Low-rank solution of an optimal control problem constrained by random Navier-Stokes equations

We develop a low-rank tensor decomposition algorithm for the numerical solution of a distributed optimal control problem constrained by two-dimensional time-dependent Navier-Stokes equations with a stochastic inflow. The goal of optimization is to minimize the flow vorticity. The inflow boundary condition is assumed to be an infinite-dimensional random field, which is parametrized using a finite- (but high-) dimensional Fourier expansion and discretized using the stochastic Galerkin finite element method. This leads to a prohibitively large number of degrees of freedom in the discrete solution. Moreover, the optimality conditions in a time-dependent problem require solving a coupled saddle-point system of nonlinear equations on all time steps at once. For the resulting discrete problem, we approximate the solution by the tensor-train (TT) decomposition and propose a numerically efficient algorithm to solve the optimality equations directly in the TT representation. This algorithm is based on the alternating linear scheme (ALS), but in contrast to the basic ALS method, the new algorithm exploits and preserves the block structure of the optimality equations. We prove that this structure preservation renders the proposed block ALS method well posed, in the sense that each step requires the solution of a nonsingular reduced linear system, which might not be the case for the basic ALS. Finally, we present numerical experiments based on two benchmark problems of simulation of a flow around a von Kármán vortex and a backward step, each of which has uncertain inflow. The experiments demonstrate a significant complexity reduction achieved using the TT representation and the block ALS algorithm. Specifically, we observe that the high-dimensional stochastic time-dependent problem can be solved with the asymptotic complexity of the corresponding deterministic problem.     

Coulomb Explosion of the Debye Layer As a Mechanism for the Formation of a High-Energy Ion Flow in the Plasma of a Micropinch Discharge

Technical Physics - Flows of ions with energies on the order of megaelectronvolts, which propagate both in the axial direction and in the direction perpendicular to the symmetry axis of the...     

Justification of the Kirchhoff hypotheses and error estimation for two-dimensional models of anisotropic and inhomogeneous plates, including laminated plates

Asymptotic analysis of the problem describing deformation ofa thin cylindrical plate with clamped lateral side is performed.The problem is considered under the most general statement withthe plate being laminated and consisting of an arbitrary numberof nonhomogeneous and anisotropic (21 elastic moduli) layers.Explicit integral representations of the differential operatorswhich form the two-dimensional model of the plate are derived.In the case when the elastic moduli of each of the layers areconstant, these integral representations turn into algebraicones. The asymptotic procedure is justified with the help ofa weighted inequality of Korn's type. The error estimates obtainedgive a rigorous mathematical proof of both of Kirchhoff's hypotheses(kinematic and static) and shed light on the well-known intrinsicinconsistency of two of the hypotheses.     

Charmed penguin versus BAU

Since the Standard Model most probably cannot explain the large value of CP asymmetries recently observed in D-meson decays we propose the fourth quark-lepton generation explanation of it. As a byproduct weakly mixed leptons of the fourth generation make it possible to save the baryon number of the Universe from erasure by sphalerons. An impact of the 4th generation on BBN is briefly discussed.     

Kinetics of surface monatomic layer deposition

The filling of a surface layer with atoms incident from the outside has been studied in the framework of a one-dimensional model. Macroscopic dynamic equilibrium is regarded as the result of microscopic equilibrium between possible atomic configurations in the presence of particle flux to the surface, the evaporation of these particles, and their mutual influence. The dependences of the degree of surface coverage on the external action intensity, features of atom-substrate interaction and interaction between atoms are found. The conditions for the formation of a rarified layer, its complete filling, clot formation, and regular distribution were determined.     

Anomalous vibrational states of a monatomic surface film

Vibrational states of a one-dimentional chain of atoms which models peculiarities of a monatomic surface film are considered. A set of nontrivial equilibrium states of the system is determined in whose vicinity almost linear band vibrations are possible. Peculiarities of anomalous branches of vibrational states are discussed. It is shown that the low-frequency gap of vibrational states disappears under certain conditions. This determines the possibility of appearance of low-frequency sound vibrations which are not possible for a trivial equilibrium distribution of atoms in the film.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika No. 7, pp. 22–25, July, 1982.     

Trapped-hole centers in MgO single crystals

The properties of the majority trapped-hole centers in MgO, such as g-factors, positions of absorption and luminescence bands, and temperatures of thermal destruction, have been analyzed with the emphasis on the observed regular trends and interrelations between the properties of these centers. Particular emphasis has been placed on the positively charged [Be]⁺ and [Ca]⁺ trapped-hole centers, which have a large cross section for recombination with conduction electrons. In these centers, a hole is localized at an oxygen ion near the impurity Be²⁺ or Ca²⁺ ion located at a regular cation site. The generation and transformation of defects due to the recombination of either relaxed conduction electrons with OH⁻-containing hole centers or cold and hot electrons with [Be]⁺ and [Ca]⁺ centers have been considered. Using the interrelation of the characteristics of hole centers and taking into account that the recombination emission band revealed at ∼6.8 eV is due to the Ca²⁺-containing centers that are stable below 50 K, the prospects for the EPR detection of the [Ca]⁺ center at T < 4.2 K have been discussed.     

Explosive phenomena in modified gravity

Observational manifestations of some models of modified gravity, which have been suggested to explain the accelerated cosmological expansion, are analyzed for gravitating systems with time dependent mass density. It is shown that if the mass density rises with time, the system evolves to the singular state with infinite curvature scalar. The corresponding characteristic time is typically much shorter than the cosmological time.     

Effect of spontaneous fission models on the production of cosmochronometer nuclei in the r-process

The dependence of the yields of cosmochronometer nuclei on the spontaneous fission model has been considered. It has been shown that the spontaneous fission rates estimated within a phenomenological model constructed on the basis of the calculations of the spontaneous fission rates for superheavy nuclei within the macroscopic-microscopic model are in good agreement with the observations.