Accurate simulation estimates of phase behaviour in ternary mixtures with prescribed composition

This paper describes an isobaric semi-grand canonical ensemble Monte Carlo scheme for the accurate study of phase behaviour in ternary fluid mixtures under the experimentally relevant conditions of prescribed pressure, temperature and overall composition. It is shown how to tune the relative chemical potentials of the individual components to target some requisite overall composition and how, in regions of phase coexistence, to extract accurate estimates for the compositions and phase fractions of individual coexisting phases. The method is illustrated by tracking a path through the composition space of a model ternary Lennard-Jones mixture.Comment: 6 pages, 3 figure

Coexistence Curve Singularities at Critical End Points

We report an extensive Monte Carlo study of critical end point behaviour in a symmetrical binary fluid mixture. On the basis of general scaling arguments, singular behaviour is predicted in the diameter of the liquid-gas coexistence curve as the critical end point is approached. The simulation results show clear evidence for this singularity, as well as confirming a previously predicted singularity in the coexistence chemical potential. Both singularities should be detectable experimentally.Comment: 9 pages Revtex, 3 figures. To appear in Phys. Rev. Let

The universality class of the electroweak theory

We study the universality class and critical properties of the electroweak theory at finite temperature. Such critical behaviour is found near the endpoint m_H=m_{H,c} of the line of first order electroweak phase transitions in a wide class of theories, including the Standard Model (SM) and a part of the parameter space of the Minimal Sypersymmetric Standard Model (MSSM). We find that the location of the endpoint corresponds to the Higgs mass m_{H,c} = 72(2) GeV in the SM with sin^2 theta_W = 0, and m_{H,c} < 80 GeV with sin^2 theta_W = 0.23. As experimentally m_H > 88 GeV, there is no electroweak phase transition in the SM. We compute the corresponding critical indices and provide strong evidence that the phase transitions near the endpoint fall into the three dimensional Ising universality class.Comment: 35 pages, 15 figure

System and Process for Upgrading Hydrocarbons

In one embodiment, a system for upgrading a hydrocarbon material may include a black wax upgrade subsystem and a molten salt gasification (MSG) subsystem. The black wax upgrade subsystem and the MSG subsystem may be located within a common pressure boundary, such as within a pressure vessel. Gaseous materials produced by the MSG subsystem may be used in the process carried out within the black wax upgrade subsystem. For example, hydrogen may pass through a gaseous transfer interface to interact with black wax feed material to hydrogenate such material during a cracking process. In one embodiment, the gaseous transfer interface may include one or more openings in a tube or conduit which is carrying the black wax material. A pressure differential may control the flow of hydrogen within the tube or conduit. Related methods are also disclosed

Probability distribution of the order parameter for the 3D Ising model universality class: a high precision Monte Carlo study

We study the probability distribution P(M) of the order parameter (average magnetization) M, for the finite-size systems at the critical point. The systems under consideration are the 3-dimensional Ising model on a simple cubic lattice, and its 3-state generalization known to have remarkably small corrections to scaling. Both models are studied in a cubic box with periodic boundary conditions. The model with reduced corrections to scaling makes it possible to determine P(M) with unprecedented precision. We also obtain a simple, but remarkably accurate approximate formula describing the universal shape of P(M).Comment: 6 pages, 6 Postscript figures, uses RevTe

System and Process for Upgrading Hydrocarbons

In one embodiment, a system for upgrading a hydrocarbon material may include a black wax upgrade subsystem and a molten salt gasification (MSG) subsystem. The black wax upgrade subsystem and the MSG subsystem may be located within a common pressure boundary, such as within a pressure vessel. Gaseous materials produced by the MSG subsystem may be used in the process carried out within the black wax upgrade subsystem. For example, hydrogen may pass through a gaseous transfer interface to interact with black wax feed material to hydrogenate such material during a cracking process. In one embodiment, the gaseous transfer interface may include one or more openings in a tube or conduit which is carrying the black wax material. A pressure differential may control the flow of hydrogen within the tube or conduit. Related methods are also disclosed

Free energies of crystalline solids: a lattice-switch Monte Carlo method

We present a method for the direct evaluation of the difference between the free energies of two crystalline structures, of different symmetry. The method rests on a Monte Carlo procedure which allows one to sample along a path, through atomic-displacement-space, leading from one structure to the other by way of an intervening transformation that switches one set of lattice vectors for another. The configurations of both structures can thus be sampled within a single Monte Carlo process, and the difference between their free energies evaluated directly from the ratio of the measured probabilities of each. The method is used to determine the difference between the free energies of the fcc and hcp crystalline phases of a system of hard spheres.Comment: 5 pages Revtex, 3 figure

Are critical finite-size scaling functions calculable from knowledge of an appropriate critical exponent?

Critical finite-size scaling functions for the order parameter distribution of the two and three dimensional Ising model are investigated. Within a recently introduced classification theory of phase transitions, the universal part of the critical finite-size scaling functions has been derived by employing a scaling limit that differs from the traditional finite-size scaling limit. In this paper the analytical predictions are compared with Monte Carlo simulations. We find good agreement between the analytical expression and the simulation results. The agreement is consistent with the possibility that the functional form of the critical finite-size scaling function for the order parameter distribution is determined uniquely by only a few universal parameters, most notably the equation of state exponent.Comment: 11 pages postscript, plus 2 separate postscript figures, all as uuencoded gzipped tar file. To appear in J. Phys. A

Freezing by Monte Carlo Phase-Switch

We describe a Monte Carlo procedure which allows sampling of the disjoint configuration spaces associated with crystalline and fluid phases, within a single simulation. The method utilises biased sampling techniques to enhance the probabilities of gateway states (in each phase) which are such that a global switch (to the other phase) can be implemented. Equilibrium freezing-point parameters can be determined directly; statistical uncertainties prescribed transparently; and finite-size effects quantified systematically. The method is potentially quite general; we apply it to the freezing of hard spheres.Comment: 5 pages, 2 figure

Self-trapping at the liquid vapor critical point

Experiments suggest that localization via self-trapping plays a central role in the behavior of equilibrated low mass particles in both liquids and in supercritical fluids. In the latter case, the behavior is dominated by the liquid-vapor critical point which is difficult to probe, both experimentally and theoretically. Here, for the first time, we present the results of path-integral computations of the characteristics of a self-trapped particle at the critical point of a Lennard-Jones fluid for a positive particle-atom scattering length. We investigate the influence of the range of the particle-atom interaction on trapping properties, and the pick-off decay rate for the case where the particle is ortho-positronium.Comment: 12 pages, 3 figures, revtex4 preprin