1,663 research outputs found
First-principles derivation of density functional formalism for quenched-annealed systems
We derive from first principles (without resorting to the replica trick) a
density functional theory for fluids in quenched disordered matrices (QA-DFT).
We show that the disorder-averaged free energy of the fluid is a functional of
the average density profile of the fluid as well as the pair correlation of the
fluid and matrix particles. For practical reasons it is preferable to use
another functional: the disorder-averaged free energy plus the fluid-matrix
interaction energy, which, for fixed fluid-matrix interaction potential, is a
functional only of the average density profile of the fluid. When the matrix is
created as a quenched configuration of another fluid, the functional can be
regarded as depending on the density profile of the matrix fluid as well. In
this situation, the replica-Ornstein-Zernike equations which do not contain the
blocking parts of the correlations can be obtained as functional identities in
this formalism, provided the second derivative of this functional is
interpreted as the connected part of the direct correlation function. The
blocking correlations are totally absent from QA-DFT, but nevertheless the
thermodynamics can be entirely obtained from the functional. We apply the
formalism to obtain the exact functional for an ideal fluid in an arbitrary
matrix, and discuss possible approximations for non-ideal fluids.Comment: 19 pages, uses RevTeX
A density functional theory for general hard-core lattice gases
We put forward a general procedure to obtain an approximate free energy
density functional for any hard-core lattice gas, regardless of the shape of
the particles, the underlying lattice or the dimension of the system. The
procedure is conceptually very simple and recovers effortlessly previous
results for some particular systems. Also, the obtained density functionals
belong to the class of fundamental measure functionals and, therefore, are
always consistent through dimensional reduction. We discuss possible extensions
of this method to account for attractive lattice models.Comment: 4 pages, 1 eps figure, uses RevTeX
Cluster density functional theory for lattice models based on the theory of Mobius functions
Rosenfeld's fundamental measure theory for lattice models is given a rigorous
formulation in terms of the theory of Mobius functions of partially ordered
sets. The free-energy density functional is expressed as an expansion in a
finite set of lattice clusters. This set is endowed a partial order, so that
the coefficients of the cluster expansion are connected to its Mobius function.
Because of this, it is rigorously proven that a unique such expansion exists
for any lattice model. The low-density analysis of the free-energy functional
motivates a redefinition of the basic clusters (zero-dimensional cavities)
which guarantees a correct zero-density limit of the pair and triplet direct
correlation functions. This new definition extends Rosenfeld's theory to
lattice model with any kind of short-range interaction (repulsive or
attractive, hard or soft, one- or multi-component...). Finally, a proof is
given that these functionals have a consistent dimensional reduction, i.e. the
functional for dimension d' can be obtained from that for dimension d (d'<d) if
the latter is evaluated at a density profile confined to a d'-dimensional
subset.Comment: 21 pages, 2 figures, uses iopart.cls, as well as diagrams.sty
(included
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Effectiveness of slow motion video compared to real time video in improving the accuracy and consistency of subjective gait analysis in dogs
Objective measures of canine gait quality via force plates, pressure mats or kinematic analysis are considered superior to subjective gait assessment (SGA). Despite research demonstrating that SGA does not accurately detect subtle lameness, it remains the most commonly performed diagnostic test for detecting lameness in dogs. This is largely because the financial, temporal and spatial requirements for existing objective gait analysis equipment makes this technology impractical for
use in general practice. The utility of slow motion video as a potential tool to augment SGA is currently untested. To evaluate a more accessible way to overcome the limitations of SGA, a slow motion video study was undertaken. Three experienced veterinarians reviewed video footage of 30 dogs, 15 with a diagnosis of primary limb lameness based on history and physical examination, and 15 with no indication of limb lameness based on history and physical examination. Four different videos were made for each dog, demonstrating each dog walking and trotting in real time, and then again walking and trotting in 50% slow motion. For each video, the veterinary raters assessed both the degree of lameness, and which limb(s) they felt represented the source of the lameness. Spearman’s rho, Cramer’s V, and t-tests were performed to determine if slow motion video increased either the accuracy or consistency of raters’ SGA relative to real time video. Raters demonstrated no significant increase in consistency or accuracy in their SGA of slow motion video relative to real time video. Based on these findings, slow motion video does not increase the consistency or accuracy of SGA values. Further research is required to determine if slow motion video will benefit SGA in other ways
Lattice density-functional theory of surface melting: the effect of a square-gradient correction
I use the method of classical density-functional theory in the
weighted-density approximation of Tarazona to investigate the phase diagram and
the interface structure of a two-dimensional lattice-gas model with three
phases -- vapour, liquid, and triangular solid. While a straightforward
mean-field treatment of the interparticle attraction is unable to give a stable
liquid phase, the correct phase diagram is obtained when including a suitably
chosen square-gradient term in the system grand potential. Taken this theory
for granted, I further examine the structure of the solid-vapour interface as
the triple point is approached from low temperature. Surprisingly, a novel
phase (rather than the liquid) is found to grow at the interface, exhibiting an
unusually long modulation along the interface normal. The conventional
surface-melting behaviour is recovered only by artificially restricting the
symmetries being available to the density field.Comment: 16 pages, 6 figure
Density functional theory for nearest-neighbor exclusion lattice gasses in two and three dimensions
To speak about fundamental measure theory obliges to mention dimensional
crossover. This feature, inherent to the systems themselves, was incorporated
in the theory almost from the beginning. Although at first it was thought to be
a consistency check for the theory, it rapidly became its fundamental pillar,
thus becoming the only density functional theory which possesses such a
property. It is straightforward that dimensional crossover connects, for
instance, the parallel hard cube system (three-dimensional) with that of
squares (two-dimensional) and rods (one-dimensional). We show here that there
are many more connections which can be established in this way. Through them we
deduce from the functional for parallel hard (hyper)cubes in the simple
(hyper)cubic lattice the corresponding functionals for the nearest-neighbor
exclusion lattice gases in the square, triangular, simple cubic, face-centered
cubic, and body-centered cubic lattices. As an application, the bulk phase
diagram for all these systems is obtained.Comment: 13 pages, 13 figures; needs revtex
Fundamental measure theory for lattice fluids with hard core interactions
We present the extension of Rosenfeld's fundamental measure theory to lattice
models by constructing a density functional for d-dimensional mixtures of
parallel hard hypercubes on a simple hypercubic lattice. The one-dimensional
case is exactly solvable and two cases must be distinguished: all the species
with the same lebgth parity (additive mixture), and arbitrary length parity
(nonadditive mixture). At the best of our knowledge, this is the first time
that the latter case is considered. Based on the one-dimensional exact
functional form, we propose the extension to higher dimensions by generalizing
the zero-dimensional cavities method to lattice models. This assures the
functional to have correct dimensional crossovers to any lower dimension,
including the exact zero-dimensional limit. Some applications of the functional
to particular systems are also shown.Comment: 22 pages, 7 figures, needs IOPP LaTeX styles file
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