Related papers: Asymptotic Expansions - Methods and Applications
We give an algorithm for obtaining expansions of massive two-loop Feynman graphs in powers of the external momentum around a finite, nonzero value of the momentum. This is based on our general two-loop formalism to reduce massive two-loop…
I propose an approximation scheme for asymptotically free field theories combining both weak coupling and strong coupling series. The weak coupling expansion is used to integrate the high frequency modes and the resulting low energy…
For a singularly perturbed system of reaction--diffusion equations, assuming that the 0th order solutions in regular and singular regions are all stable, we construct matched asymptotic expansions for formal solutions to any desired order…
In this paper, insight is given in the techniques used to compute asymptotic expansions. In a broad fashion the technique is described. Most of the results apply to the paper "An expansion for the maximum likelihood estimator and its…
Considered herein are the family of nonlinear equations with both dispersive and dissipative homogeneous terms appended. Solutions of these equations that start with finite energia decay to zero as time goes to infinity. We present an…
New algorithms for computing of asymptotic expansions for stationary distributions of nonlinearly perturbed semi-Markov processes are presented. The algorithms are based on special techniques of sequential phase space reduction, which can…
We give asymptotic expressions for the number of commuting matrices over finite fields. For this, we use product expansions for the corresponding generating functions.
We discuss the program EXP used to automate the successive application of asymptotic expansions to Feynman diagrams. We focus on the generation of the relevant subgraphs and the determination of the topologies for the remaining integrals.…
A family of asymptotic solutions at infinity for the system of ordinary differential equations is considered. Existence of exact solutions which have these asymptotics is proved.
Asymptotic solutions are derived for inhomogeneous differential equations having a large real or complex parameter and a simple turning point. They involve Scorer functions and three slowly varying analytic coefficient functions. The…
Asymptotic safety is a remarkable example when fruitful ideas borrowed from statistical physics proliferate to high-energy physics. The concept of asymptotic safety is tightly connected to fixed points (FPs) of the renormalization-group…
We introduce a novel compositional description of Feynman diagrams, with well-defined categorical semantics as morphisms in a dagger-compact category. Our chosen setting is suitable for infinite-dimensional diagrammatic reasoning,…
We study the asymptotic behavior of a family of functionals which penalize a short-range interaction of convolution type between a finite perimeter set and its complement. We first compute the pointwise limit and we obtain a lower estimate…
We discuss the cosmology of axion-scalar systems in asymptotic limits of type IIB/F-theory flux compactifications. These results allow us to test a putative extension of the Distance Conjecture in a dynamical setting, which posits that…
The aim of this paper is to give a new description of the geometry appearing in the multi-specialization along a general family of submanifolds of a real analytic manifold (including some important cases as clean intersection or a…
We review and announce recent results on the asymptotic behavior of asymptotically Euclidean relativistic initial data sets and asymptotic foliations thereof. In particular, we discuss the geometrization of asymptotic flatness and of…
This article is focused on the asymptotic expansions, as time tends to infinity, of solutions of a system of ordinary differential equations with non-smooth nonlinear terms. The forcing function decays to zero in a very complicated but…
In this paper, we derive new asymptotic expansions for the solutions of higher order elliptic equations in the presence of small inclusions. As a byproduct, we derive a topological derivative based algorithm for the reconstruction of…
We discuss the status of expansion by regions, i.e. a well-known strategy to obtain an expansion of a given multiloop Feynman integral in a given limit where some kinematic invariants and/or masses have certain scaling measured in powers of…
This paper is concerned with the asymptotic expansions of the amplitude of the solution of the Helmholtz equation. The original expansions were obtained using a pseudo-differential decomposition of the Dirichlet to Neumann operator. This…