Equation of state and critical behavior of polymer models: A quantitative comparison between Wertheim's thermodynamic perturbation theory and computer simulations

We present an application of Wertheim's Thermodynamic Perturbation Theory (TPT1) to a simple coarse grained model made of flexibly bonded Lennard-Jones monomers. We use both the Reference Hyper-Netted-Chain (RHNC) and Mean Spherical approximation (MSA) integral equation theories to describe the properties of the reference fluid. The equation of state, the density dependence of the excess chemical potential, and the critical points of the liquid--vapor transition are compared with simulation results and good agreement is found. The RHNC version is somewhat more accurate, while the MSA version has the advantage of being almost analytic. We analyze the scaling behavior of the critical point of chain fluids according to TPT1 and find it to reproduce the mean field exponents: The critical monomer density is predicted to vanish as $n^{-1/2}$ upon increasing the chain length $n$ while the critical temperature is predicted to reach an asymptotic finite temperature that is attained as $n^{-1/2}$. The predicted asymptotic finite critical temperature obtained from the RHNC and MSA versions of TPT1 is found to be in good agreement with the $\Theta$ point of our polymer model as obtained from the temperature dependence of the single chain conformations.Comment: to appear in J.Chem.Phy

The Landau gauge gluon and ghost propagators in 4D SU(3) gluodynamics in large lattice volumes

We present recent results of the Landau gauge gluon and ghost propagators in SU(3) pure gauge theory at Wilson \beta=5.7 for lattice sizes up to 80^4 corresponding to physical volumes up to (13.2 fm)^4. In particular, we focus on finite-volume and Gribov copy effects. We employ a gauge fixing method that combines a simulated annealing algorithm with finalizing overrelaxation. We find the gluon propagator for the largest volumes and at q^2 ~ 0.01 GeV^2 to become flat. Although not excluded by our data, there is still no clear indication of a gluon propagator tending towards zero in the zero-momentum limit. New data for the ghost propagator are reported, too.Comment: 7 pages, 3 figures, poster presented at Lattice-2007, Regensburg, July 30 - August 4, 2007, 1 figure replace

A new stellar mixing process operating below shell convection zones following off-center ignition

During most stages of stellar evolution the nuclear burning of lighter to heavier elements results in a radial composition profile which is stabilizing against buoyant acceleration, with light material residing above heavier material. However, under some circumstances, such as off-center ignition, the composition profile resulting from nuclear burning can be destabilizing, and characterized by an outwardly increasing mean molecular weight. The potential for instabilities under these circumstances, and the consequences that they may have on stellar structural evolution, remain largely unexplored. In this paper we study the development and evolution of instabilities associated with unstable composition gradients in regions which are initially stable according to linear Schwarzschild and Ledoux criteria. In particular, we explore the mixing taking place under various conditions with multi-dimensional hydrodynamic convection models based on stellar evolutionary calculations of the core helium flash in a 1.25 \Msun star, the core carbon flash in a 9.3\,\Msun star, and of oxygen shell burning in a star with a mass of 23\,\Msun. The results of our simulations reveal a mixing process associated with regions having outwardly increasing mean molecular weight that reside below convection zones. The mixing is not due to overshooting from the convection zone, nor is it due directly to thermohaline mixing which operates on a timescale several orders of magnitude larger than the simulated flows. Instead, the mixing appears to be due to the presence of a wave field induced in the stable layers residing beneath the convection zone which enhances the mixing rate by many orders of magnitude and allows a thermohaline type mixing process to operate on a dynamical, rather than thermal, timescale. We discuss our results in terms of related laboratory phenomena and associated theoretical developments.Comment: accepted for publication in Astrophysical Journal, 9 pages, 8 figure

Molecular transport and flow past hard and soft surfaces: Computer simulation of model systems

The properties of polymer liquids on hard and soft substrates are investigated by molecular dynamics simulation of a coarse-grained bead-spring model and dynamic single-chain-in-mean-field (SCMF) simulations of a soft, coarse-grained polymer model. Hard, corrugated substrates are modelled by an FCC Lennard-Jones solid while polymer brushes are investigated as a prototypical example of a soft, deformable surface. From the molecular simulation we extract the coarse-grained parameters that characterise the equilibrium and flow properties of the liquid in contact with the substrate: the surface and interface tensions, and the parameters of the hydrodynamic boundary condition. The so-determined parameters enter a continuum description like the Stokes equation or the lubrication approximation.Comment: 41 pages, 13 figure