Green-Kubo formula for weakly coupled system with dynamical noise

We study the Green-Kubo (GK) formula $\kappa (\varepsilon, \xi)$ for the heat conductivity of an infinite chain of $d$-dimensional finite systems (cells) coupled by a smooth nearest neighbour potential $\varepsilon V$. The uncoupled systems evolve according to Hamiltonian dynamics perturbed stochastically by an energy conserving noise of strength $\xi$. Noting that $\kappa (\varepsilon, \xi)$ exists and is finite whenever $\xi> 0$, we are interested in what happens when the strength of the noise $\xi \to 0$. For this, we start in this work by formally expanding $\kappa (\varepsilon, \xi)$ in a power series in $\varepsilon$, $\kappa (\varepsilon, \xi) = \varepsilon^2 \sum_{n\ge 2} \varepsilon^{n-2} \kappa_n (\xi)$ and investigating the (formal) equations satisfied by $\kappa_n (\xi$. We show in particular that $\kappa_2 (\xi)$ is well defined when no pinning potential is present, and coincides formally with the heat conductivity obtained in the weak coupling (van Hove) limit, where time is rescaled as $\varepsilon^{-2}t$, for the cases where the latter has been established \cite{LO, DL}. For one-dimensional systems, we investigate $\kappa_2 (\xi)$ as $\xi\to 0$ in three cases: the disordered harmonic chain, the rotor chain and a chain of strongly anharmonic oscillators. Moreover, we formally identify $\kappa_2 (\xi)$ with the conductivity obtained by having the chain between two reservoirs at temperature $T$ and $T+\delta T$, in the limit $\delta T\to 0$, $N \to \infty$, $\varepsilon \to 0$.Comment: New version with many improvement

Orientation dynamics of weakly Brownian particles in periodic viscous flows

Evolution equations for the orientation distribution of axisymmetric particles in periodic flows are derived in the regime of small but non-zero Brownian rotations. The equations are based on a multiple time scale approach that allows fast computation of the relaxation processes leading to statistical equilibrium. The approach has been applied to the calculation of the effective viscosity of a thin disk suspension in gravity waves.Comment: 16 pages, 7 eps figures include

Nonequilibrium dynamics of a stochastic model of anomalous heat transport

We study the dynamics of covariances in a chain of harmonic oscillators with conservative noise in contact with two stochastic Langevin heat baths. The noise amounts to random collisions between nearest-neighbour oscillators that exchange their momenta. In a recent paper, [S Lepri et al. J. Phys. A: Math. Theor. 42 (2009) 025001], we have studied the stationary state of this system with fixed boundary conditions, finding analytical exact expressions for the temperature profile and the heat current in the thermodynamic (continuum) limit. In this paper we extend the analysis to the evolution of the covariance matrix and to generic boundary conditions. Our main purpose is to construct a hydrodynamic description of the relaxation to the stationary state, starting from the exact equations governing the evolution of the correlation matrix. We identify and adiabatically eliminate the fast variables, arriving at a continuity equation for the temperature profile T(y,t), complemented by an ordinary equation that accounts for the evolution in the bulk. Altogether, we find that the evolution of T(y,t) is the result of fractional diffusion.Comment: Submitted to Journal of Physics A, Mathematical and Theoretica

Transport properties of heavy particles in high Reynolds number turbulence

The statistical properties of heavy particle trajectories in high Reynolds numbers turbulent flows are analyzed. Dimensional analysis assuming Kolmogorov scaling is compared with the result of numerical simulation using a synthetic turbulence advecting field. The non-Markovian nature of the fluid velocity statistics along the solid particle trajectories is put into evidence, and its relevance in the derivation of Lagrangian transport models is discussed.Comment: 30 pages, 11 eps figures included. To appear in Physics of Fluid

Anomalous transport and relaxation in classical one-dimensional models

After reviewing the main features of anomalous energy transport in 1D systems, we report simulations performed with chains of noisy anharmonic oscillators. The stochastic terms are added in such a way to conserve total energy and momentum, thus keeping the basic hydrodynamic features of these models. The addition of this "conservative noise" allows to obtain a more efficient estimate of the power-law divergence of heat conductivity kappa(L) ~ L^alpha in the limit of small noise and large system size L. By comparing the numerical results with rigorous predictions obtained for the harmonic chain, we show how finite--size and --time effects can be effectively controlled. For low noise amplitudes, the alpha values are close to 1/3 for asymmetric potentials and to 0.4 for symmetric ones. These results support the previously conjectured two-universality-classes scenario

A note on a local ergodic theorem for an infinite tower of coverings

This is a note on a local ergodic theorem for a symmetric exclusion process defined on an infinite tower of coverings, which is associated with a finitely generated residually finite amenable group.Comment: Final version to appear in Springer Proceedings in Mathematics and Statistic

Altered search speed and growth: social versus independent foraging in two pelagic juvenile fishes

Prior studies have demonstrated that juvenile walleye pollock Theragra chalcogramma forage socially in schools for spatially and temporally clumped food, but forage more independently for spatially and temporally dispersed food. One advantage of social foraging is that fish in schools may be able to locate more food clumps than fish foraging individually. However, data also indicate that walleye pollock swim faster when foraging socially. We conducted laboratory experiments to evaluate the effect of food distribution upon the energetic foraging costs incurred by juvenile walleye pollock and sablefish Anaplopoma fimbria. We predicted that when given identical rations, fish receiving clumped food would swim faster, expending more energy, and therefore grow more slowly than fish receiving dispersed food. After 2 wk under these 2 foraging regimes, juvenile walleye pollock receiving clumped food swam 50 % faster, but experienced 19 % lower growth, than walleye pollock receiving dispersed food. Sablefish demonstrated only a weak swim speed response, with no difference in growth between food distributions. Our results demonstrate that although social foraging may increase encounter rates with food, in some species there may also be an energetic cost for this behavior, which will have an influence upon energetic efficiency, potentially affecting growth and survival.Keywords: Swimming, Growth, Foraging strategy, Bioenergetics, Milkshake effect, Shoalin

Effects of physical factors on the vertical distribution of larval walleye pollock Theragra chalcogramma under controlled laboratory conditions

This study examined, under controlled laboratory conditions, behavioral responses of larval walleye pollock (4 to 8 mm) to various physical factors that may potentially play a role in vertical movements and distribution. Diel periodicity in vertical distribution was evident and appeared to be under exogenous control. During the day, with light intensity at 70 μE/m⁻²s⁻¹, larvae moved downward from the surface. As light intensity decreased during simulated evening twilight, larvae moved upward. At night, with no available light, larvae continued to swim upward, apparently the result of negative geotaxis. They remained near the surface until morning when they then began moving downward. Changes in vertical distribution occurred concomitantly with changes in activity, orientation and behavior. Formation of a vertical thermal gradient caused larvae to move upward and away from cold water. Turbulence at the surface, induced by an airstream, elicited an avoidance response and resulted in larvae moving downward.Keywords: diel periodicity, vertical migrations, light intensity, Theragra chalcogramm