6,956 research outputs found
Determination of normalized electric eigenfields in microwave cavities with sharp edges
The magnetic field integral equation for axially symmetric cavities with
perfectly conducting piecewise smooth surfaces is discretized according to a
high-order convergent Fourier--Nystr\"om scheme. The resulting solver is used
to accurately determine eigenwavenumbers and normalized electric eigenfields in
the entire computational domain.Comment: 34 pages, 6 figure
Resumming double logarithms in the QCD evolution of color dipoles
The higher-order perturbative corrections, beyond leading logarithmic
accuracy, to the BFKL evolution in QCD at high energy are well known to suffer
from a severe lack-of-convergence problem, due to radiative corrections
enhanced by double collinear logarithms. Via an explicit calculation of Feynman
graphs in light cone (time-ordered) perturbation theory, we show that the
corrections enhanced by double logarithms (either energy-collinear, or double
collinear) are associated with soft gluon emissions which are strictly ordered
in lifetime. These corrections can be resummed to all orders by solving an
evolution equation which is non-local in rapidity. This equation can be
equivalently rewritten in local form, but with modified kernel and initial
conditions, which resum double collinear logs to all orders. We extend this
resummation to the next-to-leading order BFKL and BK equations. The first
numerical studies of the collinearly-improved BK equation demonstrate the
essential role of the resummation in both stabilizing and slowing down the
evolution.Comment: 16 pages, 5 figure
Small-N Collisional Dynamics: Pushing Into the Realm of Not-So-Small-N
In this paper, we study small-N gravitational dynamics involving up to six
objects. We perform a large suite of numerical scattering experiments involving
single, binary, and triple stars. This is done using the FEWBODY numerical
scattering code, which we have upgraded to treat encounters involving triple
stars. We focus on outcomes that result in direct physical collisions between
stars, within the low angular momentum and high absolute orbital energy regime.
The dependence of the collision probability on the number of objects involved
in the interaction, N, is found for fixed total energy and angular momentum.
Our results are consistent with a collision probability that increases
approximately as N^2. Interestingly, this is also what is expected from the
mean free path approximation in the limit of very large N. A more thorough
exploration of parameter space will be required in future studies to fully
explore this potentially intriguing connection. This study is meant as a first
step in an on-going effort to extend our understanding of small-N collisional
dynamics beyond the three- and four-body problems and into the realm of
larger-N.Comment: 11 pages, 6 figures, 2 tables; accepted for publication in MNRAS;
updated to match published versio
Reconciling Semiclassical and Bohmian Mechanics: II. Scattering states for discontinuous potentials
In a previous paper [J. Chem. Phys. 121 4501 (2004)] a unique bipolar
decomposition, Psi = Psi1 + Psi2 was presented for stationary bound states Psi
of the one-dimensional Schroedinger equation, such that the components Psi1 and
Psi2 approach their semiclassical WKB analogs in the large action limit.
Moreover, by applying the Madelung-Bohm ansatz to the components rather than to
Psi itself, the resultant bipolar Bohmian mechanical formulation satisfies the
correspondence principle. As a result, the bipolar quantum trajectories are
classical-like and well-behaved, even when Psi has many nodes, or is wildly
oscillatory. In this paper, the previous decomposition scheme is modified in
order to achieve the same desirable properties for stationary scattering
states. Discontinuous potential systems are considered (hard wall, step, square
barrier/well), for which the bipolar quantum potential is found to be zero
everywhere, except at the discontinuities. This approach leads to an exact
numerical method for computing stationary scattering states of any desired
boundary conditions, and reflection and transmission probabilities. The
continuous potential case will be considered in a future publication.Comment: 18 pages, 8 figure
MARCOS, a numerical tool for the simulation of multiple time-dependent non-linear diffusive shock acceleration
We present a new code aimed at the simulation of diffusive shock acceleration
(DSA), and discuss various test cases which demonstrate its ability to study
DSA in its full time-dependent and non-linear developments. We present the
numerical methods implemented, coupling the hydrodynamical evolution of a
parallel shock (in one space dimension) and the kinetic transport of the
cosmic-rays (CR) distribution function (in one momentum dimension), as first
done by Falle. Following Kang and Jones and collaborators, we show how the
adaptive mesh refinement technique (AMR) greatly helps accommodating the
extremely demanding numerical resolution requirements of realistic (Bohm-like)
CR diffusion coefficients. We also present the paral lelization of the code,
which allows us to run many successive shocks at the cost of a single shock,
and thus to present the first direct numerical simulations of linear and
non-linear multiple DSA, a mechanism of interest in various astrophysical
environments such as superbubbles, galaxy clusters and early cosmological
flows.Comment: accepted for publication in MNRAS by the Royal Astronomical Society
and Blackwell Publishin
Entanglement Perturbation Theory for Antiferromagnetic Heisenberg Spin Chains
A recently developed numerical method, entanglement perturbation theory
(EPT), is used to study the antiferromagnetic Heisenberg spin chains with
z-axis anisotropy and magnetic field B. To demonstrate the accuracy,
we first apply EPT to the isotropic spin-1/2 antiferromagnetic Heisenberg
model, and find that EPT successfully reproduces the exact Bethe Ansatz results
for the ground state energy, the local magnetization, and the spin correlation
functions (Bethe ansatz result is available for the first 7 lattice
separations). In particular, EPT confirms for the first time the asymptotic
behavior of the spin correlation functions predicted by the conformal field
theory, which realizes only for lattice separations larger than 1000. Next,
turning on the z-axis anisotropy and the magnetic field, the 2-spin and 4-spin
correlation functions are calculated, and the results are compared with those
obtained by Bosonization and density matrix renormalization group methods.
Finally, for the spin-1 antiferromagnetic Heisenberg model, the ground state
phase diagram in space is determined with help of the Roomany-Wyld RG
finite-size-scaling. The results are in good agreement with those obtained by
the level-spectroscopy method.Comment: 12 pages, 14 figure
A New Code SORD for Simulation of Polarized Light Scattering in the Earth Atmosphere
We report a new publicly available radiative transfer (RT) code for numerical simulation of polarized light scattering in plane-parallel atmosphere of the Earth. Using 44 benchmark tests, we prove high accuracy of the new RT code, SORD (Successive ORDers of scattering). We describe capabilities of SORD and show run time for each test on two different machines. At present, SORD is supposed to work as part of the Aerosol Robotic NETwork (AERONET) inversion algorithm. For natural integration with the AERONET software, SORD is coded in Fortran 90/95. The code is available by email request from the corresponding (first) author or from ftp://climate1.gsfc.nasa.gov/skorkin/SORD/
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