32,635 research outputs found
Numerical methods for computing Casimir interactions
We review several different approaches for computing Casimir forces and
related fluctuation-induced interactions between bodies of arbitrary shapes and
materials. The relationships between this problem and well known computational
techniques from classical electromagnetism are emphasized. We also review the
basic principles of standard computational methods, categorizing them according
to three criteria---choice of problem, basis, and solution technique---that can
be used to classify proposals for the Casimir problem as well. In this way,
mature classical methods can be exploited to model Casimir physics, with a few
important modifications.Comment: 46 pages, 142 references, 5 figures. To appear in upcoming Lecture
Notes in Physics book on Casimir Physic
Two-Loop integrals for CP-even heavy quarkonium production and decays: Elliptic Sectors
By employing the differential equations, we compute analytically the elliptic
sectors of two-loop master integrals appearing in the NNLO QCD corrections to
CP-even heavy quarkonium exclusive production and decays, which turns out to be
the last and toughest part in the relevant calculation. The integrals are found
can be expressed as Goncharov polylogarithms and iterative integrals over
elliptic functions. The master integrals may be applied to some other NNLO QCD
calculations about heavy quarkonium exclusive production, like
, ,~and~, heavy quarkonium exclusive
decays, and also the CP-even heavy quarkonium inclusive production and decays.Comment: 23 pages, 3 figures, more discussions and references adde
Models for the Brane-Bulk Interaction: Toward Understanding Braneworld Cosmological Perturbation
Using some simple toy models, we explore the nature of the brane-bulk
interaction for cosmological models with a large extra dimension. We are in
particular interested in understanding the role of the bulk gravitons, which
from the point of view of an observer on the brane will appear to generate
dissipation and nonlocality, effects which cannot be incorporated into an
effective (3+1)-dimensional Lagrangian field theoretic description. We
explicitly work out the dynamics of several discrete systems consisting of a
finite number of degrees of freedom on the boundary coupled to a
(1+1)-dimensional field theory subject to a variety of wave equations. Systems
both with and without time translation invariance are considered and moving
boundaries are discussed as well. The models considered contain all the
qualitative feature of quantized linearized cosmological perturbations for a
Randall-Sundrum universe having an arbitrary expansion history, with the sole
exception of gravitational gauge invariance, which will be treated in a later
paper.Comment: 47 pages, RevTeX (or Latex, etc) with 5 eps figure
Invisibility and Inverse Problems
This survey of recent developments in cloaking and transformation optics is
an expanded version of the lecture by Gunther Uhlmann at the 2008 Annual
Meeting of the American Mathematical Society.Comment: 68 pages, 12 figures. To appear in the Bulletin of the AM
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