Search results for "Methodologie"
showing 10 items of 2141 documents
Products of Bessel functions and associated polynomials
2013
The symbolic method is used to get explicit formulae for the products or powers of Bessel functions and for the relevant integrals.
Estimating the Best Reference Homography for Planar Mosaics From Videos
2015
This paper proposes a novel strategy to find the best reference homography in mosaics from video sequences. The reference homography globally minimizes the distortions induced on each image frame by the mosaic homography itself. This method is designed for planar mosaics on which a bad choice of the first reference image frame can lead to severe distortions after concatenating several successive homographies. This often happens in the case of underwater mosaics with non-flat seabed and no georeferential information available. Given a video sequence of an almost planar surface, sub-mosaics with low distortions of temporally close image frames are computed and successively merged according to…
Speeding up a few orders of magnitude the Jacobi method: high order Chebyshev-Jacobi over GPUs
2017
In this technical note we show how to reach a remarkable speed up when solving elliptic partial differential equations with finite differences thanks to the joint use of the Chebyshev-Jacobi method with high order discretizations and its parallel implementation over GPUs.
Horizons: Nuclear Astrophysics in the 2020s and Beyond
2022
Nuclear astrophysics is a field at the intersection of nuclear physics and astrophysics, which seeks to understand the nuclear engines of astronomical objects and the origin of the chemical elements. This white paper summarizes progress and status of the field, the new open questions that have emerged, and the tremendous scientific opportunities that have opened up with major advances in capabilities across an ever growing number of disciplines and subfields that need to be integrated.We take a holistic view of the field discussing the unique challenges and opportunities in nuclear astrophysics in regards to science, diversity, education, and the interdisciplinarity and breadth of the field…
Simplifying differential equations for multi-scale Feynman integrals beyond multiple polylogarithms
2017
In this paper we exploit factorisation properties of Picard-Fuchs operators to decouple differential equations for multi-scale Feynman integrals. The algorithm reduces the differential equations to blocks of the size of the order of the irreducible factors of the Picard-Fuchs operator. As a side product, our method can be used to easily convert the differential equations for Feynman integrals which evaluate to multiple polylogarithms to $\varepsilon$-form.
Simple differential equations for Feynman integrals associated to elliptic curves
2019
The $\varepsilon$-form of a system of differential equations for Feynman integrals has led to tremendeous progress in our abilities to compute Feynman integrals, as long as they fall into the class of multiple polylogarithms. It is therefore of current interest, if these methods extend beyond the case of multiple polylogarithms. In this talk I discuss Feynman integrals, which are associated to elliptic curves and their differential equations. I show for non-trivial examples how the system of differential equations can be brought into an $\varepsilon$-form. Single-scale and multi-scale cases are discussed.
Differential equations for Feynman integrals beyond multiple polylogarithms
2017
Differential equations are a powerful tool to tackle Feynman integrals. In this talk we discuss recent progress, where the method of differential equations has been applied to Feynman integrals which are not expressible in terms of multiple polylogarithms.
JaxoDraw: A graphical user interface for drawing Feynman diagrams
2003
JaxoDraw is a Feynman graph plotting tool written in Java. It has a complete graphical user interface that allows all actions to be carried out via mouse click-and-drag operations in a WYSIWYG fashion. Graphs may be exported to postscript/EPS format and can be saved in XML files to be used in later sessions. One of the main features of JaxoDraw is the possibility to produce LaTeX code that may be used to generate graphics output, thus combining the powers of TeX/LaTeX with those of a modern day drawing program. With JaxoDraw it becomes possible to draw even complicated Feynman diagrams with just a few mouse clicks, without the knowledge of any programming language.
On the computation of intersection numbers for twisted cocycles
2020
Intersection numbers of twisted cocycles arise in mathematics in the field of algebraic geometry. Quite recently, they appeared in physics: Intersection numbers of twisted cocycles define a scalar product on the vector space of Feynman integrals. With this application, the practical and efficient computation of intersection numbers of twisted cocycles becomes a topic of interest. An existing algorithm for the computation of intersection numbers of twisted cocycles requires in intermediate steps the introduction of algebraic extensions (for example square roots), although the final result may be expressed without algebraic extensions. In this article I present an improvement of this algorith…
A walk on sunset boulevard
2016
A walk on sunset boulevard can teach us about transcendental functions associated to Feynman diagrams. On this guided tour we will see multiple polylogarithms, differential equations and elliptic curves. A highlight of the tour will be the generalisation of the polylogarithms to the elliptic setting and the all-order solution for the sunset integral in the equal mass case.