Related papers: Breathers and kinks in a simulated crystal experim…
We review research on the role of nonlinear coherent phenomena (e.g breathers and kinks) in the formation linear decorations in mica crystal. The work is based on a new model for the motion of the mica hexagonal K layer, which allows…
We report the ejection of atoms at a crystal surface caused by energetic breathers which have travelled more than 10^7 unit cells in atomic chain directions. The breathers were created by bombardment of a crystal face with heavy ions. This…
We describe, for the first time, the full 2D scattering of long-lived breathers in a model hexagonal lattice of atoms. The chosen system, representing an idealized model of mica, combines a Lennard-Jones interatomic potential with an…
In this paper we consider a 2D hexagonal crystal lattice model first proposed by Marin, Eilbeck and Russell in 1998. We perform a detailed numerical study of nonlinear propagating localized modes, that is, propagating discrete breathers and…
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 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…
We present a dynamical picture of kink-anti-kink scattering in a pair of special, Frankensteinian potentials made of piece-wise quadratic and linear pieces. Specifically, we focus on models that support kinks without skin and core regions.…
This thesis presents an extensive analysis of the behavior of topological solitons when one or more of their internal modes are activated. The first part of this manuscript is devoted to the study of the simplest topological solitons in…
In this paper we complete the study of global minimizers of a forced, non autonomous, one dimensional, phase transition model, initiated in [8]. Motivated by the recent findings in [9], revealing new configurations of topological structures…
The deformed model $\tilde{\varphi}^{(6)}$ is introduced based on the $\varphi^4$ model using a deformation functional $F[\varphi]$ including a free parameter $a$. The kink solutions in different sectors and their internal modes are…
We study discrete solitons (kinks) accessible in state-of-the-art trapped ion experiments, considering zigzag crystals and quasi-3D configurations, both theoretically and experimentally. We first extend the theoretical understanding of…
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…
The resonant energy transfer mechanism, responsible for the presence of fractal patterns in the velocity diagrams of kink-antikink scattering, is analyzed for a family of two-component scalar field theory models, in which the kink solutions…
We study the dynamics of moving discrete breathers in an interfaced piecewise DNA molecule. This is a DNA chain in which all the base pairs are identical and there exists an interface such that the base pairs dipole moments at each side are…
We analyse the scattering of sine-Gordon breathers on a square potential well. We show that the scattering process depends not only on the vibration frequency of the breather and its incoming speed but also on its phase as well as the depth…
We simulate the sintering of particle aggregates due to surface diffusion. As a method we use Kinetic Monte-Carlo simulations in which elasticity can explicitly be taken into account. Therefore it is possible to investigate the shape…
Discrete breathers, or intrinsic localized modes, are spatially localized, time--periodic, nonlinear excitations that can exist and propagate in systems of coupled dynamical units. Recently, some experiments show the sighting of a form of…
A general formalism of X-ray scattering from different kinds of surface morphologies is described. Based on a description of the surface morphology at the atomic scale through the use of the paracrystal model and discrete distributions of…
The role played by a Lorentz-violating term on the outcomes of kink scattering in the $\phi^6$ model is investigated by using the Fourier spectral method. Impacts of the Lorentz-violating term on the critical velocities, the location of…
We study the scattering of the $\varphi^8$ kinks off each other, namely, we consider those $\varphi^8$ kinks that have power-law asymptotics. The slow power-law fall-off leads to a long-range interaction between the kink and the antikink.…