Efficient numerical algorithms for surface formulations of mathematical models for biomolecule analysis and design

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.Includes bibliographical references (p. 179-183).This thesis presents a set of numerical techniques that extend and improve computational modeling approaches for biomolecule analysis and design. The presented research focuses on surface formulations of modeling problems related to the estimation of the energetic cost to transfer a biomolecule from the gas phase to aqueous solution. The thesis discusses four contributions to modeling biomolecular interactions. First, the thesis presents an approach to allow accurate discretization of the most prevalent mathematical definitions of the biomolecule-solvent interface; also presented are a number of accurate techniques for numerically integrating possibly singular functions over the discretized surfaces. Such techniques are essential for solving surface formulations numerically. The second part of the thesis presents a fast multiscale numerical algorithm, FFTSVD, that efficiently solves large boundary-element method problems in biomolecule electrostatics. The algorithm synthesizes elements of other popular fast algorithms to achieve excellent efficiency and flexibility. The third thesis component describes an integral-equation formulation and boundary-element method implementation for biomolecule electrostatic analysis.(cont.) The formulation and implementation allow the solution of complicated molecular topologies and physical models. Furthermore, by applying the methods developed in the first half of the thesis, the implementation can deliver superior accuracy for competitive performance. Finally, the thesis describes a highly efficient numerical method for calculating a biomolecular charge distribution that minimizes the free energy' change of binding to another molecule. The approach, which represents a novel PDE-constrained methodology, builds on well-developed physical theory. Computational results illustrate not only the method's improved performance but also its application to realistic biomolecule problems.by Jaydeep Porter Bardhan.Ph.D

Calibration of a microvision system for microelectromechanical system device characterization

Thesis (M.Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2001.Includes bibliographical references (leaves 56-57).With the growing use of microelectromechanical systems (MEMS), it becomes increasingly important that reliable, accurate methods for characterizing and calibrating MEMS be developed. One microsystem in need of specific characterization measurements is the polychromator, an electrically programmable, surface micromachined diffraction grating. A microvision system has been developed to measure the electromechanical behavior of the polysilicon beams that comprise this device. Proper rigor demands that the system for making characterizations should itself be characterized; its accuracy and precision should be determined, so that users may understand the possible error margins of its measurements. This thesis describes HUMS (Heavily Upsampling Microvision System), the software application developed to automate the characterization of the polychromator, and the method developed to quantify the accuracy of the HUMS application.by Jaydeep Porter Bardhan.M.Eng