and attenuation for marine sediments from the perspective of granular mechanics. We leverage recent theoretical insights from the granular physics…
The quasistatic approximation is a useful but questionable simplification for analyzing step instabilities during the growth/evaporation of vicinal surfaces. Using this approximation, we characterized in Part I of this work the effect on…
We are interested in the dynamics of interfaces, or zeros, of shock waves in general scalar viscous conservation laws with a locally Lipschitz continuous flux function, such as the modular Burgers' equation. We prove that all interfaces…
This work proposes a new way for handling obstacles to asymptotic integrability in perturbed nonlinear PDEs within the method of Normal Forms - NF - for the case of multi-wave solutions. Instead of including the whole obstacle in the NF,…
The purpose of this paper is to investigate experimental and numerical dynamic responses of a preloaded vibro-impacting Hertzian contact under sinusoidal excitation. Dynamic response under random excitation is analysed in the second part of…
In this paper we use a deterministic multi-asperity model to investigate the elastic contact of rough spheres. Synthetic rough surfaces with controllable spectra were used to identify individual asperities, their locations and curvatures.…
We study the stability of composite waves consisting of a shock profile and a rarefaction wave for the one-dimensional isothermal Navier--Stokes--Poisson (NSP) system, which describes the ion dynamics in a collision-dominated plasma. More…
We theoretically study and experimentally report the propagation of nonlinear hysteretic torsional pulses in a vertical granular chain made of cm-scale, self-hanged magnetic beads. As predicted by contact mechanics, the torsional coupling…
The inelastic hard sphere model of granular material is simple, easily accessible to theory and simulation, and captures much of the physics of granular media. It has three drawbacks, all related to the approximation that collisions are…
Wave phenomena in vibrofluidized dry and partially wet granular materials confined in a quasi-two-dimensional geometry are investigated with numerical simulations considering individual particles as hard spheres. Short ranged cohesive…
This paper introduces a novel wave front tracking framework for reconstructing unknown flux functions in $2\times 2$ hyperbolic conservation laws, extending beyond the well-studied scalar case. By analyzing Riemann solutions at fixed…
Plastic instabilities in amorphous materials are often studied using idealized models of binary mixtures that do not capture accurately molecular interactions and bonding present in real glasses. Here we study atomic scale plastic…
Interactions between solitary waves have been pivotal to understanding nonlinear phenomena across various disciplines. The dynamics of rarefaction solitary waves holds great potential, yet their fundamental characteristics and interactions…
Shocks due to hyperbolic partial differential equations (PDEs) appear throughout mathematics and science. The canonical example is shock formation in the inviscid Burgers' equation $\frac{\partial u}{\partial t}+u\frac{\partial u}{\partial…
A set of travelling wave solutions to a hyperbolic generalization of the convection-reaction-diffusion is studied by the methods of local nonlinear alnalysis and numerical simulation. Special attention is paid to displaying appearance of…