39,994 research outputs found
Volume integral equations for electromagnetic scattering in two dimensions
We study the strongly singular volume integral equation that describes the
scattering of time-harmonic electromagnetic waves by a penetrable obstacle. We
consider the case of a cylindrical obstacle and fields invariant along the axis
of the cylinder, which allows the reduction to two-dimensional problems. With
this simplification, we can refine the analysis of the essential spectrum of
the volume integral operator started in a previous paper (M. Costabel, E.
Darrigrand, H. Sakly: The essential spectrum of the volume integral operator in
electromagnetic scattering by a homogeneous body, Comptes Rendus Mathematique,
350 (2012), pp. 193-197) and obtain results for non-smooth domains that were
previously available only for smooth domains. It turns out that in the TE case,
the magnetic contrast has no influence on the Fredholm properties of the
problem. As a byproduct of the choice that exists between a vectorial and a
scalar volume integral equation, we discover new results about the symmetry of
the spectrum of the double layer boundary integral operator on Lipschitz
domains.Comment: 21 page
Fast, adaptive, high order accurate discretization of the Lippmann-Schwinger equation in two dimension
We present a fast direct solver for two dimensional scattering problems,
where an incident wave impinges on a penetrable medium with compact support. We
represent the scattered field using a volume potential whose kernel is the
outgoing Green's function for the exterior domain. Inserting this
representation into the governing partial differential equation, we obtain an
integral equation of the Lippmann-Schwinger type. The principal contribution
here is the development of an automatically adaptive, high-order accurate
discretization based on a quad tree data structure which provides rapid access
to arbitrary elements of the discretized system matrix. This permits the
straightforward application of state-of-the-art algorithms for constructing
compressed versions of the solution operator. These solvers typically require
work, where denotes the number of degrees of freedom. We
demonstrate the performance of the method for a variety of problems in both the
low and high frequency regimes.Comment: 18 page
Vector Bremsstrahlung by Ultrarelativistic Collisions in Higher Dimensions
A classical computation of vector bremsstrahlung in ultrarelativistic
gravitational-force collisions of massive point particles is presented in an
arbitrary number d of extra dimensions. Our method adapts the post-linear
formalism of General Relativity to the multidimensional case. The total emitted
energy, as well as its angular and frequency distribution and characteristic
values, are discussed in detail.
For an electromagnetic mediation propagated in the bulk, the emitted energy
of scattering with impact parameter b has magnitude , with dominant frequency . For the gravitational force the charge emits via vector field,
propagated in the bulk, energy
for , with dominant frequency and energy
for , with most of the
energy coming from a wide frequency region . For the UED model with extra space volume the emitted energy
is . Finally, for the ADD model, including
four dimensions, the electromagnetic field living on 3-brane, loses on emission
the energy , with characteristic
frequency .
The contribution of the low frequency part of the radiation (soft photons) to
the total radiated energy is shown to be negligible for all values of d. The
domain of validity of the classical result is discussed. The result is analyzed
from the viewpoint of the deWitt - Brehme - Hobbs equation (and corresponding
equations in higher dimensions).Comment: 39 pages, 4 figure
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
Vector Correlators in Lattice QCD: methods and applications
We discuss the calculation of the leading hadronic vacuum polarization in
lattice QCD. Exploiting the excellent quality of the compiled experimental data
for the e^+e^- --> hadrons cross-section, we predict the outcome of
large-volume lattice calculations at the physical pion mass, and design
computational strategies for the lattice to have an impact on important
phenomenological quantities such as the leading hadronic contribution to
(g-2)mu and the running of the electromagnetic coupling constant. First, the
R(s) ratio can be calculated directly on the lattice in the threshold region,
and we provide the formulae to do so with twisted boundary conditions. Second,
the current correlator projected onto zero spatial momentum, in a Euclidean
time interval where it can be calculated accurately, provides a potentially
critical test of the experimental R(s) ratio in the region that is most
relevant for (g-2)mu. This observation can also be turned around: the vector
correlator at intermediate distances can be used to determine the lattice
spacing in fm, and we make a concrete proposal in this direction. Finally, we
quantify the finite-size effects on the current correlator coming from
low-energy two-pion states and provide a general parametrization of the vacuum
polarization on the torus.Comment: 16 pages, 9 figure files; corrected a factor 2 in Eq. (7) over the
published versio
Volume Integral Formulation for the Calculation of Material Independent Modes of Dielectric Scatterers
In the frame of volume integral equation methods, we introduce an alternative
representation of the electromagnetic field scattered by a homogeneous object
of arbitrary shape at a given frequency, in terms of a set of modes independent
of its permittivity. This is accomplished by introducing an auxiliary
eigenvalue problem, based on a volume integral operator. With this modal basis
the expansion coefficients of the scattered field are simple rational functions
of the permittivity of the scatterer. We show, by studying the electromagnetic
scattering from a sphere and a cylinder of dimensions comparable to the
incident wavelength, that only a moderate number of modes is needed to
accurately describe the scattered far field. This method can be used to
investigate resonant scattering phenomena, including plasmonic and photonic
resonances, and to design the permittivity of the object to pursue a prescribed
tailoring of the scattered field. Moreover, the presented modal expansion is
computationally advantageous compared to direct solution of the volume integral
equation when the scattered field has to be computed for many different values
of the dielectric permittivity, given the size and shape of the dielectric
body
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