Tracer dispersion in a percolation network with spatial correlations

We analyze the transport properties of a neutral tracer in a carrier fluid flowing through percolationlike porous media with spatial correlations. We model convection in the mass transport process using the velocity field obtained by the numerical solution of the Navier-Stokes and continuity equations in the pore space. We find that the resulting statistical properties of the tracer show a transition from a subdiffusion regime at low Peclet number to an enhanced diffusion regime at high Peclet number.     

Subdiffusion and cage effect in a sheared granular material

We investigate experimentally the diffusion properties of a bidimensional bidisperse dry granular material under quasistatic cyclic shear. The comparison of these properties with results obtained both in computer simulations of hard spheres systems and Lennard-Jones liquids and experiments on colloidal systems near the glass transition demonstrates a strong analogy between the statistical behavior of granular matter and these systems, despite their intrinsic microscopic differences (thermal vs athermal). More specifically, we study in detail the cage dynamics responsible for the subdiffusion in the slow relaxation regime, and obtain the values of relevant time and length scales.     

Circular polarization memory effect in low-coherence enhanced backscattering of light

We experimentally study the propagation of circularly polarized light in the subdiffusion regime by exploiting enhanced backscattering [(EBS), also known as coherent backscattering] of light under low spatial coherence illumination. We demonstrate for the first time, to the best of our knowledge, that a circular polarization memory effect exists in EBS over a large range of scatterers' sizes in this regime. We show that low-coherence EBS signals from the helicity preserving and orthogonal helicity channels cross over as the mean free path length of light in media varies, and that the cross point indicates the transition from multiple to double scattering in EBS.     

From Weakly Chaotic Dynamics to Deterministic Subdiffusion via Copula Modeling

Copula modeling consists in finding a probabilistic distribution, called copula, whereby its coupling with the marginal distributions of a set of random variables produces their joint distribution. The present work aims to use this technique to connect the statistical distributions of weakly chaotic dynamics and deterministic subdiffusion. More precisely, we decompose the jumps distribution of Geisel–Thomae map into a bivariate one and determine the marginal and copula distributions respectively by infinite ergodic theory and statistical inference techniques. We verify therefore that the characteristic tail distribution of subdiffusion is an extreme value copula coupling Mittag–Leffler distributions. We also present a method to calculate the exact copula and joint distributions in the case where weakly chaotic dynamics and deterministic subdiffusion statistical distributions are already known. Numerical simulations and consistency with the dynamical aspects of the map support our results.     

Conciliating the nonadditive entropy approach and the fractional model formulation when describing subdiffusion

We consider here two different models describing subdiffusion. One of them is derived from Continuous Time Random Walk formalism and utilizes a subdiffusion equation with a fractional time derivative. The second model is based on Sharma-Mittal nonadditive entropy formalism where the subdiffusive process is described by a nonlinear equation with ordinary derivatives. Using these two models we describe the process of a substance released from a thick membrane and we find functions which determine the time evolution of the amount of substance remaining inside this membrane. We then find ‘the agreement conditions’ under which these two models provide the same relation defining subdiffusion and give the same function characterizing the process of the released substance. These agreement conditions enable us to determine the relation between the parameters occuring in both models.     

How to measure subdiffusion parameters

We propose a method to measure the subdiffusion parameter alpha and subdiffusion coefficient Dalpha which are defined by means of the relation chi2 = 2Dalpha / Gamma(1+alpha)(t alpha), where chi2 denotes a mean square displacement of a random walker starting from x = 0 at the initial time t = 0. The method exploits a membrane system where a substance of interest is transported in a solvent from one vessel to another across a thin membrane which plays here only an auxiliary role. We experimentally study a diffusion of glucose and sucrose in a gel solvent, and we precisely determine the parameters alpha and Dalpha, using a fully analytic solution of the fractional subdiffusion equation.     

Impurity transport in percolation media

An equation describing the impurity transport in a percolation medium is obtained and the inferences drawn from this equation are analyzed based on the scale invariance concept. A determining part in this analysis is allowance for the sinks inherent in such media. At distances shorter than the correlation length, the particles are transferred in the regime of subdiffusion; at large distances, the concentration asymptotics exhibits a characteristic “tail” shape. In the medium occurring in the state above the percolation threshold, the impurity transport over time periods longer than the characteristic time related to the correlation length is well described by the classical equation with a renormalized diffusion coefficient. In this case, the concentration tail has a Gaussian shape at moderate distances and tends to subdiffusion asymptotics at very long distances. A relation is established between the factor determining renormalization of the diffusion coefficient and the factor determining a decrease in the number of active impurity particles at large times.     

An anomalous non-self-similar infiltration and fractional diffusion equation

Problems of anomalous infiltration in porous media are considered. As follows from the analysis of experimental data, modification of the infiltration equation is necessary. A fractional diffusion equation with variable order of the time-derivative operator for describing the liquid infiltration in porous media is proposed. The physical meaning of this fractional equation is explained. This equation provides good agreement with existing experimental data for both the subdiffusion and the superdiffusion. The treatment of experimental data for the absorption of water in a fired-clay brick and for water infiltration in cement mortar using this fractional equation of diffusion is presented. Various formulae, which can be useful for applications, have been developed.     

Uphill anomalous transport in a deterministic system with speed-dependent friction coefficient

We investigate the transport of a deterministic Brownian particle theoretically, which moves in simple onedimensional, symmetric periodic potentials under the influence of both a time periodic and a static biasing force. The physical system employed contains a friction coefficient that is speed-dependent. Within the tailored parameter regime, the absolute negative mobility, in which a particle can travel in the direction opposite to a constant applied force, is observed.This behavior is robust and can be maximized at two regimes upon variation of the characteristic factor of friction coefficient. Further analysis reveals that this uphill motion is subdiffusion in terms of localization(diffusion coefficient with the form D(t) ~t~(-1) at long times). We also have observed the non-trivially anomalous subdiffusion which is significantly deviated from the localization; whereas most of the downhill motion evolves chaotically, with the normal diffusion.     

A Study on Stochastic Resonance in Biased Subdiffusive SmoluchowskiSystems within Linear Response Range

The method of matrix continued fraction is used to investigatestochastic resonance (SR) in the biased subdiffusive Smoluchowskisystem within linear response range. Numerical results of lineardynamic susceptibility and spectral amplification factor are presented and discussed in two-well potential and mono-well potential with different subdiffusion exponents. Following our observation, the introduction of a bias in the potential weakens the SR effect in the subdiffusive system just as in the normal diffusive case. Our observation also discloses that the subdiffusion inhibits the low-frequency SR, but it enhances the high-frequency SR in thebiased Smoluchowski system, which should reflect a ``flattening"influence of the subdiffusion on the linear susceptibility.     

局域浓度调控扩散系数的次氯酸-碘离子-丙二酸系统图灵斑图形成中的反常扩散

通过数值模拟及振幅方程解析解方法,从实空间和倒空间分析了受局域浓度扩散系数调控下次氯酸-碘离子-丙二酸反应扩散系统图灵斑图形成的扩散机理.在零扩散系数调节下,斑图形成为典型的菲克扩散;而在负向正向扩散系数调节下,斑图的形成依赖欠扩散和超扩散.图灵系统的浓度稳态振幅对随机初始条件敏感性随局域浓度扩散调控系数k的增大而增加.     

Mesoscale Simulation of Bacterial Chromosome and Cytoplasmic Nanoparticles in Confinement

In this study we investigated, using a simple polymer model of bacterial chromosome, the subdiffusive behaviors of both cytoplasmic particles and various loci in different cell wall confinements. Non-Gaussian subdiffusion of cytoplasmic particles as well as loci were obtained in our Langevin dynamic simulations, which agrees with fluorescence microscope observations. The effects of cytoplasmic particle size, locus position, confinement geometry, and density on motions of particles and loci were examined systematically. It is demonstrated that the cytoplasmic subdiffusion can largely be attributed to the mechanical properties of bacterial chromosomes rather than the viscoelasticity of cytoplasm. Due to the randomly positioned bacterial chromosome segments, the surrounding environment for both particle and loci is heterogeneous. Therefore, the exponent characterizing the subdiffusion of cytoplasmic particle/loci as well as Laplace displacement distributions of particle/loci can be reproduced by this simple model. Nevertheless, this bacterial chromosome model cannot explain the different responses of cytoplasmic particles and loci to external compression exerted on the bacterial cell wall, which suggests that the nonequilibrium activity, e.g., metabolic reactions, play an important role in cytoplasmic subdiffusion.     

Random walks on the Comb model and its generalizations

Microscopic models with anomalous diffusion, which include the Comb model and its generalization for the finite width of the backbone, have been considered in this paper. The physical mechanisms of the subdiffusion random walks have been established. The first comes from the permanent return of the diffusing particle to the initial point of the diffusion due to "effective reducing" of the dimensionality of the considered system to the quasi-one-dimensional system. This physical mechanism has been obtained in the Comb model and in the model with a strip. The second mechanism of the subdiffusion is connected with random capture on the traps of diffusing particles and their ensuing random release from the traps. It has been shown that these different mechanisms of subdiffusion have been described by the different generalized diffusion equations of fractional order. The solutions of these different equations have been obtained, and the physical sense of the fractional order generalized equations has been discussed.     

Numerical method for two dimensional fractional reaction subdiffusion equation

In this paper, a new numerical algorithm for solving two dimensional fractional reaction subdiffusion equation is proposed. The stability and convergency of this method are investigated by the Fourier analysis. Theoretical analysis and numerical experiment demonstrate that the proposed method is effective for solving the two dimensional fractional reaction subdiffusion equation.     

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.     

Subdiffusion in a time-dependent force field

Based on the random-barrier model and using the mean-field approximation, we derive an equation that describes the subdiffusion of particles in an external time-varying force field. The derived equation predicts the frequency dependence of the conductivity and, in this regard, is consistent with the experiment. We show that the response of the system to an external perturbation depends significantly on the structure of the inhomogeneous medium.     

A multidimensional subdiffusion model： An arbitrage-free market

<正>To capture the subdiffusive characteristics of financial markets,the subordinated process,directed by the inverse Q-stale subordinator S_α(t) for 0 <α< 1,has been employed as the model of asset prices.In this article,we introduce a multidimensional subdiffusion model that has a bond and K correlated stocks.The stock price process is a multidimensional subdiffusion process directed by the inverse Q-stable subordinator.This model describes the period of stagnation for each stock and the behavior of the dependency between multiple stocks.Moreover,we derive the multidimensional fractional backward Kolmogorov equation for the subordinated process using the Laplace transform technique.Finally, using a martingale approach,we prove that the multidimensional subdiffusion model is arbitrage-free,and also gives an arbitrage-free pricing rule for contingent claims associated with the martingale measure.     

Quantum subdiffusion with two- and three-body interactions

We study the dynamics of a few-quantum-particle cloud in the presence of two- and three-body interactions in weakly disordered one-dimensional lattices. The interaction is dramatically enhancing the Anderson localization length ξ ₁ of noninteracting particles. We launch compact wave packets and show that few-body interactions lead to transient subdiffusion of wave packets, m ₂ ~ t ^α , α< 1, on length scales beyond ξ ₁. The subdiffusion exponent is independent of the number of particles. Two-body interactions yield α ≈ 0.5 for two and three particles, while three-body interactions decrease it to α ≈ 0.2. The tails of expanding wave packets exhibit exponential localization with a slowly decreasing exponent. We relate our results to subdiffusion in nonlinear random lattices, and to results on restricted diffusion in high-dimensional spaces like e.g. on comb lattices.     

Subdiffusion in peptides originates from the fractal-like structure of configuration space

Molecular dynamics simulation of oligopeptide chains reveals configurational subdiffusion at equilibrium extending from 10(-12) to 10(-8) s. Trap models, involving a random walk with a distribution of waiting times, cannot account for the subdiffusion, which is found rather to arise from the fractal-like structure of the accessible configuration space.