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1.
The induced force method developed by Mazur and Bedeaux is applied here to two-dimensional Brownian motion. We obtain a generalized Faxén theorem which reduces to the Stokes-Basset drag force on a nonuniformly moving cylinder or disk in the special case where the fluid fluctuations are neglected. The resulting modified Langevin equation is solved numerically for the velocity autocorrelation Ø(t) and the expected long time result Ø(t)~1/t is obtained. It is perhaps surprising that the short time behavior of Ø(t) deviates considerably from that predicted on the basis of a modified Langevin equation incorporating the classic Oseen-Lamb drag force on a cylinder.  相似文献   

2.
A Hamiltonian version has been formulated for the model of axisymmetric equally rotating jet streams with a free boundary. In the framework of this approach, dominant structures, i.e., structure elements appearing in strongly disturbed jet streams at the preturbulent stage of their decay, are studied. It has been shown that compactons, i.e., solution with a compact support, can be such dominant structures. Analysis of the mechanism of the instability of compactons shows the possibility of collapse, which occurs almost without deformation of their shape but leads to the intensification of the vortex sheet at the boundary according to the law (t 0 ? t)?1, where t 0 is the collapse time.  相似文献   

3.
Large-scale genomic technologies has opened new possibilities to infer gene regulatory networks from time series data. Here, we investigate the relationship between the dynamic information of gene expression in time series and the underlying network structure. First, our results show that the distribution of gene expression fluctuations (i.e., standard deviation) follows a power-law. This finding indicates that while most genes exhibit a relatively low variation in expression level, a few genes are revealed as highly variable genes. Second, we propose a stochastic model that explains the emergence of this power-law behavior. The model derives a relationship that connects the standard deviation (variance) of each node to its degree. In particular, it allows us to identify a global property of the underlying genetic regulatory network, such as the degree exponent, by only computing dynamic information. This result not only offers an interesting link to explore the topology of real systems without knowing the real structure but also supports earlier findings showing that gene networks may follow a scale-free distribution.  相似文献   

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5.
Starting from the Smoluchowski equation without hydrodynamic interactions for two species of spherical diffusing particles, sum rules are derived here for the first three moments of Sαβ(k,ω), i.e., for the initial value of the first, second and third time-derivatives of Fαβ(k, t) (the time-dependent correlations between the fluctuations in the local concentration of diffusing particles of species α and β). These sum rules are written in terms of the potential of interaction uαβ(r) between the diffusing particles and the two- and three-particles distribution functions. This derivation is motivated by its potential use in the study of counterion effects on the diffusion of highly charged colloidal particles. Thus, we propose to approximate the memory function involved in the time evolution equation for Fαβ(k, t by a two-parameter model, with its (k-dependent) parameters being determined by the sum rules derived here. This procedure, along with Kirkwood's superposition approximation, reduces the dynamical problem to the knowledge of the radial distribution functions gαβ(r).  相似文献   

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7.
王参军  梅冬成 《物理学报》2008,57(7):3983-3988
研究了受色交叉关联噪声驱动的基因转录调节系统的瞬态性质(平均首通时间).据Novikov定理和Fox近似方法得到相应的Fokker-Planck方程,求出稳态概率分布函数的表达式.在此基础上运用最快下降法得到平均首通时间的近似表达式.经过数值计算,结果表明:在强关联,小关联时间条件下,蛋白质的浓度经历了开→关→开;在弱关联,大关联时间条件下,蛋白质的浓度经历了开→关.在基因转录过程中出现了重入现象. 关键词: 色交叉关联噪声 基因转录调节系统 平均首通时间  相似文献   

8.
We propose a method for analyzing the data for the rates of exchange of various currencies versus the U.S. dollar. The method analyzes the return time series of the data as a Markov process, and develops an effective equation which reconstructs it. We find that the Markov time scale, i.e., the time scale over which the data are Markov-correlated, is one day for the majority of the daily exchange rates that we analyze. We derive an effective Langevin equation to describe the fluctuations in the rates. The equation contains two quantities, D(1) and D(2), representing the drift and diffusion coefficients, respectively. We demonstrate how the two coefficients are estimated directly from the data, without using any assumptions or models for the underlying stochastic time series that represent the daily rates of exchange of various currencies versus the U.S. dollar.  相似文献   

9.
N D Sen Gupta 《Pramana》1974,3(6):363-369
The object of this paper is to point out that the hypothesis of decaying states,i.e., states with amplitude having a factor eγt (γ-real) is not compatible with the wave equation with a hermitian hamiltonian. An attempt has been made to obtain the expression for relative population density in general. It is shown that the usual expressions for the transition rates, which are proportional to time, may be obtained for a very restricted interval of time.  相似文献   

10.
Stochasticity is an inherent feature of complex systems with nanoscale structure. In such systems information is represented by small collections of elements (e.g., a few electrons on a quantum dot), and small variations in the populations of these elements may lead to big uncertainties in the information. Unfortunately, little is known about how to work within this inherently noisy environment to design robust functionality into complex nanoscale systems. Here, we look to the biological cell as an intriguing model system where evolution has mediated the trade-offs between fluctuations and function, and in particular we look at the relationships and trade-offs between stochastic and deterministic responses in the gene expression of budding yeast (Saccharomyces cerevisiae). We find gene regulatory arrangements that control the stochastic and deterministic components of expression, and show that genes that have evolved to respond to stimuli (stress) in the most strongly deterministic way exhibit the most noise in the absence of the stimuli. We show that this relationship is consistent with a bursty two-state model of gene expression, and demonstrate that this regulatory motif generates the most uncertainty in gene expression when there is the greatest uncertainty in the optimal level of gene expression.  相似文献   

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The blinking of quantum dots under the action of laser radiation is described based on a model of a binary (two-state) renewal process with on (fluorescent) and off (non fluorescent) states. The T on and T off sojourn times in the on and off states are random and power-law distributed with exponents 0 < α < 1 and 0 < β < 1; the averages of the on and off times are infinite. As a consequence of this, the Gaussian statistics is inapplicable and the process is described using a more general statistics. An equation for the density of distribution p(t on|t) of the total on time during the observation time t is derived that contains derivatives of fractional orders α and β. A solution to this equation is found in terms of fractional stable distributions. The Poisson transform of the density p(t on|t) leads to the photon counting distribution and determines the fluorescence statistics. It is demonstrated that, if a blinking process with exponents α < β is implemented, then, at fairly long times, the on time will considerably prevail over the off time, i.e., blinking will be suppressed. This behavior is evidenced by the types of distributions of the total fluorescence time, the decay of relative fluctuations, and the Monte Carlo simulated trajectories of the process.  相似文献   

13.
We discuss the conditions under which an anomaly occurs in conductance and localization length of Anderson model on a lattice. Using the ladder Hamiltonian and analytical calculation of average conductance we find the set of resonance conditions which complements the π-coupling rule for anomalies. We identify those anomalies that might vanish due to the symmetry of the lattice or the distribution of the disorder. In terms of the dispersion relation it is known from strictly one-dimensional model that the lowest order (i.e., the most strong) anomalies satisfy the equation E(k)=E(3k). We show that the anomalies of the generalized model studied here are also the solutions of the same equation with modified dispersion relation.  相似文献   

14.
We present two models that exhibit self-organized criticality at the mean-field level. These can be variously interpreted in epidemiological or chemical reaction terms. By studying the master equation for these models we find, however, that only in one of them does the self-organized critical behavior survive in the face of fluctuations. For this model we show the spectrum of the evolution operator to have spectral collapse, i.e., instead of a gap, as would occur in noncritical behavior, there are eigenvalues that approach zero as an inverse power of system size.  相似文献   

15.
We investigate an N-dimensional fractional diffusion equation with radial symmetry by taking a spatial and time dependent diffusion coefficient into account, i.e.,  with . The equation is considered in a confined region and subjected to time dependent boundary conditions which may be related to inhomogeneous characteristics of the surfaces confining the system. The results show an anomalous spreading of the solutions and an unusual behavior of the survival probability.  相似文献   

16.
Abstract

For the first time we show that the quasiclassical limit of the symmetry constraint of the Sato operator for the KP hierarchy leads to the generalized Zakharov reduction of the Sato function for the dispersionless KP (dKP) hierarchy which has been proved to be result of symmetry constraint of the dKP hierarchy recently. By either regarding the symmetry constrained dKP hierarchy as its stationary case or taking the dispersionless limit of the KP hierarchy with self-consistent sources directly, we construct a new integrable dispersionless hierarchy, i.e., the dKP hierarchy with self-consistent sources and find its associated conservation equations (or equations of Hamilton-Jacobi type). Some solutions of the dKP equation with self-consistent sources are also obtained by hodograph transformations.  相似文献   

17.
《Physics letters. A》2001,286(1):47-54
In a previous paper an inverse system with two hierarchies for a given symmetry was proposed. The scheme was found to have so constructive structure that relation between members of the hierarchies was systematically determined. In this Letter, with the proposed system we find simply and directly recursion formulae for two hierarchies for the su(2) algebra, i.e., the localized induction hierarchy and the hierarchy with the dispersionless equation. We show that, as a special case, the recursion formulae reduce to those of the modified Korteweg–de Vries hierarchy and the sine–Gordon hierarchy.  相似文献   

18.
《Nuclear Physics B》2001,600(2):378-386
The problem of time and the quantization of three-dimensional gravity in the strong coupling regime is studied following path integral methods. The time is identified with the volume of spacetime. We show that the effective action describes an infinite set of massless relativistic particles moving in a curved three-dimensional target space, i.e., a tensionless 3-brane on a curved background. If the cosmological constant is zero the target space is flat and there is no ‘‘ graviton" propagation (i.e., G[gij(2),gij(1)]=0). If the cosmological constant is different from zero, 3D gravity is both classical and quantum mechanically soluble. Indeed, we find the following results: (i) the general exact solutions of the Einstein equations are singular at t=0 showing the existence of a big-bang in this regime and (ii) the propagation amplitude between two geometries 〈gij(2),t2|gij(1),t1〉 vanishes as t→0, suggesting that big-bang is suppressed quantum mechanically. This result is also valid for D>3.  相似文献   

19.
20.
For random growing networks, Barabás and Albert proposed a kind of model in Barabás et al. [Physica A 272 (1999) 173], i.e. model A. In this paper, for model A, we give the differential format of master equation of degree distribution and obtain its analytical solution. The obtained result P(kt) is the time evolution of degree distribution. P(kt) is composed of two terms. At given finite time, one term decays exponentially, the other reflects size effect. At infinite time, the degree distribution is the same as that of Barabás and Albert. In this paper, we also discuss the normalization of degree distribution P(kt) in detail.  相似文献   

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