Geometry of Control-Affine Systems

Motivated by control-affine systems in optimal control theory, we introduce the notion of a point-affine distribution on a manifold X - i.e., an affine distribution F together with a distinguished vector field contained in F. We compute local invariants for point-affine distributions of constant type when dim(X)=n, rank(F)=n-1, and when dim(X)=3, rank(F)=1. Unlike linear distributions, which are characterized by integer-valued invariants - namely, the rank and growth vector - when dim(X)<=4, we find local invariants depending on arbitrary functions even for rank 1 point-affine distributions on manifolds of dimension 2

Online learning : towards enabling choice

Education is rapidly evolving from an opportunity that was provided mainly for an elite to one that is available to a mass markets and as such is prone to the forces generated by this environment. Where, in the established pattern, commercial interest was limited mainly to the use of skills developed during the educational process, the future model of educational provision will involve extensive commercial activity in the production, delivery and marketing of material. Already there are a number of commercial companies offering framework products enabling "off the shelf solutions" for the construction and delivery of web based courses in any subject area. The commercialisation of education is underway and it is inevitable that it will be viewed, by entrepreneurs and customers alike, as any other commercial product. It would seem reasonable that the consumer should be able to evaluate the performance of these new modes of working in a similar manner to other commercial products. This paper draws together current thinking on the problems associated with evaluating computer and communication based learning

Instrumentation design study for testing a hypersonic ramjet engine on the x-15 a-2. volume 2- preliminary design of in-flight thrust/drag measuring device

Inflight thrust and drag measuring device for hypersonic ramjet engine on X-15A-2 aircraf

Matching of analytical and numerical solutions for neutron stars of arbitrary rotation

We demonstrate the results of an attempt to match the two-soliton analytical solution with the numerically produced solutions of the Einstein field equations, that describe the spacetime exterior of rotating neutron stars, for arbitrary rotation. The matching procedure is performed by equating the first four multipole moments of the analytical solution to the multipole moments of the numerical one. We then argue that in order to check the effectiveness of the matching of the analytical with the numerical solution we should compare the metric components, the radius of the innermost stable circular orbit ($R_{ISCO}$), the rotation frequency $\Omega\equiv\frac{d\phi}{dt}$ and the epicyclic frequencies $\Omega_{\rho},\;\Omega_z$. Finally we present some results of the comparison.Comment: Contribution at the 13th Conference on Recent Developments in Gravity (NEB XIII), corrected typo in $M_4$ of eq. 5 of the published versio

Superfluid turbulence from quantum Kelvin wave to classical Kolmogorov cascades

A novel unitary quantum lattice gas algorithm is used to simulate quantum turbulence of a BEC described by the Gross-Pitaevskii equation on grids up to 5760^3. For the first time, an accurate power law scaling for the quantum Kelvin wave cascade is determined: k^{-3}. The incompressible kinetic energy spectrum exhibits very distinct power law spectra in 3 ranges of k-space: a classical Kolmogorov k^{-5/3} spectrum at scales much greater than the individual quantum vortex cores, and a quantum Kelvin wave cascade spectrum k^{-3} on scales of order the vortex cores. In the semiclassical regime between these two spectra there is a pronounced steeper spectral decay, with non-universal exponent. The Kelvin k^{-3} spectrum is very robust, even on small grids, while the Kolmogorov k^{-5/3} spectrum becomes more and more apparent as the grids increase from 2048^3 grids to 5760^3.Comment: 4 pages, 2 figure

Activation mechanisms in sodium-doped Silicon MOSFETs

We have studied the temperature dependence of the conductivity of a silicon MOSFET containing sodium ions in the oxide above 20 K. We find the impurity band resulting from the presence of charges at the silicon-oxide interface is split into a lower and an upper band. We have observed activation of electrons from the upper band to the conduction band edge as well as from the lower to the upper band. A possible explanation implying the presence of Hubbard bands is given.Comment: published in J. Phys. : Condens. Matte

Geometry of Optimal Control for Control-Affine Systems

Motivated by the ubiquity of control-affine systems in optimal control theory, we investigate the geometry of point-affine control systems with metric structures in dimensions two and three. We compute local isometric invariants for point-affine distributions of constant type with metric structures for systems with 2 states and 1 control and systems with 3 states and 1 control, and use Pontryagin's maximum principle to find geodesic trajectories for homogeneous examples. Even in these low dimensions, the behavior of these systems is surprisingly rich and varied

Experimental investigations on channelized coplanar waveguide

A new variant of coplanar waveguide (CPW) which was termed channelized coplanar waveguide (CCPW) is presented. Measured propagation characteristics for CCPW such as epsilon(eff) and unloaded Q as a function of geometrical parameters and frequency are presented. The measured and modeled epsilon(eff) are also compared. Equivalent circuit model element values are presented for a CCPW open circuit and a CCPW right angle bend. A CCPW matched T-junction, matched 1:3 junction, and a novel coax-to-CCPW in-phase, N-way, radial power divider are also demonstrated