Narrow Results

High radiative efficiency in moderately doped n-InP results in the transport of holes dominated by photon-assisted hopping, when radiative hole recombination at one spot produces a photon, whose interband absorption generates another hole, possibly far away. Due to "heavy tails" in the hop probability, this is a random walk with divergent diffusivity (process known as the Lévy flight). Our key evidence is derived from the ratio of transmitted and reflected luminescence spectra, measured in samples of different thicknesses. These experiments prove the non-exponential decay of the hole concentration from the initial photo-excitation spot. The power-law decay, characteristic of Lévy flights, is steep enough at short distances (steeper than an exponent) to fit the data for thin samples and slow enough at large distances to account for thick samples. The high radiative efficiency makes possible a semiconductor scintillator with efficient photon collection. It is rather unusual that the material is "opaque" at wavelengths of its own scintillation. Nevertheless, after repeated recycling most photons find their way to one of two photodiodes integrated on both sides of the semiconductor slab. We present an analytical model of photon collection in two-sided slab, which shows that the heavy tails of Lévy-flight transport lead to a high charge collection efficiency and hence high energy resolution. Finally, we discuss a possibility to increase the slab thickness while still quantifying the deposited energy and the interaction position within the slab. The idea is to use a layered semiconductor with photon-assisted collection of holes in narrow-bandgap layers spaced by distances far exceeding diffusion length. Holes collected in these radiative layers emit longwave radiation, to which the entire structure is transparent. Nearly-ideal calculated characteristics of a mm-thick layered scintillator can be scaled up to several centimeters.

Using an inverse of the standard linear congruential random number generator, large randomly occupied lattices can be visited by a random walker without having to determine the occupation status of every lattice site in advance. In seven dimensions, at the percolation threshold with L⁷ sites and L≤420, we confirm the expected time-dependence of the end-to-end distance (including the corrections to the asymptotic behavior).

A model of fission gas migration in nuclear fuel pellet is proposed. Diffusion process of fission gas in granular structure of nuclear fuel with presence of inter-granular bubbles in the fuel matrix is simulated by fractional diffusion model. The Grunwald–Letnikov derivative parameter characterizes the influence of porous fuel matrix on the diffusion process of fission gas. A finite-difference method for solving fractional diffusion equations is considered. Numerical solution of diffusion equation shows correlation of fission gas release and Grunwald–Letnikov derivative parameter. Calculated profile of fission gas concentration distribution is similar to that obtained in the experimental studies. Diffusion of fission gas is modeled for real RBMK-1500 fuel operation conditions. A functional dependence of Grunwald–Letnikov derivative parameter with fuel burn-up is established.

In this work, we investigate computationally the dynamics of a nonlinear partial differential equation with anomalous diffusion that extends the well-known double sine–Gordon equation from relativistic quantum mechanics. The problem under consideration includes the presence of constant damping along with anomalous spatial derivatives. The model is defined on a close and bounded interval of the real line, and it is at rest at the initial time. One end of the interval is subject to sinusoidal driving, and the other considers the presence of an absorbing boundary in order to simulate a semi-infinite medium. The simulation of this system is carried out using a numerical method that resembles the energy properties of the continuous medium. The computational results shown in this work establish the presence of the nonlinear phenomenon of bistability in the system considered. We obtain hysteresis cycles for some particular scenarios, and employ the bistability of the system to simulate the transmission of binary signals from the driving boundary to the opposite end.

We consider the problem of the cosmic ray spectrum formation assuming that cosmic rays are produced by galactic sources. The fractional diffusion equation proposed in our recent papers is used to describe the cosmic rays propagation in interstellar medium. We show that in the framework of this approach it is possible to explain the locally observed basic features of the cosmic rays in the energy region 10¹⁰ ÷ 10²⁰eV: difference between spectral exponents of protons and other nuclei, mass composition variation, "knee" problem, flattening of the primary spectrum for E ≥ 10¹⁸ ÷ 10¹⁹eV.

Competing styles in statistical mechanics have been introduced to investigate physico-chemical systems displaying complex structures, when one faces difficulties to handle the standard formalism in the well-established Boltzmann–Gibbs statistics. After a brief description of the question, we consider the particular case of Renyi statistical approach, which is applied to the study of the "anomalous" (non-Fickian) diffusion that is involved in experiments of cyclic voltammetry in electro-physical chemistry. In these experiments, one is dealing with the fractal-like structure of the thin film morphology present in electrodes in microbatteries. Fractional-power laws are evidenced in the voltammetry measurements and in the analysis of the interphase width obtained using atomic force microscopy. The resulting fractional-powers are related to each other and to the statistical fractal dimension, and can be expressed in terms of the index on which Renyi's statistical approach depends. The important fact that this index, which is restricted to a given interval, provides a measure of the micro-roughness of the electrode surface, and is related to the dynamics involved, the nonequilibrium thermodynamic state of the system, and to the experimental protocol is clarified.

Anomalous (non-Gaussian) kinetics is often observed in various disordered materials, such as amorphous semiconductors, porous solids, polycrystalline films, liquid-crystalline materials, polymers, etc. Recently the anomalous relaxation-diffusion processes have been observed in nanoscale systems: nanoporous silicon, glasses doped by quantum dots, quasi-one-dimensional (1D) systems, arrays of colloidal quantum dots, and some others. The paper presents a review of new approach, based on fractional kinetic equations. We give a physical basis for some fractional equations deriving them from their classical counterparts by means of averaging over statistical ensemble of disordered media. We consider self-similarity as the main feature of these processes, and explain memory phenomena in frameworks of hidden variables conception.

It has been empirically known that the disordered system exhibits a power-law behavior. We show from calculation the power law t^-1-α for the pausing-time distribution of thermal diffusion of hydrogen in the exponential density of states. This power law of the pausing-time distribution is examined by the Monte Carlo simulation. The results agree with those obtained by analytical calculation. We discuss the power law in terms of random walk in fractal structure (Cantor ensemble).

The pausing-time distribution of thermal diffusion of hydrogen is analytically shown in the Gaussian density of state. The pausing-time distribution exhibits a log-normal distribution. It has been shown that the pausing-time distribution follows approximately power law, i.e., t^-1-α(t: pausing time). The diffusion coefficient of hydrogen is also obtained to be approximately τ^α-1 (τ: diffusion time). The value of α is the ratio of hydrogen temperature T_r to T_2σ, in which T_2σ, is a temperature corresponding to 2σ (σ: standard deviation). Finally, Brownian motion is shown to correspond to the case of σ = 0. The width of the energy distribution play an important role in hydrogen diffusion.

The diffusion coefficient of hydrogen is obtained for exponential energy distribution in hydrogenated amorphous silicon (a-Si:H). It is shown that the diffusion coefficient follows the form of τ^α-1 (τ: diffusion time) in the case of α < 1 and a larger τ, in which α is the ratio of hydrogen temperature to width for energy distribution function. In the case of α ≥ 1, as α reaches infinity at the limit, the hydrogen diffusion approaches Brownian motion.

Hydrogen diffusion in a-Si:H with exponential distribution of the states in energy exhibits the fractal structure. It is shown that a probability $P(t)$ of the pausing time $t$ has a form of $t^{\alpha }$ ($\alpha$: fractal dimension). It is shown that the fractal dimension $\alpha =T_r$/$T_0$ ($T_r$: hydrogen temperature, $T_0$: a temperature corresponding to the width of exponential distribution of the states in energy) is in agreement with the Hausdorff dimension. A fractal graph for the case of $\alpha \le 1$ is like the Cantor set. A fractal graph for the case of $\alpha >1$ is like the Koch curves. At $\alpha =\infty$, hydrogen migration exhibits Brownian motion. Hydrogen diffusion in a-Si:H should be the fractal process.

Granular materials as typical soft matter, their transport properties play significant roles in durability and service life in relevant practical engineering structures. Physico-mechanical properties of materials are generally dependent of their microstructures including interfacial and porous characteristics. The formation of such microstructures is directly related to particle components in granular materials. Understanding the interactive mechanism of particle components, microstructures, and transport properties is a problem of great interest in materials research community. The resulting rigorous component-structure-property relations are also valuable for material design and microstructure optimization. This review article describes state-of-the-art progresses on modeling particle components, interfacial and porous configurations and incorporating these internal structural characteristics into modeling transport properties of granular materials. We mainly focus on three issues involving the simulation for geometrical components, the quantitative characterization for interfacial and porous microstructures, and the modeling strategies for diffusive behaviors of granular materials. In the first aspect, in-depth reviews are presented to realize complex morphologies of geometrical particles, to detect the overlap between adjacent nonspherical particles, and to simulate the random packings of nonspherical particles. In the second aspect, we emphasize the development progresses on the interfacial thickness and porosity distribution, the interfacial volume fraction, and the continuum percolation of soft particles representing compliant interfaces and discrete pores. In the final aspect, a literature review is also provided on modeling of transport properties on the forefront of the effective diffusion and anomalous diffusion in multiphase granular materials. Finally, some conclusions and perspectives for future studies are provided.

It is shown that a fractional oscillator (FO) noise, which is a generalization of the ordinary overdamped linear oscillator driven by the white noise may be ‘applied to diverse systems; its stationary correlation function presents

power-law-like function, exponential-like function, exponential function, and oscillatory decays. The model may be employed to describe the fluctuation of the distance between a fluorescein–tyrosine pair within a single protein complex and the internal dynamics of a lysozyme molecule in solution. It also has the possibility of describing a Brownian particle in an oscillatory viscoelastic shear flow.

We describe the transport of a finite chain of $N$ identical particles in a thermal bath, through thin channels that forbid any crossing with a conceptually and technically simple method, that is neither restricted to the thermodynamic limit (infinite systems with finite density) nor to overdamped systems. We obtain analytically the mean squared displacement of each particle. Regardless of the damping, we identify a correlated regime for which chain transport is dominated by the correlations between individual particles. At large damping, the mean squared displacement evidences the typical single file behavior, with a time dependence that scales as $t^{1/2}$. At small damping, the correlated regime is rather described by a diffusion-like behavior, with a diffusivity which is neither the individual particle diffusivity nor the Fickian diffusivity of the chain as a whole. We emphasize that, for a chain with free ends, the fluctuations of the chain ends are larger by a factor two than the fluctuations of its center. This effect is observed whatever the damping $\gamma$, but the duration of this fluctuations enhancement is found to scale as $N$ for low damping and as $N^2\gamma$ for high damping. We discuss the relevance of this model to the transport of actual systems in confined geometries.

Based on the experimental measurement results of fluid particle transverse accelerations in fully developed pipe turbulence published in Nature (2001) by La Porta et al, the present authors recently develop a multiscale statistical model which considers both normal diffusion in molecular scale and anomalous diffusion in vortex scale. This model gives rise to a new probability density function, called Power-Stretched Gaussian Distribution model (PSGD). In this study, we make a further comparison of this statistical distribution model with the well-known Lévy distribution, Tsallis distribution and stretched-exponential distribution. Our model is found to have the following merits: 1) fewer parameters, 2) better fitting with experimental data, 3) more explicit physical interpretation.

We report, in this paper, a recent study on the dynamical mechanism of Brownian particles diffusing in the fractional damping environment, where several important quantities such as the mean square displacement (MSD) and mean square velocity are calculated for dynamical analysis. A particular type of backward motion is found in the diffusion process. The reason of it is analyzed intrinsically by comparing with the diffusion in various dissipative environments. Results show that the diffusion in the fractional damping environment obeys the Langevin dynamics which is quite different form what is expected.

In the anomalous diffusions, the transition phenomena from superdiffusion (or subdiffusion) to normal diffusion have been found in several experiments and studied by stochastic models. In this study, we found the diffusion transition which occurs twice in a stochastic process, first from superdiffusion to subdiffusion, and then from subdiffusion to normal diffusion by using the nonstationary Markovian replication process with the memory of the previous step exponentially decaying with time. In the early stage, when the walker strongly follows the previous step, superdiffusive behaviors occur, while in the intermediate stage in which the memory effect decays exponentially, the motion of the walker shows subdiffusive behaviors. Eventually, as the memory effect almost disappears, the motion reduces to normal diffusion. We also found that the Hurst exponent in the intermediate subdiffusive region becomes smaller when the change of the memory effect is more abrupt.

Variable-order fractional diffusion equation model is a recently developed and promising approach to characterize time-dependent or concentration-dependent anomalous diffusion, or diffusion process in inhomogeneous porous media. To further study the properties of variable-order time fractional subdiffusion equation models, the efficient numerical schemes are urgently needed. This paper investigates numerical schemes for variable-order time fractional diffusion equations in a finite domain. Three finite difference schemes including the explicit scheme, the implicit scheme and the Crank–Nicholson scheme are studied. Stability conditions for these three schemes are provided and proved via the Fourier method, rigorous convergence analysis is also performed. Two numerical examples are offered to verify the theoretical analysis of the above three schemes and illustrate the effectiveness of suggested schemes. The numerical results illustrate that, the implicit scheme and the Crank–Nicholson scheme can achieve high accuracy compared with the explicit scheme, and the Crank–Nicholson scheme claims highest accuracy in most situations. Moreover, some properties of variable-order time fractional diffusion equation model are also shown by numerical simulations.

In this article, we have applied the Weyl differential operator in an epidemic model with the standard incidence rate to study pattern formation among species with superdiffusive movement in space. A thorough linear stability analysis predicts the various Turing pattern regions. Further, the analysis shows the relationship between the wavenumber of the Turing pattern and the superdiffusive exponent, which are supported by numerical results. A Fourier spectral method in space and a fourth-order exponential time differentiating Runge–Kutta method are used for numerical simulation. Simulations are done for the Turing pattern regions for 2D and 3D problems, showing the only quantitative change in patterns for varying superdiffusive exponents.

During the inflationary regime, the expansion of the Universe is driven by a scalar field ϕ(t) which may be in thermal contact with the radiation fluid. In this work, we study the influence of the thermal bath assuming that it is responsible for the stochastic evolution of the inflaton field. Assuming that the fluctuation dynamics is described by a Langevin-type equation of motion, a large set of analytical solutions including white and colored noises are derived. It is found that even in the case of white noise the field experience an anomalous diffusion. Such results may be important for studying thermally induced initial density perturbations in inflationary cosmologies, mainly in the framework of warm inflation.