The triangular Ising model with nearest- and next-nearest-neighbor couplings in a field

We study the Ising model on the triangular lattice with nearest-neighbor couplings $K_{\rm nn}$, next-nearest-neighbor couplings $K_{\rm nnn}>0$, and a magnetic field $H$. This work is done by means of finite-size scaling of numerical results of transfer matrix calculations, and Monte Carlo simulations. We determine the phase diagram and confirm the character of the critical manifolds. The emphasis of this work is on the antiferromagnetic case $K_{\rm nn}<0$, but we also explore the ferromagnetic regime $K_{\rm nn}\ge 0$ for H=0. For $K_{\rm nn}<0$ and H=0 we locate a critical phase presumably covering the whole range $-\infty < K_{\rm nn}<0$. For $K_{\rm nn}<0$, $H\neq 0$ we locate a plane of phase transitions containing a line of tricritical three-state Potts transitions. In the limit $H \to \infty$ this line leads to a tricritical model of hard hexagons with an attractive next-nearest-neighbor potential

Lattice Boltzmann Equation: Failure or Success?

The lattice Boltzmann equation (LBE) is a microscopically-inspired method designed to solve macroscopic fluid dynamics problems. As a such, it lives at the interface between the microscopic (molecular) and macroscopic (continuum) worlds, hopefully capturing the best of the two. In this paper we shall discuss whether or not, after almost a decade since its inception, LBE has lived up to the initial expectations. Open problems and future research developments are also briefly outlined

A Lattice Boltzmann method for simulations of liquid-vapor thermal flows

We present a novel lattice Boltzmann method that has a capability of simulating thermodynamic multiphase flows. This approach is fully thermodynamically consistent at the macroscopic level. Using this new method, a liquid-vapor boiling process, including liquid-vapor formation and coalescence together with a full coupling of temperature, is simulated for the first time.Comment: one gzipped tar file, 19 pages, 4 figure

Lattice Boltzmann Simulation of Non-Ideal Fluids

A lattice Boltzmann scheme able to model the hydrodynamics of phase separation and two-phase flow is described. Thermodynamic consistency is ensured by introducing a non-ideal pressure tensor directly into the collision operator. We also show how an external chemical potential can be used to supplement standard boundary conditions in order to investigate the effect of wetting on phase separation and fluid flow in confined geometries. The approach has the additional advantage of reducing many of the unphysical discretisation problems common to previous lattice Boltzmann methods.Comment: 11 pages, revtex, 4 Postscript figures, uuencode

The influence of collective neutrino oscillations on a supernova r-process

Recently, it has been demonstrated that neutrinos in a supernova oscillate collectively. This process occurs much deeper than the conventional matter-induced MSW effect and hence may have an impact on nucleosynthesis. In this paper we explore the effects of collective neutrino oscillations on the r-process, using representative late-time neutrino spectra and outflow models. We find that accurate modeling of the collective oscillations is essential for this analysis. As an illustration, the often-used "single-angle" approximation makes grossly inaccurate predictions for the yields in our setup. With the proper multiangle treatment, the effect of the oscillations is found to be less dramatic, but still significant. Since the oscillation patterns are sensitive to the details of the emitted fluxes and the sign of the neutrino mass hierarchy, so are the r-process yields. The magnitude of the effect also depends sensitively on the astrophysical conditions - in particular on the interplay between the time when nuclei begin to exist in significant numbers and the time when the collective oscillation begins. A more definitive understanding of the astrophysical conditions, and accurate modeling of the collective oscillations for those conditions, is necessary.Comment: 27 pages, 10 figure

Neutrino flavor conversion in a neutrino background: single- versus multi-particle description

In the early Universe, or near a supernova core, neutrino flavor evolution may be affected by coherent neutrino-neutrino scattering. We develop a microscopic picture of this phenomenon. We show that coherent scattering does not lead to the formation of entangled states in the neutrino ensemble and therefore the evolution of the system can always be described by a set of one-particle equations. We also show that the previously accepted formalism overcounts the neutrino interaction energy; the correct one-particle evolution equations for both active-active and active-sterile oscillations contain additional terms. These additional terms modify the index of refraction of the neutrino medium, but have no effect on oscillation physics.Comment: 12 pages, 3 figures, minor typos correcte