Anomalous transport in fluid field with random waiting time depending on the preceding jump length

Anomalous (or non-Fickian) transport behaviors of particles have been widely observed in complex porous media. To capture the energy-dependent characteristics of non-Fickian transport of a particle in flow fields, in the present paper a generalized continuous time random walk model whose waiting time probability distribution depends on the preceding jump length is introduced, and the corresponding master equation in Fourier-Laplace space for the distribution of particles is derived. As examples, two generalized advection-dispersion equations for Gaussian distribution and lévy flight with the probability density function of waiting time being quadratic dependent on the preceding jump length are obtained by applying the derived master equation.     

Continuous time random walk with jump length correlated with waiting time

A coupled continuous time random walk (CTRW) model is proposed, in which the jump length of a walker is correlated with waiting time. The power law distribution is chosen as the probability density function of waiting time and the Gaussian-like distribution as the probability density function of jump length. Normal diffusion, subdiffusion and superdiffusion can be realized within the present model. It is shown that the competition between long-tailed distribution and correlation of jump length and waiting time will lead to different diffusive behavior.     

Anomalous quantum heat transport in a one-dimensional harmonic chain with random couplings

We investigate quantum heat transport in a one-dimensional harmonic system with random couplings. In the presence of randomness, phonon modes may normally be classified as ballistic, diffusive or localized. We show that these modes can roughly be characterized by the local nearest-neighbor level spacing distribution, similarly to their electronic counterparts. We also show that the thermal conductance G(th) through the system decays rapidly with the system size (G(th)?～?L(-α)). The exponent α strongly depends on the system size and can change from α??1 with increasing system size, indicating that the system undergoes a transition from a heat conductor to a heat insulator. This result could be useful in thermal control of low-dimensional systems.     

Light transport and correlation length in a random laser

A random laser is a strongly disordered, laser‐active optical medium. The coherent laser feedback, which has been demonstrated experimentally to be present in these systems beyond doubt, requires the existence of spatially localized photonic quasimodes. However, the origin of these quasimodes has remained controversial. We develop an analytical theory for diffusive random lasers by coupling the transport theory of the disordered medium to the semiclassical laser rate equations, accounting for (coherent) stimulated and (incoherent) spontaneous emission. From the causality of wave propagation in an amplifying, diffusive medium we derive a novel length scale which we identify with the average mode radius of the lasing quasi‐modes. We show that truly localized modes do not exist in the system without photon number conservation. However, we find that causality in the amplifying medium implies the existence of a novel, finite intensity correlation length which we identify with the average mode volume of the lasing quasimodes. We show further that the surface of the laser‐active medium is crucial in order to stabilize a stationary lasing state. We solve the laser transport theory with appropriate surface boundary conditions to obtain the spatial distributions of the light intensity and of the occupation inversion. The dependence of the intensity correlation length on the pump rate agrees with experimental findings.     

Anomalous fluid transport in porous media induced by biofilm growth

Magnetic resonance measurements of the transition from normal to anomalous hydrodynamic dispersion in porous media due to biological activity are presented. Fractional advection-diffusion equations are shown to provide models for the measured impact of biofilm growth on porous media transport dynamics.     

Quantum transport in a time-dependent random potential with a finite correlation time

Using an earlier density matrix formalism in momentum space we study the motion of a particle in a time-dependent random potential with a finite correlation time τ, for 0 < t ? τ. Within this domain we consider two subdomains bounded by kinetic time scales (t _c ² = 2m? ^-1 c ², c ² = σ ², ξ ², σξ, with 2σ the width of an initial wavepacket and the correlation length of the gaussian potential fluctuations), where we obtain power law scaling laws for the effect of the random potential in the mean squared displacement 〈x ²〉 and in the mean kinetic energy 〈E _kin〉. At short times, ? min (t _σ ², 1/2t _ξ ²), 〈x ²〉 and 〈E _kin〉 scale classically as t ⁴ and t ², respectively. At intermediate times, t _σξ ? t ? 2t _σ ² and 1/2t _ξ ² ? t ? t _σξ, these quantities scale quantum mechanically as t ^3/2 and as √t, respectively. These results lie in the perspective of recent studies of the existence of (fractional) power law behavior of 〈x ²〉 and 〈E _kin〉 at intermediate times. We also briefly discuss the scaling laws for 〈x ²〉 and 〈E _kin〉 at short times in the case of spatially uncorrelated potential.     

Turbulent transport processes in a plasma as a diffusion process with random time

It is proposed to apply the statistical analysis of the increments of fluctuating particle fluxes to analyzing the probability characteristics of turbulent transport processes in plasma. Such an approach makes it possible to analyze the dynamic probability characteristics of the process under study. It is shown that, in the plasmas of the L-2M stellarator and the TAU-1 linear device, the increments of local fluctuating particle fluxes are of stochastic character and that their distributions are scale mixtures of Gaussians. In particular, for TAU-1, the increments have the Laplacian distribution (which is a scale mixture of Gaussians with an exponential mixing distribution). This implies that the rate of flux variations is a diffusion process with random time. It is shown that the characteristic growth (damping) time of fluctuations is one order of magnitude shorter than their characteristic correlation time. Physical mechanisms that may be responsible for the random character of the growth (damping) of fluctuations are discussed.     

Anomalous dispersion in correlated porous media: a coupled continuous time random walk approach

We study the causes of anomalous dispersion in Darcy-scale porous media characterized by spatially heterogeneous hydraulic properties. Spatial variability in hydraulic conductivity leads to spatial variability in the flow properties through Darcy’s law and thus impacts on solute and particle transport. We consider purely advective transport in heterogeneity scenarios characterized by broad distributions of heterogeneity length scales and point values. Particle transport is characterized in terms of the stochastic properties of equidistantly sampled Lagrangian velocities, which are determined by the flow and conductivity statistics. The persistence length scales of flow and transport velocities are imprinted in the spatial disorder and reflect the distribution of heterogeneity length scales. Particle transitions over the velocity length scales are kinematically coupled with the transition time through velocity. We show that the average particle motion follows a coupled continuous time random walk (CTRW), which is fully parameterized by the distribution of flow velocities and the medium geometry in terms of the heterogeneity length scales. The coupled CTRW provides a systematic framework for the investigation of the origins of anomalous dispersion in terms of heterogeneity correlation and the distribution of conductivity point values. We derive analytical expressions for the asymptotic scaling of the moments of the spatial particle distribution and first arrival time distribution (FATD), and perform numerical particle tracking simulations of the coupled CTRW to capture the full average transport behavior. Broad distributions of heterogeneity point values and lengths scales may lead to very similar dispersion behaviors in terms of the spatial variance. Their mechanisms, however are very different, which manifests in the distributions of particle positions and arrival times, which plays a central role for the prediction of the fate of dissolved substances in heterogeneous natural and engineered porous materials.     

The effect of zinc concentration on vacancies jump rate, diffusion coefficient and jump length in Cu-Zn ferrite

Samples with the chemical formula Cu_1−xZn_xFe₂O₄ (x=0.2, 0.4, 0.6, 0.8 and 1) were prepared by the standard ceramic method. The dielectric constant and dielectric loss tangent were studied as a function of vacancy jump rate. The results show that the dielectric constant and dielectric loss tangent decrease with increasing vacancy jump rate. In addition, the electron jump length in the octahedral sites was studied as a function of zinc concentration. The increase in jump length with Zn concentration has been attributed to the substitution of Fe⁺³ for Zn²⁺ at the A-sites, which increases the B-B interaction. The increase of diffusion coefficient with increasing Zn concentration was reinforced by the increase of jump rate.     

Subdiffusion with the disappearance of particles at the time of a jump

The reaction-subdiffusion equations corresponding to a monomolecular chemical reaction at the time of a diffusion jump are derived. It is shown that the approach to deriving such equations suggested previously in [8] gives the correct result in the case of asymptotic subdiffusion but is inapplicable in the practically important case of transient subdiffusion.     

Prediction problem for target events based on the inter-event waiting time

In this paper we address the problem of forecasting the target events of a time series given the distribution ξ of time gaps between target events. Strong earthquakes and stock market crashes are the two types of such events that we are focusing on. In the series of earthquakes, as McCann et al. show [W.R. Mc Cann, S.P. Nishenko, L.R. Sykes, J. Krause, Seismic gaps and plate tectonics: seismic potential for major boundaries, Pure and Applied Geophysics 117 (1979) 1082-1147], there are well-defined gaps (called seismic gaps) between strong earthquakes. On the other hand, usually there are no regular gaps in the series of stock market crashes [M. Raberto, E. Scalas, F. Mainardi, Waiting-times and returns in high-frequency financial data: an empirical study, Physica A 314 (2002) 749-755]. For the case of seismic gaps, we analytically derive an upper bound of prediction efficiency given the coefficient of variation of the distribution ξ. For the case of stock market crashes, we develop an algorithm that predicts the next crash within a certain time interval after the previous one. We show that this algorithm outperforms random prediction. The efficiency of our algorithm sets up a lower bound of efficiency for effective prediction of stock market crashes.     

利用稳频激光稳定F-P腔腔长的研究

为实现对F-P腔腔长的控制,设计了F-P腔腔长锁定控制系统。该系统以633nm稳频激光作为基准光源,通过控制系统驱动压电陶瓷调节F-P腔的腔长,以实现将F-P腔的谐振频率锁定到基准光源的频率上。实验结果表明,该方案切实可行,锁定后的F-P腔腔长的不确定度可达10-10量级。该方法在原子沉积技术中对于实现沉积台的稳定具有重要的指导意义。     

Percolation transport in random flows with weak dissipation effects

In the present paper, we consider the influence of weak dissipative effects on the passive scalar behavior in the framework of continuum percolation approach. The renormalization method of a small parameter in continuum percolation models is reviewed. It is shown that there is a characteristic velocity scale, which corresponds to the dissipative process. The modification of the renormalization condition of the small percolation parameter is suggested in accordance with additional external influences superimposed on the system. In the framework of mean-field arguments, the balance of correlation scales is considered. This gives the characteristic time that corresponds to the percolation regime. The expression for the effective coefficient of diffusion is obtained.     

Noise-induced escape on time scales preceding quasistationarity: New developments in the Kramers problem

Noise-induced escape from the metastable part of a potential is considered on time scales preceding the formation of quasiequilibrium within that part of the potential. It is shown that, counterintuitively, the escape flux may then depend exponentially strongly, and in a complicated manner, on time and friction. (c) 2001 American Institute of Physics.     

Anomalous Hall effect in ferromagnetic semiconductors in the hopping transport regime

We present a theory of the anomalous Hall effect in ferromagnetic (Ga,Mn)As in the regime when conduction is due to phonon-assisted hopping of holes between localized states in the impurity band. We show that the microscopic origin of the anomalous Hall conductivity in this system can be attributed to a phase that a hole gains when hopping around closed-loop paths in the presence of spin-orbit interactions and background magnetization of the localized Mn moments. Mapping the problem to a random resistor network, we derive an analytic expression for the macroscopic anomalous Hall conductivity sigma(AH)(xy). We show that sigma(AH)(xy) is proportional to the first derivative of the density of states varrho(epsilon) and thus can be expected to change sign as a function of impurity band filling. We also show that sigma(AH)(xy) depends on temperature as the longitudinal conductivity sigma(xx) within logarithmic accuracy.     

Influence of the phase coherence length on ballistic transport

The characteristic length scales for the transport in disordered metals are discussed. Based on a phenomenological model of phase randomising scattering processes, the influence of the phase coherence length on the conductance of ballistic systems is studied. It is argued that the frequency dependence of the conductance of quasi-one dimensional systems can be used in order to determine not only the statistical average but the whole distribution function of the phase coherence length. Various cases of distributions, the -function, the exponential, and the Gamma distribution, are discussed. It is shown that due to quantum coherence effects deviations from the classical (Drude) behavior of the conductance exist. For independent scattering processes the probability distribution function is given by the Poisson distribution function. In this case an expression for the conductance can be derived which contains the ballistic transport, and the result for the exponential distribution.