176 research outputs found
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
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