Fast Bounds on the Distribution of Smooth Numbers

In this paper we present improvements to Bernstein’s algorithm, which finds rigorous upper and lower bounds for (x, y)

Dynamic Evolution of a Quasi-Spherical General Polytropic Magnetofluid with Self-Gravity

In various astrophysical contexts, we analyze self-similar behaviours of magnetohydrodynamic (MHD) evolution of a quasi-spherical polytropic magnetized gas under self-gravity with the specific entropy conserved along streamlines. In particular, this MHD model analysis frees the scaling parameter $n$ in the conventional polytropic self-similar transformation from the constraint of $n+\gamma=2$ with $\gamma$ being the polytropic index and therefore substantially generalizes earlier analysis results on polytropic gas dynamics that has a constant specific entropy everywhere in space at all time. On the basis of the self-similar nonlinear MHD ordinary differential equations, we examine behaviours of the magnetosonic critical curves, the MHD shock conditions, and various asymptotic solutions. We then construct global semi-complete self-similar MHD solutions using a combination of analytical and numerical means and indicate plausible astrophysical applications of these magnetized flow solutions with or without MHD shocks.Comment: 21 pages, 7 figures, accepted for publication in APS

Monte Carlo Methods for Estimating Interfacial Free Energies and Line Tensions

Excess contributions to the free energy due to interfaces occur for many problems encountered in the statistical physics of condensed matter when coexistence between different phases is possible (e.g. wetting phenomena, nucleation, crystal growth, etc.). This article reviews two methods to estimate both interfacial free energies and line tensions by Monte Carlo simulations of simple models, (e.g. the Ising model, a symmetrical binary Lennard-Jones fluid exhibiting a miscibility gap, and a simple Lennard-Jones fluid). One method is based on thermodynamic integration. This method is useful to study flat and inclined interfaces for Ising lattices, allowing also the estimation of line tensions of three-phase contact lines, when the interfaces meet walls (where "surface fields" may act). A generalization to off-lattice systems is described as well. The second method is based on the sampling of the order parameter distribution of the system throughout the two-phase coexistence region of the model. Both the interface free energies of flat interfaces and of (spherical or cylindrical) droplets (or bubbles) can be estimated, including also systems with walls, where sphere-cap shaped wall-attached droplets occur. The curvature-dependence of the interfacial free energy is discussed, and estimates for the line tensions are compared to results from the thermodynamic integration method. Basic limitations of all these methods are critically discussed, and an outlook on other approaches is given

Constraining Strong Baryon-Dark Matter Interactions with Primordial Nucleosynthesis and Cosmic Rays

Self-interacting dark matter (SIDM) was introduced by Spergel & Steinhardt to address possible discrepancies between collisionless dark matter simulations and observations on scales of less than 1 Mpc. We examine the case in which dark matter particles not only have strong self-interactions but also have strong interactions with baryons. The presence of such interactions will have direct implications for nuclear and particle astrophysics. Among these are a change in the predicted abundances from big bang nucleosynthesis (BBN) and the flux of gamma-rays produced by the decay of neutral pions which originate in collisions between dark matter and Galactic cosmic rays (CR). From these effects we constrain the strength of the baryon--dark matter interactions through the ratio of baryon - dark matter interaction cross section to dark matter mass, $s$. We find that BBN places a weak upper limit to this ratio $< 10^8 cm^2/g$. CR-SIDM interactions, however, limit the possible DM-baryon cross section to $< 5 \times 10^{-3} cm^2/g$; this rules out an energy-independent interaction, but not one which falls with center-of-mass velocity as $s \propto 1/v$ or steeper.Comment: 17 pages, 2 figures; plain LaTeX. To appear in PR

Atoms to phenotypes: Molecular design principles of cellular energy metabolism

We report a 100-million atom-scale model of an entire cell organelle, a photosynthetic chromatophore vesicle from a purple bacterium, that reveals the cascade of energy conversion steps culminating in the generation of ATP from sunlight. Molecular dynamics simulations of this vesicle elucidate how the integral membrane complexes influence local curvature to tune photoexcitation of pigments. Brownian dynamics of small molecules within the chromatophore probe the mechanisms of directional charge transport under various pH and salinity conditions. Reproducing phenotypic properties from atomistic details, a kinetic model evinces that low-light adaptations of the bacterium emerge as a spontaneous outcome of optimizing the balance between the chromatophore’s structural integrity and robust energy conversion. Parallels are drawn with the more universal mitochondrial bioenergetic machinery, from whence molecular-scale insights into the mechanism of cellular aging are inferred. Together, our integrative method and spectroscopic experiments pave the way to first-principles modeling of whole living cells

How to move ionized gas: an introduction to the dynamics of HII regions

This review covers the dynamic processes that are important in the evolution and structure of galactic HII regions, concentrating on an elementary presentation of the physical concepts and recent numerical simulations of HII region evolution in a non-uniform medium. The contents are as follows: (1) The equations (Euler equations; Radiative transfer; Rate equations; How to avoid the dynamics; How to avoid the atomic physics). (2) Physical concepts (Static photoionization equilibrium; Ionization front propagation; Structure of a D-type front; Photoablation flows; Other ingredients - Stellar winds, Radiation pressure, Magnetic fields, Instabilities). (3) HII region evolution (Early phases: hypercompact and ultracompact regions; Later phases: compact and extended regions; Clumps and turbulence).Comment: To be published as a chapter in 'Diffuse Matter from Star Forming Regions to Active Galaxies' - A volume Honouring John Dyson. Eds. T. W. Harquist, J. M. Pittard and S. A. E. G. Falle. 25 pages, 7 figures. Some figures degraded to meet size restriction. Full-resolution version available at http://www.ifront.org/wiki/Dyson_Festschrift_Chapte