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

Meshfree exponential integrators

For the numerical solution of time-dependent partial dierential equations, a class ofmeshfree exponential integrators is proposed. These methods are of particular interest in situationswhere the solution of the dierential equation concentrates on a small part of the computationaldomain which may vary in time. For the space discretization, radial basis functions with compactsupport are suggested. The reason for this choice are stability and robustness of the resultinginterpolation procedure. The time integration is performed with an exponential Rosenbrock method.The required matrix functions are computed by Newton interpolation based on Leja points. Theproposed integrators are fully adaptive in space and time. Numerical examples that illustrate therobustness and the good stability properties of the method are included

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

A minimisation approach for computing the ground state of Gross\u2013Pitaevskii systems

In this paper, we present a minimisation method for computing the ground stateof systems of coupled Gross\u2013Pitaevskii equations. Our approach relies on a spectral decomposition of the solution into Hermite basis functions. Inserting the spectral representation into the energy functional yields a constrained nonlinear minimisation problem for the coefficients. For its numerical solution, we employ a Newton-like method with an approximate line-search strategy. We analyse this method and prove global convergence. Appropriate starting values for the minimisation process are determined by a standard continuation strategy. Numerical examples with two and three-component two-dimensional condensates are included. These experiments demonstrate the reliability of our method and nicely illustrate the effect of phase segregation

Comparison of software for computing the action of the matrix exponential

The implementation of exponential integrators requires the action of the matrix exponential and related functions of a large matrix. There are various methods in the literature for carrying out this task. In this paper we describe a new implementation of a method based on interpolation at Leja points. We numerically compare this method with others from the literature. As we are interested in exponential intergrators we choose the test examples from spatial discretization of time dependent partial differential equations in two and three space dimensions. The test matrices thus have large eigenvalues and can be nonnormal

O deslocamento do sujeito: a saga identitária em Hotel Atlântico de João Gilberto Noll

O objetivo desta pesquisa é analisar a questão identitária presente no romance Hotel Atlântico, do escritor João Gilberto Noll, acompanhando a trajetória errante do narrador-personagem, um indivíduo que transita à deriva, na contramão da sociedade, em busca de novas circunstâncias que lhe permitam experimentar a possibilidade de ser outro, utilizando máscaras que representam diferentes identidades. Noll faz emergir, no cenário literário, a representação da fragmentação, do desassossego e da solidão, características próprias do homem pós-moderno e de sua conturbada relação com o tempo. Ao criar uma linguagem que projeta imagens distorcidas no espaço e no tempo, o escritor gaúcho busca promover a reflexão e o questionamento acerca dos sentimentos de insegurança e de estranheza vividos pelos indivíduos no mundo efêmero e descentralizado da pós-modernidade. Para discorrer sobre esse tema complexo e provisório que é a identidade, serão fundamentais as considerações de Stuart Hall e as abordagens de Zygmunt Bauman que, ao discorrer sobre o mundo líquido-moderno, mostra como a identidade se tornou um tema necessário para o entendimento das transformações sociais e de suas implicações na individualidade pessoal

Anisotropic osmosis filtering for shadow removal in images

We present an anisotropic extension of the isotropic osmosis model that has been introduced by Weickert et al.~(Weickert, 2013) for visual computing applications, and we adapt it specifically to shadow removal applications. We show that in the integrable setting, linear anisotropic osmosis minimises an energy that involves a suitable quadratic form which models local directional structures. In our shadow removal applications we estimate the local structure via a modified tensor voting approach (Moreno, 2012) and use this information within an anisotropic diffusion inpainting that resembles edge-enhancing anisotropic diffusion inpainting (Weickert, 2006, Gali\'c, 2008). Our numerical scheme combines the nonnegativity preserving stencil of Fehrenbach and Mirebeau (Fehrenbach, 2014) with an exact time stepping based on highly accurate polynomial approximations of the matrix exponential. The resulting anisotropic model is tested on several synthetic and natural images corrupted by constant shadows. We show that it outperforms isotropic osmosis, since it does not suffer from blurring artefacts at the shadow boundaries

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

Efeito do tempo e condições de encharcamento sobre a estabilidade do farelo de arroz parboilizado.

O objetivo deste trabalho foi avaliar o efeito do tempo e da temperatura da água de encharcamento sobre a degradação hidrolítica e peroxidação do farelo de arroz na parboilização