Survey of classical density functionals for modelling hydrogen physisorption at 77 K

This work surveys techniques based on classical density functionals for modeling the quantum dispersion of physisorbed hydrogen at 77 K. Two such techniques are examined in detail. The first is based on the "open ring approximation" (ORA) of Broukhno et al., and it is compared with a technique based on the semiclassical approximation of Feynman and Hibbs (FH). For both techniques, a standard classical density functional is used to model hydrogen molecule-hydrogen molecule (i.e., excess) interactions. The three-dimensional (3D) quantum harmonic oscillator (QHO) system and a model of molecular hydrogen adsorption into a graphitic slit pore at 77 K are used as benchmarks. Density functional results are compared with path-integral Monte Carlo simulations and with exact solutions for the 3D QHO system. It is found that neither of the density functional treatments are entirely satisfactory. However, for hydrogen physisorption studies at 77 K the ORA based technique is generally superior to the FH based technique due to a fortunate cancellation of errors in the density functionals used. But, if more accurate excess functionals are used, the FH technique would be superior

Self-referential Monte Carlo method for calculating the free energy of crystalline solids

A self-referential Monte Carlo method is described for calculating the free energy of crystalline solids. All Monte Carlo methods for the free energy of classical crystalline solids calculate the free-energy difference between a state whose free energy can be calculated relatively easily and the state of interest. Previously published methods employ either a simple model crystal, such as the Einstein crystal, or a fluid as the reference state. The self-referential method employs a radically different reference state; it is the crystalline solid of interest but with a different number of unit cells. So it calculates the free-energy difference between two crystals, differing only in their size. The aim of this work is to demonstrate this approach by application to some simple systems, namely, the face centered cubic hard sphere and Lennard-Jones crystals. However, it can potentially be applied to arbitrary crystals in both bulk and confined environments, and ultimately it could also be very efficient

The self-referential method for linear rigid bodies : application to hard and Lennard-Jones dumbbells

The self-referential (SR) method incorporating thermodynamic integration (TI) [Sweatman et al., J. Chem. Phys. 128, 064102 (2008)] is extended to treat systems of rigid linear bodies. The method is then applied to obtain the canonical ensemble Helmholtz free energy of the alpha-N2 and plastic face centered cubic phases of systems of hard and Lennard-Jones dumbbells using Monte Carlo simulations. Generally good agreement with reference literature data is obtained, which indicates that the SR-TI method is potentially very general and robust

Gamma-ray emission from dark matter wakes of recoiled black holes

A new scenario for the emission of high-energy gamma-rays from dark matter annihilation around massive black holes is presented. A black hole can leave its parent halo, by means of gravitational radiation recoil, in a merger event or in the asymmetric collapse of its progenitor star. A recoiled black hole which moves on an almost-radial orbit outside the virial radius of its central halo, in the cold dark matter background, reaches its apapsis in a finite time. Near or at the apapsis passage, a high-density wake extending over a large radius of influence, forms around the black hole. It is shown that significant gamma-ray emission can result from the enhancement of neutralino annihilation in these wakes. At its apapsis passage, a black hole is shown to produce a flash of high-energy gamma-rays whose duration is determined by the mass of the black hole and the redshift at which it is ejected. The ensemble of such black holes in the Hubble volume is shown to produce a diffuse high-energy gamma-ray background whose magnitude is compared to the diffuse emission from dark matter haloes alone.Comment: version to appear in Astrophysical Journal letters (labels on Fig. 3 corrected

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

Existence and Stability of Symmetric Periodic Simultaneous Binary Collision Orbits in the Planar Pairwise Symmetric Four-Body Problem

We extend our previous analytic existence of a symmetric periodic simultaneous binary collision orbit in a regularized fully symmetric equal mass four-body problem to the analytic existence of a symmetric periodic simultaneous binary collision orbit in a regularized planar pairwise symmetric equal mass four-body problem. We then use a continuation method to numerically find symmetric periodic simultaneous binary collision orbits in a regularized planar pairwise symmetric 1, m, 1, m four-body problem for $m$ between 0 and 1. Numerical estimates of the the characteristic multipliers show that these periodic orbits are linearly stability when $0.54\leq m\leq 1$, and are linearly unstable when $0<m\leq0.53$.Comment: 6 figure

The self-referential method combined with thermodynamic integration

The self-referential method [M. B. Sweatman, Phys. Rev. E 72, 016711 (2005)] for calculating the free energy of crystalline solids via molecular simulation is combined with thermodynamic integration to produce a technique that is convenient and efficient. Results are presented for the chemical potential of hard sphere and Lennard-Jones face centered cubic crystals that agree well with this previous work. For the small system sizes studied, this technique is about 100 times more efficient than the parameter hopping technique used previously

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

The Extreme Microlensing Event OGLE-2007-BLG-224: Terrestrial Parallax Observation of a Thick-Disk Brown Dwarf

Parallax is the most fundamental technique to measure distances to astronomical objects. Although terrestrial parallax was pioneered over 2000 years ago by Hipparchus (ca. 140 BCE) to measure the distance to the Moon, the baseline of the Earth is so small that terrestrial parallax can generally only be applied to objects in the Solar System. However, there exists a class of extreme gravitational microlensing events in which the effects of terrestrial parallax can be readily detected and so permit the measurement of the distance, mass, and transverse velocity of the lens. Here we report observations of the first such extreme microlensing event OGLE-2007-BLG-224, from which we infer that the lens is a brown dwarf of mass M=0.056 +- 0.004 Msun, with a distance of 525 +- 40 pc and a transverse velocity of 113 +- 21 km/s. The velocity places the lens in the thick disk, making this the lowest-mass thick-disk brown dwarf detected so far. Follow-up observations may allow one to observe the light from the brown dwarf itself, thus serving as an important constraint for evolutionary models of these objects and potentially opening a new window on sub-stellar objects. The low a priori probability of detecting a thick-disk brown dwarf in this event, when combined with additional evidence from other observations, suggests that old substellar objects may be more common than previously assumed.Comment: ApJ Letters, in press, 15 pages including 2 figure