7,021 research outputs found
Package-X: A Mathematica package for the analytic calculation of one-loop integrals
Package-X, a Mathematica package for the analytic computation of one-loop
integrals dimensionally regulated near 4 spacetime dimensions is described.
Package-X computes arbitrarily high rank tensor integrals with up to three
propagators, and gives compact expressions of UV divergent, IR divergent, and
finite parts for any kinematic configuration involving real-valued external
invariants and internal masses. Output expressions can be readily evaluated
numerically and manipulated symbolically with built-in Mathematica functions.
Emphasis is on evaluation speed, on readability of results, and especially on
user-friendliness. Also included is a routine to compute traces of products of
Dirac matrices, and a collection of projectors to facilitate the computation of
fermion form factors at one-loop. The package is intended to be used both as a
research tool and as an educational tool.Comment: Package files are available at http://packagex.hepforge.or
Computing Periods of Hypersurfaces
We give an algorithm to compute the periods of smooth projective
hypersurfaces of any dimension. This is an improvement over existing algorithms
which could only compute the periods of plane curves. Our algorithm reduces the
evaluation of period integrals to an initial value problem for ordinary
differential equations of Picard-Fuchs type. In this way, the periods can be
computed to extreme-precision in order to study their arithmetic properties.
The initial conditions are obtained by an exact determination of the cohomology
pairing on Fermat hypersurfaces with respect to a natural basis.Comment: 33 pages; Final version. Fixed typos, minor expository changes.
Changed code repository lin
Development of an integrated BEM approach for hot fluid structure interaction
The progress made toward the development of a boundary element formulation for the study of hot fluid-structure interaction in Earth-to-Orbit engine hot section components is reported. The convective viscous integral formulation was derived and implemented in the general purpose computer program GP-BEST. The new convective kernel functions, in turn, necessitated the development of refined integration techniques. As a result, however, since the physics of the problem is embedded in these kernels, boundary element solutions can now be obtained at very high Reynolds number. Flow around obstacles can be solved approximately with an efficient linearized boundary-only analysis or, more exactly, by including all of the nonlinearities present in the neighborhood of the obstacle. The other major accomplishment was the development of a comprehensive fluid-structure interaction capability within GP-BEST. This new facility is implemented in a completely general manner, so that quite arbitrary geometry, material properties and boundary conditions may be specified. Thus, a single analysis code (GP-BEST) can be used to run structures-only problems, fluids-only problems, or the combined fluid-structure problem. In all three cases, steady or transient conditions can be selected, with or without thermal effects. Nonlinear analyses can be solved via direct iteration or by employing a modified Newton-Raphson approach
A Simple and Efficient Regularization Method for 3D BEM: Application to Frequency-Domain Elastodynamics
An efficient and easy-to-implement method is proposed to regularize integral
equations in the 3D boundary element method (BEM). The method takes advantage
of an assumed three-noded triangle discretization of the boundary surfaces. The
method is based on the derivation of analytical expressions of singular
integrals. To demonstrate the accuracy of the method, three elastodynamic
problems are numerically worked out in the frequency domain: a cavity under
harmonic pressure, diffraction of a plane wave by a spherical cavity, and
amplification of seismic waves in a semispherical alluvial basin (the second
one is also investigated in the time domain). The numerical results are
compared to semi-analytical solutions; a close agreement is found for all
problems, showing the accuracy of the proposed method
Non-abelian -theory: Berends-Giele recursion for the -expansion of disk integrals
We present a recursive method to calculate the -expansion of disk
integrals arising in tree-level scattering of open strings which resembles the
approach of Berends and Giele to gluon amplitudes. Following an earlier
interpretation of disk integrals as doubly partial amplitudes of an effective
theory of scalars dubbed as -theory, we pinpoint the equation of motion of
-theory from the Berends-Giele recursion for its tree amplitudes. A computer
implementation of this method including explicit results for the recursion up
to order is made available on the website
http://repo.or.cz/BGap.gitComment: 58 pages, harvmac TeX, v2: cosmetic changes, published versio
- …