57 research outputs found
Anomalous phase behavior of a soft-repulsive potential with a strictly monotonic force
We study the phase behavior of a classical system of particles interacting
through a strictly convex soft-repulsive potential which, at variance with the
pairwise softened repulsions considered so far in the literature, lacks a
region of downward or zero curvature. Nonetheless, such interaction is
characterized by two length scales, owing to the presence of a range of
interparticle distances where the repulsive force increases, for decreasing
distance, much more slowly than in the adjacent regions. We investigate, using
extensive Monte Carlo simulations combined with accurate free-energy
calculations, the phase diagram of the system under consideration. We find that
the model exhibits a fluid-solid coexistence line with multiple re-entrant
regions, an extremely rich solid polymorphism with solid-solid transitions, and
water-like anomalies. In spite of the isotropic nature of the interparticle
potential, we find that, among the crystal structures in which the system can
exist, there are also a number of non-Bravais lattices, such as cI16 and
diamond.Comment: 21 pages, 7 figures, in press on Phys. Rev.
A probabilistic model for the equilibration of an ideal gas
I present a generalization of the Ehrenfest urn model that is aimed at
simulating the approach to equilibrium in a dilute gas. The present model
differs from the original one in two respects: 1) the two boxes have different
volumes and are divided into identical cells with either multiple or single
occupancy; 2) particles, which carry also a velocity vector, are subjected to
random, but elastic, collisions, both mutual and against the container walls. I
show, both analytically and numerically, that the number and energy of
particles in a given urn evolve eventually to an equilibrium probability
density which, depending on cell occupancy, is binomial or hypergeometric
in the particle number and beta-like in the energy. Moreover, the Boltzmann
entropy takes precisely the same form as the thermodynamic entropy of
an ideal gas. This exercise can be useful for pedagogical purposes in that it
provides, although in an extremely simplified case, a probabilistic
justification for the maximum-entropy principle.Comment: 9 pages, 2 figure
Hexatic phase and water-like anomalies in a two-dimensional fluid of particles with a weakly softened core
We study a two-dimensional fluid of particles interacting through a
spherically-symmetric and marginally soft two-body repulsion. This model can
exist in three different crystal phases, one of them with square symmetry and
the other two triangular. We show that, while the triangular solids first melt
into a hexatic fluid, the square solid is directly transformed on heating into
an isotropic fluid through a first-order transition, with no intermediate
tetratic phase. In the low-pressure triangular and square crystals melting is
reentrant provided the temperature is not too low, but without the necessity of
two competing nearest-neighbor distances over a range of pressures. A whole
spectrum of water-like fluid anomalies completes the picture for this model
potential.Comment: 26 pages, 14 figures; printed article available at
http://link.aip.org/link/?jcp/137/10450
- …