Related papers: Wave manipulation using a bistable chain with reve…
We have studied properties of nonlinear waves in a mathematical model of a predator-prey system with pursuit and evasion. We demonstrate a new type of propagating wave in this system. The mechanism of propagation of these waves essentially…
We expand on prior results on noise supported signal propagation in arrays of coupled bistable elements. We present and compare experimental and numerical results for kink propagation under the influence of local and global fluctuations. As…
We develop a theoretical model to investigate wave propagation in media with random time-varying properties, where temporal fluctuations lead to complex scattering dynamics. Focusing on the ensemble-averaged field, we derive an exact…
We review recent progress in analysing wave scattering in systems with both intrinsic chaos and/or disorder and internal losses, when the scattering matrix is no longer unitary. By mapping the problem onto a nonlinear supersymmetric…
Studying wave propagation in nonlinear discrete systems is essential for understanding energy transfer in lattices. While linear systems prohibit wave propagation within the natural band gap, nonlinear systems exhibit {supratransmission},…
We describe various types of traveling fronts of bistable reaction-diffusion cellular automata. These dynamical systems with discrete time, space, and state spaces can be seen as fully discrete versions of widely studied bistable…
We experimentally and computationally analyze impact-shock-induced stress wave propagation in packings of disordered flexible fibers. We find that dispersive wave propagation, associated with large stress attenuation, occurs much more…
In this paper, the effect of weak nonlinearities in 1D locally resonant metamaterials is investigated via the method of multiple scales. Commonly employed to the investigate the effect of weakly nonlinear interactions on the free wave…
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 paper is concerned with the existence and qualitative properties of pulsating fronts for spatially periodic reaction-diffusion equations with bistable nonlinearities. We focus especially on the influence of the spatial period and,…
We report on the strongly nonlinear dynamics of an array of weakly coupled, non-compressed, parallel granular chains subject to a local initial impulse. The motion of the granules in each chain is constrained to be in one direction which…
In this Letter we describe a novel class of dynamical excitations -- accelerating oscillatory fronts in a new genre of nonlinear sonic vacua with strongly non-local effects. Indeed, it is surprising that such models naturally arise in…
Motivated by earlier studies of artificial perceptions of light called phosphenes, we analyze traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators modeling this phenomenon. We examine the discrete model…
Perturbative partial-wave amplitudes diverge in cases with a massless exchanged particle in the $t$-channel. We argue that the divergence is an artifact of perturbation theory and give a prescription for the all-orders correction factor…
An integro-differential expression for the diffusion current of the impurities diffusing by the mechanism of bound impurity-defect pairs has been derived. The ensuing nonlocal diffusion equation generalizes the existing theories of…
We investigate the propagation of Rayleigh waves in a half-space coupled to a nonlinear metasurface. The metasurface consists of an array of nonlinear oscillators attached to the free surface of a homogeneous substrate. We describe,…
We analyze mechanisms and regimes of wave packet spreading in nonlinear disordered media. We predict that wave packets can spread in two regimes of strong and weak chaos. We discuss resonance probabilities, nonlinear diffusion equations,…
The dynamics of random weakly nonlinear waves is studied in the framework of vibrating thin elastic plates. Although it has been previously predicted that no stationary inverse cascade of constant wave action flux could exist in the…
The propagation of incoherent elastic energy in a three-dimensional solid due to the scattering by many, randomly placed and oriented, pinned dislocation segments, is considered in a continuum mechanics framework. The scattering mechanism…
The spatial structure of the inhomogeneity in a disordered medium determines how waves scatter and propagate in it. We present a theoretical model of how the Fourier components of the disorder control wave scattering in a two-dimensional…