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

Leishmania promastigotes evade interleukin 12 (IL-12) induction by macrophages and stimulate a broad range of cytokines from CD4+ T cells during initiation of infection.

Leishmania major are intramacrophage parasites whose eradication requires the induction of T helper 1 (Th1) effector cells capable of activating macrophages to a microbicidal state. Interleukin 12 (IL-12) has been recently identified as a macrophage-derived cytokine capable of mediating Th1 effector cell development, and of markedly enhancing interferon gamma (IFN-gamma) production by T cells and natural killer cells. Infection of macrophages in vitro by promastigotes of L. major caused no induction of IL-12 p40 transcripts, whereas stimulation using heat-killed Listeria or bacterial lipopolysaccharide induced readily detectable IL-12 mRNA. Using a competitor construct to quantitate a number of transcripts, a kinetic analysis of cytokine induction during the first few days of infection by L. major was performed. All strains of mice examined, including susceptible BALB/c and resistant C57BL/6, B10.D2, and C3H/HeN, had the appearance of a CD4+ population in the draining lymph nodes that contained transcripts for IL-2, IL-4, and IFN-gamma (and in some cases, IL-10) that peaked 4 d after infection. In resistant mice, the transcripts for IL-2, IL-4, and IL-10 were subsequently downregulated, whereas in susceptible BALB/c mice, these transcripts were only slightly decreased, and IL-4 continued to be reexpressed at high levels. IL-12 transcripts were first detected in vivo by 7 d after infection, consistent with induction by intracellular amastigotes. Challenge of macrophages in vitro confirmed that amastigotes, in contrast to promastigotes, induced IL-12 p40 mRNA. Reexamination of the cytokine mRNA at 4 d revealed expression of IL-13 in all strains analyzed, suggesting that IL-2 and IL-13 may mediate the IL-12-independent production of IFN-gamma during the first days after infection. Leishmania have evolved to avoid inducing IL-12 from host macrophages during transmission from the insect vector, and cause a striking induction of mRNAs for IL-2, IL-4, IL-10, and IL-13 in CD4+ T cells. Each of these activities may favor survival of the organism

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