A Compilation Strategy for Numerical Programs Based on Partial Evaluation

This work demonstrates how partial evaluation can be put to practical use in the domain of high-performance numerical computation. I have developed a technique for performing partial evaluation by using placeholders to propagate intermediate results. For an important class of numerical programs, a compiler based on this technique improves performance by an order of magnitude over conventional compilation techniques. I show that by eliminating inherently sequential data-structure references, partial evaluation exposes the low-level parallelism inherent in a computation. I have implemented several parallel scheduling and analysis programs that study the tradeoffs involved in the design of an architecture that can effectively utilize this parallelism. I present these results using the 9- body gravitational attraction problem as an example.

KAM: Automatic Planning and Interpretation of Numerical Experiments Using Geometrical Methods

KAM is a computer program that can automatically plan, monitor, and interpret numerical experiments with Hamiltonian systems with two degrees of freedom. The program has recently helped solve an open problem in hydrodynamics. Unlike other approaches to qualitative reasoning about physical system dynamics, KAM embodies a significant amount of knowledge about nonlinear dynamics. KAM's ability to control numerical experiments arises from the fact that it not only produces pictures for us to see, but also looks at (sic---in its mind's eye) the pictures it draws to guide its own actions. KAM is organized in three semantic levels: orbit recognition, phase space searching, and parameter space searching. Within each level spatial properties and relationships that are not explicitly represented in the initial representation are extracted by applying three operations ---(1) aggregation, (2) partition, and (3) classification--- iteratively.

Explorations of the Practical Issues of Learning Prediction-Control Tasks Using Temporal Difference Learning Methods

There has been recent interest in using temporal difference learning methods to attack problems of prediction and control. While these algorithms have been brought to bear on many problems, they remain poorly understood. It is the purpose of this thesis to further explore these algorithms, presenting a framework for viewing them and raising a number of practical issues and exploring those issues in the context of several case studies. This includes applying the TD(lambda) algorithm to: 1) learning to play tic-tac-toe from the outcome of self-play and of play against a perfectly-playing opponent and 2) learning simple one-dimensional segmentation tasks.

The Kineticist's Workbench: Combining Symbolic and Numerical Methods in the Simulation of Chemical Reaction Mechanisms

The Kineticist's Workbench is a program that simulates chemical reaction mechanisms by predicting, generating, and interpreting numerical data. Prior to simulation, it analyzes a given mechanism to predict that mechanism's behavior; it then simulates the mechanism numerically; and afterward, it interprets and summarizes the data it has generated. In performing these tasks, the Workbench uses a variety of techniques: graph- theoretic algorithms (for analyzing mechanisms), traditional numerical simulation methods, and algorithms that examine simulation results and reinterpret them in qualitative terms. The Workbench thus serves as a prototype for a new class of scientific computational tools---tools that provide symbiotic collaborations between qualitative and quantitative methods.

Numerical Simulation of Electroosmotic Flow with Step Change in Zeta Potential

Electroosmotic flow is a convenient mechanism for transporting polar fluid in a microfluidic device. The flow is generated through the application of an external electric field that acts on the free charges that exists in a thin Debye layer at the channel walls. The charge on the wall is due to the chemistry of the solid-fluid interface, and it can vary along the channel, e.g. due to modification of the wall. This investigation focuses on the simulation of the electroosmotic flow (EOF) profile in a cylindrical microchannel with step change in zeta potential. The modified Navier-Stoke equation governing the velocity field and a non-linear two-dimensional Poisson-Boltzmann equation governing the electrical double-layer (EDL) field distribution are solved numerically using finite control-volume method. Continuities of flow rate and electric current are enforced resulting in a non-uniform electrical field and pressure gradient distribution along the channel. The resulting parabolic velocity distribution at the junction of the step change in zeta potential, which is more typical of a pressure-driven velocity flow profile, is obtained.

A Two-level Prediction Model for Deep Reactive Ion Etch (DRIE)

We contribute a quantitative and systematic model to capture etch non-uniformity in deep reactive ion etch of microelectromechanical systems (MEMS) devices. Deep reactive ion etch is commonly used in MEMS fabrication where high-aspect ratio features are to be produced in silicon. It is typical for many supposedly identical devices, perhaps of diameter 10 mm, to be etched simultaneously into one silicon wafer of diameter 150 mm. Etch non-uniformity depends on uneven distributions of ion and neutral species at the wafer level, and on local consumption of those species at the device, or die, level. An ion–neutral synergism model is constructed from data obtained from etching several layouts of differing pattern opening densities. Such a model is used to predict wafer-level variation with an r.m.s. error below 3%. This model is combined with a die-level model, which we have reported previously, on a MEMS layout. The two-level model is shown to enable prediction of both within-die and wafer-scale etch rate variation for arbitrary wafer loadings.

Numerical comparison between Maxwell stress method and equivalent multipole approach for calculation of the dielectrophoretic force in octupolar cell traps

This work presents detailed numerical calculations of the dielectrophoretic force in octupolar traps designed for single-cell trapping. A trap with eight planar electrodes is studied for spherical and ellipsoidal particles using an indirect implementation of the boundary element method (BEM). Multipolar approximations of orders one to three are compared with the full Maxwell stress tensor (MST) calculation of the electrical force on spherical particles. Ellipsoidal particles are also studied, but in their case only the dipolar approximation is available for comparison with the MST solution. The results show that the full MST calculation is only required in the study of non-spherical particles.