A stable three-level finite difference scheme for solving the parabolic two-step model in a 3D micro-sphere heated by ultrashort-pulsed lasers

Ultrashort-pulsed lasers with pulse durations of the order of sub-picosecond to femtosecond domain possess exclusive capabilities in limiting the undesirable spread of the thermal process zone in the heated sample. Parabolic two-step micro heat transport equations have been widely applied for thermal analysis of thin metal films exposed to picosecond thermal pulses. In this study, we develop a three level finite difference scheme for solving the heat transport equations in a three-dimensional micro-sphere heated by ultrashort-pulsed lasers. It is shown that the scheme is unconditionally stable. The method is illustrated by numerical examples.     

An algebraic representation of the affine Bäcklund transformation

In 1980 Chern and Terng defined a Bäcklund transformation for affine minimal surfaces. In this paper we show that this Bäcklund transformation can be simply represented by an involution and translation of the affine conormal.     

One-dimensional global attractor for strongly damped wave equations

We consider the dynamical behavior of the strongly damped wave equations under homogeneous Neumann boundary condition. By the property of limit set of asymptotic autonomous differential equations, we prove that in certain parameter region, the system has a one-dimensional global attractor, which is a periodic horizontal curve.     

A class of subgrid-scale models preserving the symmetry group of Navier–Stokes equations

Navier–Stokes equations (NS) admit transformations which transform a solution to another solution (galilean transformation, scaling transformation, …). They also admit viscosity dependent transformations which transform a solution to a solution of another NS with different viscosity. These particular transformations are called symmetries of NS. Each of them has a physical role (such as conservation laws, …). A consistent turbulence model should then remain invariant under these symmetry transformations. Unfortunately, this is not the case of several models.In this article, a class of subgrid-scale models preserving the symmetries of NS is built. This class is then refined such that the models respect the second law of thermodynamics. One of the simplest models of the class is tested to the flow in a ventilated room. Better results than those provided by Smagorinsky and dynamic models are obtained.     

Characterization of supercommuting matrices

For a given n-by-n matrix A, we consider the set of matrices which commute with A and all of whose principal submatrices commute with the corresponding principal submatrices of A. The properties of this set are examined, with particular attention to its dimension.     

Static dust sphere in Einstein-Cartan theory

Physically meaningful solutions of the field equations for static spherical dust distributions in the Einstein-Cartan theory have been obtained. There is one in which the spin is zero at the center and another with zero spin at the boundary of the sphere.     

Existence and multiplicity of positive periodic solutions to functional differential equations with impulse effects

This paper deals with a new existence theory for single and multiple positive periodic solutions to a kind of nonautonomous functional differential equations with impulse actions at fixed moments by employing a fixed point theorem in cones. Easily verifiable sufficient criteria are established. The paper extends some previous results and reports some new results about impulsive functional differential equations.     

The completely positive and doubly nonnegative completion problems

We prove the following. Let G be an undirected graph. Every partially specified symmetric matrix, the graph of whose specified entries is G and each of whose fully specified submatrices is completely positive (equal to BB^T for some entrywise nonnegative matrix B), may be completed to a completely positive matrix if and only if G is a block-clique graph (a chordal graph in which distinct maximal cliques overlap in at most one vertex). The same result holds for matrices that are doubly nonnegative (entrywise nonnegative and positive semidefinite).