Design Criteria for Zero Leakage Connectors for Launch Vehicles. Mathematical Model of Interface Sealing Phenomenon, Volume 2 Final Report

Mathematical model of interface sealing phenomenon in determining design criteria for zero leakage connectors for launch vehicle

Four-qubit entanglement from string theory

We invoke the black hole/qubit correspondence to derive the classification of four-qubit entanglement. The U-duality orbits resulting from timelike reduction of string theory from D=4 to D=3 yield 31 entanglement families, which reduce to nine up to permutation of the four qubits.Comment: 4 pages, 1 figure, 2 tables, revtex; minor corrections, references adde

Polarizations and Nullcone of Representations of Reductive Groups

The paper starts with the following simple observation. Let V be a representation of a reductive group G, and let f_1,f_2,...,f_n be homogeneous invariant functions. Then the polarizations of f_1,f_2,...,f_n define the nullcone of k 0} h(t) x = 0 for all x in L. This is then applied to many examples. A surprising result is about the group SL(2,C) where almost all representations V have the property that all linear subspaces of the nullcone are annihilated. Again, this has interesting applications to the invariants on several copies. Another result concerns the n-qubits which appear in quantum computing. This is the representation of a product of n copies of $SL_2$ on the n-fold tensor product C^2 otimes C^2 otimes ... otimes C^2. Here we show just the opposite, namely that the polarizations never define the nullcone of several copies if n <= 3. (An earlier version of this paper, distributed in 2002, was split into two parts; the first part with the title ``On the nullcone of representations of reductive groups'' is published in Pacific J. Math. {bf 224} (2006), 119--140.

A general form of Gelfand-Kazhdan criterion

We formalize the notion of matrix coefficients for distributional vectors in a representation of a real reductive group, which consist of generalized functions on the group. As an application, we state and prove a Gelfand-Kazhdan criterion for a real reductive group in very general settings.Comment: 16 pages, to appear in Manuscripta Mathematic

Transfer of K-types on local theta lifts of characters and unitary lowest weight modules

In this paper we study representations of the indefinite orthogonal group O(n,m) which are local theta lifts of one dimensional characters or unitary lowest weight modules of the double covers of the symplectic groups. We apply the transfer of K-types on these representations of O(n,m), and we study their effects on the dual pair correspondences. These results provide examples that the theta lifting is compatible with the transfer of K-types. Finally we will use these results to study subquotients of some cohomologically induced modules

Uniqueness of Bessel models: the archimedean case

In the archimedean case, we prove uniqueness of Bessel models for general linear groups, unitary groups and orthogonal groups.Comment: 22 page

Statistical Mechanics of Membrane Protein Conformation: A Homopolymer Model

The conformation and the phase diagram of a membrane protein are investigated via grand canonical ensemble approach using a homopolymer model. We discuss the nature and pathway of $\alpha$-helix integration into the membrane that results depending upon membrane permeability and polymer adsorptivity. For a membrane with the permeability larger than a critical value, the integration becomes the second order transition that occurs at the same temperature as that of the adsorption transition. For a nonadsorbing membrane, the integration is of the first order due to the aggregation of $\alpha$-helices.Comment: RevTeX with 5 postscript figure

The resource theory of quantum reference frames: manipulations and monotones

Every restriction on quantum operations defines a resource theory, determining how quantum states that cannot be prepared under the restriction may be manipulated and used to circumvent the restriction. A superselection rule is a restriction that arises through the lack of a classical reference frame and the states that circumvent it (the resource) are quantum reference frames. We consider the resource theories that arise from three types of superselection rule, associated respectively with lacking: (i) a phase reference, (ii) a frame for chirality, and (iii) a frame for spatial orientation. Focussing on pure unipartite quantum states (and in some cases restricting our attention even further to subsets of these), we explore single-copy and asymptotic manipulations. In particular, we identify the necessary and sufficient conditions for a deterministic transformation between two resource states to be possible and, when these conditions are not met, the maximum probability with which the transformation can be achieved. We also determine when a particular transformation can be achieved reversibly in the limit of arbitrarily many copies and find the maximum rate of conversion. A comparison of the three resource theories demonstrates that the extent to which resources can be interconverted decreases as the strength of the restriction increases. Along the way, we introduce several measures of frameness and prove that these are monotonically nonincreasing under various classes of operations that are permitted by the superselection rule.Comment: 37 pages, 4 figures, Published Versio

Ancient habitat shifts and organismal diversification are decoupled in the African viper genus Bitis (Serpentes: Viperidae)

Aim: The expansion of open habitats during the mid-Miocene has been hypothesized as a driver of allopatric speciation for many African taxa. This habitat-dependent mode of diversification has been implicated in the shift from C3 (e.g. forest/woodland) to C4 dominated systems (i.e. open savanna, grasslands) in a number of African squamates. We examined this hypothesis using a genus of African viperid snakes (Bitis) with both open habitat and forest-dwelling representatives. Location: Africa. Methods: A comprehensive multilocus dataset was used to generate a calibrated species tree using a multispecies coalescent model. Individual gene trees and patterns of nuclear allele sharing were used to assess species monophyly and isolation. To test the habitat-dependent evolution hypothesis, we generated an ancestral character state reconstruction for open and closed habitats using the dated phylogeny. This was related to the timing of open habitat expansion and forest/woodland contraction in Africa. Results: The genus Bitis originated in the Oligocene, with species level diversification in the late Miocene/Pliocene. Four well-supported clades correspond to the recognized subgenera Bitis, Keniabitis, Macrocerastes and Calechidna. Several previously unrecognized lineages potentially represent cryptic species. Main conclusions Habitat-dependent evolution does not appear to have been a main driver for generic level viperine diversification: the ancestral state for Bitis was open habitat and at least one clade moved into forest in the Miocene, long after forest had contracted and fragmented. Forest-dependent species diversified only in the late Miocene, presumably as forest became further reduced in extent, fitting an allopatric model of speciation. Although our results do not favour a general pattern of habitat-dependent diversification in Bitis, cladogenesis within the subgenus Calechidna for “arenicolous” species (Bitis caudalis complex) and “rupicolous” species (B. Atropos-cornuta complex), corresponds to the aridification of southwest Africa. This suggests there are subtleties not captured in the broad open habitat category, which are relevant for understanding the role of habitat-dependent evolution