Related papers: Complex functions as lumps of energy
A general approach allowing to find the analytical expressions for equilibrium magnetic structures in small and flat magnetic nano-sized cylinders of arbitrary shape made of soft magnetic material is presented. The resulting magnetization…
Given a charge and current distribution with compact support, the associated potentials and fields are generally not integrable in the classical sense. However, it is convenient to be able to define their Fourier transform in order to…
The aim of this paper is to give the text of a recent introduction to nonlinear generalized functions exposed in my talk in the congress gf2011, which was asked by several participants. Three representative topics were presented: two…
By using Cauchy integral formula in the theory of complex functions, the authors establish some integral representations for the principal branches of several complex functions involving the logarithmic function, find some properties, such…
The article provides an introduction to infinite-dimensional differential calculus over topological fields and surveys some of its applications, notably in the areas of infinite-dimensional Lie groups and dynamical systems.
A subclass of complex-valued close-to-convex harmonic functions that are univalent and sense-preserving in the open unit disc is investigated. The coefficient estimates, growth results, area theorem, boundary behavior, convolution and…
Q-lumps are spinning planar topological solitons with stationary solutions that satisfy first-order Bogomolny equations. Q-lump scattering has previously been studied only in the charge two sector, by approximating time evolution by motion…
Dynamical topological solitons are studied in classical two-dimensional Heisenberg easy-axis ferromagnets. The properties of such solitons are treated both analytically in the continuum limit and numerically by spin dynamics simulations of…
Roughly speaking, functional analysis is the study of vector spaces of arbitrary dimension over the field of real or complex numbers, and the continuous linear mappings between such spaces. Naturally, the notion of continuity requires a…
We develop a Hamiltonian theory for 2D soliton equations. In particular, we identify the spaces of doubly periodic operators on which a full hierarchy of commuting flows can be introduced, and show that these flows are Hamiltonian with…
Topos theory has been suggested first by Isham and Butterfield, and then by Isham and Doering, as an alternative mathematical structure within which to formulate physical theories. In particular, it has been used to reformulate standard…
The phenomenon of quantum number fractionalization is explained. The relevance of non-trivial phonon field topology is emphasized.
We use the homological perturbation lemma to produce explicit formulas computing the class in the twisted de Rham complex represented by an arbitrary polynomial. This is a non-asymptotic version of the method of Feynman diagrams. In…
New CP1-soliton behaviour on a flat torus is reported. Defined by the Weierstrass elliptic function and numerically-evolved from rest, each soliton splits up in two lumps which eventually reunite, divide and get back together again, etc..…
A generalized reciprocal theorem is formulated for the motion and hydrodynamic force moments of an active particle in an arbitrary background flow of a (weakly nonlinear) complex fluid. This formalism includes as special cases a number of…
We establish the plurisubharmonicity of the envelope of the Poisson functional on almost complex manifolds. That is, we generalize the corresponding result for complex manifolds and almost complex manifolds of complex dimension two.
Topological excitations are believed to play an important role in different areas of physics. For example, one case of topical interest is the use of dual models of quantum cromodynamics to understand properties of its vacuum and…
Topological phases of matter are ubiquitous in crystals, but less is known about their existence in amorphous systems, that lack long-range order. In this perspective, we review the recent progress made on theoretically defining amorphous…
Ultrafunctions are a particular class of functions defined on a hyperreal field $\mathbb{R}^{\ast}\supset\mathbb{R}$. They have been introduced and studied in some previous works. In this paper we introduce a particular space of…
In the 6th Int. Symposium on OPSFA there were several communications dealing with concrete applications of orthogonal polynomials to experimental and theoretical physics, chemistry, biology and statistics. Here I make suggestions concerning…