Related papers: A numerical test of differential equations for one…
We apply the bootstrap technique to find the moments of certain multi-trace and multi-matrix random matrix models suggested by noncommutative geometry. Using bootstrapping we are able to find the relationships between the coupling constant…
In this talk, we discuss our recent computation of the two-loop sunrise integral with arbitrary non-zero particle masses. In two space-time dimensions, we arrive at a result in terms of elliptic dilogarithms. Near four space-time…
We present the two-loop sunrise integral with arbitrary non-zero masses in two space-time dimensions in terms of elliptic dilogarithms. We find that the structure of the result is as simple and elegant as in the equal mass case, only the…
The moments of Bessel functions and Bessel-trigonometric functions play a basic role in many practical problems and numerical analysis. This paper presents a complete analysis for these moments based on the recursive relations of Bessel…
The main steps of the process of obtaining the result [1] in terms of elliptic polylogarithms for a two-loop sunrise integral with two different internal masses with pseudothreshold kinematics for all orders of the dimensional regulator are…
By use of the threshold expansion we develop an algorithm for analytical evaluation, within dimensional regularization, of arbitrary terms in the expansion of the (two-loop) sunset diagram with general masses m_1, m_2 and m_3 near its…
The calculation of exclusive observables beyond the one-loop level requires elaborate techniques for the computation of multi-leg two-loop integrals. We discuss how the large number of different integrals appearing in actual two-loop…
A set of algorithms is presented for efficient numerical calculation of the time evolution of classical dynamical systems. Starting with a first approximation for solving the differential equations that has a "reversible" character, we show…
An unsteady problem is considered for a space-fractional equation in a bounded domain. A first-order evolutionary equation involves the square root of an elliptic operator of second order. Finite element approximation in space is employed.…
One problem which plagues the numerical evaluation of one-loop Feynman diagrams using recursive integration by part relations is a numerical instability near exceptional momentum configurations. In this contribution we will discuss a…
An explicit investigation about the equal-mass two-loop sunrise Feynman graph is performed. Such perturbative amplitude is related with many important physical process treated in the standard model context. The background of this…
The program package XLOOPS calculates massive one- and two-loop Feynman diagrams. It consists of five parts: i) a graphical user interface ii) routines for generating diagrams from particle input iii) procedures for calculating one-loop…
We present an example of the practical implementation of a protocol for experimental bifurcation detection based on on-line identification and feedback control ideas. The idea is to couple the experiment with an on-line computer-assisted…
We discuss a progress in calculation of Feynman integrals which has been done with help of the differential equation method and demonstrate the results for a class of two-point two-loop diagrams.
Numerical methods for stochastic partial differential equations typically estimate moments of the solution from sampled paths. Instead, we shall directly target the deterministic equations satisfied by the first and second moments, as well…
We discuss a progress in calculation of Feynman integrals which has been done with help of the Differential Equation Method and demonstrate the results for a class of two-point two-loop diagrams.
We show that one can employ well-established numerical continuation methods to efficiently calculate the phase diagram for thermodynamic systems. In particular, this involves the determination of lines of phase coexistence related to first…
In this study, we introduce a refined method for ascertaining error estimations in numerical simulations of dynamical systems via an innovative application of composition techniques. Our approach involves a dual application of a basic…
A comprehensive study is performed of general massive, scalar, two-loop Feynman diagrams with three external legs. Algorithms for their numerical evaluation are introduced and discussed, numerical results are shown for all different…
Accurately evaluating configurational integrals for dense solids remains a central and difficult challenge in the statistical mechanics of condensed systems. Here, we present a novel tensor network approach that reformulates the…