Lattice-gas crystallization

This paper presents a new lattice-gas method for molecular dynamics modeling. A mean-field treatment is given and is applied to a linear stability analysis. Exact numerical simulations of the solid-phase crystallization are presented, as is a finite-temperature multiphase liquid-gas system. The lattice-gas method, a discrete dynamical method, is therefore capable of representing a variety of collective phenomena in multiple regimes from the hydrodynamic scale down to a molecular dynamics scale.     

Asynchronous algorithm for integration of reaction-diffusion equations for inhomogeneous excitable media

An asynchronous algorithm for the integration of reaction-diffusion equations for inhomogeneous excitable media is described. Since many physical systems are inhomogeneous where either the local kinetics or the diffusion or conduction properties vary significantly in space, integration schemes must be able to account for wide variations in the temporal and spatial scales of the solutions. The asynchronous algorithm utilizes a fixed spatial grid and automatically adjusts the time step locally to achieve an efficient simulation where the errors in the solution are controlled. The scheme does not depend on the specific form of the local kinetics and is easily applied to systems with complex geometries. (c) 2000 American Institute of Physics.     

Master equations for coupled systems

A formalism to cope with the problem of dynamically coupled systems is developed. A time-dependent projection operator of the type given by Willis-Picard and Grabert-Weidlich is used to derive a time-convolutionless master equation from the Liouville equation for the total composite system. A systematic perturbational expansion formula with respect to the interaction between systems is also given. Finally, the comparison with the usual non-Markoffian master equation is discussed.     

Symmetries of non-linear reaction-diffusion equations and their solutions

This paper is concerned with the symmetries of a certain class of non-linear reaction-diffusion equations. The symmetries are used for deriving solutions of these equations. Subsequently, we compare the solutions with those given by other authors.     

From atomistic lattice-gas models for surface reactions to hydrodynamic reaction-diffusion equations

Atomistic lattice-gas models for surface reactions can accurately describe spatial correlations and ordering in chemisorbed layers due to adspecies interactions or due to limited mobility of some adspecies. The primary challenge in such modeling is to describe spatiotemporal behavior in the physically relevant "hydrodynamic" regime of rapid diffusion of (at least some) reactant adspecies. For such models, we discuss the development of exact reaction-diffusion equations (RDEs) describing mesoscale spatial pattern formation in surface reactions. Formulation and implementation of these RDEs requires detailed analysis of chemical diffusion in mixed reactant adlayers, as well as development of novel hybrid and parallel simulation techniques. (c) 2002 American Institute of Physics.     

Speed selection for coupled wave equations

We discuss models for coupled wave equations describing interacting fields, focusing on the speed of travelling wave solutions. In particular, we propose a general mechanism for selecting and tuning the speed of the corresponding (multi-component) travelling wave solutions under certain physical conditions. A number of physical models (molecular chains, coupled Josephson junctions, propagation of kinks in chains of adsorbed atoms and domain walls) are considered as examples.     

Time-space white noise eliminates global solutions in reaction-diffusion equations

We prove that perturbing the reaction-diffusion equation u_t=u_xx+(u₊)^p (p>1), with time-space white noise produces that solutions explodes with probability one for every initial datum, opposite to the deterministic model where a positive stationary solution exists.     

Global solutions for the coupled maxwell-dirac equations

This letter is a result announcement. The evolution group of coupled Maxwell-Dirac equations is intertwined with the evolution group of the free equations by a time-independent mapping on a domain which contains more than the free electromagnetic field. As a consequence, there exist global solutions with a nonzero electron field.     

Nonlinear analysis of a reaction-diffusion system: Amplitude equations

A reaction-diffusion system with a nonlinear diffusion term is considered. Based on nonlinear analysis, the amplitude equations are obtained in the cases of the Hopf and Turing instabilities in the system. Turing pattern-forming regions in the parameter space are determined for supercritical and subcritical instabilities in a two-component reaction-diffusion system.     

Lattice-gas model of multiple layer adsorption

The phase diagram for a lattice-gas model of physical adsorption on a homogeneous substrate has been calculated in a mean-field approximation. The first-order phase transitions corresponding to the addition of successive layers terminate in individual critical points as the temperature increases. The critical temperatures of successive layers increase, monotonically with layer number, from the critical temperature of the two-dimensional lattice gas to that of the bulk three-dimensional lattice gas. This last feature is probably an artifact of the mean-field approximation.     

Multi-symplectic method for the coupled Schrodinger-KdV equations

In this paper, we present a multi-symplectic Hamiltonian formulation of the coupled Schrtidinger-KdV equations （CS＇KE） with periodic boundary conditions. Then we develop a novel multi-symplectic Fourier pseudospectral （MSFP） scheme for the CSKE. In numerical experiments, we compare the MSFP method with the Crank-Nicholson （CN） method. Our results show high accuracy, effectiveness, and good ability of conserving the invariants of the MSFP method.     

Cosmological solutions for the coupled Einstein-Yang-Mills-Higgs equations

The coupled system of Einstein-Yang-Mills-Higgs equations is solved numerically for a Robertson-Walker symmetric universe. The open universe must be excluded because, for this situation, the coupled system is unable to produce energy-momentum densityT in agreement with the Robertson-Walker symmetry. For the closed universe, inflation solutions do occur if an early re-collapse is avoided by suitable choice of the initial conditions. The energy exchange between the minimally coupled Higgs and Yang-Mills subsystems is very small so that the inflating power of the Higgs field cannot be disturbed by the presence of the Yang-Mills field. After the inflation phase the influence of the Yang-Mills field is completely negligible (cosmic no-hair theorem).     

光-力耦合受激布里渊散射方程组

 采用位移形式表征各向同性介质的运动，从而对传统的SBS耦合波方程组进行改造，使之适用于多维的情况并体现光学理论和力学理论的耦合。采用有限差分方法数值求解了光学-力学耦合型后向SBS方程组，得到了瞬态的位移场、速度场和应力场。计算结果表明，当泵浦光光强为2.0×10 ¹⁵W/m ²时，SBS可激发厚度为1cm的K9玻璃样品的表面产生出0.1nm量级的位移和10m/s量级的速度，对应的应力幅度达到10MPa量级。     

Oscillatory Turing patterns in reaction-diffusion systems with two coupled layers

A model reaction-diffusion system with two coupled layers yields oscillatory Turing patterns when oscillation occurs in one layer and the other supports stationary Turing structures. Patterns include "twinkling eyes," where oscillating Turing spots are arranged as a hexagonal lattice, and localized spiral or concentric waves within spot-like or stripe-like Turing structures. A new approach to generating the short-wave instability is proposed.     

The periodic solutions for coupled integrable dispersionless equations

By using the Jacobi elliptic-function method,this paper obtains the periodic solutions for coupled integrable dispersionless equations. The periodic solutions include some kink and anti-kink solitons.