Thesis (M.S.)--University of Wisconsin--Madison, 1962. / Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaf 66).

The project has been to design, build and calibrate a current integrator for use in the measurement of the target ion current of a Van de Graaff generator and a 50 K.V. ion accelerator. Various methods of measuring small fluctuating currents used by previous workers are discussed with reference to the particular needs of this problem. Errors due to the target cooling system, target contamination, neutralization of the beam at low energies and secondary electron emission are also discussed. The integrator was designed using a Miller integrating circuit consisting of a pair of condensers connected from the grid of the input tube to the plate of the output tube of an amplifier having an unfed-back gain of approximately 4000, The conditions for accurate operation of the Miller circuit have been derived. To comply with them the input tube of the amplifier is connected as an electrometer tube and the condensers used are low leakage polystyrene condensers. Any incoming charge is stored on the condensers and the integral of this charge is indicated by the decreasing anode voltage of the last tube of the amplifier. At the end of a rundown a Schmitt trigger circuit operates a relay which recharges one of the pair of condensers to a fixed potential and thereby adds a known quantity of charge to it, and then reconnects it, also actuating a mechanical counter. The virtue of this scheme is that there is always one condenser in the Miller circuit and thus no dead time errors arise. Currents from 4 x 10ˉ⁸ amperes to 2 x 10ˉ⁴ amperes are measurable on four overlapping ranges. The integrator sensitivity (in coulombs required to produce a count) is found to vary with the counting rate. Mean sensitivities accurate to ± 3% on each of the ranges are given. For higher accuracy (± 1%) it is necessary to read the sensitivity appropriate to the counting rate from a calibration graph. The variation in sensitivity with counting rate appears to arise from the time required for the relay to switch the recharging condenser. The sensitivity varies less than ± ½% during the day, and about ± 2% in a week. If all voltages are adjusted as recommended, the sensitivity is found to be constant to 1% or better two months after the original calibration. The lower limit of measurable currents is set by drift currents of the order of 3 x l0ˉ¹⁰ amps. The upper limit of measurable currents is set by the bottoming of the amplifier during the recharging time. Two simple air ionization chamber gamma radiation health monitors have also been built (using a shielded electrometer tube in a d.c, amplifier) and calibrated. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

No description available.

Thesis (M.S. in E.E.)--School of Electrical and Computer Engineering, Georgia Institute of Technology, 2004. Directed by David V. Anderson. / Includes bibliographical references (leaves 55-56).

Alan B. Macnee. / "August 17, 1949." / Bibliography: p. 20-21. / Army Signal Corps Contract No. W36-039-sc-32037 Project No. 102B Dept. of the Army Project No. 3-99-10-022

Graduation date: 1993

A Lagrange--d'Alembert integrator is a geometric numerical method for finding numerical solutions to the Lagrange--d'Alembert equations for mechanical systems with nonholonomic constraints that are linear in the velocities. The integrator is developed from geometry and principles that are analogues of the continuous theory.<p>Using discrete analogues of the symplectic form and momentum map, the resulting methods are symplectic and momentum preserving whenever the continuous system is symplectic and momentum preserving. In addition, it is possible to, in principle, generate Lagrange--d'Alembert integrators of any method order.

A Lagrange--d'Alembert integrator is a geometric numerical method for finding numerical solutions to the Lagrange--d'Alembert equations for mechanical systems with nonholonomic constraints that are linear in the velocities. The integrator is developed from geometry and principles that are analogues of the continuous theory.<p>Using discrete analogues of the symplectic form and momentum map, the resulting methods are symplectic and momentum preserving whenever the continuous system is symplectic and momentum preserving. In addition, it is possible to, in principle, generate Lagrange--d'Alembert integrators of any method order.

Thesis (Ph. D. in engineering science)--Washington State University. / Includes bibliographical references.

Simulation and optimization of complex physical systems are an integral part of modern science and engineering. The systems of interest in many fields have a multiphysics nature, with complex interactions between physical, chemical and in some cases even biological processes. This dissertation seeks to advance forward and adjoint numerical time integration methodologies for the simulation and optimization of semi-discretized multiphysics partial differential equations (PDEs), and to estimate and control numerical errors via a goal-oriented a posteriori error framework. We extend exponential propagation iterative methods of Runge-Kutta type (EPIRK) by [Tokman, JCP 2011], to build EPIRK-W and EPIRK-K time integration methods that admit approximate Jacobians in the matrix-exponential like operations. EPIRK-W methods extend the W-method theory by [Steihaug and Wofbrandt, Math. Comp. 1979] to preserve their order of accuracy under arbitrary Jacobian approximations. EPIRK-K methods extend the theory of K-methods by [Tranquilli and Sandu, JCP 2014] to EPIRK and use a Krylov-subspace based approximation of Jacobians to gain computational efficiency. New families of partitioned exponential methods for multiphysics problems are developed using the classical order condition theory via particular variants of T-trees and corresponding B-series. The new partitioned methods are found to perform better than traditional unpartitioned exponential methods for some problems in mild-medium stiffness regimes. Subsequently, partitioned stiff exponential Runge-Kutta (PEXPRK) methods -- that extend stiffly accurate exponential Runge-Kutta methods from [Hochbruck and Ostermann, SINUM 2005] to a multiphysics context -- are constructed and analyzed. PEXPRK methods show full convergence under various splittings of a diffusion-reaction system. We address the problem of estimation of numerical errors in a multiphysics discretization by developing a goal-oriented a posteriori error framework. Discrete adjoints of GARK methods are derived from their forward formulation [Sandu and Guenther, SINUM 2015]. Based on these, we build a posteriori estimators for both spatial and temporal discretization errors. We validate the estimators on a number of reaction-diffusion systems and use it to simultaneously refine spatial and temporal grids. / Doctor of Philosophy / The study of modern science and engineering begins with descriptions of a system of mathematical equations (a model). Different models require different techniques to both accurately and effectively solve them on a computer. In this dissertation, we focus on developing novel mathematical solvers for models expressed as a system of equations, where only the initial state and the rate of change of state as a function are known. The solvers we develop can be used to both forecast the behavior of the system and to optimize its characteristics to achieve specific goals. We also build methodologies to estimate and control errors introduced by mathematical solvers in obtaining a solution for models involving multiple interacting physical, chemical, or biological phenomena. Our solvers build on state of the art in the research community by introducing new approximations that exploit the underlying mathematical structure of a model. Where it is necessary, we provide concrete mathematical proofs to validate theoretically the correctness of the approximations we introduce and correlate with follow-up experiments. We also present detailed descriptions of the procedure for implementing each mathematical solver that we develop throughout the dissertation while emphasizing on means to obtain maximal performance from the solver. We demonstrate significant performance improvements on a range of models that serve as running examples, describing chemical reactions among distinct species as they diffuse over a surface medium. Also provided are results and procedures that a curious researcher can use to advance the ideas presented in the dissertation to other types of solvers that we have not considered. Research on mathematical solvers for different mathematical models is rich and rewarding with numerous open-ended questions and is a critical component in the progress of modern science and engineering.