Related papers: Improved Conformal Mapping of the Borel Plane
Recently, Weniger (delta sequence) method has been proposed by the authors of Ref. [1] (Jentschura et al.) for resummation of truncated perturbation series in quantum field theories. Those authors presented numerical evidence suggesting…
The improvement of resummation algorithms for divergent perturbative expansions in quantum field theory by asymptotic information about perturbative coefficients is investigated. Various asymptotically optimized resummation prescriptions…
Our goal is to provide a novel method of representing 2D shapes, where each shape will be assigned a unique fingerprint - a computable approximation to a conformal map of the given shape to a canonical shape in 2D or 3D space (see page 22…
The aim of this study is to analyze the properties of harmonic fields in the vicinity of rough boundaries where either a constant potential or a zero flux is imposed, while a constant field is prescribed at an infinite distance from this…
Conformal mapping, a classical topic in complex analysis and differential geometry, has become a subject of great interest in the area of surface parameterization in recent decades with various applications in science and engineering.…
The knowledge of capacitance in semiconductor micro-strip detectors is important for a correct design, simulation and understanding of the detectors. Analytical approaches can efficiently complement numerical methods providing quick results…
Generalized Polynomial Chaos (gPC) expansions are well established for forward uncertainty propagation in many application areas. Although the associated computational effort may be reduced in comparison to Monte Carlo techniques, for…
Summation methods play a very important role in quantum field theory because all perturbation series are divergent and the expansion parameter is not always small. A number of methods have been tried in this context, most notably Pade…
In these Notes, a comprehensive description of the universal fractal geometry of conformally-invariant scaling curves or interfaces, in the plane or half-plane, is given. The present approach focuses on deriving critical exponents…
F. Stenger proposed efficient approximation formulas for derivatives over infinite intervals. These formulas were derived by combining the Sinc approximation with appropriate conformal maps. It has been demonstrated that these formulas can…
Many observables in quantum field theory can be expressed in terms of trans-series, in which one adds to the perturbative series a typically infinite sum of exponentially small corrections, due to instantons or to renormalons. Even after…
We use a conformal mapping technique to study the Laplacian transfer across a rough interface. Natural Dirichlet or Von Neumann boundary condition are simply read by the conformal map. Mixed boundary condition, albeit being more complex can…
Recently-developed variational perturbation expansions converge exponentially fast for positive coupling constants. They do not, however, possess the correct left-hand cut in the complex coupling constant plane, implying a wrong large-order…
To study asymptotic structures, we regularize Einstein's field equations by means of conformal transformations. The conformal factor is chosen so that it carries a dimensional scale that captures crucial asymptotic features. By choosing a…
The algorithm for finding the optimal consistent approximation of an inconsistent pairwise comparisons matrix is based on a logarithmic transformation of a pairwise comparisons matrix into a vector space with the Euclidean metric.…
In this paper, we present an algorithm for reparametrizing algebraic plane curves from a numerical point of view. That is, we deal with mathematical objects that are assumed to be given approximately. More precisely, given a tolerance…
The article provides a pedagogical review aimed at graduate students in materials science, physics, and applied mathematics, focusing on recent developments in the subject. Following a brief summary of concepts from complex analysis, the…
In this note we report an improved determination of the scaling dimensions and OPE coefficients of the minimal supersymmetric extension of the 3d Ising model using the conformal bootstrap. We also show how this data can be used as input to…
Perturbative QCD corrections to hadronic $\tau$ decays and $e^+e^-$ annihilation into hadrons below charm are obtained from the Adler function, which at present is known in the chiral limit to five-loop accuracy. Extractions of the strong…
Borel summation techniques are developed to obtain exact invariants from formal adiabatic invariants (given as divergent series in a small parameter) for a class of differential equations, under assumptions of analyticity of the…