Related papers: Origin of Jumping Oscillons in an Excitable Reacti…
A remarkable phenomenon in turbulent flows is the spontaneous emergence of coherent large spatial scale zonal jets. Geophysical examples of this phenomenon include the Jovian banded winds and the Earth's polar front jet. In this work a…
Oscillons are localized, non-singular, time-dependent, spherically-symmetric solutions of nonlinear scalar field theories which, although unstable, are extremely long-lived. We show that they naturally appear during the collapse of…
The possibility that extremely long-lived, time-dependent, and localized field configurations (``oscillons'') arise during the collapse of asymmetrical bubbles in 2+1 dimensional phi^4 models is investigated. It is found that oscillons can…
We report the discovery of highly localized structures traveling over a one-dimensional pattern of Faraday waves in a vertically-vibrated fluid layer confined in a thin annular cell. These propagating structures emerge spontaneously beyond…
We propose a general framework for studying jump-diffusion systems driven by both Gaussian noise and a jump process with state-dependent intensity. Of particular natural interest are the jump locations: the system evaluated at the jump…
In the past the study of reaction-diffusion systems has greatly contributed to our understanding of the behavior of many-body systems far from equilibrium. In this paper we aim at characterizing the properties of diffusion limited reactions…
We consider a (1+1) dimensional scalar field theory that supports oscillons, which are localized, oscillatory, stable solutions to nonlinear equations of motion. We study this theory in an expanding background and show that oscillons now…
Self-oscillators are intriguing due to their ability to sustain periodic motion without periodic stimulus. They remain rare as achieving such behavior requires a balance of energy input, dissipation and non-linear feedback mechanism. Here,…
We examine the effects of a periodically varying flow velocity on the standing and travelling wave patterns formed by the flow-distributed oscillation (FDO) mechanism. In the kinematic (or diffusionless) limit, the phase fronts undergo a…
Random metastability occurs when an externally forced or noisy system possesses more than one state of apparent equilibrium. This work investigates fluctuations in a class of random dynamical systems, arising from randomly perturbing a…
We consider the stability of position control of traveling waves in reaction-diffusion system as proposed in {[}J. L\"ober, H. Engel, arXiv:1304.2327{]}. Instead of analyzing the controlled reaction-diffusion system, stability is studied on…
We consider networks of reaction-diffusion systems of Hodgkin-Huxley type. We give a general mathematical framework, in which we prove existence and unicity of solutions as well as existence of invariant regions and of the attractor. Then,…
Coupling diffusion process of signaling molecules with nonlinear interactions of intracellular processes and cellular growth/transformation leads to a system of reaction-diffusion equations coupled with ordinary differential equations…
Classical models of pattern formation are based on diffusion-driven instability (DDI) of constant stationary solutions of reaction-diffusion equations, which leads to emergence of stable, regular Turing patterns formed around that…
In an experiment of oscillatory media, domains and walls are formed under the parametric resonance with a frequency double the natural one. In this bi-stable system, %phase jumps $\pi$ by crossing walls. a nonequilibrium transition from…
The universal equations describing collective oscillations of the multidomain patterns of small period in an arbitrary $d$-dimensional reaction-diffusion system of the activator-inhibitor type are asymptotically derived. It is shown that…
We demonstrate the emergence of self-organized structures in the course of the relaxation of an initially excited, dissipative and finite chain of interacting particles in a periodic potential towards its many particle equilibrium…
Excitable waves arise in many spatially-extended systems of either biological, chemical, or physical nature due to the interplay between local reaction and diffusion processes. Here we demonstrate that similar phenomena are encoded in the…
We study the dynamics of an infinite system of point particles of two types. They perform random jumps in $\mathbf{R}^d$ in the course of which particles of different types repel each other whereas those of the same type do not interact.…
Boundary-induced pattern formation from a spatially uniform state is investigated using one-dimensional reaction-diffusion equations. The temporal oscillation is successively transformed into a spatially periodic pattern, triggered by…