431 research outputs found
A fundamental measure theory for the sticky hard sphere fluid
We construct a density functional theory (DFT) for the sticky hard sphere
(SHS) fluid which, like Rosenfeld's fundamental measure theory (FMT) for the
hard sphere fluid [Phys. Rev. Lett. {\bf 63}, 980 (1989)], is based on a set of
weighted densities and an exact result from scaled particle theory (SPT). It is
demonstrated that the excess free energy density of the inhomogeneous SHS fluid
is uniquely defined when (a) it is solely a function of the
weighted densities from Kierlik and Rosinberg's version of FMT [Phys. Rev. A
{\bf 42}, 3382 (1990)], (b) it satisfies the SPT differential equation, and (c)
it yields any given direct correlation function (DCF) from the class of
generalized Percus-Yevick closures introduced by Gazzillo and Giacometti [J.
Chem. Phys. {\bf 120}, 4742 (2004)]. The resulting DFT is shown to be in very
good agreement with simulation data. In particular, this FMT yields the correct
contact value of the density profiles with no adjustable parameters. Rather
than requiring higher order DCFs, such as perturbative DFTs, our SHS FMT
produces them. Interestingly, although equivalent to Kierlik and Rosinberg's
FMT in the case of hard spheres, the set of weighted densities used for
Rosenfeld's original FMT is insufficient for constructing a DFT which yields
the SHS DCF.Comment: 11 pages, 3 figure
Mode expansion for the density profile of crystal-fluid interfaces: Hard spheres as a test case
We present a technique for analyzing the full three-dimensional density
profiles of a planar crystal-fluid interface in terms of density modes. These
density modes can also be related to crystallinity order parameter profiles
which are used in coarse-grained, phase field type models of the statics and
dynamics of crystal-fluid interfaces and are an alternative to crystallinity
order parameters extracted from simulations using local crystallinity criteria.
We illustrate our results for the hard sphere system using finely-resolved,
three-dimensional density profiles from density functional theory of
fundamental measure type.Comment: submitted for the special issue of the CODEF III conferenc
Theory of ice premelting in porous media
Premelting describes the confluence of phenomena that are responsible for the
stable existence of the liquid phase of matter in the solid region of its bulk
phase diagram. Here we develop a theoretical description of the premelting of
water ice contained in a porous matrix, made of a material with a melting
temperature substantially larger than ice itself, to predict the amount of
liquid water in the matrix at temperatures below its bulk freezing point. Our
theory combines the interfacial premelting of ice in contact with the matrix,
grain boundary melting in the ice, and impurity and curvature induced
premelting, the latter occurring in regions which force the ice-liquid
interface into a high curvature configuration. These regions are typically
found at points where the matrix surface is concave, along contact lines of a
grain boundary with the matrix, and in liquid veins. Both interfacial
premelting and curvature induced premelting depend on the concentration of
impurities in the liquid, which, due to the small segregation coefficient of
impurities in ice are treated as homogeneously distributed in the premelted
liquid. Our principal result is an equation for the fraction of liquid in the
porous medium as a function of the undercooling, which embodies the combined
effects of interfacial premelting, curvature induced premelting, and
impurities. The result is analyzed in detail and applied to a range of
experimentally relevant settings.Comment: 14 pages, 10 figures, accepted for publication in Physical Review
Grain boundary melting in ice
We describe an optical scattering study of grain boundary premelting in water
ice. Ubiquitous long ranged attractive polarization forces act to suppress
grain boundary melting whereas repulsive forces originating in screened Coulomb
interactions and classical colligative effects enhance it. The liquid enhancing
effects can be manipulated by adding dopant ions to the system. For all
measured grain boundaries this leads to increasing premelted film thickness
with increasing electrolyte concentration. Although we understand that the
interfacial surface charge densities and solute concentrations can
potentially dominate the film thickness, we can not directly measure them
within a given grain boundary. Therefore, as a framework for interpreting the
data we consider two appropriate dependent limits; one is dominated by
the colligative effect and one is dominated by electrostatic interactions.Comment: 6 pages, 5 figure
Bifurcation in the growth of continental crust
Is the present-day water-land ratio a necessary outcome of the evolution of
plate tectonic planets with a similar age, volume, mass, and total water
inventory as the Earth? This would be the case - largely independent of initial
conditions - if Earth's present-day continental volume were at a stable unique
equilibrium with strong self-regulating mechanisms of continental growth
steering the evolution to this state. In this paper, we question this
conjecture. Instead we suggest that positive feedbacks in the plate tectonics
model of continental production and erosion may dominate and show that such a
model can explain the history of continental growth.
We investigate the main mechanisms that contribute to the growth of the
volume of the continental crust. In particular, we analyze the effect of the
oceanic plate speed, depending on the area and thickness of thermally
insulating continents, on production and erosion mechanisms. Effects that cause
larger continental production rates for larger values of continental volume are
positive feedbacks. In contrast, negative feedbacks act to stabilize the
continental volume. They are provided by the increase of the rate of surface
erosion, subduction erosion, and crustal delamination with the continental
volume. We systematically analyze the strengths of positive and negative
feedback contributions to the growth of the continental crust. Although the
strengths of some feedbacks depend on poorly known parameters, we conclude that
a net predominance of positive feedbacks is plausible. We explore the effect of
the combined feedback strength on the feasibility of modeling the observed
small positive net continental growth rate over the past 2-3 billion years
Message passing for vertex covers
Constructing a minimal vertex cover of a graph can be seen as a prototype for
a combinatorial optimization problem under hard constraints. In this paper, we
develop and analyze message passing techniques, namely warning and survey
propagation, which serve as efficient heuristic algorithms for solving these
computational hard problems. We show also, how previously obtained results on
the typical-case behavior of vertex covers of random graphs can be recovered
starting from the message passing equations, and how they can be extended.Comment: 25 pages, 9 figures - version accepted for publication in PR
Density functional theory for hard-sphere mixtures: the White-Bear version Mark II
In the spirit of the White-Bear version of fundamental measure theory we
derive a new density functional for hard-sphere mixtures which is based on a
recent mixture extension of the Carnahan-Starling equation of state. In
addition to the capability to predict inhomogeneous density distributions very
accurately, like the original White-Bear version, the new functional improves
upon consistency with an exact scaled-particle theory relation in the case of
the pure fluid. We examine consistency in detail within the context of
morphological thermodynamics. Interestingly, for the pure fluid the degree of
consistency of the new version is not only higher than for the original
White-Bear version but also higher than for Rosenfeld's original fundamental
measure theory.Comment: 16 pages, 3 figures; minor changes; J. Phys.: Condens. Matter,
accepte
Phase behaviour of binary mixtures of diamagnetic colloidal platelets in an external magnetic field
Using fundamental measure density functional theory we investigate
paranematic-nematic and nematic-nematic phase coexistence in binary mixtures of
circular platelets with vanishing thicknesses. An external magnetic field
induces uniaxial alignment and acts on the platelets with a strength that is
taken to scale with the platelet area. At particle diameter ratio lambda=1.5
the system displays paranematic-nematic coexistence. For lambda=2, demixing
into two nematic states with different compositions also occurs, between an
upper critical point and a paranematic-nematic-nematic triple point. Increasing
the field strength leads to shrinking of the coexistence regions. At high
enough field strength a closed loop of immiscibility is induced and phase
coexistence vanishes at a double critical point above which the system is
homogeneously nematic. For lambda=2.5, besides paranematic-nematic coexistence,
there is nematic-nematic coexistence which persists and hence does not end in a
critical point. The partial orientational order parameters along the binodals
vary strongly with composition and connect smoothly for each species when
closed loops of immiscibility are present in the corresponding phase diagram.Comment: 9 pages, to appear in J.Phys:Condensed Matte
A hard-sphere model on generalized Bethe lattices: Statics
We analyze the phase diagram of a model of hard spheres of chemical radius
one, which is defined over a generalized Bethe lattice containing short loops.
We find a liquid, two different crystalline, a glassy and an unusual
crystalline glassy phase. Special attention is also paid to the close-packing
limit in the glassy phase. All analytical results are cross-checked by
numerical Monte-Carlo simulations.Comment: 24 pages, revised versio
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