Decay rate with coordinate-dependent diffusion coefficients

Using a master equation for the reduced density matrix of open quantum system, the influence of coordinate-dependent microscopical diffusion coefficients on the decay rate from a potential well is studied. For different temperatures, frictions, heights of barrier and ratios of stiffnesses of the potential in the minimum and on the top of the barrier, the quasistationary decay rates are obtained with the sets of coordinate-dependent and -independent microscopical diffusion coefficients, and coordinate-dependent phenomenological diffusion coefficients.     

On the analysis of coordinate-dependent diffusion

Coordinate-dependent diffusion in solids, in which case the probability of presence of a vacancy, φ, and the probability of migration, γ, depend on coordinate x is analyzed. The coordinate dependence of parameters φ and γ is shown to cause the drift component of the diffusion flux. In the presence of this component, the direction of atomic motion may coincide (enhanced diffusion) or not coincide (retarded diffusion and up-diffusion) with the direction of the diffusion component. The criteria of enhanced diffusion, retarded diffusion, and up-diffusion are established. These criteria are specified by the behavior of function F(x)=φ(x)/γ(x).     

Anomalous diffusion and memory effects on the impedance spectroscopy for finite-length situations

The contribution of ions to the electrical impedance of an electrolytic cell limited by perfect blocking electrodes is determined by considering the role of the anomalous diffusion process and memory effects. Analytical solutions for fractional diffusion equations together with Poisson's equation relating the effective electric field to the net charge density are found. This procedure allows the construction of general expressions for the electrochemical impedance satisfying the Kramers-Kronig relations when the diffusion of ions in the cell is characterized by the usual, as well as by anomalous, behavior.     

Kramers rate formula with coordinate-dependent mass

We study in this paper the classical stationary fission rate including a coordinate-dependent mass and a realistic potential. The results show that our numerical rate formula is a good approximation to the realistic Langevin simulation even if the nuclear temperature is not smaller than the fission barrier.     

Anomalous diffusion in two-dimensional potentials with hexagonal symmetry

The diffusion process in a Hamiltonian dynamical system describing the motion of a particle in a two-dimensional (2D) potential with hexagonal symmetry is studied. It is shown that, depending on the energy of the particle, various transport processes can exist: normal (Brownian) diffusion, anomalous diffusion, and ballistic transport. The relationship between these transport processes and the underlying structure of the phase space of the Hamiltonian dynamical system is investigated. The anomalous transport is studied in detail in two particular cases: in the first case, inside the chaotic sea there exist self-similar structures with fractal properties while in the second case the transport takes place in the presence of multilayered structures. It is demonstrated that structures of the second type can lead to a physical situation in which the transport becomes ballistic. Also, it is shown that for all cases in which the diffusive transport is anomalous the trajectories of the diffusing particles contain long segments of regular motion, the length of these segments being described by Levy probability density functions. Finally, the numerical values of the parameters which describe the diffusion processes are compared with those predicted by existing theoretical models. (c) 2000 American Institute of Physics.     

Anomalous diffusion with absorption: exact time-dependent solutions

Recently, analytical solutions of a nonlinear Fokker-Planck equation describing anomalous diffusion with an external linear force were found using a nonextensive thermostatistical Ansatz. We have extended these solutions to the case when an homogeneous absorption process is also present. Some peculiar aspects of the interrelation between the deterministic force, the nonlinear diffusion, and the absorption process are discussed.     

Anomalous diffusion and continuum percolation

Anomalous diffusion for continuum percolation is simulated by considering systems of randomly distributed circles and spheres. Universal behavior is obtained for the case of equal local conductances and nonuniversal behavior for diverging distributions of the local conductances. Diffusion in the continuum has a behavior consistent with that of other transport properties in the continuum. In addition, the results suggest that different algorithms for diffusion, which differ only in the random walker sitting times, are equivalent.     

Anomalous diffusion in silo drainage

The silo discharge process is studied by molecular dynamics simulations. The development of the velocity profile and the probability density function for the displacements in the horizontal and vertical axis are obtained. The PDFs obtained at the beginning of the discharge reveal non-Gaussian statistics and superdiffusive behaviors. When the stationary flow is developed, the PDFs at shorter temporal scales are non-Gaussian too. For big orifices a well-defined transition between ballistic and diffusive regime is observed. In the case of a small outlet orifice, no well-defined transition is observed. We use a nonlinear diffusion equation introduced in the framework of non-extensive thermodynamics in order to describe the movements of the grains. The solution of this equation gives a well-defined relationship (γ= 2/(3-q)) between the anomalous diffusion exponent γ and the entropic parameter q introduced by the non-extensive formalism to fit the PDF of the fluctuations.     

Solution of the Fokker-Planck equation with spatial coordinate-dependent moments

The solution of the Fokker-Planck equation with spatial coordinate-dependent moments is given in the form of the path integral, involving the conditional probability expressed in terms of the moments at the “postpoint”. It is easily seen that it satisfies the Fokker-Planck equation.     

Anomalous diffusion for a correlated process with long jumps

We discuss diffusion properties of a dynamical system, which is characterised by long-tail distributions and finite correlations. The particle velocity has the stable Lévy distribution; it is assumed as a jumping process (the kangaroo process) with a variable jumping rate. Both the exponential and the algebraic form of the covariance–defined for the truncated distribution–are considered. It is demonstrated by numerical calculations that the stationary solution of the master equation for the case of power-law correlations decays with time, but a simple modification of the process makes the tails stable. The main result of the paper is a finding that–in contrast to the velocity fluctuations–the position variance may be finite. It rises with time faster than linearly: the diffusion is anomalously enhanced. On the other hand, a process which follows from a superposition of the Ornstein–Uhlenbeck–Lévy processes always leads to position distributions with a divergent variance which means accelerated diffusion.     

Anomalous diffusion in branched elliptical structure

Diffusion in narrow curved channels with dead-ends as in extracellular space in the biological tissues, e.g., brain, tumors, muscles, etc. is a geometrically induced complex diffusion and is relevant to different kinds of biological, physical, and chemical systems. In this paper, we study the effects of geometry and confinement on the diffusion process in an elliptical comb-like structure and analyze its statistical properties. The ellipse domain whose boundary has the polar equation $rho left( theta right)=frac{b}{sqrt {1-e^{2}cos^{2}theta } }$ with $0相似文献   

Anomalous diffusion and fractional stable distributions

A new set of distributions, called fractional stable distributions, is described. A subset of this set is represented by stable laws, while its particular case is the Gaussian distribution. These distributions arise as solutions to fractional-order partial differential equations that represent a generalization of the ordinary diffusion equation to the case of anomalous diffusion. The properties of multidimensional fractional stable densities are described, their expressions in terms of special functions are presented, and physical problems that lead to these densities are discussed.     

反常扩散与分数阶对流-扩散方程

反常扩散现象在自然界和社会系统中广泛存在.考虑了扩散过程的时间相关和时空相关性，用非局域性的处理方法，在传统的二阶对流 扩散方程基础上，得到了分数阶对流 扩散方程，以此方程来描述反常扩散.在此方程中，弥散项和对时间的导数为分数阶导数所代替.由此分数阶对流 扩散方程，对传统的费克扩散定律进行推广，得到了广义的分数费克扩散定律，分数费克扩散定律说明某时刻空间中某点的流量不仅与其领域内的浓度梯度有关，而且与整个空间中其他不同点的粒子浓度、浓度变化的历史，甚至初始时刻的浓度有关.讨论了方程的解——分数稳定分布，并由此说明了扩散运动的平均平方位移是运移时间的非线性函数. 关键词： 扩散 分数阶微积分 稳定分布（Lévy分布） 费克扩散定律     

Anomalous diffusion in living yeast cells

The viscoelastic properties of the cytoplasm of living yeast cells were investigated by studying the motion of lipid granules naturally occurring in the cytoplasm. A large frequency range of observation was obtained by a combination of video-based and laser-based tracking methods. At time scales from 10(-4) to 10(2) s, the granules typically perform subdiffusive motion with characteristics different from previous measurements in living cells. This subdiffusive behavior is thought to be due to the presence of polymer networks and membranous structures in the cytoplasm. Consistent with this hypothesis, we observe that the motion becomes less subdiffusive upon actin disruption.