2d Model Field Theories at Finite Temperature and Density

In certain 1+1 dimensional field theoretic toy models, one can go all the way from microscopic quarks via the hadron spectrum to the properties of hot and dense baryonic matter in an essentially analytic way. This "miracle" is illustrated through case studies of two popular large N models, the Gross-Neveu and the 't Hooft model - caricatures of the Nambu-Jona-Lasinio model and real QCD, respectively. The main emphasis will be on aspects related to spontaneous symmetry breaking (discrete or continuous chiral symmetry, translational invariance) and confinement.Comment: 90 pages, 27 figures, Contribution to the Festschrift in honor of Boris Ioffe, edited by M. Shifma

The Jang equation reduction of the spacetime positive energy theorem in dimensions less than eight

We extend the Jang equation proof of the positive energy theorem due to R. Schoen and S.-T. Yau from dimension $n=3$ to dimensions $3 \leq n <8$. This requires us to address several technical difficulties that are not present when $n=3$. The regularity and decay assumptions for the initial data sets to which our argument applies are weaker than those of R. Schoen and S.-T. Yau. In recent joint work with L.-H. Huang, D. Lee, and R. Schoen we have given a different proof of the full positive mass theorem in dimensions $3 \leq n < 8$. We pointed out that this theorem can alternatively be derived from our density argument and the positive energy theorem of the present paper.Comment: All comments welcome! Final version to appear in Comm. Math. Phy

Vehicle to grid as a household emergency generator for 2007 Toyota Prius plug-in hybrid electric vehicle.

Electric vehicles are quickly becoming one of the most rapidly growing technologies of this age. With their acceleration to prominence, the concept of Vehicle to Grid (V2G) becomes much more common as well. V2G is normally used as a supplement to the power grid to shave peak load levels, as a spinning reserve, or as a supplement to renewable energy sources. These vehicles can provide many advantages to consumers and power grid operators while also benefitting the environment. This paper explores an additional application where V2G could be of great benefit. This situation is the use of a V2G capable car to provide backup electricity generating capacity to an average American-style home (in terms of power consumption). This objective is completed in coordination with the IEEE 1547 Standard for Interconnecting Distributed Resources with Electric Power Systems. A 2007 Toyota Prius retrofitted to function as a Plug-In Hybrid Vehicle is used as a baseline. The output of the system is designated to be a single phase 240 Vrms 60 Hz signal that would connect to the house grid. All steps in designing and simulating the interface are performed as well as selection of components including gate drive support systems

Existence, Regularity, and Properties of Generalized Apparent Horizons

We prove a conjecture of Tom Ilmanen's and Hubert Bray's regarding the existence of the outermost generalized apparent horizon in an initial data set and that it is outer area minimizing.Comment: 16 pages, thoroughly revised, no major changes, to appear in Comm. Math. Phy

Changes in context as a measure of semantic flexibility

Call number: LD2668 .T4 1985 S36Master of Scienc

Proof of the double bubble conjecture

We prove that the standard double bubble provides the least-area way to enclose and separate two regions of prescribed volume in R3.Morgan has partial support from a National Science Foundation grant. Ritoré and Ros have partial support from DGICYT research group n. PB97-0785

Coarse-grained treatment of the self-assembly of colloids suspended in a nematic host phase

The complex interplay of molecular scale effects, nonlinearities in the orientational field and long-range elastic forces makes liquid-crystal physics very challenging. A consistent way to extract information from the microscopic, molecular scale up to the meso- and macroscopic scale is still missing. Here, we develop a hybrid procedure that bridges this gap by combining extensive Monte Carlo (MC) simulations, a local Landau-de Gennes theory, classical density functional theory, and finite-size scaling theory. As a test case to demonstrate the power and validity of our novel approach we study the effective interaction among colloids with Boojum defect topology immersed in a nematic liquid crystal. In particular, at sufficiently small separations colloids attract each other if the angle between their center-of-mass distance vector and the far-field nematic director is about 30 degrees. Using the effective potential in coarse-grained two-dimensional MC simulations we show that self-assembled structures formed by the colloids are in excellent agreement with experimental data.DFG, GRK 1524, Self-Assembled Soft-Matter Nanostructures at Interface

Disclination lines at homogeneous and heterogeneous colloids immersed in a chiral liquid crystal

In the present work we perform Monte Carlo simulations in the isothermal-isobaric ensemble to study defect topologies formed in a cholesteric liquid crystal due to the presence of a spherical colloidal particle. Topological defects arise because of the competition between anchoring at the colloidal surface and the local director. We consider homogeneous colloids with either local homeotropic or planar anchoring to validate our model by comparison with earlier lattice Boltzmann studies. Furthermore, we perform simulations of a colloid in a twisted nematic cell and discuss the difference between induced and intrinsic chirality on the formation of topological defects. We present a simple geometrical argument capable of describing the complex three-dimensional topology of disclination lines evolving near the surface of the colloid. The presence of a Janus colloid in a cholesteric host fluid reveals a rich variety of defect structures. Using the Frank free energy we analyze these defects quantitatively indicating a preferred orientation of the Janus colloid relative to the cholesteric helix.DFG, GRK 1524, Self-Assembled Soft-Matter Nanostructures at Interface