273 research outputs found
Green-Kubo formula for weakly coupled system with dynamical noise
We study the Green-Kubo (GK) formula for the heat
conductivity of an infinite chain of -dimensional finite systems (cells)
coupled by a smooth nearest neighbour potential . The uncoupled
systems evolve according to Hamiltonian dynamics perturbed stochastically by an
energy conserving noise of strength . Noting that exists and is finite whenever , we are interested in what happens
when the strength of the noise . For this, we start in this work by
formally expanding in a power series in
, and investigating the (formal) equations
satisfied by . We show in particular that 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 , for the cases where the latter has
been established \cite{LO, DL}. For one-dimensional systems, we investigate
as in three cases: the disordered harmonic chain,
the rotor chain and a chain of strongly anharmonic oscillators. Moreover, we
formally identify with the conductivity obtained by having the
chain between two reservoirs at temperature and , in the limit
, , .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
Influence of morpho-structural parameters on the environmental stress cracking of polyethylene
The environmental stress cracking resistance (ESCR) of four polyethylenes in active medium (10% Tergitol solution) was investigated.
The four materials were chosen to explore a broad range of performance and applications; they are listed according to increasing expected ESCR:
- an injection moulding, low-molecular weight (MW) HDPE homopolymer
- two rotomoulding LLDPE copolymers with a different comonomer (butene or hexene)
- a blown film extrusion high MW HDPE copolymer (hexene)
The fracture resistance of the hexene LLDPE copolymer was expected to be slightly higher than that of the butene one, because of the longer alkyl group. The two materials were chosen to challenge the ability of the different testing methods to discriminate between similar levels of ESCR.
Several analytical techniques were employed to obtain relevant morpho-structural parameters: density, degree of crystallinity, MW distribution, short chain branch content and average lamellar thickness.
ESCR was evaluated by employing three well-known but widely different approaches:
- the Bell Telephone test (ASTMD1693), performed on notched specimens immersed in the active environment at 50°C
- strain hardening modulus (SHM), obtained from tensile tests performed in air at 80°C
- fracture mechanics (FM) tests on three- and four-point bending notched specimens, performed at varying temperatures both in air and in the active environment; two different loading histories were considered (creep and constant displacement rate)
MW distribution seems to have a greater effect on ESCR behaviour with respect to other morpho-structural parameters. There was instead a strong consistency of the different ESCR testing methods, so that SHM could replace ASTMD1693 as an industrial test aimed at ranking ESCR of polyethylenes. FM, while being more complex to carry out, provides a wealth of additional information which could be used to actually predict the lifetime of products working in an ESC environment
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
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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
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