Orientational prewetting of planar solid substrates by a model liquid crystal

We present grand canonical ensemble Monte Carlo simulations of prewetting transitions in a model liquid crystal at structureless solid substrates. Molecules of the liquid crystal interact via anisometric Lennard-Jones potentials and can be anchored planar or homeotropically at the substrates. Fluid-substrate attraction is modeled by a Yukawa potential of variable range. By monitoring the grand-potential density and the nematic order parameter as functions of the chemical potential μ, several discontinuous prewetting, wetting, and isotropic-nematic phase transitions are observed. These transitions depend on both the range of the fluid-substrate attraction and the specific anchoring at the substrate. Our results show that at substrates characterized by degenerate anchoring prewetting occurs at lower μ compared with cases in which the anchoring is monostable. This indicates that prewetting transitions are driven by orientational entropy because degenerate anchoring allows for more orientationally distinct configurations of molecules compared with monostable anchoring. In addition, by analyzing local density and various local order parameters, a detailed picture of the structure of various phases emerges from our simulations.     

Specifying Angular Momentum and Center of Mass for Vacuum Initial Data Sets

We show that it is possible to perturb arbitrary vacuum asymptotically flat spacetimes to new ones having exactly the same energy and linear momentum, but with center of mass and angular momentum equal to any preassigned values measured with respect to a fixed affine frame at infinity. This is in contrast to the axisymmetric situation where a bound on the angular momentum by the mass has been shown to hold for black hole solutions. Our construction involves changing the solution at the linear level in a shell near infinity, and perturbing to impose the vacuum constraint equations. The procedure involves the perturbation correction of an approximate solution which is given explicitly.     

Slit-pore sorption isotherms by the grand-canonical Monte Carlo method

The grand-canonical ensemble Monte Carlo method has been used to study sorption isotherms (plots of density versus chemical potential) for a rare-gas fluid in a slit-pore whose plane-parallel walls comprise rigidly fixed rare-gas atoms. Hysteresis in the vicinity of the capillary-condensation transition is evinced by fluctuations between liquid and vapour phases as the length of the Markov chain increases (at fixed chemical potential). The degree of hysteresis, which reflects the non-ergodic behaviour of the Markov chain, can be diminished by increasing the surface area of the pore wall and by extending the Markov chain. It is concluded that hysteresis is a non-equilibrium phenomenon that cannot be properly treated by equilibrium statistical-mechanical methods.     

Solving molecular distance geometry problems by global optimization algorithms

In this paper we consider global optimization algorithms based on multiple local searches for the Molecular Distance Geometry Problem (MDGP). Three distinct approaches (Multistart, Monotonic Basin Hopping, Population Basin Hopping) are presented and for each of them a computational analysis is performed. The results are also compared with those of two other approaches in the literature, the DGSOL approach (Moré, Wu in J. Glob. Optim. 15:219–234, 1999) and a SDP based approach (Biswas et al. in An SDP based approach for anchor-free 3D graph realization, Technical Report, Operations Research, Stanford University, 2005).     

Mesoscale modeling of complex binary fluid mixtures: towards an atomistic foundation of effective potentials

This paper is devoted to equilibrium molecular-dynamics (MD) simulations of a fully atomistic model of binary mixtures of water (component 1) and ethanol (component 2). We investigate ways to extract from these simulations effective, pairwise additive potentials suitable to describe the interactions between coarse-grained molecules (i.e., beads) in corresponding mesoscale dissipative particle-dynamics simulations. The fully atomistic model employed in MD simulations is mapped onto an implicit water model, where the internal degrees of freedom of ethanol and all the degrees of freedom of water are integrated out. This gives us an effective one-component system consisting only of ethanol beads. The effective interaction potential between a pair of ethanol beads, Phi(R), is approximated at three levels of sophistication. At the lowest one, we approximate Phi(R) by the potential of mean force between the centers of mass of two ethanol beads calculated in the fully atomistic MD simulations; at the second level, we take Phi(R) to be the potential linked to total and direct correlation functions in the hypernetted-chain closure of the Ornstein-Zernike equation. At the third level we approximate Phi(R) numerically by improving it iteratively through the Boltzmann inversion scheme. Our results indicate that the level-one approach works only at the lowest (8 wt %) concentration; the level-two approach works only up to intermediate ethanol concentrations (ca. 50 wt %). Only the Boltzmann inversion scheme works for all, up to the highest concentration considered (70 wt %).     

The energy and the linear momentum of space-times in general relativity

We extend our previous proof of the positive mass conjecture to allow a more general asymptotic condition proposed by York. Hence we are able to prove that for an isolated physical system, the energy momentum four vector is a future timelike vector unless the system is trivial. Furthermore, we allow singularities of the type of black holes.Supported in part by an NSF grant