介观振荡化学反应体系的内噪声随机共振

用化学Langevin方程研究了内噪声对介观振荡化学反应体系的影响.研究发现,在确定性体系处于定态条件下,内噪声可以导致体系振荡:随着内噪声强度的变化,诱导振荡信号的信噪比通过一个极大值,表明内噪声随机共振的出现;由于内噪声强度随着系统体积的变化而改变,因此,这一现象也证明了系统尺度共振,即最佳尺度效应的存在.     

Particle dynamics simulations of Turing patterns

The direct simulation Monte Carlo method is used to reproduce Turing patterns at the microscopic level in reaction-diffusion systems. In order to satisfy the basic condition for the development of such a spatial structure, we propose a model involving a solvent, which allows for disparate diffusivities of individual reactive species. One-dimensional structures are simulated in systems of various lengths. Simulation results agree with the macroscopic predictions obtained by integration of the reaction-diffusion equations. Additional effects due to internal fluctuations are observed, such as temporal transitions between structures of different wavelengths in a confined system. For a structure developing behind a propagating wave front, the fluctuations suppress the induction period and accelerate the formation of the Turing pattern. These results support the ability of reaction-diffusion models to robustly reproduce axial segmentation including the formation of early vertebrae or somites in noisy biological environments.     

介观化学体系中的动力学尺度效应

以生命和表面催化体系为对象,研究了介观化学体系中内涨落对体系非线性动力学行为的调控作用。内涨落可以诱导随机振荡,其强度在体系处于最佳尺度时会出现一个甚至多个极大值,并且在耦合体系中会得到进一步增强,表现为尺度共振效应、尺度选择效应和双重尺度效应,揭示了介观化学体系中尺度效应的新机制。     

介观化学体系中的动力学尺度效应

以生命和表面催化体系为对象,研究了介观化学体系中内涨落对体系非线性动力学行为的调控作用。内涨落可以诱导随机振荡,其强度在体系处于最佳尺度时会出现一个甚至多个极大值,并且在耦合体系中会得到进一步增强,表现为尺度共振效应、尺度选择效应和双重尺度效应,揭示了介观化学体系中尺度效应的新机制。     

Exact on-lattice stochastic reaction-diffusion simulations using partial-propensity methods

Stochastic reaction-diffusion systems frequently exhibit behavior that is not predicted by deterministic simulation models. Stochastic simulation methods, however, are computationally expensive. We present a more efficient stochastic reaction-diffusion simulation algorithm that samples realizations from the exact solution of the reaction-diffusion master equation. The present algorithm, called partial-propensity stochastic reaction-diffusion (PSRD) method, uses an on-lattice discretization of the reaction-diffusion system and relies on partial-propensity methods for computational efficiency. We describe the algorithm in detail, provide a theoretical analysis of its computational cost, and demonstrate its computational performance in benchmarks. We then illustrate the application of PSRD to two- and three-dimensional pattern-forming Gray-Scott systems, highlighting the role of intrinsic noise in these systems.     

The Gray-Scott model under the influence of noise: reentrant spatiotemporal intermittency in a reaction-diffusion system

We investigate the influence of noise on the spatiotemporal behavior of the Gray-Scott model, a prototype for a simple reaction-diffusion system. In the parameter regime studied it is characterized deterministically by a stable fixed point. As the noise increases a regular periodic pattern is replaced first by an irregularly oscillating periodic pattern and then by spatiotemporal intermittency. With further increasing noise strength the spatiotemporal intermittency is first replaced by a low amplitude noisy regime followed by spatiotemporal intermittency (STI) embedded into a noisy background. At sufficiently high noise intensity high amplitude noise prevails. We point out that the transition from spatiotemporal intermittency to low amplitude noise can be traced back to the fact that the spatially homogeneous state is a global attractor. As the noise strength grows further the "noisy" fixed point starts to communicate with STI leading to noise-induced spatiotemporal intermittency as an excitable state. At high enough noise strength high amplitude noise is left over wiping out all details of the underlying deterministic dynamical system.     

Enhancement of stochastic oscillations by colored noise or internal noise in NO reduction by CO on small platinum surfaces

In this paper, based on the stochastic model of NO reduction by CO on Pt crystal surfaces and taking Gaussian colored noise as external fluctuations of the NO partial pressure, we study the effect of the colored noise on the internal noise-induced stochastic oscillations (INSOs) and the effect of internal noise on the colored noise-induced stochastic oscillations (CNSOs). It is found that the INSO can be enhanced by the colored noise with appropriate correlation time or noise strength and, interestingly, the CNSO can be enhanced by the internal noise as well and, moreover, the enhanced CNSO can reach the best oscillatory states repetitively via proper internal noises. This effect of the internal noise is different from its effect on the stochastic oscillations induced by the external Gaussian white noise, which probably results from the interaction of the correlated colored noise and the internal noise.     

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

We have studied the influence of internal noise on the reaction rate oscillation during carbon-monoxide oxidation on single crystal platinum surfaces using chemical Langevin equations. Considering that the surface is divided into small well-mixed cells, we have focused on the dynamic behavior inside a single cell. Internal noise can induce rate oscillations and the performance of the stochastic rate oscillations shows double maxima with the variation of the internal noise intensity, demonstrating the occurrence of internal noise coherent biresonance. The relationship between such a phenomenon with the deterministic bifurcation features of the system is also discussed.     

Stochastic bi-resonance induced by external noise for Ca~(2+) signaling in hepatocytes

Noise-induced effects have been widely studied theoretically and experimentally in different fields of science, one of the most interesting phenomena is sto- chastic resonance (SR), and the traditional SR was confined to the single-peak form. However, in …     

Isometric graphing and multidimensional scaling for reaction-diffusion modeling on regular and fractal surfaces with spatiotemporal pattern recognition

Heterogeneous surface reactions exhibiting complex spatiotemporal dynamics and patterns can be studied as processes involving reaction-diffusion mechanisms. In many realistic situations, the surface has fractal characteristics. This situation is studied by isometric graphing and multidimensional scaling (IGMDS) of fractal surfaces for extracting geodesic distances (i.e., shortest scaled distances that obtain edges of neighboring surface nodes and their interconnections) and the results obtained used to model effects of surface diffusion with nonlinear reactions. Further analysis of evolved spatiotemporal patterns may be carried out by IGMDS because high-dimensional snapshot data can be efficiently projected to a transformed subspace with reduced dimensions. Validation of the IGMDS methodology is carried out by comparing results with reduction capabilities of conventional principal component analysis for simple situations of reaction and diffusion on surfaces. The usefulness of the IGMDS methodology is shown for analysis of complex patterns formed on both regular and fractal surfaces, and using generic nonlinear reaction-diffusion systems following FitzHugh Nagumo and cubic reaction kinetics. The studies of these systems with nonlinear kinetics and noise show that effects of surface disorder due to fractality can become very relevant. The relevance is shown by studying properties of dynamical invariants in IGMDS component space, viz., the Lyapunov exponents and the KS entropy for interesting situations of spiral formation and turbulent patterns.     

Stochastic bi-resonance induced by external noise for Ca<Superscript>2+</Superscript> signaling in hepatocytes

The influence of external noise on intracellular Ca²⁺ oscillations dynamics in a single cell of rat hepatocytes is studied. The coherence of noise-induced intracellular Ca²⁺ oscillations reached two maxima for multiple external noise intensity, indicating the occurrence of external noise stochastic bi-resonance (SBR). This phenomenon is compared with our previous result that was induced by internal noise. Additionally, the deterministic bifurcation character of the system was also discussed.     

Catalytic conversion reactions mediated by single-file diffusion in linear nanopores: hydrodynamic versus stochastic behavior

We analyze the spatiotemporal behavior of species concentrations in a diffusion-mediated conversion reaction which occurs at catalytic sites within linear pores of nanometer diameter. Diffusion within the pores is subject to a strict single-file (no passing) constraint. Both transient and steady-state behavior is precisely characterized by kinetic Monte Carlo simulations of a spatially discrete lattice-gas model for this reaction-diffusion process considering various distributions of catalytic sites. Exact hierarchical master equations can also be developed for this model. Their analysis, after application of mean-field type truncation approximations, produces discrete reaction-diffusion type equations (mf-RDE). For slowly varying concentrations, we further develop coarse-grained continuum hydrodynamic reaction-diffusion equations (h-RDE) incorporating a precise treatment of single-file diffusion in this multispecies system. The h-RDE successfully describe nontrivial aspects of transient behavior, in contrast to the mf-RDE, and also correctly capture unreactive steady-state behavior in the pore interior. However, steady-state reactivity, which is localized near the pore ends when those regions are catalytic, is controlled by fluctuations not incorporated into the hydrodynamic treatment. The mf-RDE partly capture these fluctuation effects, but cannot describe scaling behavior of the reactivity.     

Internal noise stochastic resonance in CO oxidation on nm-sized palladium particles

The constructive roles of noise and disorder in nonlinear system have been extensively studied in the last two decades. Among them the most well known phenomenon is stochastic resonance[1], which demon-strates that noise can help a nonlinear system to det…     

Efficient stochastic simulation of simultaneous reaction and diffusion in a gas-liquid interface

A stochastic simulation of simultaneous reaction and diffusion is proposed for the gas-liquid interface formed in the surface of a gas bubble within a liquid. The interface between a carbon dioxide bubble and an aqueous solution of calcium hydroxide was simulated as an application example, taken from the integrated production of calcium carbonate. First Gillespie’s stochastic simulation algorithm was applied in separate reaction and diffusion simulations. The results from these simulations were consistent with deterministic solutions based on differential equations. However it was observed that stochastic diffusion simulations are extremely slow. The sampling of diffusion events was accelerated applying a group molecule transfer scheme based on the binomial distribution function. Simulations of the reaction-diffusion in the gas-liquid interface based on the standard Gillespie’s stochastic algorithm were also slow. However the application of the binomial distribution function scheme allowed to compute the concentration profiles in the gas-liquid interface in a fraction of the time required with the standard Gillespie’s stochastic algorithm.     

局域平衡假设和反应-扩散过程

局域平衡假设作为不可逆过程热力学理论的基础通常被认为适用于一般条件下的物理化学过程。本文从玻耳兹曼方程和涨落的随机理论出发重新研究了局域平衡假设对反应—扩散过程的适用性。表明对于涉及非线性化学动力学的反应—扩散过程, 从随机理论得到的结果和局域平衡假设是不一致的。     

Average band structure of smectic C* type random materials

We consider a Smectic C* type structure which exhibits alignment fluctuations which can be described by noise associated with both director angles. We take the propagation of axially incident electromagnetic waves, and from Maxwell equations, we establish the stochastic governing set of equations corresponding to optical phenomena. We note that this set of equations can be expressed as a linear vector stochastic system of differential equations with multiplicative noise. We use a procedure to calculate from the stochastic differential set of equations, the governing equations for the expected value of the electromagnetic transverse magnetic and electric fields for a certain autocorrelation function, and calculate explicitly their corresponding band structure for a particular spectral noise density. We have shown that the average resulting electromagnetic fields exhibit a biased decaying exponential dependence which impedes to propagate the waves in one sense while it permits them in the other sense. We have also found a remarkable widening of the band gap and the appearance of new local maxima for the modes without band gap.     

Communication: limitations of the stochastic quasi-steady-state approximation in open biochemical reaction networks

It is commonly believed that, whenever timescale separation holds, the predictions of reduced chemical master equations obtained using the stochastic quasi-steady-state approximation are in very good agreement with the predictions of the full master equations. We use the linear noise approximation to obtain a simple formula for the relative error between the predictions of the two master equations for the Michaelis-Menten reaction with substrate input. The reduced approach is predicted to overestimate the variance of the substrate concentration fluctuations by as much as 30%. The theoretical results are validated by stochastic simulations using experimental parameter values for enzymes involved in proteolysis, gluconeogenesis, and fermentation.