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## Universality in statistics of Stokes flow over a no-slip wall with random roughness

Stochastic roughness is a widespread feature of natural surfaces and is an inherent byproduct of most fabrication techniques. In view of the rapid development of microfluidics, the important question is how this inevitable problem affects the low-Reynolds-number flows that are common for micro-devices. Moreover, one could potentially turn the flaw into a virtue and control the flow properties by means of specially ‘tuned’ random roughness. In this paper we investigate theoretically the statistics of fluctuations in fluid velocity produced by the waviness irregularities at the surface of a no-slip wall. Particular emphasis is laid on the issue of the universality of our findings.

The ability of phase mixing to provide eﬃcient damping of Alfvén waves even in weakly dissipative plasmas made it a popular mechanismforexplainingthesolarcoronalheating.Initiallyitwasstudiedintheequilibriumconﬁgurationswiththestraightmagnetic ﬁeldlinesandtheAlfvénspeedonlyvaryinginthedirectionperpendiculartothemagneticﬁeld.LatertheanalysisoftheAlfvénwave phase mixing was extended in various directions. In particular it was studied in two-dimensional planar magnetic plasma equilibria. Analytical investigation was carried out under the assumption that the wavelength is much smaller than the characteristic scale of the background quantity variation. This assumption enabled using the Wentzel, Kramers, and Brillouin (WKB) method. When it is not satisﬁed the study was only carried out numerically. In general, even the wave propagation in a one-dimensional inhomogeneous equilibrium can be only studied numerically. However there is one important exception, so-called non-reﬂective equilibria. In these equilibria the wave equation with the variable phase speed reduces to the Klein-Gordon equation with constant coeﬃcients. In this paper we apply the theory of non-reﬂective wave propagation to studying the Alfvén wave phase mixing in two-dimensional planar magnetic plasma equilibria. Using curvilinear coordinates we reduce the equation describing the Alfvén wave phase mixing to the equationthatbecomesaone-dimensionalwaveequationintheabsenceofdissipation.Thisequationisfurtherreducedtotheequation which is the one-dimensional Klein-Gordon equation in the absence of dissipation. Then we show that this equation has constant coeﬃcients when a particular relation between the plasma density and magnetic ﬁeld magnitude is satisﬁed. Using the derived Klein- Gordon-type equation we study the phase mixing in various non-reﬂective equilibria. We emphasise that our analysis is valid even when the wavelength is comparable with the characteristic scale of the background quantity variation. In particular, we study the Alfvén wave damping due to phase mixing in an equilibrium with constant plasma density and exponentially divergent magnetic ﬁeld lines. We conﬁrm the result previously obtained in the WKB approximation that there is enhanced Alfvén wave damping in this equilibrium with the damping length proportional to ln(Re), where Re is the Reynolds number. Our theoretical results are applied to heating of coronal plumes. We show that, in spite of enhanced damping, Alfvén waves with periods of the order of one minute can be eﬃciently damped in the lower corona, at the height about 200 Mm, only if the shear viscosity is increased by about 6 orders of magnitude in comparison with its value given by the classical plasma theory. We believe that such increase of the shear viscosity can be provided by the turbulence.

We simulate the oscillation of the viscous drop in the viscous liquid. We combine methods of chromodynamics model and Shan-Chen pseudo-potential for the immiscible fluids. We measure the frequency of the first nontrivial eigenmode using the initial ellipsoid form of the drop. Drop oscillates about the equilibrium spherical form of radius $R$. Computed frequency as a function of the radius $R$ follows to the well known Rayleigh formula. We discuss the simulation setup in the framework of the Lattice Boltzmann method.

This paper aims to resolve the problem of formation of young objects observed in the RCW 82 H II region. In the framework of a classical trigger model the estimated time of fragmentation is larger than the estimated age of the H II region. Thus the young objects could not have formed during the dynamical evolution of the H II region. We propose a new model that helps resolve this problem. This model suggests that the H II region RCW 82 is embedded in a cloud of limited size that is denser than the surrounding interstellar medium. According to this model, when the ionization-shock front leaves the cloud it causes the formation of an accelerating dense gas shell. In the accelerated shell, the effects of the Rayleigh-Taylor (R-T) instability dominate and the characteristic time of the growth of perturbations with the observed magnitude of about 3 pc is 0.14 Myr, which is less than the estimated age of the H II region. The total time t ∑, which is the sum of the expansion time of the H II region to the edge of the cloud, the time of the R-T instability growth, and the free fall time, is estimated as 0.44 < t ∑ < 0.78 Myr. We conclude that the young objects in the H II region RCW 82 could be formed as a result of the R-T instability with subsequent fragmentation into large-scale condensations.

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.