Frequency Analysis of Reflex Velocities of Stars with Planets

Since it has become possible to discovery planets orbiting nearby solar-type stars through very precise Doppler-shift measurements, the role of methods used to analyze such observations has grown significantly. The widely employed model-dependent approach based on the least-squares fit of the Keplerian motion to the radial-velocity variations can be, as we show, unsatisfactory. Thus, in this paper, we propose a new method that may be easily and successfully applied to the Doppler-shift measurements. This method allows us to analyze the data without assuming any specific model and yet to extract all significant features of the observations. This very simple idea, based on the subsequent subtraction of all harmonic components from the data, can be easily implemented. We show that our method can be used to analyze real 16 Cygni B Doppler-shift observations with a surprising but correct result which is substantially different from that based on the least-squares fit of a Keplerian orbit. Namely, using frequency analysis we show that with the current accuracy of this star's observations it is not possible to determine the value of the orbital eccentricity which is claimed to be as high as 0.6.Comment: AASLaTeX + 5 figures (eps files), 22 pages, two figures delated, typos corrections; accepted for publication in Ap

Optimal design of solidification processes

An optimal design algorithm is presented for the analysis of general solidification processes, and is demonstrated for the growth of GaAs crystals in a Bridgman furnace. The system is optimal in the sense that the prespecified temperature distribution in the solidifying materials is obtained to maximize product quality. The optimization uses traditional numerical programming techniques which require the evaluation of cost and constraint functions and their sensitivities. The finite element method is incorporated to analyze the crystal solidification problem, evaluate the cost and constraint functions, and compute the sensitivities. These techniques are demonstrated in the crystal growth application by determining an optimal furnace wall temperature distribution to obtain the desired temperature profile in the crystal, and hence to maximize the crystal's quality. Several numerical optimization algorithms are studied to determine the proper convergence criteria, effective 1-D search strategies, appropriate forms of the cost and constraint functions, etc. In particular, we incorporate the conjugate gradient and quasi-Newton methods for unconstrained problems. The efficiency and effectiveness of each algorithm is presented in the example problem

Variational Trajectory Optimization Tool Set: Technical description and user's manual

The algorithms that comprise the Variational Trajectory Optimization Tool Set (VTOTS) package are briefly described. The VTOTS is a software package for solving nonlinear constrained optimal control problems from a wide range of engineering and scientific disciplines. The VTOTS package was specifically designed to minimize the amount of user programming; in fact, for problems that may be expressed in terms of analytical functions, the user needs only to define the problem in terms of symbolic variables. This version of the VTOTS does not support tabular data; thus, problems must be expressed in terms of analytical functions. The VTOTS package consists of two methods for solving nonlinear optimal control problems: a time-domain finite-element algorithm and a multiple shooting algorithm. These two algorithms, under the VTOTS package, may be run independently or jointly. The finite-element algorithm generates approximate solutions, whereas the shooting algorithm provides a more accurate solution to the optimization problem. A user's manual, some examples with results, and a brief description of the individual subroutines are included

A nonlinear quantum model of the Friedmann universe

A discussion is given of the quantisation of a physical system with finite degrees of freedom subject to a Hamiltonian constraint by treating time as a constrained classical variable interacting with an unconstrained quantum state. This leads to a quantisation scheme that yields a Schrodinger-type equation which is in general nonlinear in evolution. Nevertheless it is compatible with a probabilistic interpretation of quantum mechanics and in particular the construction of a Hilbert space with a Euclidean norm is possible. The new scheme is applied to the quantisation of a Friedmann Universe with a massive scalar field whose dynamical behaviour is investigated numerically.Comment: 11 pages of text + 4 pages for 8 figure

FFTPL: An Analytic Placement Algorithm Using Fast Fourier Transform for Density Equalization

We propose a flat nonlinear placement algorithm FFTPL using fast Fourier transform for density equalization. The placement instance is modeled as an electrostatic system with the analogy of density cost to the potential energy. A well-defined Poisson's equation is proposed for gradient and cost computation. Our placer outperforms state-of-the-art placers with better solution quality and efficiency