2,566 research outputs found
Towards a unification of HRT and SCOZA
The Hierarchical Reference Theory (HRT) and the Self-Consistent
Ornstein-Zernike Approximation (SCOZA) are two liquid state theories that both
furnish a largely satisfactory description of the critical region as well as
phase separation and the equation of state in general. Furthermore, there are a
number of similarities that suggest the possibility of a unification of both
theories. As a first step towards this goal we consider the problem of
combining the lowest order gamma expansion result for the incorporation of a
Fourier component of the interaction with the requirement of consistency
between internal and free energies, leaving aside the compressibility relation.
For simplicity we restrict ourselves to a simplified lattice gas that is
expected to display the same qualitative behavior as more elaborate models. It
turns out that the analytically tractable Mean Spherical Approximation is a
solution to this problem, as are several of its generalizations. Analysis of
the characteristic equations shows the potential for a practical scheme and
yields necessary conditions any closure to the Ornstein Zernike relation must
fulfill for the consistency problem to be well posed and to have a unique
differentiable solution. These criteria are expected to remain valid for more
general discrete and continuous systems, even if consistency with the
compressibility route is also enforced where possible explicit solutions will
require numerical evaluations.Comment: Minor changes in accordance with referee comment
SCOZA for Monolayer Films
We show the way in which the self-consistent Ornstein-Zernike approach
(SCOZA) to obtaining structure factors and thermodynamics for Hamiltonian
models can best be applied to two-dimensional systems such as thin films. We
use the nearest-neighbor lattice gas on a square lattice as an illustrative
example.Comment: 10 pages, 5 figure
Market forces and airline safety: an empirical reevaluation
The recent publicity with regard to commercial airline accidents and near accidents has sparked new debate over the issue of safety in the industry under deregulation, with the main issue being the unregulated market\u27s ability to impose significant penalties for poor safety attitudes. This study shows that although there are large movements in the price of airline stocks subsequent to accidents, the market imposed costs do not provide a direct motivation for enhanced safety performance. Instead, the market\u27s reaction to airline accidents is based on the nature of airline stocks as short term investment tools. It is necessary, therefore, to continue to carefully evaluate the role of government in the promotion of airline safety in a deregulated environment. One cannot assert, without qualification, that free market forces, in and of themselves, will provide individual firms with the impetus to provide the socially optimal level of safety performance
Mapping a Homopolymer onto a Model Fluid
We describe a linear homopolymer using a Grand Canonical ensemble formalism,
a statistical representation that is very convenient for formal manipulations.
We investigate the properties of a system where only next neighbor interactions
and an external, confining, field are present, and then show how a general pair
interaction can be introduced perturbatively, making use of a Mayer expansion.
Through a diagrammatic analysis, we shall show how constitutive equations
derived for the polymeric system are equivalent to the Ornstein-Zernike and
P.Y. equations for a simple fluid, and find the implications of such a mapping
for the simple situation of Van der Waals mean field model for the fluid.Comment: 12 pages, 3 figure
Solution of the Percus-Yevick equation for hard discs
We solve the Percus-Yevick equation in two dimensions by reducing it to a set
of simple integral equations. We numerically obtain both the pair correlation
function and the equation of state for a hard disc fluid and find good
agreement with available Monte-Carlo calculations. The present method of
resolution may be generalized to any even dimension.Comment: 9 pages, 3 figure
Thermodynamic and dynamic anomalies for a three dimensional isotropic core-softened potential
Using molecular dynamics simulations and integral equations (Rogers-Young,
Percus-Yevick and hypernetted chain closures) we investigate the thermodynamic
of particles interacting with continuous core-softened intermolecular
potential. Dynamic properties are also analyzed by the simulations. We show
that, for a chosen shape of the potential, the density, at constant pressure,
has a maximum for a certain temperature. The line of temperatures of maximum
density (TMD) was determined in the pressure-temperature phase diagram.
Similarly the diffusion constant at a constant temperature, , has a maximum
at a density and a minimum at a density .
In the pressure-temperature phase-diagram the line of extrema in diffusivity is
outside of TMD line. Although in this interparticle potential lacks
directionality, this is the same behavior observed in SPC/E water.Comment: 16 page
Evolution of collision numbers for a chaotic gas dynamics
We put forward a conjecture of recurrence for a gas of hard spheres that
collide elastically in a finite volume. The dynamics consists of a sequence of
instantaneous binary collisions. We study how the numbers of collisions of
different pairs of particles grow as functions of time. We observe that these
numbers can be represented as a time-integral of a function on the phase space.
Assuming the results of the ergodic theory apply, we describe the evolution of
the numbers by an effective Langevin dynamics. We use the facts that hold for
these dynamics with probability one, in order to establish properties of a
single trajectory of the system. We find that for any triplet of particles
there will be an infinite sequence of moments of time, when the numbers of
collisions of all three different pairs of the triplet will be equal. Moreover,
any value of difference of collision numbers of pairs in the triplet will
repeat indefinitely. On the other hand, for larger number of pairs there is but
a finite number of repetitions. Thus the ergodic theory produces a limitation
on the dynamics.Comment: 4 pages, published versio
Liquid Transport Due to Light Scattering
Using experiments and theory, we show that light scattering by
inhomogeneities in the index of refraction of a fluid can drive a large-scale
flow. The experiment uses a near-critical, phase-separated liquid, which
experiences large fluctuations in its index of refraction. A laser beam
traversing the liquid produces a large-scale deformation of the interface and
can cause a liquid jet to form. We demonstrate that the deformation is produced
by a scattering-induced flow by obtaining good agreements between the measured
deformations and those calculated assuming this mechanism.Comment: 4 pages, 5 figures, submitted to Physical Review Letters v2: Edited
based on comments from referee
Classification of minimal actions of a compact Kac algebra with amenable dual
We show the uniqueness of minimal actions of a compact Kac algebra with
amenable dual on the AFD factor of type II. This particularly implies the
uniqueness of minimal actions of a compact group. Our main tools are a Rohlin
type theorem, the 2-cohomology vanishing theorem, and the Evans-Kishimoto type
intertwining argument.Comment: 68 pages, Introduction rewritten; minor correction
Quantum criticality around metal-insulator transitions of strongly correlated electrons
Quantum criticality of metal-insulator transitions in correlated electron
systems is shownto belong to an unconventional universality class with
violation of Ginzburg-Landau-Wilson(GLW) scheme formulated for symmetry
breaking transitions. This unconventionality arises from an emergent character
of the quantum critical point, which appears at the marginal point between the
Ising-type symmetry breaking at nonzero temperatures and the topological
transition of the Fermi surface at zero temperature. We show that Hartree-Fock
approximations of an extended Hubbard model on square latticesare capable of
such metal-insulator transitions with unusual criticality under a preexisting
symmetry breaking. The obtained universality is consistent with the scaling
theory formulated for Mott transition and with a number of numerical results
beyond the mean-field level, implying that the preexisting symmetry breaking is
not necessarily required for the emergence of this unconventional universality.
Examinations of fluctuation effects indicate that the obtained critical
exponents remain essentially exact beyond the mean-field level. Detailed
analyses on the criticality, containing diverging carrier density fluctuations
around the marginal quantum critical point, are presented from microscopic
calculations and reveal the nature as quantum critical "opalescence". Analyses
on crossovers between GLW type at nonzero temperature and topological type at
zero temperature show that the critical exponents observed in (V,Cr)2O3 and
kappa-ET-type organic conductor provide us with evidences for the existence of
the present marginal quantum criticality.Comment: 24 pages, 19 figure
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