Xiao-Guang Wu

Catalytic CO oxidation on Pt surfaces: a lattice-gas cellular automaton model

Abstract A lattice-gas cellular automaton model for CO oxidation on metal surfaces is developed. The model treats the dynamics of the absorbed CO and O species explicitly and incorporates the effects of surface phase transformations through simple cellular automaton rules. Nucleation and growth processes are observed and studied. Oscillations associated with surface spatial structure are also obtained when surface phase transformations are possible. The model can serve as a basis for more detailed studies of the reactive dynamics of such systems.

Effects of molecular fluctuations on chemical oscillations and chaos

The effects of molecular fluctuations on chemical oscillations and chaos are investigated. The calculations are carried out using a reactive lattice‐gas automaton which provides a mesoscopic description of the reactive dynamics. A specific chemical model, the Willamowski–Rossler reaction, is used to illustrate the effects. The applicability of mass‐action rate laws and reaction‐diffusion equations are considered and the character of the fluctuations in various dynamical regimes for both spatially‐distributed and spatially‐homogeneous systems are examined. The work provides information on the molecular origin of macroscopic, self‐organized structures in far‐from‐equilibrium reacting systems.

Projected dynamics: Analysis of a chemical reaction model

The rate processes corresponding to barrier crossing dynamics in a symmetric double‐well potential driven by a white‐noise source are investigated. The rate kernels in the generalized phenomenological rate law describing the reaction involve time evolution through a projected Fokker–Planck operator. The spectral properties of the projected Fokker–Planck operator are studied, and the rate kernels are expressed in terms of the eigenvalues and eigenfunctions of this operator. The formal results are illustrated with numerical calculations. The results provide information on the nature of the generalized chemical rate law for fast processes.

Projected dynamics for BGK reaction kinetics

Abstract The time dependence of the rate kernels that determine the barrier crossing rates of a double-well system with Bhatnagar—Gross—Krook (BGK) dynamics is studied. The rate kernels evolve according to projected dynamics where that part of the evolution which is proportional to the species population numbers is removed. The rate kernels for projected and ordinary dynamics are compared for various values of the chemical and internal relaxation times, and the validity of a phenomenological rate law description is discussed.

Vortex dynamics in oscillatory chemical systems.

Vortex core dynamics is studied in the Brusselator both near to and far from the Hopf bifurcation line for random and pair initial conditions. Extensive simulations are carried out for a pair of counter-rotating vortices close to the Hopf bifurcation line. Provided the vortices are not so far apart that wave-front annihilation produces strong gradients between their centers, the simulation results compare favorably with theories based on the complex Ginzburg-Landau equation. Far from the Hopf line the vortex core dynamics changes character and phenomena such as periodic motion of the vortex centers arise.

Chemical turbulence and phase resetting dynamics

The onset of chemical turbulence in the 2‐D complex Ginzburg–Landau equation is studied for a class of finite‐amplitude, inhomogeneous, random initial conditions. Numerical simulations on a coupled map lattice corresponding to this reaction–diffusion equation are carried out in order to characterize the nature of the turbulent state. The phase diagram giving the zone of chemical turbulence in the parameter space that specifies the initial condition is determined numerically and compared with an analytical estimate.

Spatiotemporal dynamics of mesoscopic chaotic systems

Abstract An investigation of the mesoscopic dynamics of chemical systems whose mass action equation gives rise to a deterministic chaotic attractor is carried out. A reactive lattice-gas model for the three-variable autocatalator is used to provide a mesoscopic description of the dynamics. The global and local dynamics is studied as a function of system size and diffusion coefficient. When the diffusion length is comparable to the system size phase coherence is maintained but the amplitudes of the oscillations are uncorrelated due to interaction between fluctuations and the instability of the chaotic dynamics. If the diffusion length is small compared to the system size then phase turbulence serves to destroy the noisy global attractor.

Internal Noise, Oscillations, Chaos and Chemical Waves

In most circumstances the spatiotemporal dynamics of reacting systems constrained to lie far from equilibrium can be described adequately by reaction-diffusion equations. These equations are valid provided the phenomena of interest occur on distance and time scales that are sufficiently long compared to molecular scales. Naturally, the complete microscopic description of the reacting medium, whether near to or far from equilibrium, must be based on the full molecular dynamics of the system, as embodied in Newton’s or Schrodinger’s equations of motion.

Projected dynamics for fast barrier-crossing processes with BGK kinetics

Abstract We study the barrier-crossing rate processes described by the Bhatnagar—Gross—Krook (BGK) equation in the small barrier regime. The spectral properties of the rate kernels are investigated through a projected BGK equation and the chemical relaxation and characteristic microscopic times are obtained.