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 $\Phi_{\text{SHS}}$ 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 $g(x)$ and structure factor $S(k)$ 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