Quantum stochastic cocycles and completely bounded semigroups on operator spaces

An operator space analysis of quantum stochastic cocycles is undertaken. These are cocycles with respect to an ampliated CCR flow, adapted to the associated filtration of subspaces, or subalgebras. They form a noncommutative analogue of stochastic semigroups in the sense of Skorohod. One-to-one correspondences are established between classes of cocycle of interest and corresponding classes of one-parameter semigroups on associated matrix spaces. Each of these 'global' semigroups may be viewed as the expectation semigroup of an associated quantum stochastic cocycle on the corresponding matrix space. The classes of cocycle covered include completely positive contraction cocycles on an operator system, or C*-algebra; completely contractive cocycles on an operator space; and contraction operator cocycles on a Hilbert space. As indicated by Accardi and Kozyrev, the Schur-action matrix semigroup viewpoint circumvents technical (domain) limitations inherent in the theory of quantum stochastic differential equations. An infinitesimal analysis of quantum stochastic cocycles from the present wider perspective is given in a sister paper.Comment: 32 page

Further Representations of the Canonical Commutation Relations

We construct a new class of representations of the canonical commutation relations, which generalizes previously known classes. We perturb the infinitesimal generator of the initial Fock representation (i.e. the free quantum field) by a function of the field which is square-integrable with respect to the associated Gaussian measure. We characterize which such perturbations lead to representations of the canonical commutation relations. We provide conditions entailing the irreducibility of such representations, show explicitly that our class of representations subsumes previously studied classes, and give necessary and sufficient conditions for our representations to be unitarily equivalent, resp. quasi-equivalent, with Fock, coherent or quasifree representations

Active cooling design for scramjet engines using optimization methods

A methodology for using optimization in designing metallic cooling jackets for scramjet engines is presented. The optimal design minimizes the required coolant flow rate subject to temperature, mechanical-stress, and thermal-fatigue-life constraints on the cooling-jacket panels, and Mach-number and pressure contraints on the coolant exiting the panel. The analytical basis for the methodology is presented, and results for the optimal design of panels are shown to demonstrate its utility

Self-shrinkers with a rotational symmetry

In this paper we present a new family of non-compact properly embedded, self-shrinking, asymptotically conical, positive mean curvature ends $\Sigma^n\subseteq\mathbb{R}^{n+1}$ that are hypersurfaces of revolution with circular boundaries. These hypersurface families interpolate between the plane and half-cylinder in $\mathbb{R}^{n+1}$, and any rotationally symmetric self-shrinking non-compact end belongs to our family. The proofs involve the global analysis of a cubic-derivative quasi-linear ODE. We also prove the following classification result: a given complete, embedded, self-shrinking hypersurface of revolution $\Sigma^n$ is either a hyperplane $\mathbb{R}^{n}$, the round cylinder $\mathbb{R}\times S^{n-1}$ of radius $\sqrt{2(n-1)}$, the round sphere $S^n$ of radius $\sqrt{2n}$, or is diffeomorphic to an $S^1\times S^{n-1}$ (i.e. a "doughnut" as in [Ang], which when $n=2$ is a torus). In particular for self-shrinkers there is no direct analogue of the Delaunay unduloid family. The proof of the classification uses translation and rotation of pieces, replacing the method of moving planes in the absence of isometries.Comment: Trans. Amer. Math. Soc. (2011), to appear; 23 pages, 1 figur

Three-loop corrections to the lightest Higgs scalar boson mass in supersymmetry

I evaluate the largest three-loop corrections to the mass of the lightest Higgs scalar boson in the Minimal Supersymmetric Standard Model in a mass-independent renormalization scheme, using effective field theory and renormalization group methods. The contributions found here are those that depend only on strong and Yukawa interactions and on the leading and next-to-leading logarithms of the ratio of a typical superpartner mass scale to the top quark mass. The approximation assumes that all superpartners and the other Higgs bosons can be treated as much heavier than the top quark, but does not assume their degeneracy. I also discuss the consistent addition of the three-loop corrections to a complete two-loop calculation.Comment: 9 page

The Many Faces of Heterogeneous Ice Nucleation: Interplay Between Surface Morphology and Hydrophobicity

What makes a material a good ice nucleating agent? Despite the importance of heterogeneous ice nucleation to a variety of fields, from cloud science to microbiology, major gaps in our understanding of this ubiquitous process still prevent us from answering this question. In this work, we have examined the ability of generic crystalline substrates to promote ice nucleation as a function of the hydrophobicity and the morphology of the surface. Nucleation rates have been obtained by brute-force molecular dynamics simulations of coarse-grained water on top of different surfaces of a model fcc crystal, varying the water-surface interaction and the surface lattice parameter. It turns out that the lattice mismatch of the surface with respect to ice, customarily regarded as the most important requirement for a good ice nucleating agent, is at most desirable but not a requirement. On the other hand, the balance between the morphology of the surface and its hydrophobicity can significantly alter the ice nucleation rate and can also lead to the formation of up to three different faces of ice on the same substrate. We have pinpointed three circumstances where heterogeneous ice nucleation can be promoted by the crystalline surface: (i) the formation of a water overlayer that acts as an in-plane template; (ii) the emergence of a contact layer buckled in an ice-like manner; and (iii) nucleation on compact surfaces with very high interaction strength. We hope that this extensive systematic study will foster future experimental work aimed at testing the physiochemical understanding presented herein.Comment: Main + S

The reliability and validity of the Sexual Violence Risk-20 (SVR-20): An International Review

This article reports on the current state of research about the most commonly used Structured Professional Judgement (SPJ) guidelines for sexual offender risk assessment, the Sexual Violence Risk-20 (SVR-20). After describing the general characteristics as well as frequently discussed strengths and weaknesses of this risk assessment approach, we give an international overview of the empirical results of the reliability and validity of the SVR-20. We conclude by describing briefly a convergent strategy for sexual offender risk assessment incorporating the SVR-20 and offer some future directions for international research on the SPJ approach