6,431 research outputs found
Scaling and Dissipation in the GOY Shell Model
This is a paper about multi-fractal scaling and dissipation in a shell model
of turbulence, called the GOY model. This set of equations describes a one
dimensional cascade of energy towards higher wave vectors. When the model is
chaotic, the high-wave-vector velocity is a product of roughly independent
multipliers, one for each logarithmic momentum shell. The appropriate tool for
studying the multifractal properties of this model is shown to be the energy
current on each shell rather than the velocity on each shell. Using this
quantity, one can obtain better measurements of the deviations from Kolmogorov
scaling (in the GOY dynamics) than were available up to now. These deviations
are seen to depend upon the details of inertial-range structure of the model
and hence are {\em not} universal. However, once the conserved quantities of
the model are fixed to have the same scaling structure as energy and helicity,
these deviations seem to depend only weakly upon the scale parameter of the
model. We analyze the connection between multifractality in the velocity
distribution and multifractality in the dissipation. Our arguments suggest that
the connection is universal for models of this character, but the model has a
different behavior from that of real turbulence. We also predict the scaling
behavior of time correlations of shell-velocities, of the dissipation,Comment: Revised Versio
Composition of processes and related partial differential equations
In this paper different types of compositions involving independent
fractional Brownian motions B^j_{H_j}(t), t>0, j=1,$ are examined. The partial
differential equations governing the distributions of
I_F(t)=B^1_{H_1}(|B^2_{H_2}(t)|), t>0 and
J_F(t)=B^1_{H_1}(|B^2_{H_2}(t)|^{1/H_1}), t>0 are derived by different methods
and compared with those existing in the literature and with those related to
B^1(|B^2_{H_2}(t)|), t>0. The process of iterated Brownian motion I^n_F(t), t>0
is examined in detail and its moments are calculated. Furthermore for
J^{n-1}_F(t)=B^1_{H}(|B^2_H(...|B^n_H(t)|^{1/H}...)|^{1/H}), t>0 the following
factorization is proved J^{n-1}_F(t)=\prod_{j=1}^{n} B^j_{\frac{H}{n}}(t), t>0.
A series of compositions involving Cauchy processes and fractional Brownian
motions are also studied and the corresponding non-homogeneous wave equations
are derived.Comment: 32 page
Integrable hierarchy underlying topological Landau-Ginzburg models of D-type
A universal integrable hierarchy underlying topological Landau-Ginzburg
models of D-tye is presented. Like the dispersionless Toda hierarchy, the new
hierarchy has two distinct (``positive" and ``negative") set of flows. Special
solutions corresponding to topological Landau-Ginzburg models of D-type are
characterized by a Riemann-Hilbert problem, which can be converted into a
generalized hodograph transformation. This construction gives an embedding of
the finite dimensional small phase space of these models into the full space of
flows of this hierarchy. One of flat coordinates in the small phase space turns
out to be identical to the first ``negative" time variable of the hierarchy,
whereas the others belong to the ``positive" flows.Comment: 14 pages, Kyoto University KUCP-0061/9
Evaporative Deposition Patterns Revisited: Spatial Dimensions of the Deposit
A model accounting for finite spatial dimensions of the deposit patterns in
the evaporating sessile drops of colloidal solution on a plane substrate is
proposed. The model is based on the assumption that the solute particles occupy
finite volume and hence these dimensions are of the steric origin. Within this
model, the geometrical characteristics of the deposition patterns are found as
functions of the initial concentration of the solute, the initial geometry of
the drop, and the time elapsed from the beginning of the drying process. The
model is solved analytically for small initial concentrations of the solute and
numerically for arbitrary initial concentrations of the solute. The agreement
between our theoretical results and the experimental data is demonstrated, and
it is shown that the observed dependence of the deposit dimensions on the
experimental parameters can indeed be attributed to the finite dimensions of
the solute particles. These results are universal and do not depend on any free
or fitting parameters; they are important for understanding the evaporative
deposition and may be useful for creating controlled deposition patterns.Comment: 34 pages, 14 figures, LaTeX; submitted to Physical Review
Bulk viscosity of superfluid neutron stars
The hydrodynamics, describing dynamical effects in superfluid neutron stars,
essentially differs from the standard one-fluid hydrodynamics. In particular,
we have four bulk viscosity coefficients in the theory instead of one. In this
paper we calculate these coefficients, for the first time, assuming they are
due to non-equilibrium beta-processes (such as modified or direct Urca
process). The results of our analysis are used to estimate characteristic
damping times of sound waves in superfluid neutron stars. It is demonstrated
that all four bulk viscosity coefficients lead to comparable dissipation of
sound waves and should be considered on the same footing.Comment: 11 pages, 1 figure, this version with some minor stylistic changes is
published in Phys. Rev.
On mechanism of antiarrhythmic action of some dimethylphenylacetamide derivatives
The study aim was to identify essential elements of the antiarrhythmic action mechanism of tertiary and quaternary derivatives of Dimethylphenylacetamide. The study was conducted in albino rats and mice of both sexes; isolated neurons of mollusc Limnea stagnalis; and strips of rats’ right ventricle myocardium. Two compounds of Dimethylphenylacetamide LKhT- 3-00 and LKhT-12-02 were studie
Periodic and Quasi-Periodic Compensation Strategies of Extreme Outages caused by Polarization Mode Dispersion and Amplifier Noise
Effect of birefringent disorder on the Bit Error Rate (BER) in an optical
fiber telecommunication system subject to amplifier noise may lead to extreme
outages, related to anomalously large values of BER. We analyze the Probability
Distribution Function (PDF) of BER for various strategies of Polarization Mode
Dispersion (PMD) compensation. A compensation method is proposed that is
capable of more efficient extreme outages suppression, which leads to
substantial improvement of the fiber system performance.Comment: 3 pages, 1 figure, Submitted to IEEE Photonics Letter
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