A generalized Faxén theorem for two-dimensional Brownian motion

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.     

Dominant structures in jet streams

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.     

Sum rules for Sαβ(k,ω) for two diffusing species

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 S_αβ(k,ω), i.e., for the initial value of the first, second and third time-derivatives of F_αβ(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 u_αβ(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 F_αβ(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 g_αβ(r).     

色交叉关联噪声对基因转录调节系统的影响

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     

On the decaying states and the transition rates

The object of this paper is to point out that the hypothesis of decaying states,i.e., states with amplitude having a factor e^γt (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.     

Statistics of photocounts of blinking fluorescence of quantum dots

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.     

Power-law distribution of gene expression fluctuations

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.     

Fluctuations in mean-field self-organized criticality

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.     

Anomalies in Conductance and Localization Length of Disordered Ladders

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.     

Some results for a fractional diffusion equation with radial symmetry in a confined region

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.     

The quasiclassical limit of the symmetry constraint of the KP hierarchy and the dispersionless KP hierarchy with self-consistent sources

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.     

Recursion formulae for IKK system with two hierarchies

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.     

Time evolution of the degree distribution of model A of random attachment growing networks

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(k, t) is the time evolution of degree distribution. P(k, t) 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(k, t) in detail.     

Dynamic correlations in a thermalized system described by the Burgers equation

For the field u(x, t) governed by the Burgers equation with a thermal noise, short-time asymptotics of multipoint correlators are obtained. Their exponential parts are independent of the correlator number. This means that they are determined by a single rare fluctuation and exhibit an intermittency phenomenon.     

Explicit time-domain approaches based on numerical Green’s functions computed by finite differences – The ExGA family

The present paper describes a new family of time stepping methods to integrate dynamic equations of motion. The scalar wave equation is considered here; however, the method can be applied to time-domain analyses of other hyperbolic (e.g., elastodynamics) or parabolic (e.g., transient diffusion) problems. The algorithms presented require the knowledge of the Green’s function of mechanical systems in nodal coordinates. The finite difference method is used here to compute numerically the problem Green’s function; however, any other numerical method can be employed, e.g., finite elements, finite volumes, etc. The Green’s matrix and its time derivative are computed explicitly through the range [0, Δt] with either the fourth-order Runge–Kutta algorithm or the central difference scheme. In order to improve the stability of the algorithm based on central differences, an additional matrix called step response is also calculated. The new methods become more stable and accurate when a sub-stepping procedure is adopted to obtain the Green’s and step response matrices and their time derivatives at the end of the time step. Three numerical examples are presented to illustrate the high precision of the present approach.     

Sliding behavior of oil droplets on nanosphere stacking layers with different surface textures

Two facile coating techniques, gravitational sediment and spin coating, were applied for the creation of silica sphere stacking layers with different textures onto glass substrates that display various sliding abilities toward liquid drops with different surface tensions, ranged from 25.6 to 72.3 mN/m. The resulting silica surface exhibits oil repellency, long-period durability > 30 days, and oil sliding capability. The two-tier texture offers a better roll-off ability toward liquid drops with a wide range of γ_L, ranged from 30.2 to 72.3 mN/m, i.e., when the sliding angle (SA) < 15°, the oil droplet start to roll off the surface. This improvement of sliding ability can be ascribed to the fact that the two-tier texture allows for air pockets (i.e., referred to as the Cassie state), thus favoring the self-cleaning ability. Taking Young-Duprè equation into account, a linearity relationship between sine SA and work of adhesion (W_ad) appears to describe the sliding behavior within the W_ad region: 2.20-3.03 mN/m. The smaller W_ad, the easier drop sliding (i.e., the smaller SA value) takes place on the surfaces. The W_ad value ∼3.03 mN/m shows a critical kinetic barrier for drop sliding on the silica surfaces from stationary to movement states. This work proposes a mathematical model to simulate the sliding behavior of oil drops on a nanosphere stacking layer, confirming the anti-oil contamination capability.