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

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

Interplay of local hydrogen-bonding and long-ranged dipolar forces in simulations of confined water

Spherical truncations of Coulomb interactions in standard models for water permit efficient molecular simulations and can give remarkably accurate results for the structure of the uniform liquid. However truncations are known to produce significant errors in nonuniform systems, particularly for electrostatic properties. Local molecular field (LMF) theory corrects such truncations by use of an effective or restructured electrostatic potential that accounts for effects of the remaining long-ranged interactions through a density-weighted mean field average and satisfies a modified Poisson's equation defined with a Gaussian-smoothed charge density. We apply LMF theory to three simple molecular systems that exhibit different aspects of the failure of a naive application of spherical truncations -- water confined between hydrophobic walls, water confined between atomically-corrugated hydrophilic walls, and water confined between hydrophobic walls with an applied electric field. Spherical truncations of 1/r fail spectacularly for the final system in particular, and LMF theory corrects the failings for all three. Further, LMF theory provides a more intuitive way to understand the balance between local hydrogen bonding and longer-ranged electrostatics in molecular simulations involving water.Comment: Submitted to PNA

Local molecular field theory for effective attractions between like charged objects in systems with strong Coulomb interactions

Strong short ranged positional correlations involving counterions can induce a net attractive force between negatively charged strands of DNA, and lead to the formation of ion pairs in dilute ionic solutions. But the long range of the Coulomb interactions impedes the development of a simple local picture. We address this general problem by mapping the properties of a nonuniform system with Coulomb interactions onto those of a simpler system with short ranged intermolecular interactions in an effective external field that accounts for the averaged effects of appropriately chosen long ranged and slowly varying components of the Coulomb interactions. The remaining short ranged components combine with the other molecular core interactions and strongly affect pair correlations in dense or strongly coupled systems. We show that pair correlation functions in the effective short ranged system closely resemble those in the uniform primitive model of ionic solutions, and illustrate the formation of ion pairs and clusters at low densities. The theory accurately describes detailed features of the effective attraction between two equally charged walls at strong coupling and intermediate separations of the walls. New analytical results for the minimal coupling strength needed to get any attraction and for the separation where the attractive force is a maximum are presented.Comment: 8 pages, 5 figures. To be published in PNA

Seam tracking performance of a Coaxial Weld Vision System and pulsed welding

This report describes a continuation of a series of tests on the Coaxial Weld Vision System at MSFC. The ability of the system to compensate for transients associated with pulsed current welding is analyzed. Using the standard image processing approach for root pass seam tracking, the system is also tested for the ability to track the toe of a previous weld bead, for tracking multiple pass weld joints. This Coaxial Weld Vision System was developed by the Ohio State University (OSU) Center for Welding Research and is a part of the Space Shuttle Main Engine Robotic Welding Development System at MSFC

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

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

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

Special Theory of Relativity through the Doppler Effect

We present the special theory of relativity taking the Doppler effect as the starting point, and derive several of its main effects, such as time dilation, length contraction, addition of velocities, and the mass-energy relation, and assuming energy and momentum conservation, we discuss how to introduce the 4-momentum in a natural way. We also use the Doppler effect to explain the "twin paradox", and its version on a cylinder. As a by-product we discuss Bell's spaceship paradox, and the Lorentz transformation for arbitrary velocities in one dimension.Comment: 20 pages, 1 figur