Related papers: Propagation Failure in Excitable Media
We investigate the dynamical properties of a strongly disordered micropolar lattice made up of cubic block units. This phononic lattice model supports both transverse and rotational degrees of freedom hence its disordered variant posses an…
It is known that an explosive instability can occur when nonlinear waves propagate in certain media that admit 3-wave mixing. The purpose of this paper is to show that explosive instabilities can occur even in media that admit no 3-wave…
Particles suspended in fluid flow through a closed duct can focus to specific stable locations in the duct cross-section due to hydrodynamic forces arising from the inertia of the disturbed fluid. Such particle focusing is exploited in…
We investigate propagation of few-photon pulses in waveguides coupled to a two-level system by means of the method of distribution functions in coordinate-momentum space that provides a detailed description of photon systems. We find that…
Starting from the wave equation for a medium with material properties that vary periodically, we study a system of recurrence relations that describe propagation of wave packets that oscillate on the microscale (i.e. on lengths of the order…
Based on boundary conditions and dispersion relations, the anomalous propagation of waves incident from regular isotropic media into quasiisotropic media is investigated. It is found that the anomalous negative refraction, anomalous total…
The displacement of a viscous liquid by air in the narrow gap between two parallel plates - a Hele-Shaw channel - is an exemplar of complex pattern formation. Typically, bubbles or fingers of air propagate steadily at low values of the…
We study the exchange of stability in scalar reaction-diffusion equations which feature a slow passage through transcritical and pitchfork type singularities in the reaction term, using a novel adaptation of the geometric blow-up method.…
Modeling of radiation-enhanced diffusion of boron and phosphorus atoms during irradiation of silicon substrates respectively with high- and low-energy protons was carried out. The results obtained confirm the previously arrived conclusion…
We study a 2D scalar harmonic wave transmission problem between a classical dielectric and a medium with a real-valued negative permittivity/permeability which models a metal at optical frequency or an ideal negative metamaterial. We…
Weakly nonlinear amplitude equations are derived for the onset of spatially extended patterns on a general class of n-component bulk-surface reaction-diffusion systems in a ball, under the assumption of linear kinetics in the bulk and…
The time-frequency integrals and the two-dimensional stationary phase method are applied to study the electromagnetic waves radiated by moving modulated sources in dispersive media. We show that such unified approach leads to explicit…
Polymerization of microtubules is ubiquitous in biological cells and under certain conditions it becomes oscillatory in time. Here simple reaction models are analyzed that capture such oscillations as well as the length distribution of…
For ultrashort pulses having different states of polarization, the experienced time delay when passing through small apertures is different. In the case of a small slit (or a circular aperture), we report a significantly stronger dispersion…
A kinetic equation describing the nonlinear evolution of intense electromagnetic pulses in electron-positron (e-p) plasmas is presented. The modulational instability is analyzed for a relativistically intense partially coherent pulse, and…
The archetypal instability of a structure is associated with the eponymous Euler beam, modeled as an inextensible curve which exhibits a supercritical bifurcation at a critical compressive load. In contrast, a soft compressible beam is…
SUMMARY This work aims at quantifying the effect of inherent uncertainties from cardiac output on the sensitivity of a human compliant arterial network response based on stochastic simulations of a reduced-order pulse wave propagation…
This work is concerned with the propagation of electromagnetic waves in isotropic chiral media and with the effects produced by a plane boundary between two such media. In analogy with the phenomena of reflection and refraction of plane…
A pitchfork bifurcation of an $(m-1)$-dimensional invariant submanifold of a dynamical system in $\mathbb{R}^m$ is defined analogous to that in $\mathbb{R}$. Sufficient conditions for such a bifurcation to occur are stated and existence of…
In the present paper, we propose a complex short pulse equation and a coupled complex short equation to describe ultra-short pulse propagation in optical fibers. They are shown to be integrable due to the existence of Lax pairs and infinite…