15,370 research outputs found
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
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 . In particular, a
universal two-qubit logic gate is attainable for this model.Comment: 13 page
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
On cross-beam monitoring of atmospheric winds and turbulence with two orbiting telescopes
Crossed beam monitoring of atmospheric winds and turbulence with two orbiting astronomical telescopes mounted on single spacecraf
Space Station long term lubrication analysis. Phase 1 preliminary tribological survey
Increases in the size, complexity, and life requirements of satellites and space vehicles have put increasing demands on the lubrication requirements for trouble-free service. Since the development costs of large systems are high, long lives with minimum maintenance are dictated. The Space Station represents the latest level of size and complexity in satellite development; it will be nearly 100 meters in major dimensions and will have a life requirement of thirty years. It will have numerous mechanisms critical to its success, some of which will be exposed to the space environment. Designing long-life lubrication systems and choosing appropriate lubricants for these systems will be necessary for their meeting the requirements and for avoiding failures with associated dependent mechanisms. The purpose of this program was to identify the various critical mechanisms and review their designs during the overall design and development stage so that problem areas could be avoided or minimized prior to the fabrication of hardware. The specific objectives were fourfold: (1) to perform a tribology survey of the Space Station for the purpose of documenting each wear point as to materials involved, environmental conditions, and operating characteristics; (2) to review each wear point (point of relative motion) as to the lubrication used and substrate materials selected in the context of its operating characteristics and the environmental conditions imposed; (3) to make recommendations for improvement in areas where the lubricant chosen and/or where the substrate (materials of the wear couple) are not considered optimum for the application; and (4) to make or recommend simulated or full scale tests in tribological areas where the state-of-the-art is being advanced, in areas where new designs are obviously being employed and a critical review would indicate that problems are a strong possibility, and/or where excessive wear, a malfunction, or excessive leakage would create fluid systems problems or contamination of exposed optical equipment
Spatial Endogenous Fire Risk and Efficient Fuel Management and Timber Harvest
This paper integrates a spatial fire behavior model and a stochastic dynamic optimization model to determine the optimal spatial pattern of fuel management and timber harvest. Each years fire season causes the loss of forest values and lives in the western US. This paper uses a multi-plot analysis and incorporates uncertainty about fire ignition locations and weather conditions to inform policy by examining the role of spatial endogenous risk - where management actions on one stand affect fire risk in that and adjacent stands. The results support two current strategies, but question two other strategies, for managing forests with fire risk.Resource /Energy Economics and Policy,
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