Study of passive optical techniques for detecting clear air turbulence

Passive optical techniques evaluated for detecting clear air turbulence

Symmetry Reduction of Optimal Control Systems and Principal Connections

This paper explores the role of symmetries and reduction in nonlinear control and optimal control systems. The focus of the paper is to give a geometric framework of symmetry reduction of optimal control systems as well as to show how to obtain explicit expressions of the reduced system by exploiting the geometry. In particular, we show how to obtain a principal connection to be used in the reduction for various choices of symmetry groups, as opposed to assuming such a principal connection is given or choosing a particular symmetry group to simplify the setting. Our result synthesizes some previous works on symmetry reduction of nonlinear control and optimal control systems. Affine and kinematic optimal control systems are of particular interest: We explicitly work out the details for such systems and also show a few examples of symmetry reduction of kinematic optimal control problems.Comment: 23 pages, 2 figure

Power dissipation in nanoscale conductors: classical, semi-classical and quantum dynamics

Modelling Joule heating is a difficult problem because of the need to introduce correct correlations between the motions of the ions and the electrons. In this paper we analyse three different models of current induced heating (a purely classical model, a fully quantum model and a hybrid model in which the electrons are treated quantum mechanically and the atoms are treated classically). We find that all three models allow for both heating and cooling processes in the presence of a current, and furthermore the purely classical and purely quantum models show remarkable agreement in the limit of high biases. However, the hybrid model in the Ehrenfest approximation tends to suppress heating. Analysis of the equations of motion reveals that this is a consequence of two things: the electrons are being treated as a continuous fluid and the atoms cannot undergo quantum fluctuations. A means for correcting this is suggested

Apparent suppression of turbulent magnetic dynamo action by a dc magnetic field

Numerical studies of the effect of a dc magnetic field on dynamo action (development of magnetic fields with large spatial scales), due to helically-driven magnetohydrodynamic turbulence, are reported. The apparent effect of the dc magnetic field is to suppress the dynamo action, above a relatively low threshold. However, the possibility that the suppression results from an improper combination of rectangular triply spatially-periodic boundary conditions and a uniform dc magnetic field is addressed: heretofore a common and convenient computational convention in turbulence investigations. Physical reasons for the observed suppression are suggested. Other geometries and boundary conditions are offered for which the dynamo action is expected not to be suppressed by the presence of a dc magnetic field component.Comment: To appear in Physics of Plasma

Chow's theorem and universal holonomic quantum computation

A theorem from control theory relating the Lie algebra generated by vector fields on a manifold to the controllability of the dynamical system is shown to apply to Holonomic Quantum Computation. Conditions for deriving the holonomy algebra are presented by taking covariant derivatives of the curvature associated to a non-Abelian gauge connection. When applied to the Optical Holonomic Computer, these conditions determine that the holonomy group of the two-qubit interaction model contains $SU(2) \times SU(2)$. In particular, a universal two-qubit logic gate is attainable for this model.Comment: 13 page

The Economics of Spruce Budworm Outbreaks in the Lake States: An Overview

Economic effects of spruce budworm outbreaks in the Lake States were examined. The recent outbreak caused spruce and fir mortality on 420 thousand ha (I.OS million acres) of commercial forest land in the Lake States. Two models of Lake States spruce-fir markets were developed. A Static Economic Model established the nature of the Lake States spruce-fir market and a Comparative Static Model examined changes brought about by spruce budworm outbreaks. Outbreaks result in short-run supply shifts which probably decrease total revenue to stumpage owners but do not affect demand. The magnitude of long-run impacts were dependent on developing Lake States markets and forest management techniques. Further research is necessary on the value of short-run losses to stumpage owners so that the costs of forest management can be compared with outbreak losses. Long-run shifts in demand can be facilitated by attracting new industry to the area, developing new markets for the spruce-fir resource, and demonstrating that the spruce-fir resource can provide a continuous fiber source in the future. These shifts would provide the price incentives that land managers require to undertake intensive forest management. Research on the development of new markets for the spruce-fir resource is needed. As markets develop, the long-run impacts become less severe. Technology transfer programs already exist to aid land managers in developing management strategies to increase yields of spruce-fir and minimize outbreak impact

Wildfire Risk Management on a Landscape with Public and Private Ownership: Who Pays?

Resource /Energy Economics and Policy,

A Self-Consistent Marginally Stable State for Parallel Ion Cyclotron Waves

We derive an equation whose solutions describe self-consistent states of marginal stability for a proton-electron plasma interacting with parallel-propagating ion cyclotron waves. Ion cyclotron waves propagating through this marginally stable plasma will neither grow nor damp. The dispersion relation of these waves, {\omega} (k), smoothly rises from the usual MHD behavior at small |k| to reach {\omega} = {\Omega}p as k \rightarrow \pm\infty. The proton distribution function has constant phase-space density along the characteristic resonant surfaces defined by this dispersion relation. Our equation contains a free function describing the variation of the proton phase-space density across these surfaces. Taking this free function to be a simple "box function", we obtain specific solutions of the marginally stable state for a range of proton parallel betas. The phase speeds of these waves are larger than those given by the cold plasma dispersion relation, and the characteristic surfaces are more sharply peaked in the v\bot direction. The threshold anisotropy for generation of ion cyclotron waves is also larger than that given by estimates which assume bi-Maxwellian proton distributions.Comment: in press in Physics of Plasma

Velocity field distributions due to ideal line vortices

We evaluate numerically the velocity field distributions produced by a bounded, two-dimensional fluid model consisting of a collection of parallel ideal line vortices. We sample at many spatial points inside a rigid circular boundary. We focus on ``nearest neighbor'' contributions that result from vortices that fall (randomly) very close to the spatial points where the velocity is being sampled. We confirm that these events lead to a non-Gaussian high-velocity ``tail'' on an otherwise Gaussian distribution function for the Eulerian velocity field. We also investigate the behavior of distributions that do not have equilibrium mean-field probability distributions that are uniform inside the circle, but instead correspond to both higher and lower mean-field energies than those associated with the uniform vorticity distribution. We find substantial differences between these and the uniform case.Comment: 21 pages, 9 figures. To be published in Physical Review E (http://pre.aps.org/) in May 200

A New Timescale for Period Change in the Pulsating DA White Dwarf WD 0111+0018

We report the most rapid rate of period change measured to date for a pulsating DA (hydrogen atmosphere) white dwarf (WD), observed in the 292.9 s mode of WD 0111+0018. The observed period change, faster than 10^{-12} s/s, exceeds by more than two orders of magnitude the expected rate from cooling alone for this class of slow and simply evolving pulsating WDs. This result indicates the presence of an additional timescale for period evolution in these pulsating objects. We also measure the rates of period change of nonlinear combination frequencies and show that they share the evolutionary characteristics of their parent modes, confirming that these combination frequencies are not independent modes but rather artifacts of some nonlinear distortion in the outer layers of the star.Comment: 10 pages, 6 figures, accepted for publication in The Astrophysical Journa