Solution domain decomposition with finite difference methods for partial differential equations

The Solution Domain Decomposition method of Nguyen and Paik [J. Sci. Comput. 4 , 357 (1993)] originally developed in a pseudospectral context is extended for use with finite difference techniques to solve partial differential equations. The essential idea behind this method lies in an application of the superposition principle, which allows interactions between adjacent subdomains to be decoupled and the resulting equations to be solved in parallel. Several tests are performed to assess its accuracy and efficiency based on a model problem arising from thermal convection inside a fluid-saturated porous cavity with heating from a side. The results reveal a well adaptation of the methodology into the framework of finite differences. © 1995 John Wiley & Sons, Inc.     

The intensity-dependent dielectric function of an exciton system

The nonlinear dielectric function of a direct band gap semiconductor is calculated using non-equilibrium Green's function technique. The interaction between the semiconductor and the intense radiation field is assumed to occur via excitons. As an example we calculate the polariton dispersion relation and the intensity-dependent changes of refraction index for GaAs.The author would like to thank Prof. Nguyen Van Hieu for projecting the problem and helpful discussions.     

Graphs with Prescribed Mean Curvature on Poincare Disk

We establish the existence and uniqueness of a solution of aquasilinear elliptic equation in the unit disk of R². Usingthis result, we obtain the existence of graphs with prescribedcurvature on the Poincaré disk.     

Decomposition of nondegenerate singularities of integrable Hamiltonian systems

The main perpose of this letter is to give a topological classification of stable nondegenerate singularities of smooth integrable Hamiltonian systems. Namely, we show that all such singularities can be decomposed diffeomorphically, after a finite covering, to the direct product of simplest (codimension 1 and codimension 2 focus-focus) singularities.     

Doubly ordered superconducting state in a doped antiferromagnet

In a weakly doped quasi-two-dimensional antiferromagnet with a Fermi contour in the form of small pockets, the Coulomb repulsion gives rise to a doubly ordered superconducting state of coexisting condensates with a large pair momentum and a zero one. The pairing with the large momentum determines the superconducting transition temperature, below which the order with zero momentum coexists as an induced order until the temperature corresponding to the initiation of the phonon pairing mechanism is reached. The superconductivity-induced orbital current density wave eliminates the pairing-repulsion-caused zero points from the two-gap quasiparticle spectrum and leads to a deviation of the relative phase of the superconducting order parameter components from π.     

Transport and structural properties of polymerized AC60 (A = K, Rb) under zero and high pressure conditions

60 display transport properties vastly different from their unpolymerized counterparts. We here describe structural (X-ray diffraction and transmission electron microscopy) and dc resistivity measurements of polymerized AC₆₀ (A = K, Rb) at zero and high pressures. The structural and electronic properties are rich, and evidence is found for unusual phase transitions in both materials. Received: 28 October 1996/Accepted: 13 December 1996     

Studies of picosecond spectro-temporal selection lasers using different dyes in microcavities with a two-stage-arrangement

Received: 18 April 1996/Revised version: 14 August 1996