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## Diffusion of charged particles in a stochastic force-free magnetic field

We study diffusion of charged particles in stationary stochastic magnetic field ${\bf B}$ with zero mean, $ \mean{\bf B} = 0 $. In the case when electric current is carried by electrons, the field is force-free, $\mathrm{curl} \,{\bf B} = \alpha{\bf B} $, where $\alpha({\bf r})$ is an arbitrary scalar function. In a small region where the function $\alpha $ and the field magnitude $|{\bf B}|$ are approximately constant, the equations of motion of charged particles are integrated and reduced to the equation of mathematical pendulum. The transition from trapped to untrapped particles is continuously traced. Averaging over the magnetic field spectrum gives the spatial diffusion coefficient $D$ of particles as a function of the Larmor radius $r_L$ in the large-scale magnetic fields ($B_{LS}$) and magnetic field correlation length $L_0$. The diffusion coefficient turns out to be proportional to the Larmor radius, $D\propto r_L $, for $r_L <L_0 / 2\pi $, and to the Larmor radius squared, $ D \propto r_L^2 $, for $ r_L> L_0 /2\pi $. We apply obtained results to the diffusion of cosmic rays in the Galaxy, which contains a large number of independent regions with parameters $L_0$ and $B_{LS}$ varying in wide range.

We average over $B_{LS}$ with the Kolmogorov spectrum

and over $L_0$ with the distribution function $f(L_0)\propto L_0^{- 1+ \sigma}$. For

the practically flat spectrum $\sigma = 1/15$, we have $ D\propto r_m^{0.7}$, which is consistent with observations.

In this paper the numerical simulation of surfactant dynamics in the topographically trapped long waves over a cylindrical shelf is described. Numerical modeling is based on the balance equation of the surface concentration. The dynamics of impurities was considered in the advection - diffusion - relaxation model. The comparison of different models of the shelf: endless slope, shelf - step concave exponential shelf has been made. It was established that the transverse bottom topography does not signifi cantly affect the geometry of the distribution of the pellicle, but it has an impact on the quantitative parameters of concentration. The infl uence of the number of mode on the concentration level for various models of the shelf was studied. The growth of the modes number increases the derivative concentration extremes from the equilibrium level.

A semiphenomenological model of the transport processes under the action of power energy sources is proposed. To explain the observed deviations of the linear system response to an external perturbation in the transport processes induced by intense energy fluxes, it is proposed to take into account the effect of inertia of the medium. The semiphenomenological model of processes is reduced to a system with two basis states. The techniques of the theory of microscopic objects for the solution of the system are applied. It is shown that the inertia of the medium is due to the finite time of establishing the equilibrium between the basis states.

This classic survey considers passive scalar and vector transport processes in a random nonstationary medium, which are described by linear parabolic equations. Integration over random paths is used, along with the asymptotic behavior of the product of a large number of independent identically distributed random matrices. The most interesting effect is the appearance of concentrated structures (intermittency) of a smooth initial distribution of the transported quantity. The occurrence of intermittent distributions in the linear problem is due to the fact that the coefficients of the transport equation are stochastic. The intermittency shows itself in the rates of exponential growth of the successive moments (Lyapunov exponents) as the moment number increases. Moment equations are obtained for the scalar and vector, and are used to study temperature evolution and magnetic-field generation in a random fluid flow. These equations are differential in a medium with short time correlations and integral in the general case. The range of application of the diffusion description is analyzed. The behavior of the diffusion coefficients in the case of time reversal is examined. The properties of an individual realization of a scalar and vector are also explained, and a dynamo theorem is given on the exponential growth of the magnetic field in a random flow with renewal.

In this study we investigate the successive approximation procedure allowed us to derive new equation, valid for the transport of dissolved matter in porous media, or in random force fields, on the macroscopic scale. To do this the diagram technique was exploited.

Cooling of tokamak boundary plasma owing to radiation of non-fully stripped lithium ions is considered as a promising way for protection of plasma facing elements (PFE) in tokamak. It may be effectively realized when the main part of lithium ions are involved in the closed circuit of migration between plasma and PFE surface. Such an approach may be implemented with the use of lithium device whose hot (500-600 °C) area to be effected by plasma serves as a Li-emitter and the cold part (∼180 °C) as a Li-collector in the shadow. Capillary-pore system (CPS) provides the returning of collected and condensed lithium to emitting zone by capillary forces. The main goals of the last T-11M lithium experiments were investigating Li ions transport in the tokamak scrape of layer (SOL) and their collecting by different kinds of limiters. The design of devices based on lithium CPS with different ratio of emitting/collecting area is the main subject of this paper. © 2015 The Authors.

The dynamics of a two-component Davydov-Scott (DS) soliton with a small mismatch of the initial location or velocity of the high-frequency (HF) component was investigated within the framework of the Zakharov-type system of two coupled equations for the HF and low-frequency (LF) fields. In this system, the HF field is described by the linear Schrödinger equation with the potential generated by the LF component varying in time and space. The LF component in this system is described by the Korteweg-de Vries equation with a term of quadratic influence of the HF field on the LF field. The frequency of the DS soliton`s component oscillation was found analytically using the balance equation. The perturbed DS soliton was shown to be stable. The analytical results were confirmed by numerical simulations.

Radiation conditions are described for various space regions, radiation-induced effects in spacecraft materials and equipment components are considered and information on theoretical, computational, and experimental methods for studying radiation effects are presented. The peculiarities of radiation effects on nanostructures and some problems related to modeling and radiation testing of such structures are considered.

This volume presents new results in the study and optimization of information transmission models in telecommunication networks using different approaches, mainly based on theiries of queueing systems and queueing networks .

The paper provides a number of proposed draft operational guidelines for technology measurement and includes a number of tentative technology definitions to be used for statistical purposes, principles for identification and classification of potentially growing technology areas, suggestions on the survey strategies and indicators. These are the key components of an internationally harmonized framework for collecting and interpreting technology data that would need to be further developed through a broader consultation process. A summary of definitions of technology already available in OECD manuals and the stocktaking results are provided in the Annex section.