Related papers: Numerical Domain Wall Type Solutions in phi**4 The…
This work is devoted to infinite-energy solutions of semi-linear wave equations in unbounded smooth domains of $\mathbb{R}^3$ with fractional damping of the form $(-\Delta_x+1)^\frac{1}{2}\partial_t u$. The work extends previously known…
We discuss several problems concerning domain walls in the spin $S$ Ising model at zero temperature in a magnetic field, $H/(2S)$, applied in the $x$ direction. Some results are also given for the planar ($y$-$z$) model in a transverse…
Magnetic domain walls in antiferromagnets have been proposed as key components for faster conventional information processing, thanks to their enhanced stability and ultrafast propagation. However, how non-conventional computing methods…
We give a summary of a talk delivered at the 2012 International Congress on Mathematical Physics. We review d=4, N=2 quantum field theory and some of the exact statements which can be made about it. We discuss the wall-crossing phenomenon.…
Numerical simulations are performed of the gravitational collapse of a scalar field with a \lambda \phi^4 potential. Comparisons are made with the thin shell approximation.
We propose a new class of fundamental solutions for the numerical analysis of boundary value problems for the Maxwell equations. We prove completeness of systems of such fundamental solutions in appropriate Sobolev spaces on a smooth…
Relativistic domain walls are studied in the framework of a polynomial approximation to the field interpolating between different vacua and forming the domain wall. In this approach we can calculate evolution of a core and of a width of the…
We show that all kinds of biasing of cosmological phase transitions produce qualitatively new type of domain wall networks. The biased networks consist of compact, finite size, bag-like wall structures and exhibit a generic instability. The…
We study the properties of domain walls and domain patterns in ultrathin epitaxial magnetic films with two orthogonal in-plane easy axes, which we call fourfold materials. In these materials, the magnetization vector is constrained to lie…
In the Ginzburg-Landau equation, there are domain walls connecting two metastable states. The dynamics of domain walls has been intensively studied, but there remain still unsolved but crucial problems even for a single domain. We study the…
Existence and uniqueness of the solution are proved for the `master equation' derived from the BPS equation for the vector multiplet scalar in the U(1) gauge theory with Nf charged matter hypermultiplets with eight supercharges. This proof…
In the present paper we establish the solvability of the Regularity boundary value problem in domains with (flat and Lipschitz) lower dimensional boundaries for operators whose coefficients exhibit small oscillations analogous to the…
A piecewise continuous biharmonic problem in domains with corner points and a corresponding Schwarz type boundary value problem for monogenic functions in a commutative biharmonic algebra are considered. A method for reducing the problems…
Analytical multi-domain solutions to the dynamical (Landau-Lifshitz-Gilbert) equation of a one-dimensional ferromagnet including an external magnetic field and spin-polarized electric current are found using the Hirota bilinearization…
In this paper we analyze the Hilbert boundary-value problem of the theory of analytic functions for an $(N+1)$-connected circular domain. An exact series-form solution has already been derived for the case of continuous coefficients.…
We describe the results of the largest and most accurate three-dimensional field theory simulations of domain wall networks with junctions. We consider a previously introduced class of models which, in the limit of large number $N$ of…
We consider N=2 supersymmetric quantum electrodynamics (SQED) with 2 flavors, the Fayet--Iliopoulos parameter, and a mass term $\beta$ which breaks the extended supersymmetry down to N=1. The bulk theory has two vacua; at $\beta=0$ the…
Numerical evidence for a cosmological version of the Bartnik-McKinnon family of particle-like solutions of the Einstein-Yang-Mills system is presented. Our solutions are also static, but space has the topology of a three-sphere. By…
We study BPS saturated domain walls in the supersymmetric SU(2) gauge theory. For a theory with a very light adjoint scalar (mass <~ Lambda/400) we use the perturbed N=2 Seiberg-Witten theory to calculate the actual field configuration of…
We prove conditions for existence of analytical solutions for boundary value problems with the Hilfer fractional derivative, generalizing the commonly used Riemann-Liouville and Caputo operators. The boundary values, referred to in this…