51 research outputs found
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
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
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.
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
Adsorbate transport in nanopores
We present a tractable theory of transport of simple fluids in cylindrical nanopores, considering trajectories of molecules between diffuse wall collisions at low-density, and including viscous flow contributions at higher densities. The model is validated through molecular dynamics simulations of supercritical methane transport, over a wide range of conditions. We find excellent agreement between model and simulation at low to medium densities. However, at high densities the model tends to over-predict the transport behaviour, due to a large decrease in surface slip that is not well represented by the model. It is also seen that the concept of activated diffusion, commonly associated with diffusion in small pores, is fundamentally invalid for smooth pores
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