Related papers: Dynamics of a planar domain wall with oscillating …
In this paper, neural network approximation methods are developed for elliptic partial differential equations with multi-frequency solutions. Neural network work approximation methods have advantages over classical approaches in that they…
We consider wave propagation problems over 2-dimensional domains with piecewise-linear boundaries, possibly including scatterers. We assume that the wave speed is constant, and that the initial conditions and forcing terms are radially…
We study collisions between nearly planar domain walls including the effects of small initial nonplanar fluctuations. These perturbations represent the small fluctuations that must exist in a quantum treatment of the problem. In a previous…
We study the propagation of a domain wall (kink) of the $\phi^4$ model in a radially symmetric environment defined by a gravity source. This source deforms the standard Euclidian metric into a Schwarzschild-like one. We introduce an…
Cosmological dynamics of scalar field with a monomial potential $\phi^{n}$ with a general background equation of state is revisited. It is known that if $n$ is smaller than a critical value, the scalar field exhibits a coherent oscillation…
The linearized problem of plasma oscillations in layer (particularly, in thin films) in external longitudinal alternating electric field is solved analytically. Specular - accommodative boundary conditions of electron reflection from the…
An inhomogeneous Kaluza-Klein compactification of a higher dimensional spacetime may give rise to an effective 4d spacetime with distinct domains having different sizes of the extra dimensions. The domains are separated by domain walls…
In this paper, we consider the plasmon resonance in multi-layer structures. The conductivity problem associated with uniformly distributed background field is considered. We show that the plasmon mode is equivalent to the eigenvalue problem…
By methods of numerical simulation the interaction of 180-degree domain walls with oscillating solitons in (2+1)-dimensional O(3) nonlinear sigma model is investigated. A model of the collisions in which there is observed a reflection of…
We calculate the vacuum fluctuations that may affect the evolution of cosmological domain walls. Considering domain walls, which are classically stable and have interaction with a scalar field, we show that explicit symmetry violation in…
We present the applications of methods from nonlinear local harmonic analysis in variational framework to calculations of nonlinear motions in polynomial/rational approximations (up to any order) of arbitrary n-pole fields. Our approach is…
We investigate the presence of static solutions in generalized models described by a real scalar field in four-dimensional space-time. We study models in which the scalar field engenders higher-order derivatives and spontaneous symmetry…
Steady-state solutions of the Poisson-Nernst-Planck model are studied in the asymptotic limit of large, but finite domains. By using asymptotic matching for integrals, we derive an approximate solution for the steady-state equation with…
Diffuse domain methods (DDMs) have garnered significant attention for approximating solutions to partial differential equations on complex geometries. These methods implicitly represent the geometry by replacing the sharp boundary interface…
We study the asymptotic scaling properties of domain wall networks with three different tensions in various cosmological epochs. We discuss the conditions under which a scale-invariant evolution of the network (which is well established for…
The diffuse domain method for partial differential equations on complicated geometries recently received strong attention in particular from practitioners, but many fundamental issues in the analysis are still widely open. In this paper we…
We construct a domain wall solution in $F(R)$ gravity. We reconstruct a static domain wall solution in a scalar field theory. We also reconstruct an explicit $F(R)$ gravity model in which a static domain wall solution can be realized.…
We consider a simply supported plate with constant thickness, defined on an unknown multiply connected domain. We optimize its shape according to some given performance functional. Our method is of fixed domain type, easy to be implemented,…
We discuss a self-consistent solution for a fermion coupled to static scalar field in the form of a kink (domain wall). In particular, we study the case when the fermion occupies an excited non-zero frequency level in the presence of the…
Polynomial chaos methods have been extensively used to analyze systems in uncertainty quantification. Furthermore, several approaches exist to determine a low-dimensional approximation (or sparse approximation) for some quantity of interest…