Effects of internal noise for rate oscillations during CO oxidation on platinum surfaces

Chemical Langevin Equation for Complex Reactions

The stochastic dynamical behaviors of an elementary reaction system can be investigated by the chemical Langevin equation (CLE). However, most of the reactions in engineering belong to complex reactions. It is not appropriate to describe the random evolution process of a complex chemical reaction system by directly using CLE because the foundation of the deviation of CLE is the equilibrium equation of the number of molecules in elementary reaction systems. In the study, the chemical Langevin equation for complex reactions (CLE-CR) is proposed based on the random process theory by introducing the extent of reactions to express the reaction rates of complex reactions. The reaction rates of complex reactions are regarded as some random variables following Poisson distribution. To illustrate the essential consistency of CLE-CR and CLE, the physical meaning of the propensity function in CLE is comprehensively discussed. A numerical example from chemical engineering is employed to demonstrate the effectiveness of CLE-CR and the solving procedure. The results show that CLE-CR can be conveniently applied into engineering to investigate the stochastic dynamical behaviors of complex reaction systems, giving the probabilistic information of the concentration evolution of chemical constituents.

Effect of internal noise on the oscillation of N2O decomposition over Cu-ZSM-5 zeolites using a stochastic description

When considering stochastic oscillations of heterogeneous catalyst systems, most researches have focused on the surface of a metal or its oxide catalysts, but there have been few studies on porous catalysts. In this work, the effects of internal noise on oscillations of N2O decomposition over Cu-ZSM-5 zeolites are investigated, using the chemical Langevin equation and a mesoscopic stochastic model. Considering that Cu-ZSM-5 particles are finely divided particles, the number of Cu ions (Ns) is proportional to the particle size at a certain Cu/Al, and the internal noise is inversely proportional to Ns. Stochastic oscillations can be observed outside the deterministic oscillatory region. Furthermore, the performance of the oscillation characterized by the signal-to-noise ratio has a maximum within the optimal size range of 4-8 nm. This suggests that a nanometer-sized zeolite may be best for oscillations.

Entropy production in a mesoscopic chemical reaction system with oscillatory and excitable dynamics

Stochastic thermodynamics of chemical reaction systems has recently gained much attention. In the present paper, we consider such an issue for a system with both oscillatory and excitable dynamics, using catalytic oxidation of carbon monoxide on the surface of platinum crystal as an example. 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 (HB). In the large system size (weak noise) limit, we find that P ∼ N(β) with β = 0 or 1, when the system is below or above the HB, 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 parameter approaches the so-called CANARD point where the maximum disappears. This phenomenon could be qualitatively understood by partitioning the total entropy production into the contributions of spikes and of small amplitude oscillations.

Internal Noise Coherent Resonance for Mesoscopic Chemical Oscillations: A Fundamental Study

The effect of internal noise for a mesoscopic chemical oscillator is studied analytically in a parameter region outside, but close to, the supercritical Hopf bifurcation. By normal form calculation and a stochastic averaging procedure, we obtain stochastic differential equations for the oscillation amplitude r and phase theta that is solvable. Noise-induced oscillation and internal noise coherent resonance, which has been observed in many numerical experiments, are reproduced well by the theory.

Critical threshold of noise-induced energy transduction in molecular machinery system

Responses of energy transduction of molecular machinery to random perturbation were investigated at the conditions where the system stayed near the bifurcation point. It was found that noise-induced oscillation (NIO) could occur. But how far from bifurcation point could one get the admissible region of NIO? We proposed and demonstrated numerically that there existed a critical threshold of NIO for each fixed noise intensity. Furthermore, it was found that noise intensity was a key factor for the determination of critical threshold. Finally, the detailed bifurcation diagram depending on noise intensity was replotted.