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A stochastic process describing the behavior of the solid-on-solid interface in a strip of widthL is studied. The invariant and reversible measure for the process is the Gibbs state with HamiltonianH|(x)–(x+1)|. Under free boundary conditions, we show that the height of the moving interface at any site converges, when suitable renormalized, to Brownian motion with a diffusion coefficient proportional toL –1.  相似文献   

Anwarud Din  黎永锦 《中国物理 B》2022,31(2):20202-020202
Norovirus is one of the most common causes of viral gastroenteritis in the world,causing significant morbidity,deaths,and medical costs.In this work,we look at stochastic modelling methodologies for norovirus transmission by water,human to human transmission and food.To begin,the proposed stochastic model is shown to have a single global positive solution.Second,we demonstrate adequate criteria for the existence of a unique ergodic stationary distribution R0 s>1 by developing a Lyapunov function.Thirdly,we find sufficient criteria Rs<1 for disease extinction.Finally,two simulation examples are used to exemplify the analytical results.We employed optimal control theory and examined stochastic control problems to regulate the spread of the disease using some external measures.Additional graphical solutions have been produced to further verify the acquired analytical results.This research could give a solid theoretical foundation for understanding chronic communicable diseases around the world.Our approach also focuses on offering a way of generating Lyapunov functions that can be utilized to investigate the stationary distribution of epidemic models with nonlinear stochastic disturbances.  相似文献   

刘茂省  阮炯 《中国物理 B》2009,18(12):5111-5116
In this paper, a stochastic SIS epidemic model on homogeneous networks is considered. The largest Lyapunov exponent is calculated by Oseledec multiplicative ergodic theory, and the stability condition is determined by the largest Lyapunov exponent. The probability density function for the proportion of infected individuals is found explicitly, and the stochastic bifurcation is analysed by a probability density function. In particular, the new basic reproductive number R*, that governs whether an epidemic with few initial infections can become an endemic or not, is determined by noise intensity. In the homogeneous networks, despite of the basic productive number R0>1, the epidemic will die out as long as noise intensity satisfies a certain condition.  相似文献   

李鑫  Janet M. Wang  唐卫清 《物理学报》2009,58(6):3603-3610
提出了一种基于工艺参数扰动的随机点匹配时延评估算法.该算法通过Cholesky分解将具有强相关性的工艺随机扰动转化为独立随机变量,并结合随机点匹配方法和多项式混沌理论对耦合随机互连线模型进行时延分析.最后,利用数值计算方法给出互连时延的有限维表达式.仿真实验结果表明,该算法与HSPICE仿真时延的相对误差不超过2%,且相比于HSPICE显著降低了电路模拟时间. 关键词: 工艺参数扰动 随机互连模型 随机点匹配方法 多项式混沌理论  相似文献   

The theory of adsorption of particles on macromolecules is considered. The theory is based on the notion that the adsorption is a discrete Markovian process. In the context of this theory the average number and the variance of the number of ligands adsorbed on macromolecules are calculated exactly. The results are compared with the frequently used approximation where the number of adsorbed particles is smaller than that in the solution. It is shown that for small values of the equilibrium constant the exact and approximate values coincide practically.  相似文献   

We study metastability and nucleation for the Blume-Capel model: a ferromagnetic nearest neighbor two-dimensional lattice system with spin variables taking values in {–1,0, +1}. We consider large but finite volume, small fixed magnetic fieldh, and chemical potential in the limit of zero temperature; we analyze the first excursion from the metastable –1 configuration to the stable +1 configuration. We compute the asymptotic behavior of the transition time and describe the typical tube of trajectories during the transition. We show that, unexpectedly, the mechanism of transition changes abruptly when the lineh=2 is crossed.  相似文献   

The relation between the aperiodic solution of the Lorenz model and that of a stochastic anharmonic oscillator is explored. The stochastic oscillator is constructed by replacing (t) in the Lorenz model by a stochastic variable(t) of specified statistics. The resulting system is of course not isomorphic to the Lorenz model, but does share with it a number of statistical properties. Thus, within the confines of these measures the two systems are physically very similar.  相似文献   

We study a stochastic neural-network model in which neurons and synapses change with a priori probability p and 1–p, respectively, in the limit p0. This implies neuron activity competing with fast fluctuations of the synaptic connections—in fact, random oscillations around values given by a learning (for example, Hebb's) rule. The consequences for the system performance of a dynamics constantly checking at random the set of memorized patterns is thus studied both analytically and numerically. We describe various nonequilibrium phase transitions whose nature depends on the properties of fluctuations. We find, in particular, that under rather general conditions locally stable mixture states do not occur, and pattern recognition and retrieval processes are substantially improved for some classes of synaptic fluctuations.  相似文献   

A formula is presented which can be regarded as the analytic basis for irreducible diagram expansions. It expresses the off-diagonal elements of the inverse of a matrix of operators by the off-diagonal elements and by diagonal elements of various inverses of the original operator. The formula can be obtained by purely analytic means without reference to statistical considerations. No infinite processes are involved if one deals with a finite matrix of operators.  相似文献   

用改进的随机轨道模型数值模拟突扩液固两相流动   总被引:2,自引:0,他引:2  
用改进的随机轨道模型数值模拟了突扩湍流液固两相流动。两相的轴向速度和湍动能的预报结果与实验符合得很好,同时还给出了不同计算截面上颗粒数密度和质量流量合理分布.预报结果对计算颗粒数敏感程度的研究表明:与通常的随机轨道不同,改进的随机轨道模型只需要很少的计算颗粒就可以给出合理正确的颗粒相分布。  相似文献   

A K Sood  S Dattagupta 《Pramana》1981,17(4):315-326
The three dominant mechanisms giving major contributions to vibrational relaxation in molecular systems are (a) pure dephasing, (b) depopulation (or energy relaxation), and (c) resonant transfer. Here (c) is not considered but the effects due to thesimultaneous occurrence of (a) and (b) are treated within a stochastic model. In dealing with (a), the vibrational frequency is assumed to undergo random uncorrelated ‘jump’, due to fluctuations in the environment of the active molecule between a continuous set of values. The ensuing results are somewhat different from those of the commonly used Kubo model of vibrational dephasing, especially at long times and appear to be better suited in interpreting certain experimental data. The model is next extended to include the simultaneous occurrence of (b). The calculation leads to two important conclusions: (i) the lineshape is not just the convolution of those due to (a) and (b), and (ii) the lineshape is asymmetric, if the intermolecular interactions are not isotropic.  相似文献   

We investigate metastability in the two dimensional Ising model in a square with free boundary conditions at low temperatures. Starting with all spins down in a small positive magnetic field, we show that the exit from this metastable phase occurs via the nucleation of a critical droplet in one of the four corners of the system. We compute the lifetime of the metastable phase analytically in the limit T 0, h 0 and via Monte Carlo simulations at fixed values of T and h and find good agreement. This system models the effects of boundary domains in magnetic storage systems exiting from a metastable phase when a small external field is applied.  相似文献   

We establish upper bounds for the spectral gap of the stochastic Ising model at low temperature in an N×N box, with boundary conditions which are plus except for small regions at the corners which are either free or minus. The spectral gap decreases exponentially in the size of the corner regions, when these regions are of size at least of order logN. This means that removing as few as O(logN) plus spins from the corners produces a spectral gap far smaller than the order N –2 gap believed to hold under the all-plus boundary condition. Our results are valid at all subcritical temperatures.  相似文献   

We establish upper bounds for the spectral gap of the stochastic Ising model at low temperatures in an l×l box with boundary conditions which are not purely plus or minus; specifically, we assume the magnitude of the sum of the boundary spins over each interval of length l in the boundary is bounded by l, where <1. We show that for any such boundary condition, when the temperature is sufficiently low (depending on ), the spectral gap decreases exponentially in l.  相似文献   

改进的随机轨道模型   总被引:5,自引:0,他引:5  
在随机轨道模型中,由于气相脉动速度对分散相颗粒作用的间歇性,使得井非在控制体内轨道上的每一点都可以代表该轨道参与颗粒相平均特性的统计计算,从而出现随机轨道模型往往低估颗粒相湍流脉动的情况.为此,本文提出了一种改进的随机轨道模型,在该模型中,分散相的时平均量在由其自身湍流脉动所确定的随机轨道上输运.与常用的随机轨道模型相比,其具有计算量小、计算结果合理且易于得到和分散相入口湍流脉动状况易于考虑等特点.对一简单已知流场的预报结果合理正确,克服了常用的随机轨道模型低估颗粒相湍流脉动的困难.  相似文献   

杨立兴  李峰  高自友  李克平 《中国物理 B》2010,19(10):100510-100510
This paper presents a discrete-time model to describe the movements of a group of trains, in which some operational strategies, including traction operation, braking operation and impact of stochastic disturbance, are defined. To show the dynamic characteristics of train traffic flow with stochastic disturbance, some numerical experiments on a railway line are simulated. The computational results show that the discrete-time movement model can well describe the movements of trains on a rail line with the moving-block signalling system. Comparing with the results of no disturbance, it finds that the traffic capacity of the rail line will decrease with the influence of stochastic disturbance. Additionally, the delays incurred by stochastic disturbance can be propagated to the subsequent trains, and then prolong their traversing time on the rail line. It can provide auxiliary information for rescheduling trains when the stochastic disturbance occurs on the railway.  相似文献   

We present results on the Swendsen-Wang dynamics for the Ising ferromagnet in the low-temperature case without external field in the thermodynamic limit. We discuss in particular the rate of convergence to the equilibrium Gibbs state in finite and infinite volume, the absence of ergodicity in the infinite volume, and the long-time behavior of the probability distribution of the dynamics for various starting configurations. Our results are purely dynamical in nature in the sense that we never use the reversibility of the process with respect to the Gibbs state, and they apply to a stochastic particle system withnon- Gibbsian invariant measure.  相似文献   

关联白噪声对抗肿瘤体系免疫效果的影响   总被引:1,自引:0,他引:1       下载免费PDF全文
在免疫监视的Logistic肿瘤生长动力学模型中引入关联的乘性白噪声,并考虑抗肿瘤体系的免疫系统激活阈值存在差异,对上述动力学生长方程进行数值仿真计算.发现噪声关联强度能够调节抗肿瘤体系个体的免疫效果,但调节的结果存在差异;噪声关联强度λ的取值存在一个最佳区间,在该区间内更多的抗肿瘤体系个体能实现最大免疫效果. 关键词: Logistic生长模型 随机涨落 肿瘤 免疫  相似文献   

The growth of bcc crystals is studied using van Beijeren's mapping onto the six-vertex model. The growth-evaporation processes are described in terms of vertices. The time evolution is given by a master equation for the probability of the six-vertex configurations. The model, studied in the finite-size case by both Monte Carlo and analytic methods, applies to the (001) surface and its vicinal surfaces. Different growth modes (including nucleation) are found, depending on the strength of disequilibrium and on temperature, and the transition between them is investigated.On leave of absence from the Institute of Physics, Czechoslovak Academy of Science, Prague, Czechoslovakia.  相似文献   

湍流边界层中重粒子弥散的随机模型   总被引:1,自引:0,他引:1  
在重粒子轨道模型的基础上,引入了Saffman力,并考虑了粒子-固壁碰撞和粒子-粒子碰撞的影响,建立了重粒子运动方程,耦合湍流脉动的随机方程,发展了重粒子弥散的随机模型,并在湍流边界层中考察该模型.将数值计算结果与实验结果进行比较,同时考察了Saffman力和粒子碰撞对计算结果的影响.  相似文献   

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