On the accuracy of the melting curves drawn from modelling a solid as an elastic medium

An ongoing problem in the study of a classical many-body system is the characterization of its equilibrium behaviour by theory or numerical simulation. For purely repulsive particles, locating the melting line in the pressure-temperature plane can be especially hard if the interparticle potential has a softened core or contains some adjustable parameters. A method is hereby presented that yields reliable melting-curve topologies with negligible computational effort. It is obtained by combining the Lindemann melting criterion with a description of the solid phase as an elastic continuum. A number of examples are given in order to illustrate the scope of the method and possible shortcomings. For a two-body repulsion of Gaussian shape, the outcome of the present approach compares favourably with the more accurate but also more computationally demanding self-consistent harmonic approximation.Comment: 25 pages, 7 figure

Adiabatic and Non-Adiabatic Contributions to the Free Energy from the Electron-Phonon Interaction for Na, K, Al, and Pb

We calculate the adiabatic contributions to the free energy due to the electron--phonon interaction at intermediate temperatures, $0 \leqslant k_{B} T < \epsilon_{F}$ for the elemental metals Na, K, Al, and Pb. Using our previously published results for the nonadiabatic contributions we show that the adiabatic contribution, which is proportional to $T^{2}$ at low temperatures and goes as $T^{3}$ at high temperatures, dominates the nonadiabatic contribution for temperatures above a cross--over temperature, $T_{c}$, which is between 0.5 and 0.8 $T_{m}$, where $T_{m}$ is the melting temperature of the metal. The nonadiabatic contribution falls as $T^{-1}$ for temperatures roughly above the average phonon frequency.Comment: Updated versio

Can Everett be Interpreted Without Extravaganza?

Everett's relative states interpretation of quantum mechanics has met with problems related to probability, the preferred basis, and multiplicity. The third theme, I argue, is the most important one. It has led to developments of the original approach into many-worlds, many-minds, and decoherence-based approaches. The latter especially have been advocated in recent years, in an effort to understand multiplicity without resorting to what is often perceived as extravagant constructions. Drawing from and adding to arguments of others, I show that proponents of decoherence-based approaches have not yet succeeded in making their ontology clear.Comment: Succinct analysis forthcoming in Found. Phy

Equation of state of cubic boron nitride at high pressures and temperatures

We report accurate measurements of the equation of state (EOS) of cubic boron nitride by x-ray diffraction up to 160 GPa at 295 K and 80 GPa in the range 500-900 K. Experiments were performed on single-crystals embedded in a quasi-hydrostatic pressure medium (helium or neon). Comparison between the present EOS data at 295 K and literature allows us to critically review the recent calibrations of the ruby standard. The full P-V-T data set can be represented by a Mie-Gr\"{u}neisen model, which enables us to extract all relevant thermodynamic parameters: bulk modulus and its first pressure-derivative, thermal expansion coefficient, thermal Gr\"{u}neisen parameter and its volume dependence. This equation of state is used to determine the isothermal Gr\"{u}neisen mode parameter of the Raman TO band. A new formulation of the pressure scale based on this Raman mode, using physically-constrained parameters, is deduced.Comment: 8 pages, 7 figure

Reply to comments by A. Douglas, J. B. Young, and N. S. Lyman and a note on the revised moments for Pahute Mesa tectonic release

In two earlier papers (Wallace et al., 1983, 1985), we discussed the evidence for tectonic release from underground nuclear explosions on Pahute Mesa at the Nevada Test Site (NTS) as observed in long-period body waves. It has been shown for some time that the nonisotropic component of the surface waves from most of these events could be explained by an equivalent double-couple source; namely strike-slip motion on north-striking faults

Reconstruction of Causal Networks by Set Covering

We present a method for the reconstruction of networks, based on the order of nodes visited by a stochastic branching process. Our algorithm reconstructs a network of minimal size that ensures consistency with the data. Crucially, we show that global consistency with the data can be achieved through purely local considerations, inferring the neighbourhood of each node in turn. The optimisation problem solved for each individual node can be reduced to a Set Covering Problem, which is known to be NP-hard but can be approximated well in practice. We then extend our approach to account for noisy data, based on the Minimum Description Length principle. We demonstrate our algorithms on synthetic data, generated by an SIR-like epidemiological model.Comment: Under consideration for the ECML PKDD 2010 conferenc

The Kumaraswamy-G Poisson Family of Distributions

For any baseline continuous G distribution, we propose a new generalized family called the Kumaraswamy-G Poisson (denoted with the prefix “Kw-GP”) with three extra positive parameters. Some special distributions in the new family such as the Kw-Weibull Poisson, Kw-gamma Poisson and Kw-beta Poisson distributions are introduced. We derive some mathematical properties of the new family including the ordinary moments, generating function and order statistics. The method of maximum likelihood is used to fit the distributions in the new family. We illustrate its potentiality by means of an application to a real data set

Dynamics of monatomic liquids

We present a theory of the dynamics of monatomic liquids built on two basic ideas: (1) The potential surface of the liquid contains three classes of intersecting nearly-harmonic valleys, one of which (the ``random'' class) vastly outnumbers the others and all whose members have the same depth and normal mode spectrum; and (2) the motion of particles in the liquid can be decomposed into oscillations in a single many-body valley, and nearly instantaneous inter-valley transitions called transits. We review the thermodynamic data which led to the theory, and we discuss the results of molecular dynamics (MD) simulations of sodium and Lennard-Jones argon which support the theory in more detail. Then we apply the theory to problems in equilibrium and nonequilibrium statistical mechanics, and we compare the results to experimental data and MD simulations. We also discuss our work in comparison with the QNM and INM research programs and suggest directions for future research.Comment: 53 pages, 16 figures. Differs from published version in using American English spelling and grammar (published version uses British English

Elastic constants of beta-eucryptite: A density functional theory study

The five independent elastic constants of hexagonal $\beta$-eucryptite have been determined using density functional theory (DFT) total energy calculations. The calculated values agree well, to within 15%, with the experimental data. Using the calculated elastic constants, the linear compressibility of $\beta$-eucryptite parallel to the c-axis, $\chi_c$, and perpendicular to it, $\chi_a$, have been evaluated. These values are in close agreement to those obtained from experimentally known elastic constants, but are in contradiction to the direct measurements based on a three-terminal technique. The calculated compressibility parallel to the c-axis was found to positive as opposed to the negative value obtained by direct measurements. We have demonstrated that $\chi_c$ must be positive and discussed the implications of a positive $\chi_c$ in the context of explaining the negative bulk thermal expansion of $\beta$-eucryptite.Comment: 3 eps figures, submitted for publicatio