87,796 research outputs found
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
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
Correlation length by measuring empty space in simulated aggregates
We examine the geometry of the spaces between particles in diffusion-limited
cluster aggregation, a numerical model of aggregating suspensions. Computing
the distribution of distances from each point to the nearest particle, we show
that it has a scaled form independent of the concentration phi, for both two-
(2D) and three-dimensional (3D) model gels at low phi. The mean remoteness is
proportional to the density-density correlation length of the gel, xi, allowing
a more precise measurement of xi than by other methods. A simple analytical
form for the scaled remoteness distribution is developed, highlighting the
geometrical information content of the data. We show that the second moment of
the distribution gives a useful estimate of the permeability of porous media.Comment: 4 page
Factorised steady states for multi-species mass transfer models
A general class of mass transport models with Q species of conserved mass is
considered. The models are defined on a lattice with parallel discrete time
update rules. For one-dimensional, totally asymmetric dynamics we derive
necessary and sufficient conditions on the mass transfer dynamics under which
the steady state factorises. We generalise the model to mass transfer on
arbitrary lattices and present sufficient conditions for factorisation. In both
cases, explicit results for random sequential update and continuous time limits
are given.Comment: 11 page
Construction of the factorized steady state distribution in models of mass transport
For a class of one-dimensional mass transport models we present a simple and
direct test on the chipping functions, which define the probabilities for mass
to be transferred to neighbouring sites, to determine whether the stationary
distribution is factorized. In cases where the answer is affirmative, we
provide an explicit method for constructing the single-site weight function. As
an illustration of the power of this approach, previously known results on the
Zero-range process and Asymmetric random average process are recovered in a few
lines. We also construct new models, namely a generalized Zero-range process
and a binomial chipping model, which have factorized steady states.Comment: 6 pages, no figure
Diffusion and rheology in a model of glassy materials
We study self-diffusion within a simple hopping model for glassy materials.
(The model is Bouchaud's model of glasses [J.-P. Bouchaud, J. Physique I 2,
1705 (1992)], as extended to describe rheological properties [P. Sollich, F.
Lequeux, P. Hebraud and M.E. Cates, Phys. Rev. Lett. 78, 2020 (1997)].) We
investigate the breakdown, near the glass transition, of the (generalized)
Stokes-Einstein relation between self-diffusion of a tracer particle and the
(frequency-dependent) viscosity of the system as a whole. This stems from the
presence of a broad distribution of relaxation times of which different moments
control diffusion and rheology. We also investigate the effect of flow
(oscillatory shear) on self-diffusion and show that this causes a finite
diffusivity in the temperature regime below the glass transition (where this
was previously zero). At higher temperatures the diffusivity is enhanced by a
power law frequency dependence that also characterises the rheological
response. The relevance of these findings to soft glassy materials (foams,
emulsions etc.) as well as to conventional glass-forming liquids is discussed.Comment: 39 page (double spaced), 2 figure
Factorised Steady States in Mass Transport Models on an Arbitrary Graph
We study a general mass transport model on an arbitrary graph consisting of
nodes each carrying a continuous mass. The graph also has a set of directed
links between pairs of nodes through which a stochastic portion of mass, chosen
from a site-dependent distribution, is transported between the nodes at each
time step. The dynamics conserves the total mass and the system eventually
reaches a steady state. This general model includes as special cases various
previously studied models such as the Zero-range process and the Asymmetric
random average process. We derive a general condition on the stochastic mass
transport rules, valid for arbitrary graph and for both parallel and random
sequential dynamics, that is sufficient to guarantee that the steady state is
factorisable. We demonstrate how this condition can be achieved in several
examples. We show that our generalized result contains as a special case the
recent results derived by Greenblatt and Lebowitz for -dimensional
hypercubic lattices with random sequential dynamics.Comment: 17 pages 1 figur
The three dimensional motion and stability of a rotating space station: Cable-counterweight configuration
The three dimensional equations of motion for a cable connected space station--counterweight system are developed using a Lagrangian formulation. The system model employed allows for cable and end body damping and restoring effects. The equations are then linearized about the equilibrium motion and nondimensionalized. To first degree, the out-of-plane equations uncouple from the inplane equations. Therefore, the characteristic polynomials for the in-plane and out-of-plane equations are developed and treated separately. From the general in-plane characteristic equation, necessary conditions for stability are obtained. The Routh-Hurwitz necessary and sufficient conditions for stability are derived for the general out-of-plane characteristic equation. Special cases of the in-plane and out-of-plane equations (such as identical end masses, and when the cable is attached to the centers of mass of the two end bodies) are then examined for stability criteria
Liquid drops on a surface: using density functional theory to calculate the binding potential and drop profiles and comparing with results from mesoscopic modelling
The contribution to the free energy for a film of liquid of thickness on
a solid surface, due to the interactions between the solid-liquid and
liquid-gas interfaces is given by the binding potential, . The precise
form of determines whether or not the liquid wets the surface. Note that
differentiating gives the Derjaguin or disjoining pressure. We develop a
microscopic density functional theory (DFT) based method for calculating
, allowing us to relate the form of to the nature of the molecular
interactions in the system. We present results based on using a simple lattice
gas model, to demonstrate the procedure. In order to describe the static and
dynamic behaviour of non-uniform liquid films and drops on surfaces, a
mesoscopic free energy based on is often used. We calculate such
equilibrium film height profiles and also directly calculate using DFT the
corresponding density profiles for liquid drops on surfaces. Comparing
quantities such as the contact angle and also the shape of the drops, we find
good agreement between the two methods. We also study in detail the effect on
of truncating the range of the dispersion forces, both those between the
fluid molecules and those between the fluid and wall. We find that truncating
can have a significant effect on and the associated wetting behaviour of
the fluid.Comment: 16 pages, 13 fig
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