Search results for "Heat equation"

On the relativistic heat equation in one space dimension

2012

We study the relativistic heat equation in one space dimension. We prove a local regularity result when the initial datum is locally Lipschitz in its support. We propose a numerical scheme that captures the known features of the solutions and allows for analysing further properties of their qualitative behaviour. J.A.C. acknowledges partial support by MINECO project, reference MTM2011-27739-C04-02, by GRC 2009 SGR 345 by the Generalitat de Catalunya, and by the Engineering and Physical Sciences Research Council grant number EP/K008404/1. J.A.C. also acknowledges support from the Royal Society through a Wolfson Research Merit Award. V.C. acknowledges partial support by MINECO project, refere…

A theorem of Radò’s type for the solutions of a quasi-linear equation

2004

Modelling of Systems with a Dispersed Phase: “Measuring” Small Sets in the Presence of Elliptic Operators

2016

When modelling systems with a dispersed phase involving elliptic operators, as is the case of the Stokes or Navier-Stokes problem or the heat equation in a bounded domain, the geometrical structure of the space occupied by the dispersed phase enters in the homogenization process through its capacity, a quantity which can be used to define the equivalence classes in \(H^1\). We shall review the relationship between capacity and homogenization terms in the limit when the number of inclusions becomes large, focusing in particular on the situation where the distribution of inclusions is not necessarily too regular (i.e. it is not periodic).

FPGA Implementation Of Diffusive Realization For A Distributed Control Operator

2010

International audience; We focus on the question of real-time computation for optimal distributed filtering or control applicable to MEMS Arrays. We present an algorithm for the realization of a linear operator solution to a functional equation through its application to a Lyapunov operatorial equation associated to the heat equation in one dimension. It is based on the diffusive realization, and turns to be well suited for fined grained parallel computer architecture as Field Programmable Gate Arrays (FPGA). An effective FPGA implementation has been successfully carried out. Here, we report the main implementation steps and the final measured performances.

On the adoption of the Monte Carlo method to solve one-dimensional steady state thermal diffusion problems for non-uniform solids

2013

Abstract The present paper is focussed on the investigation of the potential adoption of the Monte Carlo method to solve one-dimensional, steady state, thermal diffusion problems for continuous solids characterised by an isotropic, space-dependent conductivity tensor and subjected to non-uniform heat power deposition. To this purpose the steady state form of Fourier’s heat diffusion equation relevant to a continuous, heterogeneous and isotropic solid, undergoing a space-dependent heat power density has been solved in a closed analytical form for the general case of Cauchy’s boundary conditions. The thermal field obtained has been, then, put in a peculiar functional form, indicating that it …

Nonstationary heat conduction in a stator

1996

In this chapter we describe a method for computing the 3d nonstationary temperature field in the lamination pack of a stator of a synchronous or asynchronous (induction) motor with a centrifugal, meander or chamber ventilation (see [Křižek, Preiningerova]). The stator of a motor has quite a complicated geometrical form. Moreover, it consists of anisotropic materials which have very different heat conductivities, e.g., 332.8 [W/mK] for copper wires and 0.2 [W/mK] for their insulations. This causes big jumps in coefficients of the appropriate heat conduction equation, and is the main source of numerical difficulties in practical calculations.

Conservative Averaging Method for Solutions of Inverse Problems for Heat Equation

2004

Inverse problems arise in various fields of science, technology and agriculture where from measurements of state of the system or process it is required to determine a certain typesetting of the causal characteristics. It is known that infrigement of the natural causal relationships can entail incorrectness of the mathematical formulation of inverse problem. Therefore the development of efficient methods for solving such problems allow us to simplify experimental research considerably and to increase the accuracy and reliability of the obtained results due to certain complication of algoritms for processing the experemental data. The problem of the determination of the coefficient of therma…

Fokker–Planck equation with respect to heat measures on loop groups

2011

Abstract The Dirichlet form on the loop group L e ( G ) with respect to the heat measure defines a Laplacian Δ DM on L e ( G ) . In this note, we will use Wasserstein distance variational method to solve the associated heat equation for a given data of finite entropy.

Efficient High-Order Iterative Methods for Solving Nonlinear Systems and Their Application on Heat Conduction Problems

2017

[EN] For solving nonlinear systems of big size, such as those obtained by applying finite differences for approximating the solution of diffusion problem and heat conduction equations, three-step iterative methods with eighth-order local convergence are presented. The computational efficiency of the new methods is compared with those of some known ones, obtaining good conclusions, due to the particular structure of the iterative expression of the proposed methods. Numerical comparisons are made with the same existing methods, on standard nonlinear systems and a nonlinear one-dimensional heat conduction equation by transforming it in a nonlinear system by using finite differences. From these…

QUALITATIVE PROPERTIES OF THE SOLUTIONS OF A NONLINEAR FLUX-LIMITED EQUATION ARISING IN THE TRANSPORT OF MORPHOGENS

2011

In this paper we study some qualitative properties of the solutions of a nonlinear flux-limited equation arising in the transport of morphogens in biological systems. Questions related to the existence of steady states, the finite speed of propagating fronts or the regularization in the interior of the support are studied from analytical and numerical points of view.