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 $\beta \approx 0.0001$ 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