相关论文: Arbitrarily weak head-on collision can induce anni…

We use geometric singular perturbation techniques combined with an action functional approach to study traveling pulse solutions in a three-component FitzHugh--Nagumo model. First, we derive the profile of traveling $1$-pulse solutions with…

A two dimensional self-gravitating Hamiltonian model made by $N$ fully-coupled classical particles exhibits a transition from a collapsing phase (CP) at low energy to a homogeneous phase (HP) at high energy. From a dynamical point of view,…

We investigate diffusion-driven instabilities in a FitzHugh-Nagumo reaction-diffusion system with superdiffusive transport, modeled by fractional Laplacian operators with different diffusion orders for the activator and the inhibitor. A…

For a coupled slow--fast FitzHugh--Nagumo(FHN) equation derived from a reaction-diffusion-mechanics (RDM) model, Holzer, Doelman and Kaper in 2013 studied existence and stability of the travelling pulse, which consists of two fast orbit…

We consider a one-dimensional system with particles having either positive or negative velocity, which annihilate on contact. To the ballistic motion of the particle, a diffusion is superimposed. The annihilation may represent a reaction in…

We investigate the instabilities and bifurcations of traveling pulses in a model excitable medium; in particular we discuss three different scenarios for the loss of stability resp. the disappearance of stable pulses. In numerical…

This work deals with a parametric linear interpolation between an autonomous FitzHugh-Nagumo model and a nonautonomous skewed-problem with the same fundamental structure. This paradigmatic example allows to construct a family of…

The emergence of particle irreversibility in periodically driven colloidal suspensions has been interpreted as resulting either from a nonequilibrium phase transition to an absorbing state or from the chaotic nature of particle…

In this paper, we provide a mathematical framework in studying the wave propagation with the annihilation phenomenon in excitable media. We deal with the existence and uniqueness of solutions to a one-dimensional free boundary problem…

We consider one-dimensional asymmetric exclusion processes with a simple attractive interaction, where the distance between consecutive particles is not allowed to exceed a certain limit and investigate the consequences of this coupling on…

Recently it has been shown that the transition of the 1+1-dimensional annihilation-fission process 2X->3X, 2X->0 exhibits an unusual type of nonequilibrium critical behavior. The phenomenological properties of critical clusters are…

The interplay between 1D traveling pulses with oscillatory tails (TPO) and heterogeneities of bump type is studied for a generalized three-component FitzHugh-Nagumo equation. First, we present that stationary pulses with oscillatory tails…

The quasi-coherent effects in two-dimensional incompressible turbulence are analyzed starting from the test particle trajectories. They can acquire coherent aspects when the stochastic potential has slow time variation and the motion is not…

In recent years, nonreciprocally coupled systems have received growing attention. Previous work has shown that the interplay of nonreciprocal coupling and Goldstone modes can drive the emergence of temporal order such as traveling waves. We…

The kinetics of the annihilation process, $A+A\to 0$, with ballistic particle motion is investigated when the distribution of particle velocities is {\it discrete}. This discreteness is the source of many intriguing phenomena. In the mean…

Ballistic annihilation is an interacting system in which particles placed throughout the real line move at preassigned velocities and annihilate upon colliding. The longstanding conjecture that in the symmetric three-velocity setting there…

Impact phenomena of nanoclusters subject to thermal fluctuations are numerically investigated. From the molecular dynamics simulation for colliding two identical clusters, it is found that the restitution coefficient for head-on collisions…

We consider diffusion-limited annihilating systems with mobile $A$-particles and stationary $B$-particles placed throughout a graph. Mutual annihilation occurs whenever an $A$-particle meets a $B$-particle. Such systems, when ran in…

We establish the existence and nonlinear stability of travelling pulse solutions for the discrete FitzHugh-Nagumo equation with infinite-range interactions close to the continuum limit. For the verification of the spectral properties, we…

For systems out of equilibrium and subjected to a static bias force it can often be expected that particle transport will usually follow the direction of this bias. However, counter-examples exist where particles exhibit uphill motion…