Fractal dimension of transport coefficients in a deterministic dynamical system

In many low-dimensional dynamical systems transport coefficients are very irregular, perhaps even fractal functions of control parameters. To analyse this phenomenon we study a dynamical system defined by a piece-wise linear map and investigate the dependence of transport coefficients on the slope of the map. We present analytical arguments, supported by numerical calculations, showing that both the Minkowski-Bouligand and Hausdorff fractal dimension of the graphs of these functions is 1 with a logarithmic correction, and find that the exponent $\gamma$ controlling this correction is bounded from above by 1 or 2, depending on some detailed properties of the system. Using numerical techniques we show local self-similarity of the graphs. The local self-similarity scaling transformations turn out to depend (irregularly) on the values of the system control parameters.Comment: 17 pages, 6 figures; ver.2: 18 pages, 7 figures (added section 5.2, corrected typos, etc.

Random walk approach to the d-dimensional disordered Lorentz gas

A correlated random walk approach to diffusion is applied to the disordered nonoverlapping Lorentz gas. By invoking the Lu-Torquato theory for chord-length distributions in random media [J. Chem. Phys. 98, 6472 (1993)], an analytic expression for the diffusion constant in arbitrary number of dimensions d is obtained. The result corresponds to an Enskog-like correction to the Boltzmann prediction, being exact in the dilute limit, and better or nearly exact in comparison to renormalized kinetic theory predictions for all allowed densities in d=2,3. Extensive numerical simulations were also performed to elucidate the role of the approximations involved.Comment: 5 pages, 5 figure

Anomalous Processes with General Waiting Times: Functionals and Multipoint Structure

Many transport processes in nature exhibit anomalous diffusive properties with non-trivial scaling of the mean square displacement, e.g., diffusion of cells or of biomolecules inside the cell nucleus, where typically a crossover between different scaling regimes appears over time. Here, we investigate a class of anomalous diffusion processes that is able to capture such complex dynamics by virtue of a general waiting time distribution. We obtain a complete characterization of such generalized anomalous processes, including their functionals and multi-point structure, using a representation in terms of a normal diffusive process plus a stochastic time change. In particular, we derive analytical closed form expressions for the two-point correlation functions, which can be readily compared with experimental data.Comment: Accepted in Phys. Rev. Let

Метод экспертных оценок в лингводидактике

Рассматривается использование метода экспертных оценок как в общей системе научно-педагогической экспертной деятельности, так и в рамках ее лингводидактического аспекта. Дается характеристика процедуры проведения экспертизы, а также оценивается перспективность обращения к интеллектуальным компьютерным системам как инструментам экспертного анализа

Asymptotic solutions of decoupled continuous-time random walks with superheavy-tailed waiting time and heavy-tailed jump length distributions

We study the long-time behavior of decoupled continuous-time random walks characterized by superheavy-tailed distributions of waiting times and symmetric heavy-tailed distributions of jump lengths. Our main quantity of interest is the limiting probability density of the position of the walker multiplied by a scaling function of time. We show that the probability density of the scaled walker position converges in the long-time limit to a non-degenerate one only if the scaling function behaves in a certain way. This function as well as the limiting probability density are determined in explicit form. Also, we express the limiting probability density which has heavy tails in terms of the Fox $H$-function and find its behavior for small and large distances.Comment: 16 pages, 1 figur

Stationary states for underdamped anharmonic oscillators driven by Cauchy noise

Using methods of stochastic dynamics, we have studied stationary states in the underdamped anharmonic stochastic oscillators driven by Cauchy noise. Shape of stationary states depend both on the potential type and the damping. If the damping is strong enough, for potential wells which in the overdamped regime produce multimodal stationary states, stationary states in the underdamped regime can be multimodal with the same number of modes like in the overdamped regime. For the parabolic potential, the stationary density is always unimodal and it is given by the two dimensional $\alpha$-stable density. For the mixture of quartic and parabolic single-well potentials the stationary density can be bimodal. Nevertheless, the parabolic addition, which is strong enough, can destroy bimodlity of the stationary state.Comment: 9 page

Escape Behavior of Quantum Two-Particle Systems with Coulomb Interactions

Quantum escapes of two particles with Coulomb interactions from a confined one-dimensional region to a semi-infinite lead are discussed by the probability of particles remaining in the confined region, i.e. the survival probability, in comparison with one or two free particles. For free-particle systems the survival probability decays asymptotically in power as a function of time. On the other hand, for two-particle systems with Coulomb interactions it shows an exponential decay in time. A difference of escape behaviors between Bosons and Fermions is considered as quantum effects of identical two particles such as the Pauli exclusion principle. The exponential decay in the survival probability of interacting two particles is also discussed in a viewpoint of quantum chaos based on a distribution of energy level spacings.Comment: 10 pages, 7 figure

Temporal variation of cephalopods in the diet of Cape fur seals in Namibia

Cape fur seal (Arctocephalus pusillus pusillus) scats were sampled over a period of eight years (1994-2001) at Atlas and Wolf Bay seal colonies in order to assess the cephalopod component of the diet of these seals and cephalopod diversity off the coast of Namibia. The temporal variation within the cephalopod component was investigated. A low diversity of cephalopods, only six species, are preyed upon, with Todarodes angolensis being the most important component both in numbers and wet weight in all years. Its lowered weight contribution during winter coincided with a greater diversity of other cephalopod species in the diet, which showed higher proportional weight contribution relative to Todarodes angolensis. Scat sampling was found to be an unreliable method of providing estimates of total prey weight consumption by seals, but was considered an acceptable method for proportional comparisons, especially given the ease of scat collection over extended periods