Wall mediated transport in confined spaces: Exact theory for low density

We present a theory for the transport of molecules adsorbed in slit and cylindrical nanopores at low density, considering the axial momentum gain of molecules oscillating between diffuse wall reflections. Good agreement with molecular dynamics simulations is obtained over a wide range of pore sizes, including the regime of single-file diffusion where fluid-fluid interactions are shown to have a negligible effect on the collective transport coefficient. We show that dispersive fluid-wall interactions considerably attenuate transport compared to classical hard sphere theory

Modeling molecular transport in slit pores

We examine the transport of methane in microporous carbon by performing equilibrium and nonequilibrium molecular dynamics simulations over a range of pore sizes, densities, and temperatures. We interpret these simulation results using two models of the transport process. At low densities, we consider a molecular flow model, in which intermolecular interactions are neglected, and find excellent agreement between transport diffusion coefficients determined from simulation, and those predicted by the model. Simulation results indicate that the model can be applied up to fluid densities of the order to 0.1-1 nm(-3). Above these densities, we consider a slip flow model, combining hydrodynamic theory with a slip condition at the solid-fluid interface. As the diffusion coefficient at low densities can be accurately determined by the molecular flow model, we also consider a model where the slip condition is supplied by the molecular flow model. We find that both density-dependent models provide a useful means of estimating the transport coefficient that compares well with simulation. (C) 2004 American Institute of Physics

Anomalous interactions in confined charge-stabilized colloid

Charge-stabilized colloidal spheres dispersed in weak 1:1 electrolytes are supposed to repel each other. Consequently, experimental evidence for anomalous long-ranged like-charged attractions induced by geometric confinement inspired a burst of activity. This has largely subsided because of nagging doubts regarding the experiments' reliability and interpretation. We describe a new class of thermodynamically self-consistent colloidal interaction measurements that confirm the appearance of pairwise attractions among colloidal spheres confined by one or two bounding walls. In addition to supporting previous claims for this as-yet unexplained effect, these measurements also cast new light on its mechanism.Comment: 8 pages, 5 figures, RevTeX4. Conference proceedings for CODEF-04, Colloidal Dispersions in External Fields, March 29 - April 1, 200

Microcanonical temperature for a classical field: application to Bose-Einstein condensation

We show that the projected Gross-Pitaevskii equation (PGPE) can be mapped exactly onto Hamilton's equations of motion for classical position and momentum variables. Making use of this mapping, we adapt techniques developed in statistical mechanics to calculate the temperature and chemical potential of a classical Bose field in the microcanonical ensemble. We apply the method to simulations of the PGPE, which can be used to represent the highly occupied modes of Bose condensed gases at finite temperature. The method is rigorous, valid beyond the realms of perturbation theory, and agrees with an earlier method of temperature measurement for the same system. Using this method we show that the critical temperature for condensation in a homogeneous Bose gas on a lattice with a UV cutoff increases with the interaction strength. We discuss how to determine the temperature shift for the Bose gas in the continuum limit using this type of calculation, and obtain a result in agreement with more sophisticated Monte Carlo simulations. We also consider the behaviour of the specific heat.Comment: v1: 9 pages, 5 figures, revtex 4. v2: additional text in response to referee's comments, now 11 pages, to appear in Phys. Rev.

Fluctuations in Nonequilibrium Statistical Mechanics: Models, Mathematical Theory, Physical Mechanisms

The fluctuations in nonequilibrium systems are under intense theoretical and experimental investigation. Topical ``fluctuation relations'' describe symmetries of the statistical properties of certain observables, in a variety of models and phenomena. They have been derived in deterministic and, later, in stochastic frameworks. Other results first obtained for stochastic processes, and later considered in deterministic dynamics, describe the temporal evolution of fluctuations. The field has grown beyond expectation: research works and different perspectives are proposed at an ever faster pace. Indeed, understanding fluctuations is important for the emerging theory of nonequilibrium phenomena, as well as for applications, such as those of nanotechnological and biophysical interest. However, the links among the different approaches and the limitations of these approaches are not fully understood. We focus on these issues, providing: a) analysis of the theoretical models; b) discussion of the rigorous mathematical results; c) identification of the physical mechanisms underlying the validity of the theoretical predictions, for a wide range of phenomena.Comment: 44 pages, 2 figures. To appear in Nonlinearity (2007

Steady state fluctuation relation and time-reversibility for non-smooth chaotic maps

Steady state fluctuation relations for dynamical systems are commonly derived under the assumption of some form of time-reversibility and of chaos. There are, however, cases in which they are observed to hold even if the usual notion of time reversal invariance is violated, e.g. for local fluctuations of Navier-Stokes systems. Here we construct and study analytically a simple non-smooth map in which the standard steady state fluctuation relation is valid, although the model violates the Anosov property of chaotic dynamical systems. Particularly, the time reversal operation is performed by a discontinuous involution, and the invariant measure is also discontinuous along the unstable manifolds. This further indicates that the validity of fluctuation relations for dynamical systems does not rely on particularly elaborate conditions, usually violated by systems of interest in physics. Indeed, even an irreversible map is proved to verify the steady state fluctuation relation.Comment: 23 pages,8 figure

Colour conductivity of hard spheres

We present an analytic solution for the d-dimensional (d>1) hard-sphere free flight trajectories in a thermostatted colour field. The solution shows that particles can only reach a finite distance in the direction perpendicular to the field in the absence of collisions. Using a numerical algorithm we designed to simulate many-body hard-sphere systems with curved trajectories, we study the onset of the instability leading to phase separation in the two-dimensional case for a range of field strengths and three densities. For the two fluid densities we find that phase separation occurs for sufficiently strong fields regardless of the initial configuration, and that the phase-separated state eventually becomes a collisionless, nonergodic steady state. For solid densities the phase-separated configuration is stable and conducting, but is not an attractor for other charge distributions because of the impossibility of particle rearrangement

Deterministic thermostats, theories of nonequilibrium systems and parallels with the ergodiccondition

Deterministic 'thermostats' are mathematical tools used to model nonequilibrium steady states of fluids. The resulting dynamical systems correctly represent the transport properties of these fluids and are easily simulated on modern computers. More recently, the connection between such thermostats and entropy production has been exploited in the development of nonequilibrium fluid theories. The purpose and limitations of deterministic thermostats are discussed in the context of irreversible thermodynamics and the development of theories of nonequilibrium phenomena. We draw parallels between the development of such nonequilibrium theories and the development of notions of ergodicity in equilibrium theories.No Full Tex