Studies Of Mesocopic Theories And Methodsin Non-equilibrium Surface Reaction-Diffusion System

Chemical processes included in the systems of surface catalysis, material growth and biomolecules, are always involved in multiscales from microscopic to mesoscopic scales, even to macroscopic spatiotemporal scales. With the advancement of experi-mental technology, a lot of self-organized non-equilibrium dissipation structures are observed at nanoscales on surface, such as oscillations, spiral waves, Turing patterns and turbulence. These structures result from the co-operations between the physical interactions at short length on the microscopic atomic scale and the reaction diffusion or interactions at long length on the mesoscopic scale. So it is very important and in-teresting to theoretically investigate and predict these complex multiscale dynamic phenomena in the systems of surface catalysis, material growth and biomolecules. On the other hand, very recently, non-equilibrium thermodynamics on the mesoscopic scale, especially, stochastic thermodynamics (ST) which based on a stochastic trajec-tory, proposed by Udo Seifert, has recently gained much attention. ST provides a framework for describing small systems like colloids or biomolecules driven out of equilibrium but still in contact with a heat bath. So it is also important and interesting to investigate the self-organized phenomena by ST and to find out the influence of bifurcation on the characteristic of non-equilibrium thermodynamics.This dissertation includes two chapters. In the first chapter, we introduce a kind of effective CG-KMC method to investigate the chemical oscillation on the lattice-gas Brusselator model. Moreover, we use CG-KMC and SPDE methods to simulate the spiral wave (SW) on the lattice-gas Gray-Scott model, respectively. In the second chapter, we use the ST to study the influence of system size on entropy productions in a model system, carbon monoxide (CO) oxidation on platinum (Pt) surface, with both oscillatory and excitable dynamics.CG methods of non-equilibrium reaction-diffusion processes on surfaceAt the stage of being, various methods of simulation and calculation have been constructed which are applicable to different temporal and spatial scales. But for many self-organized non-equilibrium dissipation structures observed on the na-noscales, on the one hand, conventional reaction-diffusion equations cannot describe accurately these phenomena due to the loss of microscopic mechanisms, such as lat-eral interactions between adsorbed molecules, and molecular fluctuations. On the other hand, traditional KMC based on microscopic lattice model, although takes ex- plicitly the molecular interactions and fluctuations into account, also fails to simulate these structures on the mesocopic scale, due to the limitation of memory and speed of available computer. Therefore, a promising way is to develop coarse-grained (CG) approaches, aiming at significantly reducing the degree of freedom to accelerate the simulation on large length scale while properly preserving the microscopic fluctua-tion information and correct dynamics.In the first chapter, we have tried to apply a CG-KMC approach to simulate the os-cillation behavior on the surface lattice-gas Brusselator model. Owing to the correla-tions between adjacent cells resulted from the nonlinear trimolecular reaction, the CG approach based on simple local mean field (LMF) approximation almost fails. By properly taking into account the boundary corrections, we have introduced a so-called b-LMF CG-KMC approach, which can reproduce the microscopic KMC results quite well, given that the diffusion is not too slow and the CG cell size is optimally chosen. Our work thus unravels the very role of reaction correlations which should be care-fully considered in any CG approach and mesoscopic modeling for non-equilibrium spatiotemporal dynamics at nanoscales.Moreover, we have used a CG-KMC method and SPDE, respectively, which are based on LMF approximation, to simulate the spatiotemporal spiral wave on two-dimension (2D) surface lattice Gray-Scott model. Particular attention is paid to the effects of internal noise on the spiral wave. In this model, spatiotemporal SW ex-ists in narrow region of deterministic parameter space. When the coarse cell size is small, the effect of internal fluctuation becomes prominence. If the internal noise is intensive enough, nucleation is interrupted and spiral wave disappears. In an appro-priate strength of noise, a robust spiral wave is induced. In addition, the corresponding relations between CGKMC and SPDE methods are also discussed.ST on chemical reaction system with oscillatory and excitable dynamicsIn two recent papers, our group mainly investigated the entropy production along a stochastic limit cycle in state space. By numerical simulation, we calculated the mean entropy production P and found out that P shows distinct scaling behaviors with the system size V at different side of the Hopf bifurcation. Furthermore, we studied the ST on a general reaction network based on chemical Langevin equation, and then we theoretically investigated the influence of internal noise and bifurcation of system on the mean entropy production.In the second chapter, we have applied the concept of ST to a model system, carbon monoxide (CO) oxidation on platinum (Pt) surface. Starting from the chemical Langevin equations, we are able to calculate the stochastic entropy production P along a random trajectory in the concentration state space. Particular attention is paid to the dependence of the time averaged entropy production P on the system size N in a parameter region close to the deterministic Hopf bifurcation. In the large system size (weak noise) limit, we find that ~ with 0 or 1 when the system is below or above the Hopf bifurcation, respectively. In the small system size (strong noise) limit, P always increases linearly with N regardless of the bifurcation parameter. More interestingly, P could even reach a maximum for some intermediate system size in a parameter region where the corresponding deterministic system shows steady state or small amplitude oscillation. The maximum value of P decreases as the system param-eter approaches the so-called CANARD point where the maximum disappears. This phenomenon could be qualitatively understood by partitioning the total entropy pro-duction into the contributions of spikes and of small amplitude oscillations.