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

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

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

Experimental investigations of the liquid-film instabilities forming on a wire under the action of a die

a b s t r a c t The liquid film remaining on a wire withdrawn from a liquid bath and forced through an annular die is experimentally investigated on a dedicated facility. An optical laser-based technique recently introduced to study liquid-film instabilities on small-radius cylinders allows the measurement of the mean final thickness and wave characteristics. Experimental results are compared to analytical predictions obtained with simple models specifically derived for this configuration and based on liquid-film properties (density, viscosity and surface tension) and operating parameters (wire speed and die dimensions). The experimental measurement of surface-perturbation features (wave amplitude, wavelength and amplification factor) as a function of the operating parameters reveals the presence of a single wavelength for low values of the withdrawing velocity and a progressive wave disappearance for high speeds, in accordance with theoretical predictions