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

Factorizations of some weighted spanning tree enumerators

We give factorizations for weighted spanning tree enumerators of Cartesian products of complete graphs, keeping track of fine weights related to degree sequences and edge directions. Our methods combine Kirchhoff's Matrix-Tree Theorem with the technique of identification of factors.Comment: Final version, 12 pages. To appear in the Journal of Combinatorial Theory, Series A. The paper has been reorganized, and the proof of Theorem 4 shortened, in light of a more general result appearing in reference [6

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

Infinite compressibility states in the Hierarchical Reference Theory of fluids. II. Numerical evidence

Continuing our investigation into the Hierarchical Reference Theory of fluids for thermodynamic states of infinite isothermal compressibility kappa[T] we now turn to the available numerical evidence to elucidate the character of the partial differential equation: Of the three scenarios identified previously, only the assumption of the equations turning stiff when building up the divergence of kappa[T] allows for a satisfactory interpretation of the data. In addition to the asymptotic regime where the arguments of part I (cond-mat/0308467) directly apply, a similar mechanism is identified that gives rise to transient stiffness at intermediate cutoff for low enough temperature. Heuristic arguments point to a connection between the form of the Fourier transform of the perturbational part of the interaction potential and the cutoff where finite difference approximations of the differential equation cease to be applicable, and they highlight the rather special standing of the hard-core Yukawa potential as regards the severity of the computational difficulties.Comment: J. Stat. Phys., in press. Minor changes to match published versio

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

Pseudodeterminants and perfect square spanning tree counts

The pseudodeterminant $\textrm{pdet}(M)$ of a square matrix is the last nonzero coefficient in its characteristic polynomial; for a nonsingular matrix, this is just the determinant. If $\partial$ is a symmetric or skew-symmetric matrix then $\textrm{pdet}(\partial\partial^t)=\textrm{pdet}(\partial)^2$. Whenever $\partial$ is the $k^{th}$ boundary map of a self-dual CW-complex $X$, this linear-algebraic identity implies that the torsion-weighted generating function for cellular $k$-trees in $X$ is a perfect square. In the case that $X$ is an \emph{antipodally} self-dual CW-sphere of odd dimension, the pseudodeterminant of its $k$th cellular boundary map can be interpreted directly as a torsion-weighted generating function both for $k$-trees and for $(k-1)$-trees, complementing the analogous result for even-dimensional spheres given by the second author. The argument relies on the topological fact that any self-dual even-dimensional CW-ball can be oriented so that its middle boundary map is skew-symmetric.Comment: Final version; minor revisions. To appear in Journal of Combinatoric

The World War II Experience and the Leadership of Entrepreneurship and Venture Investing around Stanford University

Dr. Frederick Terman has been widely recognized as the godfather of Silicon Valley (Lowood, 1982). Terman, a Stanford University electrical engineering professor, managed Harvard University\u27s Radio Research Laboratory during World War II and returned as Stanford\u27s dean of engineering. His commitment to seeing California companies in science-based industries seize postwar opportunities to push ahead of their Eastern counterparts influenced the venture investing as well as the entrepreneurship that built a thriving high-technology industrial community around Stanford University. Terman\u27s wartime experience shaped his postwar role as a leader of high-technology entrepreneurship. Wartime experiences similarly influenced individuals who invested in California ventures after the war. Environmental shifts during World War II did much to foster the industrial community now known as Silicon Valley

Evaluating the use of Flow-Through Larval Culture for the Eastern Oyster, Crassostrea virginica

One system used for bivalve mollusc culture is flowthrough larval culture, which provides a continuous flow of food and seawater to the tank. Flowthrough culture enables larvae to be reared at stocking densities up to 100 larvae/mL, a characteristic that should recommend it as the culture system of choice for the East coast; however, Eastern oyster larvae have never been tested in flowthrough culture, discouraging implementation of the system. The thesis objectives are designed to address questions regarding the survival, growth, competent period, cell consumption, growth efficiency, and cell selection of oyster larvae reared in flowthrough culture. The objectives are: to describe larval tolerance to metabolic waste products, to determine how stocking densities influence clogging of the banjo screen and how those stocking densities coupled with exchange rate influence survival, growth, duration of the competent period, cell consumption, and cell selectivity, and to examine replication of flowthrough culture and establish data for the variables measured. To obtain a basic understanding of larval tolerance to their metabolic waste, twelve static tanks were set up at the Aquaculture Genetics and Breeding Technology Center’s hatchery at the Virginia Institute of Marine Science. Larvae were exposed to a range of concentrations of ammonia, nitrite, and nitrate and their survival and growth were monitored. Ammonia was the only metabolic waste that caused detrimental effects to larvae at a concentration of 10 mg/L. To address the remaining objectives, six 400 L conical flowthrough tanks were set up at Oyster Seed Holdings, a commercial hatchery. To determine if banjo screen clogging (the cause of tank overflow) was affected by the day and density at which larvae were introduced to flowthrough culture, larvae were introduced at two days old at three different stocking densities. The banjo screen, a circular plastic band with mesh screen on both sides, retains larvae in flowthrough culture while allowing water to exit. The banjo screen was monitored for clogging every 12 hours for 60 hours. Larvae can be introduced to flowthrough culture at two days old at densities as high as 50 larvae/mL without risking banjo clogging. To examine the effects of different flowthrough culture parameters on larval development, larvae were stocked in flowthrough cultures at 10, 20, and 50 larvae/mL and reared at five and ten exchanges of water/day. Five exchanges of water/day and a stocking density between 10 – 20 larvae/mL resulted in the highest survival, fastest growth, and greatest amount of competent larvae harvested. Variation among flowthrough cultures stocked with 10 larvae/mL and reared at five and ten exchanges of water/day was examined. Five exchanges of water/day generally had lower variation, with the smallest being survival and length. The results for survival, length, cell consumption, duration of the competent period, and growth efficiency were characterized as the established values for the thesis’s flowthrough system and were compared with data obtained from the controls in Chapter Three to distinguish anomalous data