Chebyshev, Legendre, Hermite and other orthonormal polynomials in D-dimensions

We propose a general method to construct symmetric tensor polynomials in the D-dimensional Euclidean space which are orthonormal under a general weight. The D-dimensional Hermite polynomials are a particular case of the present ones for the case of a gaussian weight. Hence we obtain generalizations of the Legendre and of the Chebyshev polynomials in D dimensions that reduce to the respective well-known orthonormal polynomials in D=1 dimensions. We also obtain new D-dimensional polynomials orthonormal under other weights, such as the Fermi-Dirac, Bose-Einstein, Graphene equilibrium distribution functions and the Yukawa potential. We calculate the series expansion of an arbitrary function in terms of the new polynomials up to the fourth order and define orthonormal multipoles. The explicit orthonormalization of the polynomials up to the fifth order (N from 0 to 4) reveals an increasing number of orthonormalization equations that matches exactly the number of polynomial coefficients indication the correctness of the present procedure.Comment: 20 page

Three-dimensional Ginzburg-Landau simulation of a vortex line displaced by a zigzag of pinning spheres

A vortex line is shaped by a zigzag of pinning centers and we study here how far the stretched vortex line is able to follow this path. The pinning center is described by an insulating sphere of coherence length size such that in its surface the de Gennes boundary condition applies. We calculate the free energy density of this system in the framework of the Ginzburg-Landau theory and study the critical displacement beyond which the vortex line is detached from the pinning center.Comment: Submitted to special issue of Prammna-Journal of Physics devoted to the Vortex State Studie

Fully dissipative relativistic lattice Boltzmann method in two dimensions

In this paper, we develop and characterize the fully dissipative Lattice Boltzmann method for ultra-relativistic fluids in two dimensions using three equilibrium distribution functions: Maxwell-J\"uttner, Fermi-Dirac and Bose-Einstein. Our results stem from the expansion of these distribution functions up to fifth order in relativistic polynomials. We also obtain new Gaussian quadratures for square lattices that preserve the spatial resolution. Our models are validated with the Riemann problem and the limitations of lower order expansions to calculate higher order moments are shown. The kinematic viscosity and the thermal conductivity are numerically obtained using the Taylor-Green vortex and the Fourier flow respectively and these transport coefficients are compared with the theoretical prediction from Grad's theory. In order to compare different expansion orders, we analyze the temperature and heat flux fields on the time evolution of a hot spot

Optimal control technique for Many Body Quantum Systems dynamics

We present an efficient strategy for controlling a vast range of non-integrable quantum many body one-dimensional systems that can be merged with state-of-the-art tensor network simulation methods like the density Matrix Renormalization Group. To demonstrate its potential, we employ it to solve a major issue in current optical-lattice physics with ultra-cold atoms: we show how to reduce by about two orders of magnitudes the time needed to bring a superfluid gas into a Mott insulator state, while suppressing defects by more than one order of magnitude as compared to current experiments [1]. Finally, we show that the optimal pulse is robust against atom number fluctuations.Comment: 5 pages, 4 figures, published versio

Matching fields of a long superconducting film

We obtain the vortex configurations, the matching fields and the magnetization of a superconducting film with a finite cross section. The applied magnetic field is normal to this cross section, and we use London theory to calculate many of its properties, such as the local magnetic field, the free energy and the induction for the mixed state. Thus previous similar theoretical works, done for an infinitely long superconducting film, are recovered here, in the special limit of a very long cross section.Comment: Contains a REVTeX file and 4 figure

Post-COVID-19 arthritis: a case report and literature review

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV2) is the novel pathogen responsible for the coronavirus disease 19 (COVID-19) outbreak. Researchers and clinicians are exploring the pathogenetic mechanisms of the viral-induced damage and growing interest is focusing on the short-term and long-term immune-mediated consequences triggered by the infection. We will focus on post-SARS-CoV2 infection arthritis which may arise as a new pathological condition associated with COVID-19. In this article, we describe a case of acute oligoarthritis occurring 13 days after a SARS-CoV2 severe pneumonia in a middle-aged Caucasian man and we go over a brief review of the current available literature. We hypothesize that molecular mimicry might be the basic immunological mechanism responsible for the onset of COVID-19-related arthritis based on the current knowledge of SARS-CoV2 and on the known pathogenetic mechanism of viral-induced arthritis

Determination of recombination length of a non-equilibrium plasma produced by laser ablation

An experimental study of the laser ablation produced plasma evolution is necessary for its deeper understanding, since plasma expansion has both spatially and temporally varying characteristics. We irradiated a Cu target with a KrF laser beam. A small Faraday cup array and an axial Faraday cup were used as diagnostic systems, in order to study the spatial variation in the total charge carried by plasma ions. Charge loss during the plasma expansion was observed, which was attributed to the charged species recombination. This occurred upstream to the critical distance where the plasma density is high enough. Downstream the critical distance the plasma particles collisions were negligible and the ion charge remained frozen. In these experiments it was observed that the critical distance for charge recombination was a function of laser fluence