272 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
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
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
Structural properties of hard disks in a narrow tube
Positional ordering of a two-dimensional fluid of hard disks is examined in
such narrow tubes where only the nearest-neighbor interactions take place.
Using the exact transfer-matrix method the transverse and longitudinal pressure
components and the correlation function are determined numerically. Fluid-solid
phase transition does not occur even in the widest tube, where the method just
loses its exactness, but the appearance of the dramatic change in the equation
of state and the longitudinal correlation function shows that the system
undergoes a structural change from a fluid to a solid-like order. The pressure
components show that the collisions are dominantly longitudinal at low
densities, while they are transverse in the vicinity of close packing density.
The transverse correlation function shows that the size of solid-like domains
grows exponentially with increasing pressure and the correlation length
diverges at close packing. It is managed to find an analytically solvable model
by expanding the contact distance up to first order. The approximate model,
which corresponds to the system of hard parallel rhombuses, behaves very
similarly to the system of hard disks.Comment: Acceped in Journal of Statistical Mechanics: Theory and Experimen
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
Structural motifs of biomolecules
Biomolecular structures are assemblies of emergent anisotropic building
modules such as uniaxial helices or biaxial strands. We provide an approach to
understanding a marginally compact phase of matter that is occupied by proteins
and DNA. This phase, which is in some respects analogous to the liquid crystal
phase for chain molecules, stabilizes a range of shapes that can be obtained by
sequence-independent interactions occurring intra- and intermolecularly between
polymeric molecules. We present a singularityfree self-interaction for a tube
in the continuum limit and show that this results in the tube being positioned
in the marginally compact phase. Our work provides a unified framework for
understanding the building blocks of biomolecules.Comment: 13 pages, 5 figure
On the decay of the pair correlation function and the line of vanishing excess isothermal compressibility in simple fluids
We re-visit the competition between attractive and repulsive interparticle
forces in simple fluids and how this governs and connects the macroscopic phase
behavior and structural properties as manifest in pair correlation functions.
We focus on the asymptotic decay of the total correlation function which
is, in turn, controlled by the form of the pair direct correlation function
. The decay of to zero can be either exponential (monotonic) if
attraction dominates repulsion and exponentially damped oscillatory otherwise.
The Fisher-Widom (FW) line separates the phase diagram into two regions
characterized by the two different types of asymptotic decay. We show that
there is a new and physically intuitive thermodynamic criterion which
approximates well the actual FW line. This new criterion defines a line where
the isothermal compressibility takes its ideal gas value
. We test our hypothesis by considering four commonly
used models for simple fluids. In all cases the new criterion yields a line in
the phase diagram that is close to the actual FW line for the thermodynamic
state points that are most relevant. We also investigate (Widom) lines of
maximal correlation length, emphasizing the importance of distinguishing
between the true and Ornstein-Zernike correlation length
Spin models on random graphs with controlled topologies beyond degree constraints
We study Ising spin models on finitely connected random interaction graphs
which are drawn from an ensemble in which not only the degree distribution
can be chosen arbitrarily, but which allows for further fine-tuning of
the topology via preferential attachment of edges on the basis of an arbitrary
function Q(k,k') of the degrees of the vertices involved. We solve these models
using finite connectivity equilibrium replica theory, within the replica
symmetric ansatz. In our ensemble of graphs, phase diagrams of the spin system
are found to depend no longer only on the chosen degree distribution, but also
on the choice made for Q(k,k'). The increased ability to control interaction
topology in solvable models beyond prescribing only the degree distribution of
the interaction graph enables a more accurate modeling of real-world
interacting particle systems by spin systems on suitably defined random graphs.Comment: 21 pages, 4 figures, submitted to J Phys
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