The Structure of Close Binaries in Two Dimensions

The structure and evolution of close binary stars has been studied using the two-dimensional (2D) stellar structure algorithm developed by Deupree (1995). We have calculated a series of solar composition stellar evolution sequences of binary models, where the mass of the 2D model is 8Msun with a point-mass 5Msun companion. We have also studied the structure of the companion in 2D, by considering the zero-age main-sequence (ZAMS) structure of a 5Msun model with an 8Msun point-mass companion. In all cases the binary orbit was assumed to be circular and co-rotating with the rotation rate of the stars. We considered binary models with three different initial separations, a = 10, 14 and 20Rsun. These models were evolved through central hydrogen burning or until the more massive star expanded to fill its critical potential surface or Roche lobe. The calculations show that evolution of the deep interior quantities is only slightly modified from those of single star evolution. Describing the model surface as a Roche equipotential is also satisfactory until very close to the time of Roche lobe overflow, when the self gravity of the model about to lose mass develops a noticeable aspherical component and the surface time scale becomes sufficiently short that it is conceivable that the actual surface is not an equipotential.Comment: 22 pages, 10 figures, accepted by Ap

Self-driven lattice-model Monte Carlo simulations of alloy thermodynamic

Monte Carlo (MC) simulations of lattice models are a widely used way to compute thermodynamic properties of substitutional alloys. A limitation to their more widespread use is the difficulty of driving a MC simulation in order to obtain the desired quantities. To address this problem, we have devised a variety of high-level algorithms that serve as an interface between the user and a traditional MC code. The user specifies the goals sought in a high-level form that our algorithms convert into elementary tasks to be performed by a standard MC code. For instance, our algorithms permit the determination of the free energy of an alloy phase over its entire region of stability within a specified accuracy, without requiring any user intervention during the calculations. Our algorithms also enable the direct determination of composition-temperature phase boundaries without requiring the calculation of the whole free energy surface of the alloy system

Exact sampling of self-avoiding paths via discrete Schramm-Loewner evolution

We present an algorithm, based on the iteration of conformal maps, that produces independent samples of self-avoiding paths in the plane. It is a discrete process approximating radial Schramm-Loewner evolution growing to infinity. We focus on the problem of reproducing the parametrization corresponding to that of lattice models, namely self-avoiding walks on the lattice, and we propose a strategy that gives rise to discrete paths where consecutive points lie an approximately constant distance apart from each other. This new method allows us to tackle two non-trivial features of self-avoiding walks that critically depend on the parametrization: the asphericity of a portion of chain and the correction-to-scaling exponent.Comment: 18 pages, 4 figures. Some sections rewritten (including title and abstract), numerical results added, references added. Accepted for publication in J. Stat. Phy