Related papers: Fluctuating solutions for the evolution of domain …
Wagner's modularity inducing problem domain is a key contribution to the study of the evolution of modularity, including both evolutionary theory and evolutionary computation. We study its behavior under classical genetic algorithms. Unlike…
Using a variational method, we prove the existence of heteroclinic solutions for a 6dimensional system of ordinary differential equations. We derive this system from the classical B{\'e}nard-Rayleigh problem near the convective instability…
Given a nonlinear evolution equation in (1+n) dimensions, which has spatially extended traveling wave solutions, it can be extended into a system of two coupled equations, one of which generates the original traveling waves, and the other…
Using a Ginzburg--Landau--Devonshire model that includes the coupling of polarization to strain, we calculate the fluctuation spectra of ferroelectric domain walls. The influence of the strain coupling differs between 180 degree and 90…
The elastic interaction between kinks (and antikinks) within domain walls plays a pivotal role in shaping the domain structure, and their dynamics. In bulk materials, kinks interact as elastic monopoles, dependent on the distance between…
We construct and analyse two-dimensional, current-carrying ring solutions, known as kinky vortons, in the $\mathbb{Z}_2$-symmetric global two-Higgs-doublet model (2HDM). We demonstrate the existence of multiple dynamically stable…
The phenomenon of bursting, in which streaks in turbulent boundary layers oscillate and then eject low speed fluid away from the wall, has been studied experimentally, theoretically, and computationally for more than 50 years because of its…
We show that domain walls separating coexisting extremal current phases in driven diffusive systems exhibit complex stochastic dynamics, with a subdiffusive temporal growth of position fluctuations due to long-range anticorrelated current…
We study a number of domain wall forming models where various types of defect junctions can exist. These illustrate some of the mechanisms that will determine the evolution of defect networks with junctions. Understanding these mechanisms…
Discrete symmetries are commonplace in field theoretical models but pose a severe problem for cosmology since they lead to the formation of domain walls during spontaneous symmetry breaking in the early universe. However if one of the…
We study the evolution of thick domain walls in the different models of cosmological inflation, in the matter-dominated and radiation-dominated universe, or more generally in the universe with the equation of state $p=w\rho$. We have found…
In this paper, we define and study Loewner chains and evolution families on finitely multiply-connected domains in the complex plane. These chains and families consist of conformal mappings on parallel slit half-planes and have one and two…
We study numerically domain growth and interface fluctuations in one- and two-dimensional lattice systems composed of four species that interact in a cyclic way. Particle mobility is implemented through exchanges of particles located on…
We consider a system of two discrete nonlinear Schr\"{o}dinger equations, coupled by nonlinear and linear terms. For various physically relevant cases, we derive a modulational instability criterion for plane-wave solutions. We also find…
It is argued that in the case of a smooth transition across a (dilaton-driven) curvature bounce the growing mode of the vector fluctuations matches continuously with a decaying mode at later times. Analytical examples of this observation…
The domain wall response under constant external magnetic fields reveals a complex behavior where sample disorder plays a key role. Furthermore, the response to alternating magnetic fields has only been explored in limited cases and…
The effective Nambu-Goto description of $(2+1)$-dimensional domain walls predicts singular behavior of its worldsheet resulting in swallowtail bifurcations. This phenomenon is intimately related to the formation of cusps, which emerge in…
In loop quantum cosmology, the values of volume fluctuations and correlations determine whether the dynamics of an evolving state exhibits a bounce. Of particular interest are states that are supported only on either the positive or the…
A relativistic generalisation of a well-known method for approximating the dynamics of topological defects in condensed matter is constructed, and applied to the evolution of domain walls in a cosmological context. It is shown that there…
The motion of domain walls in ferromagnetic, cylindrical nanowires is investigated numerically by solving the Landau-Lifshitz-Gilbert equation for a classical spin model in which energy contributions from exchange, crystalline anisotropy,…