Effects of Confinement on Critical Adsorption: Absence of Critical Depletion for Fluids in Slit Pores

The adsorption of a near-critical fluid confined in a slit pore is investigated by means of density functional theory and by Monte Carlo simulation for a Lennard-Jones fluid. Our work was stimulated by recent experiments for SF_6 adsorbed in a mesoporous glass which showed the striking phenomenon of critical depletion, i.e. the adsorption excess "Gamma" first increases but then decreases very rapidly to negative values as the bulk critical temperature T_c is approached from above along near-critical isochores. By contrast, our density functional and simulation results, for a range of strongly attractive wall-fluid potentials, show Gamma monotonically increasing and eventually saturating as the temperature is lowered towards T_c along both the critical (rho=rho_c) and sub-critical isochores (rho<\rho_c). Such behaviour results from the increasingly slow decay of the density profile away from the walls, into the middle of the slit, as T->T_c. For rho < rho_c we find that in the fluid the effective bulk field, which is negative and which favours desorption, is insufficient to dominate the effects of the surface fields which favour adsorption. We compare this situation with earlier results for the lattice gas model with a constant (negative) bulk field where critical depletion was found. Qualitatively different behaviour of the density profiles and adsorption is found in simulations for intermediate and weakly attractive wall-fluid potentials but in no case do we observe the critical depletion found in experiments. We conclude that the latter cannot be accounted for by a single pore model.Comment: 21 pages Revtex. Submitted to Phys. Rev.

Phase Transition in the ABC Model

Recent studies have shown that one-dimensional driven systems can exhibit phase separation even if the dynamics is governed by local rules. The ABC model, which comprises three particle species that diffuse asymmetrically around a ring, shows anomalous coarsening into a phase separated steady state. In the limiting case in which the dynamics is symmetric and the parameter $q$ describing the asymmetry tends to one, no phase separation occurs and the steady state of the system is disordered. In the present work we consider the weak asymmetry regime $q=\exp{(-\beta/N)}$ where $N$ is the system size and study how the disordered state is approached. In the case of equal densities, we find that the system exhibits a second order phase transition at some nonzero $\beta_c$. The value of $\beta_c = 2 \pi \sqrt{3}$ and the optimal profiles can be obtained by writing the exact large deviation functional. For nonequal densities, we write down mean field equations and analyze some of their predictions.Comment: 18 pages, 3 figure

Spontaneous Symmetry Breaking in a Non-Conserving Two-Species Driven Model

A two species particle model on an open chain with dynamics which is non-conserving in the bulk is introduced. The dynamical rules which define the model obey a symmetry between the two species. The model exhibits a rich behavior which includes spontaneous symmetry breaking and localized shocks. The phase diagram in several regions of parameter space is calculated within mean-field approximation, and compared with Monte-Carlo simulations. In the limit where fluctuations in the number of particles in the system are taken to zero, an exact solution is obtained. We present and analyze a physical picture which serves to explain the different phases of the model

Exact solution of the zero-range process: fundamental diagram of the corresponding exclusion process

In this paper, we propose a general way of computing expectation values in the zero-range process, using an exact form of the partition function. As an example, we provide the fundamental diagram (the flux-density plot) of the asymmetric exclusion process corresponding to the zero-range process.We express the partition function for the steady state by the Lauricella hypergeometric function, and thereby have two exact fundamental diagrams each for the parallel and random sequential update rules. Meanwhile, from the viewpoint of equilibrium statistical mechanics, we work within the canonical ensemble but the result obtained is certainly in agreement with previous works done in the grand canonical ensemble.Comment: 12 pages, 2 figure

An exactly solvable dissipative transport model

We introduce a class of one-dimensional lattice models in which a quantity, that may be thought of as an energy, is either transported from one site to a neighbouring one, or locally dissipated. Transport is controlled by a continuous bias parameter q, which allows us to study symmetric as well as asymmetric cases. We derive sufficient conditions for the factorization of the N-body stationary distribution and give an explicit solution for the latter, before briefly discussing physically relevant situations.Comment: 7 pages, 1 figure, submitted to J. Phys.

Yang-Lee Theory for a Nonequilibrium Phase Transition

To analyze phase transitions in a nonequilibrium system we study its grand canonical partition function as a function of complex fugacity. Real and positive roots of the partition function mark phase transitions. This behavior, first found by Yang and Lee under general conditions for equilibrium systems, can also be applied to nonequilibrium phase transitions. We consider a one-dimensional diffusion model with periodic boundary conditions. Depending on the diffusion rates, we find real and positive roots and can distinguish two regions of analyticity, which can identified with two different phases. In a region of the parameter space both of these phases coexist. The condensation point can be computed with high accuracy.Comment: 4 pages, accepted for publication in Phys.Rev.Let

Condensation Transitions in Two Species Zero-Range Process

We study condensation transitions in the steady state of a zero-range process with two species of particles. The steady state is exactly soluble -- it is given by a factorised form provided the dynamics satisfy certain constraints -- and we exploit this to derive the phase diagram for a quite general choice of dynamics. This phase diagram contains a variety of new mechanisms of condensate formation, and a novel phase in which the condensate of one of the particle species is sustained by a `weak' condensate of particles of the other species. We also demonstrate how a single particle of one of the species (which plays the role of a defect particle) can induce Bose-Einstein condensation above a critical density of particles of the other species.Comment: 17 pages, 4 Postscript figure

Conserved mass models with stickiness and chipping

We study a chipping model in one dimensional periodic lattice with continuous mass, where a fixed fraction of the mass is chipped off from a site and distributed randomly among the departure site and its neighbours; the remaining mass sticks to the site. In the asymmetric version, the chipped off mass is distributed among the site and the right neighbour, whereas in the symmetric version the redistribution occurs among the two neighbours. The steady state mass distribution of the model is obtained using a perturbation method for both parallel and random sequential updates. In most cases, this perturbation theory provides a steady state distribution with reasonable accuracy.Comment: 17 pages, 4 eps figure