Related papers: Influence of moving breathers on vacancies migrati…
In this paper a Frenkel--Kontorova model with a nonlinear interaction potential is used to describe a vacancy defect in a crystal. According to recent numerical results [Cuevas et al, Phys. Lett. A 315, 364 (2003)] the vacancy can migrate…
In this paper, interstitial migration generated by scattering with a mobile breather is investigated numerically in a Frenkel-Kontorova one-dimensional lattice. Consistent with experimental results it is shown that interstitial diffusion is…
In the present chapter, we explore the possibility of a Frenkel-Kontorova (discrete sine-Gordon) model to bear interactions that decay algebraically with space, inspired by the continuum limit of the corresponding fractional derivative. In…
We study the properties of moving breathers in a bent DNA-related model with short range interaction, due to the stacking of the base pairs, and long range interaction, due to the finite dipole moment of the bonds within each base pair. We…
Breathers may be mobile close to an instability threshold where the frequency of a pinning mode vanishes. The translation mode is a marginal mode that is a solution of the linearized (Hill) equation of the breather which grows linearly in…
We study the properties of discrete breathers, also known as intrinsic localized modes, in the one-dimensional Frenkel-Kontorova lattice of oscillators subject to damping and external force. The system is studied in the whole range of…
We present a theoretical study of the interaction of vacancies with a tilt grain boundary in aluminum based on the density functional theory. The grain boundary volume expansion and vacancy induced contraction are calculated and compared…
A 1D model of interacting particles moving over a periodic substrate and in a position dependent temperature profile is considered. When the substrate and the temperature profile are spatially asymmetric a center-of-mass velocity develops,…
We consider random walkers that deform the medium as they move, enabling a faster motion in regions which have been recently visited. This induces an effective attraction between walkers mediated by the medium, which can be regarded as a…
We analyze the influence of an impurity in the evolution of moving discrete breathers in a Klein--Gordon chain with non-weak nonlinearity. Three different behaviours can be observed when moving breathers interact with the impurity: they…
The features of alternative approach of non-equilibrium evolution thermodynamics are shown on the example of theory of vacancies by opposed to the classic prototype of Landau theory. On this foundation a strict theory of the melting of…
The ability for real-time control of topological defects can open up prospects for dynamical manipulation of macroscopic properties of solids. A sub-category of these defects, formed by particle dislocations, can be effectively described…
In this communication, we examine a nonlinear model with an impurity emulating a bend. We justify the geometric interpretation of the model and connect it with earlier work on models including geometric effects. We focus on both the…
The scattering of kinks and low-frequency breathers of the nonlinear sine-Gordon (SG) equation on a spatially localized $\mathcal{PT}$-symmetric perturbation (defect) with a balanced gain and loss is investigated numerically. It is…
A formalism using a double Laplace Fourier transform of the transport equation yields the return probabilities of the vacancy in the vicinity of the tracer atom in the presence of solute-vacancy interactions of arbitrary extension. Studying…
Invasion fronts in ecology are well studied but very few mathematical results concern the case with variable motility (possibly due to mutations). Based on an apparently simple reaction-diffusion equation, we explain the observed phenomena…
The dynamics of a system composed of elastic hard particles confined by an isotropic harmonic potential are studied. In the low-density limit, the Boltzmann equation provides an excellent description, and the system does not reach…
We consider a generalized one-dimensional chain in a periodic potential (the Frenkel-Kontorova model), with dissipative, pulsating (or ratchet) dynamics as a model of transport when the average force on the system is zero. We find lower…
We study some of the salient features of the arrival statistics and exploration properties of mortal random walkers, that is, walkers that may die as they move, or as they wait to move. Such evanescence or death events have profound…
Active matter systems under confinement display persistent surface motion and a strong boundary affinity. However, despite extensive studies of their positional dynamics, much less attention has been given to the corresponding orientational…