Relationship between stochastic flows and connection forms

In this article I will prove new representation for the Levi-Civita connection in terms of the stochastic flow corresponding to Brownian motion on manifold.Comment: 6 page

Duality, Vector advection and the Navier-Stokes equations

In this article we show that three dimensional vector advection equation is self dual in certain sense defined below. As a consequence, we infer classical result of Serrin of existence of strong solution of Navier-Stokes equation. Also we deduce Feynman-Kac type formula for solution of the vector advection equation and show that the formula is not unique i.e. there exist flows which differ from standard flow along which vorticity is conserved.Comment: 51 pages; Some minor mistakes are correcte

Backward Uniqueness and the existence of the spectral limit for some parabolic SPDEs

The aim of this article is to study the asymptotic behaviour for large times of solutions to a certain class of stochastic partial differential equations of parabolic type. In particular, we will prove the backward uniqueness result and the existence of the spectral limit for abstract SPDEs and then show how these results can be applied to some concrete linear and nonlinear SPDEs. For example, we will consider linear parabolic SPDEs with gradient noise and stochastic NSEs with multiplicative noise. Our results generalize the results proved in \cite{[Ghidaglia-1986]} for deterministic PDEs.Comment: 31 pages;Major Changes: New theorem which covers the case of SPDEs with quadratic nonlinearity (such as stochastic Navier-Stokes equation with multiplicative noise) is adde

Global evolution of random vortex filament equation

We prove the existence of a global solution for the filament equation with inital condition given by a geometric rough path in the sense of Lyons (1998).Our work gives a positive answer to a question left open in recent publications: Berselli and Gubinelli (2007) showed the existence of global solution for a smooth initial condition while Bessaih, Gubinelli, Russo (2005) proved the existence of a local solution for a general initial condition given by a rough path.Comment: 19 pages; minor revision

Ergodicity for infinite particle systems with locally conserved quantities

We analyse certain degenerate infinite dimensional sub-elliptic generators, and obtain estimates on the long-time behaviour of the corresponding Markov semigroups that describe a certain model of heat conduction. In particular, we establish ergodicity of the system for a family of invariant measures, and show that the optimal rate of convergence to equilibrium is polynomial. Consequently, there is no spectral gap, but a Liggett-Nash type inequality is shown to hold.Comment: 34 pages; introduction rewritten, minor corrections, references adde

Distribution of small dispersive coal dust particles and absorbed radioactive chemical elements in conditions of forced acoustic resonance in iodine air filter at nuclear power plant

The physical features of distribution of the small dispersive coal dust particles and the adsorbed radioactive chemical elements and their isotopes in the absorber with the granular filtering medium with the cylindrical coal granules were researched in the case of the intensive air dust aerosol stream flow through the iodine air filter (IAF). It was shown that, at the certain aerodynamic conditions in the IAF, the generation of the acoustic oscillations is possible. It was found that the acoustic oscillations generation results in an appearance of the standing acoustic waves of the air pressure (density) in the IAF. In the case of the intensive blow of the air dust aerosol, it was demonstrated that the standing acoustic waves have some strong influences on both: 1) the dynamics of small dispersive coal dust particles movement and their accumulation in the IAF; 2) the oversaturation of the cylindrical coal granules by the adsorbed radioactive chemical elements and their isotopes in the regions, where the antinodes of the acoustic waves are positioned. Finally, we completed the comparative analysis of the theoretical calculations with the experimental results, obtained for the cases of: 1) the experimental aerodynamic modeling of physical processes of the absorbed radioactive chemical elements and their isotopes distribution in the IAF; and 2) the gamma-activation spectroscopy analysis of the absorbed radioactive chemical elements and their isotopes distribution in the IAF. We made the innovative propositions on the necessary technical modifications with the purpose to improve the IAF technical characteristics and increase its operational time at the nuclear power plant (NPP), going from the completed precise characterization of the IAF parameters at the long term operation.Comment: 8 pages, 2 figures, http://vant.kipt.kharkov.ua/ARTICLE/VANT_2013_2/article_2013_2_94.pd

Physical features of accumulation and distribution processes of small disperse coal dust precipitations and absorbed radioactive chemical elements in iodine air filter at nuclear power plant

The physical features of absorption process of radioactive chemical elements and their isotopes in the iodine air filters of the type of AU-1500 at the nuclear power plants are researched. It is shown that the non-homogenous spatial distribution of absorbed radioactive chemical elements and their isotopes in the iodine air filter, probed by the gamma-activation analysis method, is well correlated with the spatial distribution of small disperse coal dust precipitations in the iodine air filter. This circumstance points out to an important role by the small disperse coal dust fractions of absorber in the absorption process of radioactive chemical elements and their isotopes in the iodine air filter. The physical origins of characteristic interaction between the radioactive chemical elements and the accumulated small disperse coal dust precipitations in an iodine air filter are considered. The analysis of influence by the researched physical processes on the technical characteristics and functionality of iodine air filters at nuclear power plants is completed.Comment: 6 pages, 7 figures http://vant.kipt.kharkov.ua/ARTICLE/VANT_2006_4/article_2006_4_164.pd

Features of coal dust dynamics at action of differently oriented forces in granular filtering medium

The process of the coal dust particles transportation and structurization in the experimental horizontal model of air filter with the cylindrical coal adsorbent granules as in the iodine air filter at the nuclear power plant is researched. In the investigated case the vector of carrying away force of air flow and the vector of gravitation force are mutually perpendicular, and the scattering of the dust particles on the granules occurs in the normal directions. It is found that the phenomenon of non controlled spontaneous sharp increase of aerodynamic resistance in the iodine air filter under the big integral volumes of filtered air and the big masses of introduced coal dust particles is not observed at the described experimental conditions in distinction from the case of the parallel orientation of this forces as in the vertical iodine air filters at the nuclear power plant. The quantitative measurements of the main parameters of the process of the dust masses transportation and structurization are made on a developed experimental model of the iodine air filter with the cylindrical coal adsorbent granules.Comment: 8 pages, 9 figures, 2 table

Stages of destruction and elastic compression of granular nanoporous carbon medium at high pressures

The granular nanoporous carbon medium, made of the cylindrical coal granules of the adsorbent of SKT 3, at an influence by the high pressures from 1MPa to 3GPa has been researched. The eight consecutive stages of the materials specific volume change, which is characterized by a certain dependence of the volume change on the pressure change, have been registered. It is shown that there is a linear dependence on the double log log plot of the materials specific volume change on the pressure for an every stage of considered process. The two stages are clearly distinguished such as a stage of materials mechanical destruction, and a stage of elastic compression of material without the disintegration of structure at a nanscale. The hysteresis dependence of the materials specific volume change on the pressure change at the pressure decrease is observed. The small disperse coal dust particles jettisoning between the high pressure cell and the base plate was observed, resulting in the elastic stress reduction in relation to the small disperse coal dust particles volume. The obtained research data can be used to improve the designs of air filters for the radioactive chemical elements absorption at the NPP with the aims to protect the environment.Comment: 4 pages, 5 figures http://vant.kipt.kharkov.ua/ARTICLE/VANT_2015_2/article_2015_2_182.pdf. Series: Physics of radiation damages and radiation materials. ISSN 1562-6016 (2015

Influence by small dispersive coal dust particles of different fractional consistence on characteristics of iodine air filter at nuclear power plant

The main purpose of research is to determine the influence by the small dispersive coal dust particles of the different fractional consistence on the technical characteristics of the vertical iodine air filter at nuclear power plant. The research on the transport properties of the small dispersive coal dust particles in the granular filtering medium of absorber in the vertical iodine air filter is completed in the case, when the modeled aerodynamic conditions are similar to the real aerodynamic conditions. It is shown that the appearance of the different fractional consistence of small dispersive coal dust particles with the decreasing dimensions down to the micro and nano sizes at the action of the air dust aerosol stream normally results in a significant change of distribution of the small dispersive coal dust particles masses in the granular filtering medium of an absorber in the vertical iodine air filter, changing the vertical iodine air filter aerodynamic characteristics. The precise characterization of the aerodynamic resistance of a model of the vertical iodine air filter is completed. The comparative analysis of the technical characteristics of the vertical and horizontal iodine air filters is also made.Comment: 6 pages, 5 figures http://vant.kipt.kharkov.ua/ARTICLE/VANT_2009_2/a rticle_2009_2_104.pd