Related papers: Dynamics of a planar domain wall with oscillating …
We study lower bounds for the norm of the product of polynomials and their applications to the so called \emph{plank problem.} We are particularly interested in polynomials on finite dimensional Banach spaces, in which case our results…
Multiple solutions are common in various non-convex problems arising from industrial and scientific computing. Nonetheless, understanding the nontrivial solutions' qualitative properties seems limited, partially due to the lack of efficient…
We investigate several models described by real scalar fields, searching for topological defects, and investigating their linear stability. We also find bosonic zero modes and examine the thermal corrections at the one-loop level. The…
We conjecture that for a plasma in a spatial domain with a boundary, the specular reflection effect of the boundary can be approximated by a large magnetic confinement field in the near-boundary region. In this paper, we verify this…
We investigate collision of a point particle and an infinitely thin planar domain wall interacting gravitationally within the linearized gravity in Minkowski space-time of arbitrary dimension. In this setting we are able to describe…
We consider domain walls embedded in curved backgrounds as an approximation for braneworld scenarios. We give a large class of new exact solutions, exhausting the possibilities for describing one and two walls for the cases where the…
The energy production through thermo-nuclear fusion requires the confinement of the plasma into a bounded domain. In most of the cases, such configurations are obtained by using strong magnetic fields. Several models exist for describing…
Common approach to radial distortion is by the means of polynomial approximation, which introduces distortion-specific parameters into the camera model and requires estimation of these distortion parameters. The task of estimating radial…
We construct a piecewise linear approximation for the dynamical $\Phi_3^4$ model on $\mathbb{T}^3$ by the theory of regularity structures in [Hai14]. For the dynamical $\Phi^4_3$ model it is proved in [Hai14] that a renormalisation has to…
A method is presented for tracing the locus of a specific peak in the frequency response under variation of a parameter. It is applicable to periodic, steady-state vibrations of harmonically forced nonlinear mechanical systems. It operates…
In this paper we present applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. According to variational approach in the general case we have the solution as a…
The dynamics of a domain wall in magnetostrictive materials is investigated. The domain wall is modeled by a d-dimensional interface moving in a d+1-dimensional environment. Long-range demagnetization effects and quenched disorder are…
We explore the connection between fractional order partial differential equations in two or more spatial dimensions with boundary integral operators to develop techniques that enable one to efficiently tackle the integral fractional…
We explore the stability of domain wall and bubble solutions in theories with compact extra dimensions. The energy density stored inside of the wall can destabilize the volume modulus of a compactification, leading to solutions containing…
We enhance the approximation capabilities of algebraic polynomials by composing them with homeomorphisms. This composition yields families of functions that remain dense in the space of continuous functions, while enabling more accurate…
The problem of the harmonic oscillator with a centrally located delta function potential can be exactly solved in one dimension where the eigenfunctions are expressed as superpositions of the Hermite polynomials or as confluent…
We perform real-space imaging of propagating magnetic domains in the fractional quantum Hall system using spin-sensitive photoluminescence microscopy. The propagation is continuous and proceeds in the direction of the conventional current,…
We analyze the propagation of two-dimensional dispersive and relativistic wavepackets localized in the vicinity of the zero level set $\Gamma$ of a domain wall. The main applications we consider are a topologically non-trivial Dirac model…
Surfaces and structures capable of multiple stable configurations have attracted growing interest for on-demand shape morphing. In this work, we consider an elastic compliant plate coupled to a two-dimensional foundation comprising an array…
We discuss the construction of oscillator-like systems associated with orthogonal polynomials on the example of the Fibonacci oscillator. In addition, we consider the dimension of the corresponding lie algebras.