Existence and homogenization of the Rayleigh-B\'enard problem

The Navier-Stokes equation driven by heat conduction is studied. As a prototype we consider Rayleigh-B\'enard convection, in the Boussinesq approximation. Under a large aspect ratio assumption, which is the case in Rayleigh-B\'enard experiments with Prandtl number close to one, we prove the existence of a global strong solution to the 3D Navier-Stokes equation coupled with a heat equation, and the existence of a maximal B-attractor. A rigorous two-scale limit is obtained by homogenization theory. The mean velocity field is obtained by averaging the two-scale limit over the unit torus in the local variable

Flying mirror model for interaction of a super-intense nonadiabatic laser pulse with a thin plasma layer: Dynamics of electrons in a linearly polarized external field

Interaction of a high-power laser pulse having a sharp front with a thin plasma layer is considered. General one-dimensional numerical-analytical model is elaborated, in which the plasma layer is represented as a large collection of electron sheets, and a radiation reaction force is derived analytically. Using this model, trajectories of the electrons of the plasma layer are calculated numerically and compared with the electron trajectories obtained in particle-in-cell simulations, and a good agreement is found. Two simplified analytical models are considered, in which only one electron sheet is used, and it moves transversely and longitudinally in the fields of an ion sheet and a laser pulse (longitudinal displacements along the laser beam axis can be considerably larger than the laser wavelength). In the model I, a radiation reaction is included self-consistently, while in the model II a radiation reaction force is omitted. For the two models, analytical solutions for the dynamical parameters of the electron sheet in a linearly polarized laser pulse are derived and compared with the numerical solutions for the central electron sheet (positioned initially in the center) of the real plasma layer, which are calculated from the general numerical-analytical model. This comparison shows that the model II gives better description for the trajectory of the central electron sheet of the real plasma layer, while the model I gives more adequate description for a transverse momentum. Both models show that if the intensity of the laser pulse is high enough, even in the field with a constant amplitude, the electrons undergo not only the transverse oscillations with the period of the laser field, but also large (in comparison with the laser wavelength) longitudinal oscillations with the period, defined by the system parameters and initial conditions of particular oscillation.open282

Flying mirror model for interaction of a super-intense laser pulse with a thin plasma layer: Transparency and shaping of linearly polarized laser pulses

A self-consistent one-dimensional (1D) flying mirror model is developed for description of an interaction of an ultra-intense laser pulse with a thin plasma layer (foil). In this model, electrons of the foil can have large longitudinal displacements and relativistic longitudinal momenta. An approximate analytical solution for a transmitted field is derived. Transmittance of the foil shows not only a nonlinear dependence on the amplitude of the incident laser pulse, but also time dependence and shape dependence in the high-transparency regime. The results are compared with particle-in-cell (PIC) simulations and a good agreement is ascertained. Shaping of incident laser pulses using the flying mirror model is also considered. It can be used either for removing a prepulse or for reducing the length of a short laser pulse. The parameters of the system for effective shaping are specified. Predictions of the flying mirror model for shaping are compared with the 1D PIC simulations, showing good agreement.open

Comment: Superconducting transition in Nb nanowires fabricated using focused ion beam

In a recent paper Tettamanzi et al (2009 Nanotechnology \bf{20} 465302) describe the fabrication of superconducting Nb nanowires using a focused ion beam. They interpret their conductivity data in the framework of thermal and quantum phase slips below $T_c$. In the following we will argue that their analysis is inappropriate and incomplete, leading to contradictory results. Instead, we propose an interpretation of the data within a SN proximity model.Comment: 3 pages, 1 figure accepted in Nanotechnolog

Efficient hydrophosphorylation of activated alkenes under phosphine catalysis

© 2016 Taylor & Francis Group, LLC.Conjugate addition of diisobutyl phosphite to activated alkenes under PBu3 catalysis affords corresponding phosphonates in high yields within short reaction times

Adhesive coatings based on aligned arrays of carbon nanostructures

This work was financially supported by Russian Foundation for Basic Research (projects 16-29-14023 and 18-32-00652) and Internal grant of the Southern Federal University (project VnGr-07/2017-26)

Asymptotics of Eigenvalues and Eigenfunctions for the Laplace Operator in a Domain with Oscillating Boundary. Multiple Eigenvalue Case

We study the asymptotic behavior of the solutions of a spectral problem for the Laplacian in a domain with rapidly oscillating boundary. We consider the case where the eigenvalue of the limit problem is multiple. We construct the leading terms of the asymptotic expansions for the eigenelements and verify the asymptotics

Vibrational instability, two-level systems and Boson peak in glasses

We show that the same physical mechanism is fundamental for two seemingly different phenomena such as the formation of two-level systems in glasses and the Boson peak in the reduced density of low-frequency vibrational states g(w)/w^2. This mechanism is the vibrational instability of weakly interacting harmonic modes. Below some frequency w_c << w_0 (where w_0 is of the order of Debye frequency) the instability, controlled by the anharmonicity, creates a new stable universal spectrum of harmonic vibrations with a Boson peak feature as well as double-well potentials with a wide distribution of barrier heights. Both are determined by the strength of the interaction I ~ w_c between the oscillators. Our theory predicts in a natural way a small value for the important dimensionless parameter C ~ 10^{-4} for two-level systems in glasses. We show that C ~ I^{-3} and decreases with increasing of the interaction strength I. We show that the number of active two-level systems is very small, less than one per ten million of oscillators, in a good agreement with experiment. Within the unified approach developed in the present paper the density of the tunneling states and the density of vibrational states at the Boson peak frequency are interrelated.Comment: 28 pages, 3 figure

Study of the dependence of Young's modulus of vertically aligned carbon nanotubes on their aspect ratio

The reported study was funded by RFBR according to the research projects No.16-29-14023 ofi_m, No.18-32-00652 and by grant of the Southern Federal University (project No. VnGr-07/2017-26)

Some generic aspects of bosonic excitations in disordered systems

We consider non-interacting bosonic excitations in disordered systems, emphasising generic features of quadratic Hamiltonians in the absence of Goldstone modes. We discuss relationships between such Hamiltonians and the symmetry classes established for fermionic systems. We examine the density \rho(\omega) of excitation frequencies \omega, showing how the universal behavior \rho(\omega) ~ \omega^4 for small \omega can be obtained both from general arguments and by detailed calculations for one-dimensional models