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The influence of nearest-neighbor diffusion on the decay of a metastable low-coverage phase (monolayer adsorption) in a square lattice-gas model of electrochemical metal deposition is investigated by kinetic Monte Carlo simulations. The…
Diffusion is a central phenomenon in almost all fields of natural science revealing microscopic processes from the observation of macroscopic dynamics. Here, we consider the paradigmatic system of a single atom diffusing in a periodic…
Many approaches to modelling reaction-diffusion systems with anomalous transport rely on deterministic equations and ignore fluctuations arising due to finite particle numbers. Starting from an individual-based model we use a…
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…
We investigate the dynamics of a single tracer exploring a course of fixed obstacles in the vicinity of the percolation transition for particles confined to the infinite cluster. The mean-square displacement displays anomalous transport,…
We provide a fully nonlinear port-Hamiltonian formulation for discrete elastodynamical systems as well as a structure-preserving time discretization. The governing equations are obtained in a variational manner and represent index-1…
The nonlinear diffusion in multicomponent liquids under chemical reactions influence has been studied. The theory is applied to the analysis of mass transfer in a solution of acetone-benzene. It has been shown, that the creation of…
We present a method to control the two-dimensional shape of traveling wave solutions to reaction-diffusion systems, as e.g. interfaces and excitation pulses. Control signals that realize a pre-given wave shape are determined analytically…
We consider a curved chain of nonlinear oscillators and show that the interplay of curvature and nonlinearity leads to a number of qualitative effects. In particular, the energy of nonlinear localized excitations centered on the bending…
The polarization and magnetization effects associated with the dynamical reduction leading to the nonlinear gyrokinetic Vlasov-Maxwell equations are shown to introduce nonlinear finite-Larmor-radius effects into a set of nonlinear…
Nonlinear damping, the change in damping rate with the amplitude of oscillations plays an important role in many electrical, mechanical and even biological oscillators. In novel technologies such as carbon nanotubes, graphene membranes or…
The effect of particle-nonconserving processes on the steady state of driven diffusive systems is studied within the context of a generalized ABC model. It is shown that in the limit of slow nonconserving processes, the large deviation…
The nonlinear response of molecular systems undergoing Markovian stochastic reorientations is calculated up to fifth order in the amplitude of the external field. Time-dependent perturbation theory is used to compute the relevant response…
A classification of dynamical systems in terms of their variational properties is reviewed. Within this classification, front propagation is discussed in a non-gradient relaxational potential flow. The model is motivated by transient…
A theoretical investigation on slow light propagation based on eletromagnetically induced transparency in a three-level quantum-dot system is performed including non-Markovian effects and correlated dephasing reservoirs. It is…
We have developed a theory of the anomalous Hall effect in two-dimensional electron gas in the case where the time of electron-electron collisions is much smaller than the transport relaxation time. The transition between the diffusion…
We study the asymptotic behaviour of a gradient system in a regime in which the driving energy becomes singular. For this system gradient-system convergence concepts are ineffective. We characterize the limiting behaviour in a different…
An impact of neutrals on anomalous edge plasma transport and zonal flow (ZF) is considered. As an example, it is assumed that edge plasma turbulence is driven by the resistive drift wave (RDW) instability. It is found that the actual effect…
The presence and evolution of defects that appear in the manufacturing process play a vital role in the failure mechanisms of engineering materials. In particular, the collective behavior of dislocation dynamics at the mesoscale leads to…
This work considers the propagation of high-frequency waves in highly-scattering media where physical absorption of a nonlinear nature occurs. Using the classical tools of the Wigner transform and multiscale analysis, we derive semilinear…