Lie theory and control systems defined on spheres

It is shown that in constructing a theory for the most elementary class of control problems defined on spheres, some results from the Lie theory play a natural role. To understand controllability, optimal control, and certain properties of stochastic equations, Lie theoretic ideas are needed. The framework considered here is the most natural departure from the usual linear system/vector space problems which have dominated control systems literature. For this reason results are compared with those previously available for the finite dimensional vector space case

Small axial turbine stator technology program

An experimental investigation was conducted to determine the effects of surface finish, fillet radius, inlet boundary layer thickness, and free-stream inlet turbulence level on the aerodynamic performance of a small axial flow turbine stator. The principal objective of this program was to help understand why large turbine efficiency is not maintained when a large turbine is scaled to a smaller size. The stator used in this program as a one-sixth scale of a 762 mm (30 in.) diameter stator design with 50 vanes having a vane height of 17 mm (0.666 in.) and an aspect ratio of 1.77. A comprehensive overall test matrix was used to provide a complete engineering understanding of the effects of each variable over the full range of all the other variables. The range of each variable investigated was as follows: surface finish 0.1 micro (4 micro in.) to 2.4 micro (95 micro in.); boundary layer thickness 2 to 25 percent of channel height at each wall; fillet radius 0 mm (0 in.) to 1.0 mm (.040 in.) and turbulence 2 to 12 percent

Assessing outgroup prejudice among secondary school pupils in northern England : introducing the Outgroup Prejudice Index

The Outgroup Prejudice Index is a six-item scale that uses social distance to assess prejudice towards ethnic and religious out groups among Asians and Whites. It was developed among a sample of 2982 teenagers attending schools in northern England who indicated their religion as either ‘Muslim’, ‘Christian’ or ‘no religion’. The scale demonstrated internal consistency reliability among both Asian (Cronbach’s alpha = .78) and White (Cronbach’s alpha = .85) pupils. The scale demonstrated construct validity in two ways: scores were correlated with a second scale based on stereotyped attitudes, and were also lower among those with friends in outgroups, suggesting the index was a valid measure of ethnic or religious outgroup prejudice

Application of system theory to power processing problems

The work in power processing is reported. Input-output models, and Lie groups in control theory are discussed along with the methods of analysis for time invariant electrical networks

Investigation of feeding devices and development of design considerations for a new feeder for micro-sheet forming

Recent review in micro-forming research and technological development suggested that the trend of the development is more focused on the manufacturing processes, machines and tooling, and efforts on the methods and systems for integrated precision material handling are insufficient. Most of the developed micro-forming machines were based on standalone concepts which do not support efficient integration to make them fully automated and integrated. At present, material feeding in micro-forming is not of sufficient precision and reliability for high throughput manufacturing applications. Precise feeding is necessary to ensure that micro-parts can be produced with sufficient accuracy, especially in multi-stage forming, while high-speed feeding is a must to meet the production-rate requirements. Therefore, design of a new high-precision and high-speed feeder for micro-forming is proposed. Several possible approaches are examined with a view to establishing feasible concepts. Based on the investigation, several concepts for thin sheet-metal feeding for micro-forming are generated, they being argued and assessed with applicable loads and forces analysis. These form a basis of designing a new feeder

Finite Controllability of Infinite-Dimensional Quantum Systems

Quantum phenomena of interest in connection with applications to computation and communication almost always involve generating specific transfers between eigenstates, and their linear superpositions. For some quantum systems, such as spin systems, the quantum evolution equation (the Schr\"{o}dinger equation) is finite-dimensional and old results on controllability of systems defined on on Lie groups and quotient spaces provide most of what is needed insofar as controllability of non-dissipative systems is concerned. However, in an infinite-dimensional setting, controlling the evolution of quantum systems often presents difficulties, both conceptual and technical. In this paper we present a systematic approach to a class of such problems for which it is possible to avoid some of the technical issues. In particular, we analyze controllability for infinite-dimensional bilinear systems under assumptions that make controllability possible using trajectories lying in a nested family of pre-defined subspaces. This result, which we call the Finite Controllability Theorem, provides a set of sufficient conditions for controllability in an infinite-dimensional setting. We consider specific physical systems that are of interest for quantum computing, and provide insights into the types of quantum operations (gates) that may be developed.Comment: This is a much improved version of the paper first submitted to the arxiv in 2006 that has been under review since 2005. A shortened version of this paper has been conditionally accepted for publication in IEEE Transactions in Automatic Control (2009

Internal consistency reliability and construct validity of the Attitude toward Muslim Proximity Index (AMPI): a measure of social distance

The Attitude toward Muslim Proximity Index (AMPI) is a six-item scale that uses tolerance to different degrees of social distance to assess prejudice towards Muslims. It was tested on 1777 teenage school children from northern England who indicated their religion as either 'Christian' or 'no religion', and demonstrated good internal reliability (Cronbach's alpha = .81). The index was higher among pupils who supported the views of the British National Party and among those who believed that British Muslims should adopt Western culture; but lower among those who knew Muslims or had Muslim friends. The AMPI is a useful measure of Islamophobic attitudes that does not rely on responses to specific events or on detailed knowledge of the Muslim religion

Double bracket dissipation in kinetic theory for particles with anisotropic interactions

We derive equations of motion for the dynamics of anisotropic particles directly from the dissipative Vlasov kinetic equations, with the dissipation given by the double bracket approach (Double Bracket Vlasov, or DBV). The moments of the DBV equation lead to a nonlocal form of Darcy's law for the mass density. Next, kinetic equations for particles with anisotropic interaction are considered and also cast into the DBV form. The moment dynamics for these double bracket kinetic equations is expressed as Lie-Darcy continuum equations for densities of mass and orientation. We also show how to obtain a Smoluchowski model from a cold plasma-like moment closure of DBV. Thus, the double bracket kinetic framework serves as a unifying method for deriving different types of dynamics, from density--orientation to Smoluchowski equations. Extensions for more general physical systems are also discussed.Comment: 19 pages; no figures. Submitted to Proc. Roy. Soc.