352 research outputs found
Hydrodynamics of thermal granular convection
A hydrodynamic theory is formulated for buoyancy-driven ("thermal") granular
convection, recently predicted in molecular dynamic simulations and observed in
experiment. The limit of a dilute flow is considered. The problem is fully
described by three scaled parameters. The convection occurs via a supercritical
bifurcation, the inelasticity of the collisions being the control parameter.
The theory is expected to be valid for small Knudsen numbers and nearly elastic
grain collisions.Comment: 4 pages, 4 EPS figures, some details adde
Long-time dynamics of Rouse-Zimm polymers in dilute solutions with hydrodynamic memory
The dynamics of flexible polymers in dilute solutions is studied taking into
account the hydrodynamic memory, as a consequence of fluid inertia. As distinct
from the Rouse-Zimm (RZ) theory, the Boussinesq friction force acts on the
monomers (beads) instead of the Stokes force, and the motion of the solvent is
governed by the nonstationary Navier-Stokes equations. The obtained generalized
RZ equation is solved approximately. It is shown that the time correlation
functions describing the polymer motion essentially differ from those in the RZ
model. The mean-square displacement (MSD) of the polymer coil is at short times
\~ t^2 (instead of ~ t). At long times the MSD contains additional (to the
Einstein term) contributions, the leading of which is ~ t^(1/2). The relaxation
of the internal normal modes of the polymer differs from the traditional
exponential decay. It is displayed in the long-time tails of their correlation
functions, the longest-lived being ~ t^(-3/2) in the Rouse limit and t^(-5/2)
in the Zimm case, when the hydrodynamic interaction is strong. It is discussed
that the found peculiarities, in particular an effectively slower diffusion of
the polymer coil, should be observable in dynamic scattering experiments.Comment: 6 page
Onset of thermal convection in a horizontal layer of granular gas
The Navier-Stokes granular hydrodynamics is employed for determining the
threshold of thermal convection in an infinite horizontal layer of granular
gas. The dependence of the convection threshold, in terms of the inelasticity
of particle collisions, on the Froude and Knudsen numbers is found. A simple
necessary condition for convection is formulated in terms of the
Schwarzschild's criterion, well-known in thermal convection of (compressible)
classical fluids. The morphology of convection cells at the onset is
determined. At large Froude numbers, the Froude number drops out of the
problem. As the Froude number goes to zero, the convection instability turns
into a recently discovered phase separation instability.Comment: 6 pages, 6 figures. An extended version. A simple and universal
necessary criterion for convection presente
Stationary convection and internal gravity waves in compressible liquids : influence of piston effect
Paper presented at the 5th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, South Africa, 1-4 July, 2007.Fundamental equations of a compressible viscous heat-conducting fluid are derived. The rigorous linear stability
analysis has been used for the onset of thermal convection and internal gravity waves. Particular emphasis is placed
upon the influence of a thermo-acoustic waves (piston effect) on these phenomena. .This recently found contra-intuitive
speeding up of thermal equilibration at constant volume replaced the traditional slowing down in a strongly compressible
liquid at constant pressure. Our analysis shows that for the onset of convection the results are coincide with those at fixed
pressure proving thereby that the piston effect does not influence the. thermodynamic phenomenon of free convection.
However, the dynamic phenomenon of propagation of the internal gravity waves is essentially dependent on the piston
effect.cs201
Coherence and Josephson oscillations between two tunnel-coupled one-dimensional atomic quasicondensates at finite temperature
We revisit the theory of tunnel-coupled atomic quasicondensates in
double-well elongated traps at finite temperatures. Using the
functional-integral approach, we calculate the relative-phase correlation
function beyond the harmonic limit of small fluctuations of the relative phase
and its conjugate relative-density variable. We show that the thermal
fluctuations of the relative phase between the two quasicondensates decrease
the frequency of Josephson oscillations and even wash out these oscillations
for small values of the tunnel coupling.Comment: revtex4, 4 figures (.eps
Diffusion-induced dephasing in nanomechanical resonators
We study resonant response of an underdamped nanomechanical resonator with
fluctuating frequency. The fluctuations are due to diffusion of molecules or
microparticles along the resonator. They lead to broadening and change of shape
of the oscillator spectrum. The spectrum is found for the diffusion confined to
a small part of the resonator and where it occurs along the whole nanobeam. The
analysis is based on extending to the continuous limit, and appropriately
modifying, the method of interfering partial spectra. We establish the
conditions of applicability of the fluctuation-dissipation relations between
the susceptibility and the power spectrum. We also find where the effect of
frequency fluctuations can be described by a convolution of the spectra without
these fluctuations and with them as the only source of the spectral broadening.Comment: 10 page
Spectrum of an oscillator with jumping frequency and the interference of partial susceptibilities
We study an underdamped oscillator with shot-noise frequency fluctuations.
The oscillator spectrum is determined by the interference of the
susceptibilities for different eigenfrequencies. Depending on the parameters,
it has a fine structure or displays a single asymmetric peak. For
nano-mechanical resonators with a fluctuating number of attached molecules, the
spectrum is found in a simple analytical form. The results bear on various
types of systems where the reciprocal correlation time of frequency
fluctuations can be comparable to the typical frequency jumps
Comment on "Ising model on a small world network"
In the recent study of the Ising model on a small-world network by A.
P\c{e}kalski [Phys. Rev. E {\bf 64}, 057104 (2001)], a surprisingly small value
of the critical exponent has been obtained for the
temperature dependence of the magnetization. We perform extensive Monte Carlo
simulations of the same model and conclude, via the standard finite-size
scaling of various quantities,that the phase transition in the model is of the
mean-field nature, in contrast to the work by A. P\c{e}kalski but in accord
with other existing studies.Comment: to be published in PR
Parametric Amplification of Nonlinear Response of Single Crystal Niobium
Giant enhancement of the nonlinear response of a single crystal Nb sample,
placed in {\it a pumping ac magnetic field}, has been observed experimentally.
The experimentally observed amplitude of the output signal is about three
orders of magnitude higher than that seen without parametric pumping. The
theoretical analysis based on the extended double well potential model provides
a qualitative explanation of the experimental results as well as new
predictions of two bifurcations for specific values of the pumping signal.Comment: 6 pages, 10 figure
Analysis of Tridiagonal Recurrence Relations in Continuum Approximation
Transition from difference to differential equation allows solving tridiagonal recurrence relations, which appear, among other things, in analysis of the rotation of an overdamped Brownian particle subjected to a periodic force. Replacement of the discrete integers in the Fourier series by continuum is justified for large numbers, i. e. for small angles. For the simplest case of the sinusoidal force, our solution, indeed, coincides with one obtained by expanding the sin in the original Fokker-Planck equation (The Ornstein-Uhlenbeck limit). However, for slightly more complicate potential the expansion for small angles does not transform the appropriate Fokker-Planck equation into the soluble. At the same time, the method suggested allows solving the problem for all periodic potentials which have finite number of terms in their Fourier series such as sinm(θ ) or cosm (θ). Even and odd functions require slightly different analysis, and are considered separately.Переход от разностного к дифференциальному уравнению позволяет решить тридиагональные рекуррентные соотношения, которые возникают, в частности, при анализе вращения броуновской частицы с трением при наличии периодической силы. Замена дискретных индексов в разложениях Фурье непрерывными оправдан для больших номеров, т. е. для малых углов. В простейшем случае синусоидальной силы наше решение действительно совпадает с решением, полученным путем разложения синуса в первоначальном уравнении Фоккера-Планка (предел Орнштейна-Уленбека). Однако уже в случае несколько более сложного потенциала разложение при малых углах не делает соответствующее уравнение Фоккера-Планка разрешимым. В то же время предлагаемый метод позволяет решить задачу для всех периодических потенциалов, для которых ряды Фурье содержат конечное число слагаемых типа sinm(θ ) или cosm (θ). Четные либо нечетные функции требуют несколько различного подхода и рассматриваются отдельно.Перехід від різницевого до диференціального рівняння дозволяє вирішити тридіагональні рекурентні співвідношення, які виникають, зокрема, при аналізі обертання броунівської частинки з тертям у присутності періодичної сили. Заміна дискретних індексів у розкладанні Фур’є неперервними виправдана для великих номерів, тобто для малих кутів. У найпростішому випадку синусоїдальної сили наше рішення співпадає із рішенням, отриманим шляхом розкладання синуса у початковому рівнянні Фоккера-Планка (границя Орнштейна-Уленбека). Однак уже у випадку дещо складнішого потенціалу розкладання при малих кутах не робить відповідне рівняння Фоккера-Планка вирішуваним. Водночас запропонований метод дозволяє вирішити задачу для всіх періодичних потенціалів, для яких ряди Фур’є містять кінцеву кількість доданків, типу sinm(θ ) або cosm (θ). Парні чи непарні функції вимагають дещо іншого підходу і розглядаються окремо
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