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Spatially extended systems can support local transient excitations in which just a part of the system is excited. The mechanisms reported so far are local excitability and excitation of a localized structure. Here we introduce an…
We investigate propagation of a pulse pair in a three-level medium under the adiabatic following condition for the general case of unequal oscillator strengths. Exact analytical solutions to the propagation equations have been obtained. It…
We study convective stability of a two-front superposition in a reaction-diffusion system. Due to the instability of the connecting equilibrium, long-range semi-strong interaction is expected between the two waves. When restricting to the…
We derive equations of motion of hydrodynamic fluctuations performing perturbative expansion of the energy-momentum conservation equations around the boost invariant solution in one-dimensional expanding system. In the course of derivation,…
We investigate diffusion of excitation in one- and two-dimensional lattices with random on-site energies and deterministic long-range couplings (hopping) inversely proportional to the distance. Three regimes of diffusion are observed in…
Long-range speckle correlations play an essential role in wave transport through disordered media, but have rarely been studied in other complex systems. Here we discover spatio-temporal intensity correlations for an optical pulse…
This paper is concerned with pulsating waves for multi-dimensional reaction-diffusion equations in spatially periodic media. First, assuming the existence of pulsating waves connecting two linearly stable steady states, we study the…
We present a non-perturbative technique to study pulse dynamics in excitable media. The method is used to study propagation failure in one-dimensional and two-dimensional excitable media. In one-dimensional media we describe the behaviour…
The paper gives a description of wave propagation in discrete-periodic one-dimensional media with block structure. For one-dimensional problems mathematical models are proposed that describe block structures in the form of a mass chain or…
In this article, we consider the energy decay of a viscoelastic wave in an heterogeneous medium. To be more specific, the medium is composed of two different homogeneous medium with a memory term located in one of the medium. We prove…
Spatial intensity correlations between waves transmitted through random media are analyzed within the framework of the random matrix theory of transport. Assuming that the statistical distribution of transfer matrices is isotropic, we found…
Persistence in spatially extended dynamical systems (like coarsening systems and other nonequilibrium systems) is reviewed. We discuss, in particular, the spatial correlations in the persistent regions and their evolution in time in these…
We study a model describing the force-extension curves of modular proteins, nucleic acids, and other biomolecules made out of several single units or modules. At a mesoscopic level of description, the configuration of the system is given by…
We experimentally investigate the lateral diffusion of dipolar excitons in coupled quantum wells in two (2D) and one (1D) dimensions. In 2D, the exciton expansion obeys non-linear temporal dynamics due to the repulsive dipole pressure at a…
The linear response of two-dimensional amorphous elastic bodies to an external delta force is determined in analogy with recent experiments on granular aggregates. For the generated forces, stress and displacement fields, we find strong…
Dispersion curves to a oscillatory reaction-diffusion system with the self-consistent flow have obtained by means of numerical calculations. The flow modulates the shape of dispersion curves and characteristics of traveling waves. The point…
Here we numerically study a model of excitable media, namely, a network with occasionally quiet nodes and connection weights that vary with activity on a short-time scale. Even in the absence of stimuli, this exhibits unstable dynamics,…
A unified electrodynamic approach to the guided wave excitation by external sources in the waveguiding structures with bianisotropic media is developed. Effect of electric, magnetic, and magneto- electric losses in such media manifests…
This work deals with a scalar nonlinear neutral delay differential equation issued from the study of wave propagation. A critical value of the coefficients is considered, where only few results are known. The difficulty follows from the…
In this paper we study the convergence of a power-law model for dilatant compressible fluids to a class of models exhibiting a maximum admissible shear rate, called thick compressible fluids. These kinds of problems were studied previously…