Related papers: Propagation Failure in Excitable Media
Motivated by the growing importance of the fidelity and fidelity susceptibility (FS) in quantum critical phenomena, we use these concepts to describe the pulse propagation inside the dispersive media. It is found that there is a dramatic…
We consider a stochastic partial differential equation close to bifurcation of pitchfork type, where a one-dimensional space changes its stability. For finite-time Lyapunov exponents we characterize regions depending on the distance from…
We investigate pitchfork bifurcations for a stochastic reaction diffusion equation perturbed by an infinite-dimensional Wiener process. It is well-known that the random attractor is a singleton, independently of the value of the bifurcation…
We study the propagation of finite bubbles in a Hele-Shaw channel, where a centred occlusion (termed a rail) is introduced to provide a small axially-uniform depth constriction. For bubbles wide enough to span the channel, the system's…
We obtain an expression for the energy of the density wave propagating in a multicomponent gravitating medium in the form well known from electrodynamics. Using the above, the possibility of "triple production" of the quasi-particles, or…
In this article we develop an effective theory of pulse propagation in a nonlinear and disordered medium. The theory is formulated in terms of a nonlinear diffusion equation. Despite its apparent simplicity this equation describes novel…
For scalar reaction-diffusion equations, a traveling wave is a front which transforms a higher energy state to a lower energy state. The same is true for a system of equations with a gradient structure. At the core of this phenomenon, the…
To obtain the most accurate pulse arrival times from radio pulsars, it is necessary to correct or mitigate the effects of the propagation of radio waves through the warm and ionised interstellar medium. We examine both the strength of…
Propagation of a two-photon pulse in a waveguide coupled to a two-level system (TLS) is studied. The pulse is formed by two spatially separated identical wavepackets. A set of equations governing the dynamics of the photon distribution in…
We consider a heavy, uniform, elastic beam rested on periodically distributed supports as a simplified model of a bridge. The supports are subjected to a partial destruction propagating as a failure wave along the beam. Three related models…
Demixing of binary fluids subjected to slow temperature ramps shows repeated waves of nucleation which arise as a consequence of the competition between generation of supersaturation by the temperature ramp and relaxation of supersaturation…
In bistable systems, the stability of front structures often influences the dynamics of extended patterns. We show how the combined effect of an instability to curvature modulations and proximity to a pitchfork front bifurcation leads to…
A unified framework is proposed to quantitatively characterize pitchfork bifurcations and associated symmetry breaking in the elliptic restricted three-body problem (ERTBP). It is known that planar/vertical Lyapunov orbits and Lissajous…
In order to describe excitable reaction-diffusion systems, we derive a two-dimensional model with a Hopf and a semilocal saddle-node homoclinic bifurcation. This model gives the theoretical framework for the analysis of the saddle-node…
We investigate the impact of the domain shape on wave propagation in excitable media. Channelled domains with sinusoidal boundaries are considered. Trains of fronts generated periodically at an extreme of the channel are found to adopt a…
A quasi-2-dimensional stationary spot in a disk-shaped chemical reactor is observed to bifurcate to an oscillating spot when a control parameter is increased beyond a critical value. Further increase of the control parameter leads to the…
Bifurcations of solitary waves propagating along the interface between two ideal fluids are considered. The study is based on a Hamiltonian approach. It concentrates on values of the density ratio close to a critical one, where the…
We prove that the famous diffusive Brusselator model can support more complicated spatial-temporal wave structure than the usual temporal-oscillation from a standard Hopf bifurcation. In our investigation, we discover that the diffusion…
The propagation of a narrow-band signal radiated by a point source in a randomly layered absorbing medium is studied asymptotically in the weak-scattering limit. It is shown that in a disordered stratified medium that is homogeneous on…
The gas breakdown produced by high-power pulsed linearly and circularly polarized microwave fields which are much weaker than the atomic fields is investigated in the non-relativistic limit. Obtained the electron distribution function…