Related papers: Breathing Spots in a Reaction-Diffusion System
Diffusion within porous media, such as biological tissues, exhibits departures from conventional Fick's laws, which could result in space-fractional diffusion. The paper considers a reaction-diffusion system with two spatial compartments --…
A one-dimensional model on a line of the length L is investigated, which involves particle diffusion as well as single particle annihilation. There are also creation and annihilation at the boundaries. The static and dynamical behaviors of…
A pure and incompressible material is confined between two plates such that it is heated from below and cooled from above. When its melting temperature is comprised between these two imposed temperatures, an interface separating liquid and…
We explore the influence of dissipation on a paradigmatic driven-dissipative model where a collection of two level atoms interact with both quadratures of a quantum cavity mode. The closed system exhibits multiple phase transitions…
We study the existence, stability, and dynamics of symmetric and anti-symmetric states of quasi-one-dimensional polariton condensates in double-well potentials, in the presence of nonresonant pumping and nonlinear damping. Some prototypical…
We study the response of one dimensional diffusive systems, consisting of particles interacting via symmetric or asymmetric exclusion, to time-periodic driving from two reservoirs coupled to the ends. The dynamical response of the system…
The consecutive microscopic solution is presented of the problem of tunneling of a particle through a potential barrier. The method is applied to the alpha and proton decay of compound systems formed in fusion reaction. Appearance of the…
We present three examples of delayed bifurcations for spike solutions of reaction-diffusion systems. The delay effect results as the system passes slowly from a stable to an unstable regime, and was previously analysed in the context of…
We investigate phase coexistence in a weakly stochastic reaction-diffusion system without assuming a continuum description. Concretely, for $(2N+1)$ diffusion-coupled vessels in which a chemical reaction exhibiting bistability occurs, we…
The study and characterization of the diversity of spatiotemporal patterns generated when a rectangular layer of fluid is locally heated beneath its free surface is presented. We focus on the instability of a stationary cellular pattern of…
Particles in a sufficiently strong electric field spontaneously rotate, provided that charge relaxation is slower in the particle than in the suspending fluid. It has long been known that drops also exhibit such "Quincke rotation," with the…
Static and dynamic properties of two-dimensional bidisperse dissipative particles are numerically studied near the jamming transition. We investigate the dependency of the critical scaling on the ratio of the different diameters and find a…
Pattern formation exhibited by a two-dimensional reaction-diffusion system in the fast inhibitor limit is considered from the point of view of interface motion. A dissipative nonlocal equation of motion for the boundary between high and low…
For a particular case of three-body scattering in 2 dimensions, we demonstrate analytically that the behaviour of the adiabatic potential is different from that of the hyperspherical coupling matrix elements, thereby leading to a phase…
This paper presents boundary observer design for space and time dependent reaction-advection-diffusion equations using backstepping method. The method uses only a single measurement at the boundary of the systems. The existence of the…
We study a non-conserved one-dimensional stochastic process which involves two species of particles $A$ and $B$. The particles diffuse asymmetrically and react in pairs as $A\emptyset\leftrightarrow AA\leftrightarrow BA \leftrightarrow…
Some quantities in the reaction-diffusion models from cellular biology or ecology depend on the spatial average of density functions instead of local density functions. We show that such nonlocal spatial average can induce instability of…
We investigate spreading properties of solutions of a large class of two-component reaction-diffusion systems, including prey-predator systems as a special case. By spreading properties we mean the long time behaviour of solution fronts…
The stationary phase method is applied to diffusion by a potential barrier for an incoming wave packet with energies greater then the barrier height. It is observed that a direct application leads to paradoxical results. The correct…
We report on the observation of a novel manifestation of saturation-induced optical bistability in a resonantly pumped optical ring cavity interacting strongly with a cloud of atoms via a narrow atomic transition. The bistability emerges,…