7,420 research outputs found
Formulation and error analysis for a generalized image point correspondence algorithm
A Generalized Image Point Correspondence (GIPC) algorithm, which enables the determination of 3-D motion parameters of an object in a configuration where both the object and the camera are moving, is discussed. A detailed error analysis of this algorithm has been carried out. Furthermore, the algorithm was tested on both simulated and video-acquired data, and its accuracy was determined
Phase behaviour of additive binary mixtures in the limit of infinite asymmetry
We provide an exact mapping between the density functional of a binary
mixture and that of the effective one-component fluid in the limit of infinite
asymmetry. The fluid of parallel hard cubes is thus mapped onto that of
parallel adhesive hard cubes. Its phase behaviour reveals that demixing of a
very asymmetric mixture can only occur between a solvent-rich fluid and a
permeated large particle solid or between two large particle solids with
different packing fractions. Comparing with hard spheres mixtures we conclude
that the phase behaviour of very asymmetric hard-particle mixtures can be
determined from that of the large component interacting via an adhesive-like
potential.Comment: Full rewriting of the paper (also new title). 4 pages, LaTeX, uses
revtex, multicol, epsfig, and amstex style files, to appear in Phys. Rev. E
(Rapid Comm.
Density Functional for Anisotropic Fluids
We propose a density functional for anisotropic fluids of hard body
particles. It interpolates between the well-established geometrically based
Rosenfeld functional for hard spheres and the Onsager functional for elongated
rods. We test the new approach by calculating the location of the the
nematic-isotropic transition in systems of hard spherocylinders and hard
ellipsoids. The results are compared with existing simulation data. Our
functional predicts the location of the transition much more accurately than
the Onsager functional, and almost as good as the theory by Parsons and Lee. We
argue that it might be suited to study inhomogeneous systems.Comment: To appear in J. Physics: Condensed Matte
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
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
Depletion potential in hard-sphere mixtures: theory and applications
We present a versatile density functional approach (DFT) for calculating the
depletion potential in general fluid mixtures. In contrast to brute force DFT,
our approach requires only the equilibrium density profile of the small
particles {\em before} the big (test) particle is inserted. For a big particle
near a planar wall or a cylinder or another fixed big particle the relevant
density profiles are functions of a single variable, which avoids the numerical
complications inherent in brute force DFT. We implement our approach for
additive hard-sphere mixtures. By investigating the depletion potential for
high size asymmetries we assess the regime of validity of the well-known
Derjaguin approximation for hard-sphere mixtures and argue that this fails. We
provide an accurate parametrization of the depletion potential in hard-sphere
fluids which should be useful for effective Hamiltonian studies of phase
behavior and colloid structure
Dynamics of a self gravitating light-like matter shell: a gauge-invariant Lagrangian and Hamiltonian description
A complete Lagrangian and Hamiltonian description of the theory of
self-gravitating light-like matter shells is given in terms of
gauge-independent geometric quantities. For this purpose the notion of an
extrinsic curvature for a null-like hypersurface is discussed and the
corresponding Gauss-Codazzi equations are proved. These equations imply Bianchi
identities for spacetimes with null-like, singular curvature. Energy-momentum
tensor-density of a light-like matter shell is unambiguously defined in terms
of an invariant matter Lagrangian density. Noether identity and
Belinfante-Rosenfeld theorem for such a tensor-density are proved. Finally, the
Hamiltonian dynamics of the interacting system: ``gravity + matter'' is derived
from the total Lagrangian, the latter being an invariant scalar density.Comment: 20 pages, RevTeX4, no figure
Dynamic Glass Transition in Two Dimensions
The question about the existence of a structural glass transition in two
dimensions is studied using mode coupling theory (MCT). We determine the
explicit d-dependence of the memory functional of mode coupling for
one-component systems. Applied to two dimensions we solve the MCT equations
numerically for monodisperse hard discs. A dynamic glass transition is found at
a critical packing fraction phi_c^{d=2} = 0.697 which is above phi_c^{d=3} =
0.516 by about 35%. phi^d_c scales approximately with phi^d_{\rm rcp} the value
for random close packing, at least for d=2, 3. Quantities characterizing the
local, cooperative 'cage motion' do not differ much for d=2 and d=3, and we
e.g. find the Lindemann criterion for the localization length at the glass
transition. The final relaxation obeys the superposition principle, collapsing
remarkably well onto a Kohlrausch law. The d=2 MCT results are in qualitative
agreement with existing results from MC and MD simulations. The mean squared
displacements measured experimentally for a quasi-two-dimensional binary system
of dipolar hard spheres can be described satisfactorily by MCT for monodisperse
hard discs over four decades in time provided the experimental control
parameter Gamma (which measures the strength of dipolar interactions) and the
packing fraction phi are properly related to each other.Comment: 14 pages, 15 figure
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