Computerized optimization of elastic booster autopilots. Volume 1: Technical manual

The philosophy and the mathematical basis of the nonlinear programming algorithm underlying the development of the COEBRA program were given. A User's Manual was given in a separate document. The purpose of this work was to convert the COEBRA program from the CDC 6400/6500 digital computer system to the UNIVAC 1108 at the George C. Marshall Space Flight Center and to provide an instruction manual on the use of the program

Convergence Rates for Newton’s Method at Singular Points

If Newton’s method is employed to find a root of a map from a Banach space into itself and the derivative is singular at that root, the convergence of the Newton iterates to the root is linear rather than quadratic. In this paper we give a detailed analysis of the linear convergence rates for several types of singular problems. For some of these problems we describe modifications of Newton’s method which will restore quadratic convergence

Newton's Method in Three Precisions

We describe a three precision variant of Newton's method for nonlinear equations. We evaluate the nonlinear residual in double precision, store the Jacobian matrix in single precision, and solve the equation for the Newton step with iterative refinement with a factorization in half precision. We analyze the method as an inexact Newton method. This analysis shows that, except for very poorly conditioned Jacobians, the number of nonlinear iterations needed is the same that one would get if one stored and factored the Jacobian in double precision. In many ill-conditioned cases one can use the low precision factorization as a preconditioner for a GMRES iteration. That approach can recover fast convergence of the nonlinear iteration. We present an example to illustrate the results.Comment: 10 page

Spatially Distributed Stochastic Systems: equation-free and equation-assisted preconditioned computation

Spatially distributed problems are often approximately modelled in terms of partial differential equations (PDEs) for appropriate coarse-grained quantities (e.g. concentrations). The derivation of accurate such PDEs starting from finer scale, atomistic models, and using suitable averaging, is often a challenging task; approximate PDEs are typically obtained through mathematical closure procedures (e.g. mean-field approximations). In this paper, we show how such approximate macroscopic PDEs can be exploited in constructing preconditioners to accelerate stochastic simulations for spatially distributed particle-based process models. We illustrate how such preconditioning can improve the convergence of equation-free coarse-grained methods based on coarse timesteppers. Our model problem is a stochastic reaction-diffusion model capable of exhibiting Turing instabilities.Comment: 8 pages, 6 figures, submitted to Journal of Chemical Physic

Self-steepening of light pulses

Self-steepening of light pulses due to propagation in medium with intensity-dependent index of refractio

Density of bulk trap states in organic semiconductor crystals: discrete levels induced by oxygen in rubrene

The density of trap states in the bandgap of semiconducting organic single crystals has been measured quantitatively and with high energy resolution by means of the experimental method of temperature-dependent space-charge-limited-current spectroscopy (TD-SCLC). This spectroscopy has been applied to study bulk rubrene single crystals, which are shown by this technique to be of high chemical and structural quality. A density of deep trap states as low as ~ 10^{15} cm^{-3} is measured in the purest crystals, and the exponentially varying shallow trap density near the band edge could be identified (1 decade in the density of states per ~25 meV). Furthermore, we have induced and spectroscopically identified an oxygen related sharp hole bulk trap state at 0.27 eV above the valence band.Comment: published in Phys. Rev. B, high quality figures: http://www.cpfs.mpg.de/~krellner

Geometry-induced pulse instability in microdesigned catalysts: the effect of boundary curvature

We explore the effect of boundary curvature on the instability of reactive pulses in the catalytic oxidation of CO on microdesigned Pt catalysts. Using ring-shaped domains of various radii, we find that the pulses disappear (decollate from the inert boundary) at a turning point bifurcation, and trace this boundary in both physical and geometrical parameter space. These computations corroborate experimental observations of pulse decollation.Comment: submitted to Phys. Rev.