Energy Transport in Stochastically Perturbed Lattice Dynamics

We consider lattice dynamics with a small stochastic perturbation of order ${\varepsilon}We consider lattice dynamics with a small stochastic perturbation of order e{\varepsilon} and prove that for a space–time scale of order e^-1{\varepsilon^{-1}} the local spectral density (Wigner function) evolves according to a linear transport equation describing inelastic collisions. For an energy and momentum conserving chain, the transport equation predicts a slow decay, as 1/?t{1/\sqrt t} , for the energy current correlation in equilibrium. This is in agreement with previous studies using a different method.     

Transport Properties of a Chain of Anharmonic Oscillators with Random Flip of Velocities

We consider the stationary states of a chain of n anharmonic coupled oscillators, whose deterministic Hamiltonian dynamics is perturbed by random independent sign change of the velocities (a random mechanism that conserve energy). The extremities are coupled to thermostats at different temperature T _ℓ and T _r and subject to constant forces τ _ℓ and τ _r . If the forces differ τ _ℓ ≠τ _r the center of mass of the system will move of a speed V _s inducing a tension gradient inside the system. Our aim is to see the influence of the tension gradient on the thermal conductivity. We investigate the entropy production properties of the stationary states, and we prove the existence of the Onsager matrix defined by Green-Kubo formulas (linear response). We also prove some explicit bounds on the thermal conductivity, depending on the temperature.     

A toroidal mode driven by ion temperature gradients and magnetic-field curvature

Summary The effect of magnetic-field curvature on the ion-mixing mode is studied in a collisionless-plasma regime. A simple plane model with an external gravity-simulating magnetic curvature is adopted. A dispersion relation which connects the ion-mixing mode to the ubiquitous mode is obtained. It is found that, within the limitations of the present local model, an inhomogeneous plasma can support fluctuations with frequencies larger than those expected in an analysis which disregards the effect of magnetic curvature. The instability threshold of this mode, which depends on the ion temperature gradient, is lowered. The effect of gravity on the ion response influences the quasi-linear ion heat transport.

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Riassunto Si studia l'effetto della curvatura del campo magnetico sul modo di mescolamento degli ioni in un regime di plasma senza collisioni. Si adotta un semplice modello piano con gravità esterna che simula curvatura magnetica. Si ottiene una relazione di dispersione che connette il modo di mescolamento degli ioni al modo ubiquitario. Si trova che, nei limiti del presente modello locale, un plasma inomogeneo può dar supporto a fluttuazioni con frequenze piú grandi dei quelle attese in un'analisi che trascura l'effetto della curvatura magnetica. La soglia d'instabilità di questo modo, che dipende dal gradiente di temperatura ionica, è abbassata. L'effectto della gravità sulla risposta ionica influenza il trasporto di calore ionico quasi lineare.

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Резюме В режиме бесстолкновительной плазмы исследуется влияние кривизны магнитного поля на моду смешивания ионов. Предлагается простая модель с внешней гравитаиый, моделирующей ккивизну магнитного поля. Выводится дисперсионное соотношение, которое связывает моду смешивания ионов с повсеместной модой. Получено, что в рамках предложенной локальной модели неоднородная плазма может испытывать флуктуации с частотчми, большими по сравнению с частотами, ожидаемыми при анализе, в котором пренеб⌕егается кривизной магнитного поля. №жидается умемьшение порога неустойчивости этой моды, которая зависит от гразиента ионной температуры. Эффект гравитации на ионный отклик влияет на квазилинейный ионный перенос тепла.

     

Effective swimming strategies in low Reynolds number flows

The optimal strategy for a microscopic swimmer to migrate across a linear shear flow is discussed. The two cases, in which the swimmer is located at large distance, and in the proximity of a solid wall, are taken into account. It is shown that migration can be achieved by means of a combination of sailing through the flow and swimming, where the swimming strokes are induced by the external flow without need of internal energy sources or external drives. The structural dynamics required for the swimmer to move in the desired direction is discussed and two simple models, based respectively on the presence of an elastic structure, and on an orientation dependent friction, to control the deformations induced by the external flow, are analyzed. In all cases, the deformation sequence is a generalization of the tank-treading motion regimes observed in vesicles in shear flows. Analytic expressions for the migration velocity as a function of the deformation pattern and amplitude are provided. The effects of thermal fluctuations on propulsion have been discussed and the possibility that noise be exploited to overcome the limitations imposed on the microswimmer by the scallop theorem have been discussed.     

Fourier’s Law for a Microscopic Model of Heat Conduction

We consider a chain of N harmonic oscillators perturbed by a conservative stochastic dynamics and coupled at the boundaries to two gaussian thermostats at different temperatures. The stochastic perturbation is given by a diffusion process that exchange momentum between nearest neighbor oscillators conserving the total kinetic energy. The resulting total dynamics is a degenerate hypoelliptic diffusion with a smooth stationary state. We prove that the stationary state, in the limit as N→ ∞, satisfies Fourier’s law and the linear profile for the energy average     

On homogenization of time-dependent random flows

We study a diffusion with a random, time dependent drift. We prove the invariance principle when the spectral measure of the drift satisfies a certain integrability condition. This result generalizes the results of [13, 7]. Received: 25 February 2000 / Revised version: 11 December 2000 /?Published online: 14 June 2001     

Ensemble Dependence of Fluctuations: Canonical Microcanonical Equivalence of Ensembles

We study the equivalence of microcanonical and canonical ensembles in continuous systems, in the sense of the convergence of the corresponding Gibbs measures and the first order corrections. We are particularly interested in extensive observables, like the total kinetic energy. This result is obtained by proving an Edgeworth expansion for the local central limit theorem for the energy in the canonical measure, and a corresponding local large deviations expansion. As an application we prove a formula due to Lebowitz–Percus–Verlet that express the asymptotic microcanonical variance of the kinetic energy in terms of the heat capacity.     

Large deviations for Gibbs random fields

A large deviation principle for Gibbs random fields on Z^d is proven and a corresponding large deviations proof of the Gibbs variational formula is given. A generalization of the Lanford theory of large deviations is also obtained.This work was partially supported by NSF-DMR81-14726