Anomalous Diffusion in Velocity Space

The problem of anomalous diffusion in the momentum space is considered on the basis of the appropriate probability transition function (PTF). New general equation for description of the diffusion of heavy particles in the gas of the light particles is formulated on basis of the new approach similar to one in coordinate space (S. Trigger et al.). The obtained results permit to describe the various situations when the probability transition function (PTF) has a long tail in the momentum space. The effective friction and diffusion coefficients are found.Comment: 11 pages, no figures and table

Relaxation Properties of Small-World Networks

Recently, Watts and Strogatz introduced the so-called small-world networks in order to describe systems which combine simultaneously properties of regular and of random lattices. In this work we study diffusion processes defined on such structures by considering explicitly the probability for a random walker to be present at the origin. The results are intermediate between the corresponding ones for fractals and for Cayley trees.Comment: 16 pages, 6 figure

Five-loop renormalization-group expansions for the three-dimensional n-vector cubic model and critical exponents for impure Ising systems

The renormalization-group (RG) functions for the three-dimensional n-vector cubic model are calculated in the five-loop approximation. High-precision numerical estimates for the asymptotic critical exponents of the three-dimensional impure Ising systems are extracted from the five-loop RG series by means of the Pade-Borel-Leroy resummation under n = 0. These exponents are found to be: \gamma = 1.325 +/- 0.003, \eta = 0.025 +/- 0.01, \nu = 0.671 +/- 0.005, \alpha = - 0.0125 +/- 0.008, \beta = 0.344 +/- 0.006. For the correction-to-scaling exponent, the less accurate estimate \omega = 0.32 +/- 0.06 is obtained.Comment: 11 pages, LaTeX, no figures, published versio

Velocity-Dependent Friction and Diffusion for Grains in Neutral Gases, Dusty Plasmas and Active Systems

A self-consistent and universal description of friction and diffusion for Brownian particles (grains) in different systems, as a gas with Boltzmann collisions, dusty plasma with ion absorption by grains, and for active particles (e.g., cells in biological systems) is suggested on the basis of the appropriate Fokker-Planck equation. Restrictions for application of the Fokker-Planck equation to the problem of velocity-dependent friction and diffusion coefficients are found. General description for this coefficient is formulated on the basis of master equation. Relation of the diffusion coefficient in the coordinate and velocity spaces is found for active (capable to transfer momentum to the ambient media) and passive particles in the framework of the Fokker-Planck equation. The problem of anomalous space diffusion is formulated on the basis of the appropriate probability transition (PT) function. The method of partial differentiation is avoided to construct the correct probability distributions for arbitrary distances, what is important for applications to different stochastic problems. Generale equation for time-dependent PT function is formulated and discussed. Generalized friction in the velocity space is determined and applied to describe the friction force itself as well as the drag force in the case of a non-zero driven ion velocity in plasmas. The negative friction due to ion scattering on grains exists and can be realized for the appropriate experimental conditions.Comment: 21 page

Five-loop \sqrt\epsilon-expansions for random Ising model and marginal spin dimensionality for cubic systems

The \sqrt\epsilon-expansions for critical exponents of the weakly-disordered Ising model are calculated up to the five-loop order and found to possess coefficients with irregular signs and values. The estimate n_c = 2.855 for the marginal spin dimensionality of the cubic model is obtained by the Pade-Borel resummation of corresponding five-loop \epsilon-expansion.Comment: 9 pages, TeX, no figure

К вопросу о биотерроризме и биобезопасности

The article offers a brief discussion of biosecurity and bioterrorism policy issues that are directly connected with genetics value determinants, responsibility and outlook of scientist engaged in biotechnology and nanotechnology and also with the problems of nanostructures used when creating genetically modified organisms and products.В статье предлагается рассмотреть вопросы биобезопасности и биотерроризма, что непосредственно связано с ценностными детерминантами генетики, мировоззрением и ответственностью ученого, занимающегося биотехнологиями, нанотехнологиями, а также вопросами применения наноструктур при создании генетически модифицированных организмов и продуктов

Chiral phase transitions: focus driven critical behavior in systems with planar and vector ordering

The fixed point that governs the critical behavior of magnets described by the $N$-vector chiral model under the physical values of $N$ ($N =2, 3$) is shown to be a stable focus both in two and three dimensions. Robust evidence in favor of this conclusion is obtained within the five-loop and six-loop renormalization-group analysis in fixed dimension. The spiral-like approach of the chiral fixed point results in unusual crossover and near-critical regimes that may imitate varying critical exponents seen in physical and computer experiments.Comment: 4 pages, 5 figures. Discussion enlarge

Carbon Nanomaterial Produced by Microwave Exfoliation of Graphite Oxide

Carbon-based graphene-like material was obtained through microwave stimulated exfoliation of graph-ite oxide (GO). Properties of this material were investigated by multiple techniques including element analysis, X-ray photoelectron spectroscopy (XPS), mass-spectroscopy, infrared (IR) and Raman spectrosco-py, scanning electron microscopy (SEM) and broadband dielectric spectroscopy. Specific surface area and volume of microwave exfoliated graphite oxide (MEGO) reached 600 m2/g and 6 cm3/g, respectively. It is shown that during such explosive reduction process the sample emits CO2, CO and H2O and, in some cases, SO2 gases. The resulting reduced material exhibits IR spectra similar to that of graphite and a dc-conductivity of 0.12 S/cm. It is also shown that prolonged storage in ambient conditions leads to elevated oxygen content and decrease of specific surface area of the samples. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/3511

Configuration Of Grafted Polystyrene Chains In The Melt: Temperature And Concentration Dependence

The concentration profiles of carboxy-terminated polystyrene chains in the melt grafted onto oxide-covered silicon substrates were measured using secondary-ion mass spectroscopy. The grafting density increased with temperature and an enthalpy of +7.4 kcal/mole was deduced for the grafting reaction, SiOH + R(COOH) ⇄ R(COOSi) + H2O. Relatively high grafting densities (σ∼6.6·mg/m2) were achieved with minimal chain distortion or displacement of long chains by shorter ones. Significant stretching of the grafted chains occurred for σ > 10 mg/m2. An equilibrium constant for the grafting reaction incorporating entropy is discussed.69577677