99,388 research outputs found
Flocking Regimes in a Simple Lattice Model
We study a one-dimensional lattice flocking model incorporating all three of
the flocking criteria proposed by Reynolds [Computer Graphics vol.21 4 (1987)]:
alignment, centring and separation. The model generalises that introduced by O.
J. O' Loan and M. R. Evans [J. Phys. A. vol. 32 L99 (1999)]. We motivate the
dynamical rules by microscopic sampling considerations. The model exhibits
various flocking regimes: the alternating flock, the homogeneous flock and
dipole structures. We investigate these regimes numerically and within a
continuum mean-field theory.Comment: 24 pages 7 figure
Criticality and Condensation in a Non-Conserving Zero Range Process
The Zero-Range Process, in which particles hop between sites on a lattice
under conserving dynamics, is a prototypical model for studying real-space
condensation. Within this model the system is critical only at the transition
point. Here we consider a non-conserving Zero-Range Process which is shown to
exhibit generic critical phases which exist in a range of creation and
annihilation parameters. The model also exhibits phases characterised by
mesocondensates each of which contains a subextensive number of particles. A
detailed phase diagram, delineating the various phases, is derived.Comment: 15 pages, 4 figure, published versi
Soft core fluid in a quenched matrix of soft core particles: A mobile mixture in a model gel
We present a density-functional study of a binary phase-separating mixture of
soft core particles immersed in a random matrix of quenched soft core particles
of larger size. This is a model for a binary polymer mixture immersed in a
crosslinked rigid polymer network. Using the replica `trick' for
quenched-annealed mixtures we derive an explicit density functional theory that
treats the quenched species on the level of its one-body density distribution.
The relation to a set of effective external potentials acting on the annealed
components is discussed. We relate matrix-induced condensation in bulk to the
behaviour of the mixture around a single large particle. The interfacial
properties of the binary mixture at a surface of the quenched matrix display a
rich interplay between capillary condensation inside the bulk matrix and
wetting phenomena at the matrix surface.Comment: 20 pages, 5 figures. Accepted for Phys. Rev.
Dynamical density functional theory and its application to spinodal decomposition
We present an alternative derivation of the dynamical density functional
theory for the one body density profile of a classical fluid developed by
Marconi and Tarazona [J. Chem. Phys., 110, 8032 (1999)]. Our derivation
elucidates further some of the physical assumptions inherent in the theory and
shows that it is not restricted to fluids composed of particles interacting
solely via pair potentials; rather it applies to general, multi-body
interactions. The starting point for our derivation is the Smoluchowski
equation and the theory is therefore one for Brownian particles and as such is
applicable to colloidal fluids. In the second part of this paper we use the
dynamical density functional theory to derive a theory for spinodal
decomposition that is applicable at both early and intermediate times. For
early stages of spinodal decomposition our non-linear theory is equivalent to
the (generalised) linear Cahn-Hilliard theory, but for later times it
incorporates coupling between different Fourier components of the density
fluctuations (modes) and therefore goes beyond Cahn-Hilliard theory. We
describe the results of calculations for a model (Yukawa) fluid which show that
the coupling leads to the growth of a second maximum in the density
fluctuations, at a wavenumber larger than that of the main peak.Comment: 23 pages, 3 figure
Why did British Electricity Prices Fall after 1998?
In an attempt to reduce high electricity prices in England and Wales the government has reduced concentration among generators and introduced New Electricity Trading Arrangements (NETA). Econometric analysis on monthly data from April 1996 to September 2002 implies support for two conflicting hypotheses. On a static view, increases in competition and the capacity margin were chiefly responsible for the fall in prices. If generators had been tacitly colluding before NETA, however, the impending change in market rules might have changed their behaviour a few months before the abolition of the Pool. That view implies that NETA reduced prices.Electricity, market power, concentration, market rules
Non-analytic curvature contributions to solvation free energies: influence of drying
We investigate the solvation of a hard spherical cavity, of radius ,
immersed in a fluid for which the interparticle forces are short ranged. For
thermodynamic states lying close to the liquid binodal, where the chemical
potential deviation is very small and
positive, complete wetting by gas (drying) occurs and two regimes of
interfacial behavior can be identified. These are characterized by the length
scale , where
is the planar gas-liquid surface tension and
is the difference in coexisting densities at temperature . For , the
interfacial free energy and the density profile of the fluid near the hard wall
can be expanded in powers of the curvature , in keeping with the
analysis of Stillinger and Cotter, J. Chem. Phys. {\bf 55}, 3449 (1971). In the
other regime, , the interfacial free energy and its derivatives acquire
terms depending on . Since can be made arbitrarily small this
implies non-analytic behavior, as , of the work of formation of a
hard spherical cavity and of the Gibbs adsorption and the fluid density at
contact with the wall. Our analysis, which is based on an effective interfacial
Hamiltonian combined with exact statistical mechanical sum rules, is confirmed
fully by the results of microscopic density functional calculations for a
square-well fluid.Comment: 17 pages, 3 figures; accepted for publication in J. Chem. Phy
Correlation function algebra for inhomogeneous fluids
We consider variational (density functional) models of fluids confined in
parallel-plate geometries (with walls situated in the planes z=0 and z=L
respectively) and focus on the structure of the pair correlation function
G(r_1,r_2). We show that for local variational models there exist two
non-trivial identities relating both the transverse Fourier transform G(z_\mu,
z_\nu;q) and the zeroth moment G_0(z_\mu,z_\nu) at different positions z_1, z_2
and z_3. These relations form an algebra which severely restricts the possible
form of the function G_0(z_\mu,z_\nu). For the common situations in which the
equilibrium one-body (magnetization/number density) profile m_0(z) exhibits an
odd or even reflection symmetry in the z=L/2 plane the algebra simplifies
considerably and is used to relate the correlation function to the finite-size
excess free-energy \gamma(L). We rederive non-trivial scaling expressions for
the finite-size contribution to the free-energy at bulk criticality and for
systems where large scale interfacial fluctuations are present. Extensions to
non-planar geometries are also considered.Comment: 15 pages, RevTex, 4 eps figures. To appear in J.Phys.Condens.Matte
Statistical Mechanics of Time Independent Non-Dissipative Nonequilibrium States
We examine the question of whether the formal expressions of equilibrium
statistical mechanics can be applied to time independent non-dissipative
systems that are not in true thermodynamic equilibrium and are nonergodic. By
assuming the phase space may be divided into time independent, locally ergodic
domains, we argue that within such domains the relative probabilities of
microstates are given by the standard Boltzmann weights. In contrast to
previous energy landscape treatments, that have been developed specifically for
the glass transition, we do not impose an a priori knowledge of the
inter-domain population distribution. Assuming that these domains are robust
with respect to small changes in thermodynamic state variables we derive a
variety of fluctuation formulae for these systems. We verify our theoretical
results using molecular dynamics simulations on a model glass forming system.
Non-equilibrium Transient Fluctuation Relations are derived for the
fluctuations resulting from a sudden finite change to the system's temperature
or pressure and these are shown to be consistent with the simulation results.
The necessary and sufficient conditions for these relations to be valid are
that the domains are internally populated by Boltzmann statistics and that the
domains are robust. The Transient Fluctuation Relations thus provide an
independent quantitative justification for the assumptions used in our
statistical mechanical treatment of these systems.Comment: 17 pages, 4 figures, minor amendment
The rheology of solid glass
As the glass transition is approached from the high temperature side, viewed as a liquid, the properties of the ever more viscous supercooled liquid are continuous functions of temperature and pressure. The point at which we decide to classify the fluid as a solid is therefore subjective. This subjective decision does, however, have discontinuous consequences for how we determine the rheological properties of the glass. We apply the recently discovered relaxation theorem to the time independent, nondissipative, nonergodic glassy state to derive an expression for the phase space distribution of an ensemble of glass samples. This distribution is then used to construct a time dependent linear response theory for aged glassysolids. The theory is verified using molecular dynamics simulations of oscillatory shear for a realistic model glass former with excellent agreement being obtained between the response theory calculations and direct nonequilibrium molecular dynamics calculations. Our numerical results confirm that unlike all the fluid states, including supercooled liquids, a solidglass (in common with crystalline states) has a nonzero value for the zero frequency shear modulus. Of all the states of matter, a supercooled fluid approaching the glass transition has the highest value for the limiting zero frequency shear viscosity. Finally, solidglasses like dilute gases and crystals have a positive temperature coefficient for the shear viscosity whereas supercooled and normal liquids have a negative temperature coefficient.We thank the National Computational Infrastructure
NCI for computational facilities and the Australian
Research Council ARC for funding
A model colloidal fluid with competing interactions: bulk and interfacial properties
Using a simple mean-field density functional theory theory (DFT), we
investigate the structure and phase behaviour of a model colloidal fluid
composed of particles interacting via a pair potential which has a hard core of
diameter , is attractive Yukawa at intermediate separations and
repulsive Yukawa at large separations. We analyse the form of the asymptotic
decay of the bulk fluid correlation functions, comparing results from our DFT
with those from the self consistent Ornstein-Zernike approximation (SCOZA). In
both theories we find rich crossover behaviour, whereby the ultimate decay of
correlation functions changes from monotonic to long-wavelength damped
oscillatory decay on crossing certain lines in the phase diagram, or sometimes
from oscillatory to oscillatory with a longer wavelength. For some choices of
potential parameters we find, within the DFT, a -line at which the
fluid becomes unstable with respect to periodic density fluctuations. SCOZA
fails to yield solutions for state points near such a -line. The
propensity to clustering of particles, which is reflected by the presence of a
long wavelength , slowly decaying oscillatory pair correlation
function, and a structure factor that exhibits a very sharp maximum at small
but non zero wavenumbers, is enhanced in states near the -line. We
present density profiles for the planar liquid-gas interface and for fluids
adsorbed at a planar hard wall. The presence of a nearby -transition
gives rise to pronounced long-wavelength oscillations in the one-body densities
at both types of interface.Comment: 14 pages, 11 figure
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