383 research outputs found
Optimal escape from metastable states driven by non-Gaussian noise
5 pages, 2 figures5 pages, 2 figures5 pages, 2 figuresWe investigate escape processes from metastable states that are driven by non-Gaussian noise. Using a path integral approach, we define a weak-noise scaling limit that identifies optimal escape paths as minima of a stochastic action, while retaining the infinite hierarchy of noise cumulants. This enables us to investigate the effect of different noise amplitude distributions. We find generically a reduced effective potential barrier but also fundamental differences, particularly for the limit when the non-Gaussian noise pulses are relatively slow. Here we identify a class of amplitude distributions that can induce a single-jump escape from the potential well. Our results highlight that higher-order noise cumulants crucially influence escape behaviour even in the weak-noise limit
Isotropic-nematic phase equilibria of polydisperse hard rods: The effect of fat tails in the length distribution
We study the phase behaviour of hard rods with length polydispersity, treated
within a simplified version of the Onsager model. We give a detailed
description of the unusual phase behaviour of the system when the rod length
distribution has a "fat" (e.g. log-normal) tail up to some finite cutoff. The
relatively large number of long rods in the system strongly influences the
phase behaviour: the isotropic cloud curve, which defines the where a nematic
phase first occurs as density is increased, exhibits a kink; at this point the
properties of the coexisting nematic shadow phase change discontinuously. A
narrow three-phase isotropic-nematic-nematic coexistence region exists near the
kink in the cloud curve, even though the length distribution is unimodal. A
theoretical derivation of the isotropic cloud curve and nematic shadow curve,
in the limit of large cutoff, is also given. The two curves are shown to
collapse onto each other in the limit. The coexisting isotropic and nematic
phases are essentially identical, the only difference being that the nematic
contains a larger number of the longest rods; the longer rods are also the only
ones that show any significant nematic ordering. Numerical results for finite
but large cutoff support the theoretical predictions for the asymptotic scaling
of all quantities with the cutoff length.Comment: 21 pages, 13 figure
Liquid-gas coexistence and critical point shifts in size-disperse fluids
Specialized Monte Carlo simulations and the moment free energy (MFE) method
are employed to study liquid-gas phase equilibria in size-disperse fluids. The
investigation is made subject to the constraint of fixed polydispersity, i.e.
the form of the `parent' density distribution of the particle
diameters , is prescribed. This is the experimentally realistic
scenario for e.g. colloidal dispersions. The simulations are used to obtain the
cloud and shadow curve properties of a Lennard-Jones fluid having diameters
distributed according to a Schulz form with a large (40%) degree of
polydispersity. Good qualitative accord is found with the results from a MFE
method study of a corresponding van der Waals model that incorporates
size-dispersity both in the hard core reference and the attractive parts of the
free energy. The results show that polydispersity engenders considerable
broadening of the coexistence region between the cloud curves. The principal
effect of fractionation in this region is a common overall scaling of the
particle sizes and typical inter-particle distances, and we discuss why this
effect is rather specific to systems with Schulz diameter distributions. Next,
by studying a family of such systems with distributions of various widths, we
estimate the dependence of the critical point parameters on . In
contrast to a previous theoretical prediction, size-dispersity is found to
raise the critical temperature above its monodisperse value. Unusually for a
polydisperse system, the critical point is found to lie at or very close to the
extremum of the coexistence region in all cases. We outline an argument showing
that such behaviour will occur whenever size polydispersity affects only the
range, rather than the strength of the inter-particle interactions.Comment: 14 pages, 12 figure
Trap models with slowly decorrelating observables
We study the correlation and response dynamics of trap models of glassy
dynamics, considering observables that only partially decorrelate with every
jump. This is inspired by recent work on a microscopic realization of such
models, which found strikingly simple linear out-of-equilibrium
fluctuation-dissipation relations in the limit of slow decorrelation. For the
Barrat-Mezard model with its entropic barriers we obtain exact results at zero
temperature for arbitrary decorrelation factor . These are then
extended to nonzero , where the qualitative scaling behaviour and all
scaling exponents can still be found analytically. Unexpectedly, the choice of
transition rates (Glauber versus Metropolis) affects not just prefactors but
also some exponents. In the limit of slow decorrelation even complete scaling
functions are accessible in closed form. The results show that slowly
decorrelating observables detect persistently slow out-of-equilibrium dynamics,
as opposed to intermittent behaviour punctuated by excursions into fast,
effectively equilibrated states.Comment: 29 pages, IOP styl
Simplified Onsager theory for isotropic-nematic phase equilibria of length polydisperse hard rods
Polydispersity is believed to have important effects on the formation of
liquid crystal phases in suspensions of rod-like particles. To understand such
effects, we analyse the phase behaviour of thin hard rods with length
polydispersity. Our treatment is based on a simplified Onsager theory, obtained
by truncating the series expansion of the angular dependence of the excluded
volume. We describe the model and give the full phase equilibrium equations;
these are then solved numerically using the moment free energy method which
reduces the problem from one with an infinite number of conserved densities to
one with a finite number of effective densities that are moments of the full
density distribution. The method yields exactly the onset of nematic ordering.
Beyond this, results are approximate but we show that they can be made
essentially arbitrarily precise by adding adaptively chosen extra moments,
while still avoiding the numerical complications of a direct solution of the
full phase equilibrium conditions.
We investigate in detail the phase behaviour of systems with three different
length distributions: a (unimodal) Schulz distribution, a bidisperse
distribution and a bimodal mixture of two Schulz distributions which
interpolates between these two cases. A three-phase isotropic-nematic-nematic
coexistence region is shown to exist for the bimodal and bidisperse length
distributions if the ratio of long and short rod lengths is sufficiently large,
but not for the unimodal one. We systematically explore the topology of the
phase diagram as a function of the width of the length distribution and of the
rod length ratio in the bidisperse and bimodal cases.Comment: 18 pages, 16 figure
Perturbative polydispersity: Phase equilibria of near-monodisperse systems
The conditions of multi-phase equilibrium are solved for generic polydisperse
systems. The case of multiple polydispersity is treated, where several
properties (e.g. size, charge, shape) simultaneously vary from one particle to
another. By developing a perturbative expansion in the width of the
distribution of constituent species, it is possible to calculate the effects of
polydispersity alone, avoiding difficulties associated with the underlying
many-body problem. Explicit formulae are derived in detail, for the
partitioning of species at coexistence and for the shift of phase boundaries
due to polydispersity. `Convective fractionation' is quantified, whereby one
property (e.g. charge) is partitioned between phases due to a driving force on
another. To demonstrate the ease of use and versatility of the formulae, they
are applied to models of a chemically-polydisperse polymer blend, and of
fluid-fluid coexistence in polydisperse colloid-polymer mixtures. In each case,
the regime of coexistence is shown to be enlarged by polydispersity.Comment: 22 pages, 3 figure
Comment on "Constant stress and pressure rheology of colloidal suspensions"
This is a comment on the recent letter by Wang and Brady on "Constant stress
and pressure rheology of colloidal suspensions", Phys. Rev. Lett. 115, 158301
(2015).Comment: 1 page; under review -> v2: publishe
Phase behaviour and particle-size cutoff effects in polydisperse fluids
We report a joint simulation and theoretical study of the liquid-vapor phase
behaviour of a fluid in which polydispersity in the particle size couples to
the strength of the interparticle interactions. Attention is focussed on the
case in which the particles diameters are distributed according to a fixed
Schulz form with degree of polydispersity . The coexistence
properties of this model are studied using grand canonical ensemble Monte Carlo
simulations and moment free energy calculations. We obtain the cloud and shadow
curves as well as the daughter phase density distributions and fractional
volumes along selected isothermal dilution lines. In contrast to the case of
size-{\em independent} interaction strengths (N.B. Wilding, M. Fasolo and P.
Sollich, J. Chem. Phys. {\bf 121}, 6887 (2004)), the cloud and shadow curves
are found to be well separated, with the critical point lying significantly
below the cloud curve maximum. For densities below the critical value, we
observe that the phase behaviour is highly sensitive to the choice of upper
cutoff on the particle size distribution. We elucidate the origins of this
effect in terms of extremely pronounced fractionation effects and discuss the
likely appearance of new phases in the limit of very large values of the
cutoff.Comment: 12 pages, 15 figure
Kinetically Constrained Models
In this chapter we summarize recent developments in the study of kinetically
constrained models (KCMs) as models for glass formers. After recalling the
definition of the KCMs which we cover we study the possible occurrence of
ergodicity breaking transitions and discuss in some detail how, before any such
transition occurs, relaxation timescales depend on the relevant control
parameter (density or temperature). Then we turn to the main issue: the
prediction of KCMs for dynamical heterogeneities. We focus in particular on
multipoint correlation functions and susceptibilities, and decoupling in the
transport coefficients. Finally we discuss the recent view of KCMs as being at
first order coexistence between an active and an inactive space-time phase.Comment: Chapter of "Dynamical heterogeneities in glasses, colloids, and
granular media", Eds.: L. Berthier, G. Biroli, J-P Bouchaud, L. Cipelletti
and W. van Saarloos (Oxford University Press, to appear), more info at
http://w3.lcvn.univ-montp2.fr/~lucacip/DH_book.ht
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