Related papers: Distributions and Integration in superspace
The immersed boundary method (IBM) of Peskin (J. Comput. Phys., 1977), and derived forms such as the projection method of Taira and Colonius (J. Comput. Phys., 2007), have been useful for simulating flow physics in problems with moving…
Diffuse interface models are widely used to describe evolution of multi-phase systems of different nature. Dispersed "inclusions", described by the phase field distribution, are usually three dimensional objects. When describing elastic…
Several aspects of the internal structure of pseudoscalar mesons, accessible through generalized parton distributions in their zero-skewness limit, are examined. These include electromagnetic and gravitational form factors related to charge…
An approach to infinite dimensional integration which unifies the case of oscillatory integrals and the case of probabilistic type integrals is presented. It provides a truly infinite dimensional construction of integrals as linear…
The scattering of scalar waves by a set of scatterers is considered. It is proven that the scattered field can be represented as an integral supported by any smooth surface enclosing the scatterers. This is a generalization of the series…
The phase-space description of bosonic quantum systems has numerous applications in such fields as quantum optics, trapped ultracold atoms, and transport phenomena. Extension of this description to the case of fermionic systems leads to…
In a previous paper we have introduced a class of multiplications of distributions in one dimension. Here we furnish different generalizations of the original definition and we discuss some applications of these procedures to the…
Let $f, g^1, \dots, g^d : \mathbb{R}^d \longrightarrow \mathbb{R}$ be H\"older continuous functions. If the H\"older exponents of these functions are less than $1$ but sufficiently large, we use the integral introduced by Z\"ust to…
We define a superspace over a ring $R$ as a functor on a subcategory of the category of supercommutative $R$-algebras. As an application the notion of a $p$-adic superspace is introduced and used to give a transparent construction of the…
We study existence, uniqueness, and distributional aspects of generalized solutions to the Cauchy problem for first-order symmetric (or Hermitian) hyperbolic systems of partial differential equations with Colombeau generalized functions as…
Stable distributions are an important class of infinitely-divisible probability distributions, of which two special cases are the Cauchy distribution and the normal distribution. Aside from a few special cases, the density function for…
We present a general mechanistic model of mass diffusion for a composite sphere placed in a large ambient medium. The multi-layer problem is described by a system of diffusion equations coupled via interlayer boundary conditions such as…
Invariant integrals of functions and forms over $q$ - deformed Euclidean space and spheres in $N$ dimensions are defined and shown to be positive definite, compatible with the star - structure and to satisfy a cyclic property involving the…
This work considers the problem of super-resolution. The goal is to resolve a Dirac distribution from knowledge of its discrete, low-pass, Fourier measurements. Classically, such problems have been dealt with parameter estimation methods.…
Aims To propose and analyze a general, dynamic, process-oriented theory of the area of distribution. Methods The area of distribution is modelled by combining (by multiplication) three matrices: one matrix represents movements, another…
We present a high-order method that provides numerical integration on volumes, surfaces, and lines defined implicitly by two smooth intersecting level sets. To approximate the integrals, the method maps quadrature rules defined on…
The definition and the properties of a Gaussian point distribution, in contrast to the well-known properties of a Gaussian random field are discussed. Constraints for the number density and the two-point correlation function arise. A simple…
We are interested in comparing probability distributions defined on Riemannian manifold. The traditional approach to study a distribution relies on locating its mean point and finding the dispersion about that point. On a general manifold…
Reaction--diffusion mechanism are a robust paradigm that can be used to represent many biological and physical phenomena over multiple spatial scales. Applications include intracellular dynamics, the migration of cells and the patterns…
The recently investigated Hilbert-Krein and other positivity structures of the superspace are considered in the framework of superdistributions. These tools are applied to problems raised by the rigorous supersymmetric quantum field theory.