634 research outputs found
Resolving velocity space dynamics in continuum gyrokinetics
Many plasmas of interest to the astrophysical and fusion communities are
weakly collisional. In such plasmas, small scales can develop in the
distribution of particle velocities, potentially affecting observable
quantities such as turbulent fluxes. Consequently, it is necessary to monitor
velocity space resolution in gyrokinetic simulations. In this paper, we present
a set of computationally efficient diagnostics for measuring velocity space
resolution in gyrokinetic simulations and apply them to a range of plasma
physics phenomena using the continuum gyrokinetic code GS2. For the cases
considered here, it is found that the use of a collisionality at or below
experimental values allows for the resolution of plasma dynamics with
relatively few velocity space grid points. Additionally, we describe
implementation of an adaptive collision frequency which can be used to improve
velocity space resolution in the collisionless regime, where results are
expected to be independent of collision frequency.Comment: 20 pages, 11 figures, submitted to Phys. Plasma
Scattering Calculations with Wavelets
We show that the use of wavelet bases for solving the momentum-space
scattering integral equation leads to sparse matrices which can simplify the
solution. Wavelet bases are applied to calculate the K-matrix for
nucleon-nucleon scattering with the s-wave Malfliet-Tjon V potential. We
introduce a new method, which uses special properties of the wavelets, for
evaluating the singular part of the integral. Analysis of this test problem
indicates that a significant reduction in computational size can be achieved
for realistic few-body scattering problems.Comment: 26 pages, Latex, 6 eps figure
A fast, high-order numerical method for the simulation of single-excitation states in quantum optics
We consider the numerical solution of a nonlocal partial differential
equation which models the process of collective spontaneous emission in a
two-level atomic system containing a single photon. We reformulate the problem
as an integro-differential equation for the atomic degrees of freedom, and
describe an efficient solver for the case of a Gaussian atomic density. The
problem of history dependence arising from the integral formulation is
addressed using sum-of-exponentials history compression. We demonstrate the
solver on two systems of physical interest: in the first, an initially-excited
atom decays into a photon by spontaneous emission, and in the second, a photon
pulse is used to an excite an atom, which then decays
Rapid Evaluation of Radiation Boundary Kernels for Time-domain Wave Propagation on Blackholes
For scalar, electromagnetic, or gravitational wave propagation on a fixed
Schwarzschild blackhole background, we describe the exact nonlocal radiation
outer boundary conditions (ROBC) appropriate for a spherical outer boundary of
finite radius enclosing the blackhole. Derivation of the ROBC is based on
Laplace and spherical-harmonic transformation of the Regge-Wheeler equation,
the PDE governing the wave propagation, with the resulting radial ODE an
incarnation of the confluent Heun equation. For a given angular index l the
ROBC feature integral convolution between a time-domain radiation boundary
kernel (TDRK) and each of the corresponding 2l+1 spherical-harmonic modes of
the radiating wave. The TDRK is the inverse Laplace transform of a
frequency-domain radiation kernel (FDRK) which is essentially the logarithmic
derivative of the asymptotically outgoing solution to the radial ODE. We
numerically implement the ROBC via a rapid algorithm involving approximation of
the FDRK by a rational function. Such an approximation is tailored to have
relative error \epsilon uniformly along the axis of imaginary Laplace
frequency. Theoretically, \epsilon is also a long-time bound on the relative
convolution error. Via study of one-dimensional radial evolutions, we
demonstrate that the ROBC capture the phenomena of quasinormal ringing and
decay tails. Moreover, carrying out a numerical experiment in which a wave
packet strikes the boundary at an angle, we find that the ROBC yield accurate
results in a three-dimensional setting. Our work is a partial generalization to
Schwarzschild wave propagation and Heun functions of the methods developed for
flatspace wave propagation and Bessel functions by Alpert, Greengard, and
Hagstrom.Comment: AMS article, 105 pages, 45 figures. Version 3 has more minor
corrections as well as extra commentary added in response to reactions by
referees. Commentary added which compares and contrasts this work with work
of Leaver and work of Andersson. For publication, article has been cut in two
and appears as two separate articles in J. Comp. Phys. 199 (2004) 376-422 and
Class. Quantum Grav. 21 (2004) 4147-419
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