63,978 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
Polar plots of diamond surface energy
Diamond surface energy sigma_hkl determines crystal habit. We discuss three aspects of a paper by Terentiev (1991).
Firstly, we compare Terentiev's algorithm for exact sigma_hkl with the analytic solution for h <= k <= l and h + k < l.
Secondly, we show that the general formula given by Terentiev should be interpreted probabilistically in order to be self consistent.
Finally, we replicate in principle the simulation results for sigma_hkl in a nickel melt using nothing more than Matlab routines
Comments on the paper by D. G. Rea and B. T. O'Leary on the composition of the Venus clouds
Comments on ice particles as major scatterers of infrared radiation from Venus atmospher
On the nonlocal viscosity kernel of mixtures
In this report we investigate the multiscale hydrodynamical response of a
liquid as a function of mixture composition. This is done via a series of
molecular dynamics simulations where the wave vector dependent viscosity kernel
is computed for three mixtures each with 7-15 different compositions. We
observe that the nonlocal viscosity kernel is dependent on composition for
simple atomic mixtures for all the wave vectors studied here, however, for a
model polymer melt mixture the kernel is independent of composition for large
wave vectors. The deviation from ideal mixing is also studied. Here it is shown
that a Lennard-Jones mixture follows the ideal mixing rule surprisingly well
for a large range of wave vectors, whereas for both the Kob-Andersen mixture
and the polymer melt large deviations are found. Furthermore, for the polymer
melt the deviation is wave vector dependent such that there exists a critical
length scale at which the ideal mixing goes from under-estimating to
over-estimating the viscosity
A universal velocity distribution of relaxed collisionless structures
Several general trends have been identified for equilibrated,
self-gravitating collisionless systems, such as density or anisotropy profiles.
These are integrated quantities which naturally depend on the underlying
velocity distribution function (VDF) of the system. We study this VDF through a
set of numerical simulations, which allow us to extract both the radial and the
tangential VDF. We find that the shape of the VDF is universal, in the sense
that it depends only on two things namely the dispersion (radial or tangential)
and the local slope of the density. Both the radial and the tangential VDF's
are universal for a collection of simulations, including controlled collisions
with very different initial conditions, radial infall simulation, and
structures formed in cosmological simulations.Comment: 13 pages, 6 figures; oversimplified analysis corrected; changed
abstract and conclusions; significantly extended discussio
Relationship between Local Molecular Field Theory and Density Functional Theory for non-uniform liquids
The Local Molecular Field Theory (LMF) developed by Weeks and co-workers has
proved successful for treating the structure and thermodynamics of a variety of
non-uniform liquids. By reformulating LMF in terms of one-body direct
correlation functions we recast the theory in the framework of classical
Density Functional Theory (DFT). We show that the general LMF equation for the
effective reference potential phi_R follows directly from the standard
mean-field DFT treatment of attractive interatomic forces. Using an accurate
(Fundamental Measures) DFT for the non-uniform hard-sphere reference fluid we
determine phi_R for a hard-core Yukawa liquid adsorbed at a planar hard wall.
In the approach to bulk liquid-gas coexistence we find the effective potentials
exhibit rich structure that can include damped oscillations at large distances
from the wall as well as the repulsive hump near the wall required to generate
the low density 'gas' layer characteristic of complete drying. We argue that it
would be difficult to obtain the same level of detail from other (non DFT
based) implementations of LMF. LMF emphasizes the importance of making an
intelligent division of the interatomic pair potential of the full system into
a reference part and a remainder that can be treated in mean-field
approximation. We investigate different divisions for an exactly solvable one-
dimensional model where the pair potential has a hard-core plus a linear
attractive tail. Results for the structure factor and the equation of state of
the uniform fluid show that including a significant portion of the attraction
in the reference system can be much more accurate than treating the full
attractive tail in mean-field approximation. We discuss further aspects of the
relationship between LMF and DFT.Comment: 35 pages, 10 Fig
Toward the Jamming Threshold of Sphere Packings: Tunneled Crystals
We have discovered a new family of three-dimensional crystal sphere packings
that are strictly jammed (i.e., mechanically stable) and yet possess an
anomalously low density. This family constitutes an uncountably infinite number
of crystal packings that are subpackings of the densest crystal packings and
are characterized by a high concentration of self-avoiding "tunnels" (chains of
vacancies) that permeate the structures. The fundamental geometric
characteristics of these tunneled crystals command interest in their own right
and are described here in some detail. These include the lattice vectors (that
specify the packing configurations), coordination structure, Voronoi cells, and
density fluctuations. The tunneled crystals are not only candidate structures
for achieving the jamming threshold (lowest-density rigid packing), but may
have substantially broader significance for condensed matter physics and
materials science.Comment: 19 pages, 5 figure
Conditional quantum state engineering in repeated 2-photon down conversion
The U(1,1) and U(2) transformations realized by three-mode interaction in the
respective parametric approximations are studied in conditional measurement,
and the corresponding non-unitary transformation operators are derived. As an
application, the preparation of single-mode quantum states using an optical
feedback loop is discussed, with special emphasis of Fock state preparation.
For that example, the influence of non-perfect detection and feedback is also
considered.Comment: 17 pages, 4 figures, using a4.st
The standard mean-field treatment of inter-particle attraction in classical DFT is better than one might expect
In classical density functional theory (DFT) the part of the Helmholtz free
energy functional arising from attractive inter-particle interactions is often
treated in a mean-field or van der Waals approximation. On the face of it, this
is a somewhat crude treatment as the resulting functional generates the simple
random phase approximation (RPA) for the bulk fluid pair direct correlation
function. We explain why using standard mean-field DFT to describe
inhomogeneous fluid structure and thermodynamics is more accurate than one
might expect based on this observation. By considering the pair correlation
function and structure factor of a one-dimensional model fluid,
for which exact results are available, we show that the mean-field DFT,
employed within the test-particle procedure, yields results much superior to
those from the RPA closure of the bulk Ornstein-Zernike equation. We argue that
one should not judge the quality of a DFT based solely on the approximation it
generates for the bulk pair direct correlation function.Comment: 9 pages, 3 figure
- …