Search results for "Numerical"
showing 10 items of 2002 documents
Kinetics of Ordered Phases in Finite Spin Systems
1989
We study the growth of the ordered phase in a spin system of finite size suddenly brought below the transition temperature. Such a growth is driven by the instability of the mode corresponding to the largest eigenvalue of the interaction matrix. The relaxation occurs through different regimes according to whether the unstable mode has a negligible or macroscopic amplitude. One regime is characterised by dynamical scaling properties whereas in the other we can distinguish the growth to a macroscopic amplitude followed by rare transitions from one equilibrium amplitude to another. The analysis is carried out in the framework of a dynamical generalisation of the spherical model assuming non-ra…
Reservoir Computing with Random Skyrmion Textures
2020
The Reservoir Computing (RC) paradigm posits that sufficiently complex physical systems can be used to massively simplify pattern recognition tasks and nonlinear signal prediction. This work demonstrates how random topological magnetic textures present sufficiently complex resistance responses for the implementation of RC as applied to A/C current pulses. In doing so, we stress how the applicability of this paradigm hinges on very general dynamical properties which are satisfied by a large class of physical systems where complexity can be put to computational use. By harnessing the complex resistance response exhibited by random magnetic skyrmion textures and using it to demonstrate pattern…
Super-critical and sub-critical bifurcations in a reaction-diffusion Schnakenberg model with linear cross-diffusion
2016
In this paper the Turing pattern formation mechanism of a two components reaction-diffusion system modeling the Schnakenberg chemical reaction is considered. In Ref. (Madzavamuse et al., J Math Biol 70(4):709–743, 2015) it was shown how the presence of linear cross-diffusion terms favors the destabilization of the constant steady state. We perform the weakly nonlinear multiple scales analysis to derive the equations for the amplitude of the Turing patterns and to show how the cross-diffusion coefficients influence the occurrence of super-critical or sub-critical bifurcations. We present a numerical exploration of far from equilibrium regimes and prove the existence of multistable stationary…
The Hubbard model beyond the two-pole approximation: a Composite Operator Method study
2014
Within the framework of the Composite Operator Method, a three-pole solution for the two-dimensional Hubbard model is presented and analyzed in detail. In addition to the two Hubbard operators, the operatorial basis comprises a third operator describing electronic transitions dressed by nearest-neighbor spin fluctuations. These latter, compared to charge and pair fluctuations, are assumed to be preeminent in the region of model-parameter space - small doping, low temperature and large on-site Coulomb repulsion - where one expects strong electronic correlations to dominate the physics of the system. This assumption and the consequent choice for the basic field, as well as the whole analytica…
Spectral broadening by incomplete thermalization of the energy in X-ray microcalorimeters with superconducting absorber and NTD-Ge thermal sensor
2004
Abstract We present a model of the response of a cryogenic microcalorimeter with superconducting absorber and phonon sensitive thermal sensor to the absorption of X-ray photons. The model is based on the main microscopic processes responsible for the thermalization of the deposited energy. We use a system of rate equations to describe the energy downconversion in the superconductor and transport to the thermal sensor. The model is a tool to investigate the thermalization efficiency with respect to the device characteristics (i.e. absorber material, geometry), in order to optimize the performances of these detectors. As a first case study, we report results of simulations for a microcalorime…
Innovative modeling of Tuned Liquid Column Damper motion
2015
Abstract In this paper a new model for the liquid motion within a Tuned Liquid Column Damper (TLCD) device is developed, based on the mathematical tool of fractional calculus. Although the increasing use of these devices for structural vibration control, it is shown that existing model does not always lead to accurate prediction of the liquid motion. A better model is then needed for accurate simulation of the behavior of TLCD systems. As regards, it has been demonstrated how correctly including the first linear liquid sloshing mode, through the equivalent mechanical analogy well established in literature, produces numerical results that highly match the corresponding experimental ones. Sin…
Memory expansion for diffusion coefficients
1998
We present a memory expansion for macroscopic transport coefficients such as the collective and tracer diffusion coefficients ${D}_{C}$ and ${D}_{T},$ respectively. The successive terms in this expansion for ${D}_{C}$ describe rapidly decaying memory effects of the center-of-mass motion, leading to fast convergence when evaluated numerically. For ${D}_{T},$ one obtains an expansion of similar form that contains terms describing memory effects in single-particle motion. As an example we evaluate ${D}_{C}$ and ${D}_{T}$ for three strongly interacting surface systems through Monte Carlo simulations, and for a simple model diffusion system via molecular dynamics calculations. We show that the n…
Grid-based Methods in Relativistic Hydrodynamics and Magnetohydrodynamics
2015
An overview of grid-based numerical methods used in relativistic hydrodynamics (RHD) and magnetohydrodynamics (RMHD) is presented. Special emphasis is put on a comprehensive review of the application of high-resolution shock-capturing methods. Results of a set of demanding test bench simulations obtained with different numerical methods are compared in an attempt to assess the present capabilities and limits of the various numerical strategies. Applications to three astrophysical phenomena are briefly discussed to motivate the need for and to demonstrate the success of RHD and RMHD simulations in their understanding. The review further provides FORTRAN programs to compute the exact solution…
The Heating of the Solar Corona
2021
The solar corona, the outer atmosphere of the Sun, is heated to millions of Kelvin. This is several orders of magnitude hotter than the photosphere, the optical surface of the Sun, below, and a mystery that has baffled scientists for centuries. The answer to the question of how the solar corona is heated lies in the crucial magnetic connection through the atmosphere of the Sun. The magnetic field that threads the corona extends below the solar photosphere, where convective motions drag the magnetic field footpoints, tangling and twisting them. The chromosphere is the atmospheric layer above the photosphere, and the magnetic field provides an important connection between these layers. The ex…
Building a numerical relativistic non-ideal magnetohydrodynamics code for astrophysical applications
2013
AbstractIncluding resistive effects in relativistic magnetized plasmas is a challenging task, that a number of authors have recently tackled employing different methods. From the numerical point of view, the difficulty in including non-ideal terms arises from the fact that, in the limit of very high plasma conductivity (i.e., close to the ideal MHD limit), the system of governing equations becomes stiff, and the standard explicit integrating methods produce instabilities that destroy the numerical solution. To deal with such a difficulty, we have extended the relativistic MHD code MR-GENESIS, to include a number of Implicit Explicit Runge-Kutta (IMEX-RK) numerical methods. To validate the i…