Complex group algebras of the double covers of the symmetric and alternating groups

We prove that the double covers of the alternating and symmetric groups are determined by their complex group algebras. To be more precise, let $n\geq 5$ be an integer, $G$ a finite group, and let \AAA and \SSS^\pm denote the double covers of \Al_n and \Sy_n, respectively. We prove that \CC G\cong \CC \AAA if and only if G\cong \AAA, and \CC G\cong \CC \SSS^+\cong\CC\SSS^- if and only if G\cong \SSS^+ or \SSS^-. This in particular completes the proof of a conjecture proposed by the second and fourth authors that every finite quasi-simple group is determined uniquely up to isomorphism by the structure of its complex group algebra. The known results on prime power degrees and relatively small degrees of irreducible (linear and projective) representations of the symmetric and alternating groups together with the classification of finite simple groups play an essential role in the proofs.Comment: 27 pages, the previous version is revised slightly, to appear in Algebra & Number Theor

Calculation of a separated turbulent boundary layer

The properties of a Navier-Stokes solution of a shock-separated turbulent flow over a flat wall are investigated. Refinements of an algebraic relaxation turbulence model previously shown to be of value for the simulation of separated flows are presented. A simplified analysis applicable near an adiabatic wall is developed and used to help verify the accuracy of the numerical solution. Features of the time-dependent response of a turbulent boundary layer to shock impingement are presented

Distributed H-infinity filtering for polynomial nonlinear stochastic systems in sensor networks

Copyright [2010] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, the distributed H1 filtering problem is addressed for a class of polynomial nonlinear stochastic systems in sensor networks. For a Lyapunov function candidate whose entries are polynomials, we calculate its first- and second-order derivatives in order to facilitate the use of Itos differential role. Then, a sufficient condition for the existence of a feasible solution to the addressed distributed H1 filtering problem is derived in terms of parameter-dependent linear matrix inequalities (PDLMIs). For computational convenience, these PDLMIs are further converted into a set of sums of squares (SOSs) that can be solved effectively by using the semidefinite programming technique. Finally, a numerical simulation example is provided to demonstrate the effectiveness and applicability of the proposed design approach.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. under Grant GR/S27658/01, the Royal Society of the U.K., the National 973 Program of China under Grant 2009CB320600, the National Natural Science Foundation of China under Grant 60974030 and the Alexander von Humboldt Foundation of Germany

Electron-photon scattering mediated by localized plasmons: A quantitative analysis by eigen-response theory

We show that the scattering interaction between a high energy electron and a photon can be strongly enhanced by different types of localized plasmons in a non-trivial way. The scattering interaction is predicted by an eigen-response theory, numerically verified by finite-difference-time-domain simulation, and experimentally verified by cathodoluminescence spectroscopy. We find that the scattering interaction associated with dark plasmons can be as strong as that of bright plasmons. Such a strong interaction may offer new opportunities to improve single-plasmon detection and high-resolution characterization techniques for high quality plasmonic materials.Comment: 4 pages, 4 figures (excluding Supporting Information

Numerical study of large-eddy breakup and its effect on the drag characteristics of boundary layers

The break-up of a field of eddies by a flat-plate obstacle embedded in a boundary layer is studied using numerical solutions to the two-dimensional Navier-Stokes equations. The flow is taken to be incompressible and unsteady. The flow field is initiated from rest. A train of eddies of predetermined size and strength are swept into the computational domain upstream of the plate. The undisturbed velocity profile is given by the Blasius solution. The disturbance vorticity generated at the plate and wall, plus that introduced with the eddies, mix with the background vorticity and is transported throughout the entire flow. All quantities are scaled by the plate length, the unidsturbed free-stream velocity, and the fluid kinematic viscosity. The Reynolds number is 1000, the Blasius boundary layer thickness is 2.0, and the plate is positioned a distance of 1.0 above the wall. The computational domain is four units high and sixteen units long

Quasi-local mass in the covariant Newtonian space-time

In general relativity, quasi-local energy-momentum expressions have been constructed from various formulae. However, Newtonian theory of gravity gives a well known and an unique quasi-local mass expression (surface integration). Since geometrical formulation of Newtonian gravity has been established in the covariant Newtonian space-time, it provides a covariant approximation from relativistic to Newtonian theories. By using this approximation, we calculate Komar integral, Brown-York quasi-local energy and Dougan-Mason quasi-local mass in the covariant Newtonian space-time. It turns out that Komar integral naturally gives the Newtonian quasi-local mass expression, however, further conditions (spherical symmetry) need to be made for Brown-York and Dougan-Mason expressions.Comment: Submit to Class. Quantum Gra

Approaching a strong fourth family

A heavy fourth family is an example of new physics which is well defined and familiar in some respects, but which nevertheless has radical implications. In particular it eliminates a light Higgs description of electroweak symmetry breaking. We discuss an early signal for heavy quarks at the LHC in the form of an excess of "$W$-jets", and as well show how $W$-jets may be useful in the reconstruction of the heavy quark masses. We argue that fourth family quarks can be distinguished from vector-like quarks of a similar mass at roughly the same time that a same sign lepton signal becomes visible. Given the large mass of the fourth neutrino we describe how a picture for neutrino mass emerges in the absence of right-handed neutrinos, and how it suggests the existence of a remnant flavor gauge symmetry. Based on talk given at "Second Workshop on Beyond 3 Generation Standard Model -- New Fermions at the Crossroads of Tevatron and LHC", January 2010, Taipei Taiwan.Comment: 14 pages, 10 figures, references added and slight change