Towards a unification of HRT and SCOZA

The Hierarchical Reference Theory (HRT) and the Self-Consistent Ornstein-Zernike Approximation (SCOZA) are two liquid state theories that both furnish a largely satisfactory description of the critical region as well as phase separation and the equation of state in general. Furthermore, there are a number of similarities that suggest the possibility of a unification of both theories. As a first step towards this goal we consider the problem of combining the lowest order gamma expansion result for the incorporation of a Fourier component of the interaction with the requirement of consistency between internal and free energies, leaving aside the compressibility relation. For simplicity we restrict ourselves to a simplified lattice gas that is expected to display the same qualitative behavior as more elaborate models. It turns out that the analytically tractable Mean Spherical Approximation is a solution to this problem, as are several of its generalizations. Analysis of the characteristic equations shows the potential for a practical scheme and yields necessary conditions any closure to the Ornstein Zernike relation must fulfill for the consistency problem to be well posed and to have a unique differentiable solution. These criteria are expected to remain valid for more general discrete and continuous systems, even if consistency with the compressibility route is also enforced where possible explicit solutions will require numerical evaluations.Comment: Minor changes in accordance with referee comment

Self-consistent Ornstein-Zernike approximation for molecules with soft cores

The Self-Consistent Ornstein-Zernike Approximation (SCOZA) is an accurate liquid state theory. So far it has been tied to interactions composed of hard core repulsion and long-range attraction, whereas real molecules have soft core repulsion at short distances. In the present work, this is taken into account through the introduction of an effective hard core with a diameter that depends upon temperature only. It is found that the contribution to the configurational internal energy due to the repulsive reference fluid is of prime importance and must be included in the thermodynamic self-consistency requirement on which SCOZA is based. An approximate but accurate evaluation of this contribution relies on the virial theorem to gauge the amplitude of the pair distribution function close to the molecular surface. Finally, the SCOZA equation is transformed by which the problem is reformulated in terms of the usual SCOZA with fixed hard core reference system and temperature-dependent interaction

The 30/20 GHZ net market assessment

By creating a number of market scenarios variations dealing with network types, network sizes, and service price levels were analyzed for their impact on market demand. Each market scenario represents a market demand forecast with results for voice, data, and video service traffic expressed in peak load megabits per second

Soft core thermodynamics from self-consistent hard core fluids

In an effort to generalize the self-consistent Ornstein-Zernike approximation (SCOZA) -- an accurate liquid-state theory that has been restricted so far to hard-core systems -- to arbitrary soft-core systems we study a combination of SCOZA with a recently developed perturbation theory. The latter was constructed by Ben-Amotz and Stell [J. Phys. Chem. B 108,6877-6882 (2004)] as a reformulation of the Week-Chandler-Andersen perturbation theory directly in terms of an arbitrary hard-sphere reference system. We investigate the accuracy of the combined approach for the Lennard-Jones fluid by comparison with simulation data and pure perturbation theory predictions and determine the dependence of the thermodynamic properties and the phase behavior on the choice of the effective hard-core diameter of the reference system.Comment: 38 pages, 10 figure

Laboratory experiments on current flow between stationary and moving electrodes in magnetoplasmas

Laboratory experiments were performed in order to investigate the basic physics of current flow between tethered electrodes in magnetoplasmas. The major findings are summarized. The experiments are performed in an effectively very large laboratory plasma in which not only the nonlinear current collection is addressed but also the propagation and spread of currents, the formation of current wings by moving electrodes, the current closure, and radiation from transmission lines. The laboratory plasma consists of a pulsed dc discharge whose Maxwellian afterglow provides a quiescent, current-free uniform background plasma. Electrodes consisting of collectors and electron emitters are inserted into the plasma and a pulsed voltage is applied between two floating electrodes via insulated transmission lines. Besides the applied current in the wire, the total current density in the plasma is obtained from space and time resolved magnetic probe measurements via Maxwell's law. Langmuir probes yield the plasma parameters

Lower algebraic K-theory of certain reflection groups

For a finite volume geodesic polyhedron P in hyperbolic 3-space, with the property that all interior angles between incident faces are integral submultiples of Pi, there is a naturally associated Coxeter group generated by reflections in the faces. Furthermore, this Coxeter group is a lattice inside the isometry group of hyperbolic 3-space, with fundamental domain the original polyhedron P. In this paper, we provide a procedure for computing the lower algebraic K-theory of the integral group ring of such Coxeter lattices in terms of the geometry of the polyhedron P. As an ingredient in the computation, we explicitly calculate some of the lower K-groups of the dihedral groups and the product of dihedral groups with the cyclic group of order two.Comment: 35 pages, 2 figure

A Kinetic Model for Grain Growth

We provide a well-posedness analysis of a kinetic model for grain growth introduced by Fradkov which is based on the von Neumann-Mullins law. The model consists of an infinite number of transport equations with a tri-diagonal coupling modelling topological changes in the grain configuration. Self-consistency of this kinetic model is achieved by introducing a coupling weight which leads to a nonlinear and nonlocal system of equations. We prove existence of solutions by approximation with finite dimensional systems. Key ingredients in passing to the limit are suitable super-solutions, a bound from below on the total mass, and a tightness estimate which ensures that no mass is transported to infinity in finite time.Comment: 24 page

The 18/30 GHz fixed communications system service demand assessment. Volume 1: Executive summary

The total demand for voice, video, and data communications services, and satellite transmission services at the 4/6 GHz, 12/14 GHz, and 18/30 GHz frequencies is discussed. Major study objectives, overall methodology, results, and general observations about a satellite systems market characteristics and trends are summarized

The 30/20 GHz fixed communications systems service demand assessment. Volume 3: Appendices

The market analysis of voice, video, and data 18/30 GHz communications systems services and satellite transmission services is discussed. Detail calculations, computer displays of traffic, survey questionnaires, and detailed service forecasts are presented