69,196 research outputs found
An iterative semi-implicit scheme with robust damping
An efficient, iterative semi-implicit (SI) numerical method for the time
integration of stiff wave systems is presented. Physics-based assumptions are
used to derive a convergent iterative formulation of the SI scheme which
enables the monitoring and control of the error introduced by the SI operator.
This iteration essentially turns a semi-implicit method into a fully implicit
method. Accuracy, rather than stability, determines the timestep. The scheme is
second-order accurate and shown to be equivalent to a simple preconditioning
method. We show how the diffusion operators can be handled so as to yield the
property of robust damping, i.e., dissipating the solution at all values of the
parameter \mathcal D\dt, where is a diffusion operator and \dt
the timestep. The overall scheme remains second-order accurate even if the
advection and diffusion operators do not commute. In the limit of no physical
dissipation, and for a linear test wave problem, the method is shown to be
symplectic. The method is tested on the problem of Kinetic Alfv\'en wave
mediated magnetic reconnection. A Fourier (pseudo-spectral) representation is
used. A 2-field gyrofluid model is used and an efficacious k-space SI operator
for this problem is demonstrated. CPU speed-up factors over a CFL-limited
explicit algorithm ranging from to several hundreds are obtained,
while accurately capturing the results of an explicit integration. Possible
extension of these results to a real-space (grid) discretization is discussed.Comment: Submitted to the Journal of Computational Physics. Clarifications and
caveats in response to referees, numerical demonstration of convergence rate,
generalized symplectic proo
PICPANTHER: A simple, concise implementation of the relativistic moment implicit Particle-in-Cell method
A three-dimensional, parallelized implementation of the electromagnetic
relativistic moment implicit particle-in-cell method in Cartesian geometry
(Noguchi et. al., 2007) is presented. Particular care was taken to keep the
C++11 codebase simple, concise, and approachable. GMRES is used as a field
solver and during the Newton-Krylov iteration of the particle pusher. Drifting
Maxwellian problem setups are available while more complex simulations can be
implemented easily. Several test runs are described and the code's numerical
and computational performance is examined. Weak scaling on the SuperMUC system
is discussed and found suitable for large-scale production runs.Comment: 29 pages, 8 figure
(2+1)D Exotic Newton-Hooke Symmetry, Duality and Projective Phase
A particle system with a (2+1)D exotic Newton-Hooke symmetry is constructed
by the method of nonlinear realization. It has three essentially different
phases depending on the values of the two central charges. The subcritical and
supercritical phases (describing 2D isotropic ordinary and exotic oscillators)
are separated by the critical phase (one-mode oscillator), and are related by a
duality transformation. In the flat limit, the system transforms into a free
Galilean exotic particle on the noncommutative plane. The wave equations
carrying projective representations of the exotic Newton-Hooke symmetry are
constructed.Comment: 30 pages, 2 figures; typos correcte
Reconstructing WKB from topological recursion
We prove that the topological recursion reconstructs the WKB expansion of a
quantum curve for all spectral curves whose Newton polygons have no interior
point (and that are smooth as affine curves). This includes nearly all
previously known cases in the literature, and many more; in particular, it
includes many quantum curves of order greater than two. We also explore the
connection between the choice of ordering in the quantization of the spectral
curve and the choice of integration divisor to reconstruct the WKB expansion.Comment: 68 pages, 9 figures. v2: published version (improved presentation
Solution of the inverse scattering problem by T-matrix completion. II. Simulations
This is Part II of the paper series on data-compatible T-matrix completion
(DCTMC), which is a method for solving nonlinear inverse problems. Part I of
the series contains theory and here we present simulations for inverse
scattering of scalar waves. The underlying mathematical model is the scalar
wave equation and the object function that is reconstructed is the medium
susceptibility. The simulations are relevant to ultrasound tomographic imaging
and seismic tomography. It is shown that DCTMC is a viable method for solving
strongly nonlinear inverse problems with large data sets. It provides not only
the overall shape of the object but the quantitative contrast, which can
correspond, for instance, to the variable speed of sound in the imaged medium.Comment: This is Part II of a paper series. Part I contains theory and is
available at arXiv:1401.3319 [math-ph]. Accepted in this form to Phys. Rev.
The Foldy-Wouthuysen transformation
The Foldy-Wouthuysen transformation of the Dirac Hamiltonian is generally
taught as simply a mathematical trick that allows one to obtain a two-component
theory in the low-energy limit. It is not often emphasized that the transformed
representation is the only one in which one can take a meaningful *classical
limit*, in terms of particles and antiparticles. We briefly review the history
and physics of this transformation.Comment: Standard LaTeX, 6 page
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