Multistep Methods for Integrating the Solar System

High order multistep methods, run at constant stepsize, are very effective for integrating the Newtonian solar system for extended periods of time. I have studied the stability and error growth of these methods when applied to harmonic oscillators and two-body systems like the Sun-Jupiter pair. I have also tried to design better multistep integrators than the traditional Stormer and Cowell methods, and I have found a few interesting ones.

Sparse Correlation Kernel Analysis and Reconstruction

This paper presents a new paradigm for signal reconstruction and superresolution, Correlation Kernel Analysis (CKA), that is based on the selection of a sparse set of bases from a large dictionary of class- specific basis functions. The basis functions that we use are the correlation functions of the class of signals we are analyzing. To choose the appropriate features from this large dictionary, we use Support Vector Machine (SVM) regression and compare this to traditional Principal Component Analysis (PCA) for the tasks of signal reconstruction, superresolution, and compression. The testbed we use in this paper is a set of images of pedestrians. This paper also presents results of experiments in which we use a dictionary of multiscale basis functions and then use Basis Pursuit De-Noising to obtain a sparse, multiscale approximation of a signal. The results are analyzed and we conclude that 1) when used with a sparse representation technique, the correlation function is an effective kernel for image reconstruction and superresolution, 2) for image compression, PCA and SVM have different tradeoffs, depending on the particular metric that is used to evaluate the results, 3) in sparse representation techniques, L_1 is not a good proxy for the true measure of sparsity, L_0, and 4) the L_epsilon norm may be a better error metric for image reconstruction and compression than the L_2 norm, though the exact psychophysical metric should take into account high order structure in images.

Implementation Workshop: High Performance Work Organizations

Since the rise of the industrial revolution, there are few challenges that compare in scale and scope with the challenge of implementing lean principles in order to achieve high performance work systems. This report summarize key insights and learning by representatives from a cross section of organizations who are on this journey. Specifically, we report on findings from the first Lean Aircraft Initiative (LAI) Implementation Workshop, which was held on February 5-6, 1997.

Plasma polymerization of C[subscript 4]F[subscript 8] thin film on high aspect ratio silicon molds

High aspect ratio polymeric micro-patterns are ubiquitous in many fields ranging from sensors, actuators, optics, fluidics and medical. Second generation PDMS molds are replicated against first generation silicon molds created by deep reactive ion etching. In order to ensure successful demolding, the silicon molds are coated with a thin layer of C[subscript 4]F[subscript 8] plasma polymer to reduce the adhesion force. Peel force and demolding status are used to determine if delamination is successful. Response surface method is employed to provide insights on how changes in coil power, passivating time and gas flow conditions affect plasma polymerization of C[subscript 4]F[subscript 8].

Implementation Workshop: High Performance Work Organizations

Since the rise of the industrial revolution, there are few challenges that compare in scale and scope with the challenge of implementing lean principles in order to achieve high performance work systems. This report summarize key insights and learning by representatives from a cross section of organizations who are on this journey. Specifically, we report on findings from the first Lean Aircraft Initiative (LAI) Implementation Workshop, which was held on February 5-6, 1997. The report is not a “cookbook” or a “how to” manual. Rather, it is a summary of the first phase in a learning process. It is designed to codify lessons learning, facilitate diffusion among people not at the session, and set the stage for further learning about implementation.

Model Order Reduction for Determining Bubble Parameters to Attain a Desired Fluid Surface Shape

In this paper, a new methodology for predicting fluid free surface shape using Model Order Reduction (MOR) is presented. Proper Orthogonal Decomposition combined with a linear interpolation procedure for its coefficient is applied to a problem involving bubble dynamics near to a free surface. A model is developed to accurately and efficiently capture the variation of the free surface shape with different bubble parameters. In addition, a systematic approach is developed within the MOR framework to find the best initial locations and pressures for a set of bubbles beneath the quiescent free surface such that the resultant free surface attained is close to a desired shape. Predictions of the free surface in two-dimensions and three-dimensions are presented.