177 research outputs found
Solving variational inequalities with Stochastic Mirror-Prox algorithm
In this paper we consider iterative methods for stochastic variational
inequalities (s.v.i.) with monotone operators. Our basic assumption is that the
operator possesses both smooth and nonsmooth components. Further, only noisy
observations of the problem data are available. We develop a novel Stochastic
Mirror-Prox (SMP) algorithm for solving s.v.i. and show that with the
convenient stepsize strategy it attains the optimal rates of convergence with
respect to the problem parameters. We apply the SMP algorithm to Stochastic
composite minimization and describe particular applications to Stochastic
Semidefinite Feasability problem and Eigenvalue minimization
Reconnections of Vortex Loops in the Superfluid Turbulent HeII. Rates of the Breakdown and Fusion processes
Kinetics of merging and breaking down vortex loops is the important part of
the whole vortex tangle dynamics. Another part is the motion of individual
lines, which obeys the Biot-Savart law in presence of friction force and of
applied external velocity fields if any. In the present work we evaluate the
coefficients of the reconnection rates and
. Quantity is a number (per unit of time and per unit of
volume) of events, when two loops with lengths and collide and
form the single loop of length . Quantity
describes the rate of events, when the single loop of the length breaks
down into two the daughter loops of lengths and . These
quantities ave evaluated as the averaged numbers of zeroes of vector
connecting two points on the loops of
and at moment of time . Statistics of the individual
loops is taken from the Gaussian model of vortex tangle. PACS-number 67.40Comment: 9 pages, 5 figures, To be submitted to JLT
Note on the paper of Fu and Wong on strictly pseudoconvex domains with K\"ahler--Einstein Bergman metrics
It is shown that the Ramadanov conjecture implies the Cheng conjecture. In
particular it follows that the Cheng conjecture holds in dimension two
Numerical simulation of stochastic vortex tangles
We present the results of simulation of the chaotic dynamics of quantized
vortices in the bulk of superfluid He II.
Evolution of vortex lines is calculated on the base of the Biot-Savart law.
The dissipative effects appeared from the interaction with the normal
component, or/and from relaxation of the order parameter are taken into
account. Chaotic dynamics appears in the system via a random forcing, e.i. we
use the Langevin approach to the problem. In the present paper we require the
correlator of the random force to satisfy the fluctuation-disspation relation,
which implies that thermodynamic equilibrium should be reached. In the paper we
describe the numerical methods for integration of stochastic differential
equation (including a new algorithm for reconnection processes), and we present
the results of calculation of some characteristics of a vortex tangle such as
the total length, distribution of loops in the space of their length, and the
energy spectrum.Comment: 8 pages, 5 figure
Vortex dynamics in rotating counterflow and plane Couette and Poiseuille turbulence in superfluid Helium
An equation previously proposed to describe the evolution of vortex line
density in rotating counterflow turbulent tangles in superfluid helium is
generalized to incorporate nonvanishing barycentric velocity and velocity
gradients. Our generalization is compared with an analogous approach proposed
by Lipniacki, and with experimental results by Swanson et al. in rotating
counterflow, and it is used to evaluate the vortex density in plane Couette and
Poiseuille flows of superfluid helium.Comment: 18 pages, 2 figure
Dynamics of coreless vortices and rotation-induced dissipation peak in superfluid films on rotating porous substrates
We analyze dynamics of 3D coreless vortices in superfluid films covering
porous substrates. The 3D vortex dynamics is derived from the 2D dynamics of
the film. The motion of a 3D vortex is a sequence of jumps between neighboring
substrate cells, which can be described, nevertheless, in terms of
quasi-continuous motion with average vortex velocity. The vortex velocity is
derived from the dissociation rate of vortex-antivortex pairs in a 2D film,
which was developed in the past on the basis of the Kosterlitz-Thouless theory.
The theory explains the rotation-induced dissipation peak in torsion-oscillator
experiments on He films on rotating porous substrates and can be used in
the analysis of other phenomena related to vortex motion in films on porous
substrates.Comment: 8 pages, 3 figures submitted to Phys. Rev.
Equilibrium rotation of a vortex bundle terminating on a lateral wall
The paper investigates possibility of equilibrium solid-body rotation of a
vortex bundle diverging at some height from a cylinder axis and terminating on
a lateral wall of a container. Such a bundle arises when vorticity expands up
from a container bottom eventually filling the whole container. The analysis
starts from a single vortex, then goes to a vortex sheet, and finally addresses
a multi-layered crystal vortex bundle. The equilibrium solid-body rotation of
the vortex bundle requires that the thermodynamic potentials in the
vortex-filled and in the vortex-free parts of the container are equal providing
the absence of a force on the vortex front separating the two parts. The paper
considers also a weakly non-equilibrium state when the bundle and the container
rotate with different angular velocities and the vortex front propagates with
the velocity determined by friction between vortices and the container or the
normal liquid moving together with the container.Comment: 16 pages, 5 figure
A Kelvin-wave cascade on a vortex in superfluid He at a very low temperature
A study by computer simulation is reported of the behaviour of a quantized
vortex line at a very low temperature when there is continuous excitation of
low-frequency Kelvin waves. There is no dissipation except by phonon radiation
at a very high frequency. It is shown that non-linear coupling leads to a net
flow of energy to higher wavenumbers and to the development of a simple
spectrum of Kelvin waves that is insensitive to the strength and frequency of
the exciting drive. The results are likely to be relevant to the decay of
turbulence in superfluid He at very low temperatures
Acceleration of the path-following method for optimization over the cone of positive semidefinite matrices
Projet META2The paper is devoted to acceleration of the path-following interior point polynomial time method for optimization over the cone of positive semidefinite matrices, with applications to quadratically constrained problems and extensions onto the general self-concordant case. In particular, we demonstrate that in a problem involving m of general type m x m linear matrix inequalities with n 3 m scalar control variables the conjugate-gradient-based acceleration allows to reduce the arithmetic cost of an e-solution by a factor of order of max {n1/3 m-1/6, n1/5}, for the Karmarkar-type acceleration this factor is of order of min {n, m1/2}. The conjugate-gradient-based acceleration turns out to be efficient also in the case of several specific "structured" problems coming from applications in control and graph theory
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