Efficient solutions of self-consistent mean field equations for dewetting and electrostatics in nonuniform liquids

We use a new configuration-based version of linear response theory to efficiently solve self-consistent mean field equations relating an effective single particle potential to the induced density. The versatility and accuracy of the method is illustrated by applications to dewetting of a hard sphere solute in a Lennard-Jones fluid, the interplay between local hydrogen bond structure and electrostatics for water confined between two hydrophobic walls, and to ion pairing in ionic solutions. Simulation time has been reduced by more than an order of magnitude over previous methods.Comment: Supplementary material included at end of main pape

A new approach for efficient simulation of Coulomb interactions in ionic fluids

We propose a simplified version of local molecular field (LMF) theory to treat Coulomb interactions in simulations of ionic fluids. LMF theory relies on splitting the Coulomb potential into a short-ranged part that combines with other short-ranged core interactions and is simulated explicitly. The averaged effects of the remaining long-ranged part are taken into account through a self-consistently determined effective external field. The theory contains an adjustable length parameter sigma that specifies the cut-off distance for the short-ranged interaction. This can be chosen to minimize the errors resulting from the mean-field treatment of the complementary long-ranged part. Here we suggest that in many cases an accurate approximation to the effective field can be obtained directly from the equilibrium charge density given by the Debye theory of screening, thus eliminating the need for a self-consistent treatment. In the limit sigma -> 0, this assumption reduces to the classical Debye approximation. We examine the numerical performance of this approximation for a simple model of a symmetric ionic mixture. Our results for thermodynamic and structural properties of uniform ionic mixtures agree well with similar results of Ewald simulations of the full ionic system. In addition we have used the simplified theory in a grand-canonical simulation of a nonuniform ionic mixture where an ion has been fixed at the origin. Simulations using short-ranged truncations of the Coulomb interactions alone do not satisfy the exact condition of complete screening of the fixed ion, but this condition is recovered when the effective field is taken into account. We argue that this simplified approach can also be used in the simulations of more complex nonuniform systems.Comment: To be published in Journal of Chemical Physic

Density fluctuations and the structure of a nonuniform hard sphere fluid

We derive an exact equation for density changes induced by a general external field that corrects the hydrostatic approximation where the local value of the field is adsorbed into a modified chemical potential. Using linear response theory to relate density changes self-consistently in different regions of space, we arrive at an integral equation for a hard sphere fluid that is exact in the limit of a slowly varying field or at low density and reduces to the accurate Percus-Yevick equation for a hard core field. This and related equations give accurate results for a wide variety of fields

Local molecular field theory for the treatment of electrostatics

We examine in detail the theoretical underpinnings of previous successful applications of local molecular field (LMF) theory to charged systems. LMF theory generally accounts for the averaged effects of long-ranged components of the intermolecular interactions by using an effective or restructured external field. The derivation starts from the exact Yvon-Born-Green hierarchy and shows that the approximation can be very accurate when the interactions averaged over are slowly varying at characteristic nearest-neighbor distances. Application of LMF theory to Coulomb interactions alone allows for great simplifications of the governing equations. LMF theory then reduces to a single equation for a restructured electrostatic potential that satisfies Poisson's equation defined with a smoothed charge density. Because of this charge smoothing by a Gaussian of width sigma, this equation may be solved more simply than the detailed simulation geometry might suggest. Proper choice of the smoothing length sigma plays a major role in ensuring the accuracy of this approximation. We examine the results of a basic confinement of water between corrugated wall and justify the simple LMF equation used in a previous publication. We further generalize these results to confinements that include fixed charges in order to demonstrate the broader impact of charge smoothing by sigma. The slowly-varying part of the restructured electrostatic potential will be more symmetric than the local details of confinements.Comment: To be published in J Phys-Cond Matt; small misprint corrected in Eq. (12) in V

Properties of cage rearrangements observed near the colloidal glass transition

We use confocal microscopy to study the motions of particles in concentrated colloidal systems. Near the glass transition, diffusive motion is inhibited, as particles spend time trapped in transient ``cages'' formed by neighboring particles. We measure the cage sizes and lifetimes, which respectively shrink and grow as the glass transition approaches. Cage rearrangements are more prevalent in regions with lower local concentrations and higher disorder. Neighboring rearranging particles typically move in parallel directions, although a nontrivial fraction move in anti-parallel directions, usually from pairs of particles with initial separations corresponding to the local maxima and minima of the pair correlation function $g(r)$, respectively.Comment: 5 pages, 4 figures; text & figures revised in v

Vacuum Energy Density for Massless Scalar Fields in Flat Homogeneous Spacetime Manifolds with Nontrivial Topology

Although the observed universe appears to be geometrically flat, it could have one of 18 global topologies. A constant-time slice of the spacetime manifold could be a torus, Mobius strip, Klein bottle, or others. This global topology of the universe imposes boundary conditions on quantum fields and affects the vacuum energy density via Casimir effect. In a spacetime with such a nontrivial topology, the vacuum energy density is shifted from its value in a simply-connected spacetime. In this paper, the vacuum expectation value of the stress-energy tensor for a massless scalar field is calculated in all 17 multiply-connected, flat and homogeneous spacetimes with different global topologies. It is found that the vacuum energy density is lowered relative to the Minkowski vacuum level in all spacetimes and that the stress-energy tensor becomes position-dependent in spacetimes that involve reflections and rotations.Comment: 25 pages, 11 figure

Task 4 supporting technology. Densification requirements definition and test objectives. Propellant densification requirements definition

The primary challenge of the X-33 CAN is to build and test a prototype LO2 and LH2 densification ground support equipment (GSE) unit, and perform tank thermodynamic testing within the 15 month phase 1 period. The LO2 and LH2 propellant densification system will be scaled for the IPTD LO2 and LH2 tank configurations. The IPTD tanks were selected for the propellant technology demonstration because of the potential benefits to the phase 1 plan: tanks will be built in time to support thermodynamic testing; minimum cost; minimum schedule risk; future testing at MSFC will build on phase 1 data base; and densification system will be available to support X-33 and RLV engine test at IPTD. The objective of the task 1 effort is to define the preliminary requirements of the propellant densification GSE and tank recirculation system. The key densification system design parameters to be established in Task 1 are: recirculation flow rate; heat exchanger inlet temperature; heat exchanger outlet temperature; maximum heat rejection rate; vent flow rate (GN2 and GH2); densification time; and tank pressure level

Circles in the Sky: Finding Topology with the Microwave Background Radiation

If the universe is finite and smaller than the distance to the surface of last scatter, then the signature of the topology of the universe is writ large on the microwave background sky. We show that the microwave background will be identified at the intersections of the surface of last scattering as seen by different ``copies'' of the observer. Since the surface of last scattering is a two-sphere, these intersections will be circles, regardless of the background geometry or topology. We therefore propose a statistic that is sensitive to all small, locally homogeneous topologies. Here, small means that the distance to the surface of last scatter is smaller than the ``topology scale'' of the universe.Comment: 14 pages, 10 figures, IOP format. This paper is a direct descendant of gr-qc/9602039. To appear in a special proceedings issue of Class. Quant. Grav. covering the Cleveland Topology & Cosmology Worksho

Reconstructing the global topology of the universe from the cosmic microwave background

If the universe is multiply-connected and sufficiently small, then the last scattering surface wraps around the universe and intersects itself. Each circle of intersection appears as two distinct circles on the microwave sky. The present article shows how to use the matched circles to explicitly reconstruct the global topology of space.Comment: 6 pages, 2 figures, IOP format. To be published in the proceedings of the Cleveland Cosmology and Topology Workshop 17-19 Oct 1997. Submitted to Class. Quant. Gra

Segue Between Favorable and Unfavorable Solvation

Solvation of small and large clusters are studied by simulation, considering a range of solvent-solute attractive energy strengths. Over a wide range of conditions, both for solvation in the Lennard-Jones liquid and in the SPC model of water, it is shown that the mean solvent density varies linearly with changes in solvent-solute adhesion or attractive energy strength. This behavior is understood from the perspective of Weeks' theory of solvation [Ann. Rev. Phys. Chem. 2002, 53, 533] and supports theories based upon that perspective.Comment: 8 pages, 7 figure