Related papers: Kinks Dynamics in One-Dimensional Coupled Map Latt…
A unified method to analyze the dynamics and topological structure associated with a class of Floquet topological insulators is presented. The method is applied to a system that describes the propagation of electromagnetic waves through the…
This work focuses on dynamics arising from reaction-diffusion equations , where the profile of propagation is no longer characterized by a single front, but by a layer of several fronts which we call a propagating terrace. This means,…
We present initial results regarding the existence, stability and interaction of linear and nonlinear vibrational modes in a system of two coupled, one dimensional lattices with unequal numbers of masses. The effects on these nonlinear…
The symmetric dynamics of two kinks and one antikink in classical (1+1)-dimensional $\phi^4$ theory is investigated. Gradient flow is used to construct a collective coordinate model of the system. The relationship between the discrete…
The frictional dynamics of interacting surfaces under forced translation are critically dependent on lattice commensurability. Performing experiments in a trapped-ion friction emulator, we observe two distinct structural and frictional…
Diffusion in an evolving environment is studied by continuos-time Monte Carlo simulations. Diffusion is modelled by continuos-time random walkers on a lattice, in a dynamic environment provided by bubbles between two one-dimensional…
It was recently proposed a novel discretization for nonlinear Klein-Gordon field theories in which the resulting lattice preserves the topological (Bogomol'nyi) lower bound on the kink energy and, as a consequence, has no Peierls-Nabarro…
We study the kink motion for the one-dimensional stochastic Allen-Cahn equation and its mass conserving counterpart. Using a deterministic slow manifold, in the sharp interface limit for sufficiently small noise strength we derive an…
We study the topological dynamics by iterations of a piecewise continuous, non linear and locally contractive map in a real finite dimensional compact ball. We consider those maps satisfying the "separation property": different continuity…
The Artificial Axon is a unique synthetic system, based on biomolecular components, which supports action potentials. Here we consider, theoretically, the corresponding space extended system, and discuss the occurrence of solitary waves, or…
Continuous limits of discrete systems with long-range interactions are considered. The map of discrete models into continuous medium models is defined. A wide class of long-range interactions that give the fractional equations in the…
In this paper we analyse the propagation of warps in protostellar circumbinary discs. We use these systems as a test environment in which to study warp propagation in the bending-wave regime, with the addition of an external torque due to…
A one dimensional lattice model is formulated to study tapping dynamics and the long time steady distribution in granular media. The dynamics conserves the number of particles in the system, and density changes are associated to the…
Frictional interfaces exhibits a very rich dynamical behavior due to frictional interactions. This work focuses on the transition between spatially localized and propagating stick-slip motion. To overcome the difficulties related to the…
Two approaches are used for description of linear transverse (kink) modes excited in a vertical thin magnetic flux tube. First one is based on the elastic thread model (Spruit, 1981). The second one follows from the the Taylor and Laurent…
This paper investigates the existence of traveling--wave--type patterns in the Keller--Segel model with logarithmic sensitivity. We consider both the linear diffusion case and the nonlinear, flux-saturated diffusion of relativistic…
We propose a simple discrete model to study the nonequilibrium fluctuations of two locally coupled 1+1 dimensional systems (interfaces). Measuring numerically the tilt-dependent velocity we construct a set of stochastic continuum equations…
We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…
This study explores the scattering dynamics of kinks within a nonlinear system governed by a parameterized potential $U_\lambda(\chi)$, examining the distinct behaviors of small and large kinks across a range of $\lambda$ values and initial…
For most discretisations of the $\phi^4$ theory, the stationary kink can only be centered either on a lattice site or midway between two adjacent sites. We search for exceptional discretisations which allow stationary kinks to be centered…