New classes of exact solutions of three-dimensional Navier-Stokes equations

New classes of exact solutions of the three-dimensional unsteady Navier-Stokes equations containing arbitrary functions and parameters are described. Various periodic and other solutions, which are expressed through elementary functions are obtained. The general physical interpretation and classification of solutions is given.Comment: 11 page

Self-gravitating spheres of anisotropic fluid in geodesic flow

The fluid models mentioned in the title are classified. All characteristics of the fluid are expressed through a master potential, satisfying an ordinary second order differential equation. Different constraints are imposed on this core of relations, finding new solutions and deriving the classical results for perfect fluids and dust as particular cases. Many uncharged and charged anisotropic solutions, all conformally flat and some uniform density solutions are found. A number of solutions with linear equation among the two pressures are derived, including the case of vanishing tangential pressure.Comment: 21 page

Mapping of Coulomb gases and sine-Gordon models to statistics of random surfaces

We introduce a new class of sine-Gordon models, for which interaction term is present in a region different from the domain over which quadratic part is defined. We develop a novel non-perturbative approach for calculating partition functions of such models, which relies on mapping them to statistical properties of random surfaces. As a specific application of our method, we consider the problem of calculating the amplitude of interference fringes in experiments with two independent low dimensional Bose gases. We calculate full distribution functions of interference amplitude for 1D and 2D gases with nonzero temperatures.Comment: final published versio

Large-Scale Structure in Brane-Induced Gravity II. Numerical Simulations

We use N-body simulations to study the nonlinear structure formation in brane-induced gravity, developing a new method that requires alternate use of Fast Fourier Transforms and relaxation. This enables us to compute the nonlinear matter power spectrum and bispectrum, the halo mass function, and the halo bias. From the simulation results, we confirm the expectations based on analytic arguments that the Vainshtein mechanism does operate as anticipated, with the density power spectrum approaching that of standard gravity within a modified background evolution in the nonlinear regime. The transition is very broad and there is no well defined Vainshtein scale, but roughly this corresponds to k_*~ 2 at redshift z=1 and k_*~ 1 at z=0. We checked that while extrinsic curvature fluctuations go nonlinear, and the dynamics of the brane-bending mode C receives important nonlinear corrections, this mode does get suppressed compared to density perturbations, effectively decoupling from the standard gravity sector. At the same time, there is no violation of the weak field limit for metric perturbations associated with C. We find good agreement between our measurements and the predictions for the nonlinear power spectrum presented in paper I, that rely on a renormalization of the linear spectrum due to nonlinearities in the modified gravity sector. A similar prediction for the mass function shows the right trends. Our simulations also confirm the induced change in the bispectrum configuration dependence predicted in paper I.Comment: 19 pages, 13 figures. v2: corrected typos, added more simulations, better test of predictions in large mass regime. v3: minor changes, published versio

Lie symmetry analysis and exact solutions of the quasi-geostrophic two-layer problem

The quasi-geostrophic two-layer model is of superior interest in dynamic meteorology since it is one of the easiest ways to study baroclinic processes in geophysical fluid dynamics. The complete set of point symmetries of the two-layer equations is determined. An optimal set of one- and two-dimensional inequivalent subalgebras of the maximal Lie invariance algebra is constructed. On the basis of these subalgebras we exhaustively carry out group-invariant reduction and compute various classes of exact solutions. Where possible, reference to the physical meaning of the exact solutions is given. In particular, the well-known baroclinic Rossby wave solutions in the two-layer model are rediscovered.Comment: Extended version, 24 pages, 1 figur

Digitalization of Processes of Small and Average Business

The role of small and medium-sized enterprises in the economic life of society cannot be overestimated: it contributes to economic growth in the country, increases the level of employment of the population, forms healthy competition, promotes the development of innovation activities and solves many social problems. In this regard, State support for entrepreneurship is essential in order to create an enabling environment for its further development. To date, a national project on the formation of support mechanisms for small and medium-sized enterprises has been adopted and is being implemented. The relevant national project is implemented within the framework of five federal projects aimed at improving the conditions of entrepreneurship, access of business entities to financial resources, acceleration of business entities, popularization of entrepreneurship, and development of rural cooperation. At the same time, in the context of digital globalization, the effective implementation of these directions is impossible without the introduction of information technologies into the activities of the business entities themselves. Research on the introduction of information technologies into business structures is not systematic and reveals certain aspects of this issue. The relevance of the study is due to the fact that within the framework of the national projects approved in our country, no mechanism has been developed to form a business model that ensures the effective introduction of such technologies into the activities of small and medium-sized businesses. Most scientific works of this topic reveal issues of implementation of specific information technologies by business entities. Therefore, the formation of a generalized model of effective introduction of IT-technologies in the activities of small and medium-sized enterprises is a pressing task that contributes to the achievement of the tasks set for national projects.The purpose of this study is to develop methodological and practical recommendations to increase the efficiency of Russian small and medium-sized enterprises on the basis of the implementation of the concept of digitalization of business. The study was aimed at national projects “Small and medium-sized entrepreneurship and support for individual entrepreneurial initiative” and “Digital economy of the Russian Federation,” interim results of their implementation. The subject of the study is the system of support for the development of Russian small and medium-sized enterprises.The scientific novelty of this study consists in the development of an algorithm for the transition of small and medium-sized enterprises to digitalization of business processes, in the systematization of business entities by the level of introduction of digital technologies into the activities, as well as in the grouping of the main directions of digitization of business entities

Integration of D-dimensional 2-factor spaces cosmological models by reducing to the generalized Emden-Fowler equation

The D-dimensional cosmological model on the manifold $M = R \times M_{1} \times M_{2}$ describing the evolution of 2 Einsteinian factor spaces, $M_1$ and $M_2$, in the presence of multicomponent perfect fluid source is considered. The barotropic equation of state for mass-energy densities and the pressures of the components is assumed in each space. When the number of the non Ricci-flat factor spaces and the number of the perfect fluid components are both equal to 2, the Einstein equations for the model are reduced to the generalized Emden-Fowler (second-order ordinary differential) equation, which has been recently investigated by Zaitsev and Polyanin within discrete-group analysis. Using the integrable classes of this equation one generates the integrable cosmological models. The corresponding metrics are presented. The method is demonstrated for the special model with Ricci-flat spaces $M_1,M_2$ and the 2-component perfect fluid source.Comment: LaTeX file, no figure

Self-consistent analytical solution of a problem of charge-carrier injection at a conductor/insulator interface

We present a closed description of the charge carrier injection process from a conductor into an insulator. Common injection models are based on single electron descriptions, being problematic especially once the amount of charge-carriers injected is large. Accordingly, we developed a model, which incorporates space charge effects in the description of the injection process. The challenge of this task is the problem of self-consistency. The amount of charge-carriers injected per unit time strongly depends on the energy barrier emerging at the contact, while at the same time the electrostatic potential generated by the injected charge- carriers modifies the height of this injection barrier itself. In our model, self-consistency is obtained by assuming continuity of the electric displacement and the electrochemical potential all over the conductor/insulator system. The conductor and the insulator are properly taken into account by means of their respective density of state distributions. The electric field distributions are obtained in a closed analytical form and the resulting current-voltage characteristics show that the theory embraces injection-limited as well as bulk-limited charge-carrier transport. Analytical approximations of these limits are given, revealing physical mechanisms responsible for the particular current-voltage behavior. In addition, the model exhibits the crossover between the two limiting cases and determines the validity of respective approximations. The consequences resulting from our exactly solvable model are discussed on the basis of a simplified indium tin oxide/organic semiconductor system.Comment: 23 pages, 6 figures, accepted to Phys.Rev.

The delayed uncoupled continuous-time random walks do not provide a model for the telegraph equation

It has been alleged in several papers that the so called delayed continuous-time random walks (DCTRWs) provide a model for the one-dimensional telegraph equation at microscopic level. This conclusion, being widespread now, is strange, since the telegraph equation describes phenomena with finite propagation speed, while the velocity of the motion of particles in the DCTRWs is infinite. In this paper we investigate how accurate are the approximations to the DCTRWs provided by the telegraph equation. We show that the diffusion equation, being the correct limit of the DCTRWs, gives better approximations in $L_2$ norm to the DCTRWs than the telegraph equation. We conclude therefore that, first, the DCTRWs do not provide any correct microscopic interpretation of the one-dimensional telegraph equation, and second, the kinetic (exact) model of the telegraph equation is different from the model based on the DCTRWs.Comment: 12 pages, 9 figure

Schwinger Pair Production in dS_2 and AdS_2

We study Schwinger pair production in scalar QED from a uniform electric field in dS_2 with scalar curvature R_{dS} = 2 H^2 and in AdS_2 with R_{AdS} = - 2 K^2. With suitable boundary conditions, we find that the pair-production rate is the same analytic function of the scalar curvature in both cases.Comment: RevTex 6 pages, no figure; replaced by the version published in PR