84 research outputs found
INFFTM: Fast evaluation of 3d Fourier series in MATLAB with an application to quantum vortex reconnections
Although Fourier series approximation is ubiquitous in computational physics
owing to the Fast Fourier Transform (FFT) algorithm, efficient techniques for
the fast evaluation of a three-dimensional truncated Fourier series at a set of
\emph{arbitrary} points are quite rare, especially in MATLAB language. Here we
employ the Nonequispaced Fast Fourier Transform (NFFT, by J. Keiner, S. Kunis,
and D. Potts), a C library designed for this purpose, and provide a Matlab and
GNU Octave interface that makes NFFT easily available to the Numerical Analysis
community. We test the effectiveness of our package in the framework of quantum
vortex reconnections, where pseudospectral Fourier methods are commonly used
and local high resolution is required in the post-processing stage. We show
that the efficient evaluation of a truncated Fourier series at arbitrary points
provides excellent results at a computational cost much smaller than carrying
out a numerical simulation of the problem on a sufficiently fine regular grid
that can reproduce comparable details of the reconnecting vortices
The phase-locked mean impulse response of a turbulent channel flow
We describe the first DNS-based measurement of the complete mean response of
a turbulent channel flow to small external disturbances. Space-time impulsive
perturbations are applied at one channel wall, and the linear response
describes their mean effect on the flow field as a function of spatial and
temporal separations. The turbulent response is shown to differ from the
response a laminar flow with the turbulent mean velocity profile as base flow.Comment: Accepted for publication in Physics of Fluid
Quantum vortex reconnections
We study reconnections of quantum vortices by numerically solving the
governing Gross-Pitaevskii equation. We find that the minimum distance between
vortices scales differently with time before and after the vortex reconnection.
We also compute vortex reconnections using the Biot-Savart law for vortex
filaments of infinitesimal thickness, and find that, in this model,
reconnection are time-symmetric. We argue that the likely cause of the
difference between the Gross-Pitaevskii model and the Biot-Savart model is the
intense rarefaction wave which is radiated away from a Gross-Pitaeveskii
reconnection. Finally we compare our results to experimental observations in
superfluid helium, and discuss the different length scales probed by the two
models and by experiments.Comment: 23 Pages, 12 Figure
Vortex reconnections in atomic condensates at finite temperature
The study of vortex reconnections is an essential ingredient of understanding
superfluid turbulence, a phenomenon recently also reported in trapped atomic
Bose-Einstein condensates. In this work we show that, despite the established
dependence of vortex motion on temperature in such systems, vortex
reconnections are actually temperature independent on the typical length/time
scales of atomic condensates. Our work is based on a dissipative
Gross-Pitaevskii equation for the condensate, coupled to a semiclassical
Boltzmann equation for the thermal cloud (the Zaremba-Nikuni-Griffin
formalism). Comparison to vortex reconnections in homogeneous condensates
further show reconnections to be insensitive to the inhomogeneity in the
background density.Comment: 6 pages, 4 figure
The Inverse Power Method for the p(x)-Laplacian Problem
We present an inverse power method for the computation of the first homogeneous eigenpair of the p(x)-Laplacian problem. The operators are discretized by the finite element method. The inner minimization problems are solved by a globally convergent inexact Newton method. Numerical comparisons are made, in one- and two-dimensional domains, with other results present in literature for the constant case p(x)=p and with other minimization techniques (namely, the nonlinear conjugate gradient) for the p(x) variable case
Reliability of the time splitting Fourier method for singular solutions in quantum fluids
We study the numerical accuracy of the well-known time splitting Fourier spectral method for the approximation of singular solutions of the Gross\u2013Pitaevskii equation. In particular, we explore its capability of preserving a steady-state vortex solution, whose density profile is approximated by an accurate diagonal Pad\ue9 expansion of degree [8,8], here explicitly derived for the first time. We show by several numerical experiments that the Fourier spectral method is only slightly more accurate than a time splitting finite difference scheme, while being reliable and efficient. Moreover, we notice that, at a post-processing stage, it allows an accurate evaluation of the solution outside grid points, thus becoming particularly appealing for applications where high resolution is needed, such as in the study of quantum vortex interactions
Quasi-Newton minimization for the p(x)-Laplacian problem
We propose a quasi-Newton minimization approach for the solution of the p(x)-Laplacian elliptic problem.This method outperforms those existing for the p(x)-variable case, which are based on general purpose minimizers such as BFGS. Moreover, when compared to ad hoc techniques available in literature for the p-constant case, and usually referred to as "mesh independent", the present method turns out to be generally superior thanks to better descent directions given by the quadratic model
Spectral methods for dissipative nonlinear Schr\uf6dinger equations
In this technical report we describe an application of spectral methods to numerically solve some nonlinear Schr\uf6dinger equations with dissipative terms and carefully study the problem of vortex formation
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