Thomas J. Higgins

Calculation of the Electrical Capacitance of a Cube

The basic theory of calculation of the capacitance of a given geometrical configuration by the use of subareas is advanced and applied to solve the long‐standing problem of the accurate evaluation of the capacitance C of a cube of side a. The best previously published determination is 0.62211a<C<0.71055a. The value obtained of C≈0.655a esu is both a lower limit and very close to the exact value.

The solution of boundary value problems by multiple Laplace transformations

By use of the multiple Laplace transform a partial differential equation and its associated boundary conditions characterizing a boundary value problem in n independent real variables can be transferred directly into an algebraic equation in n independent complex variables. This algebraic equation can be solved for the multiple transform of the solution of the boundary value problem. Multiple inversion of this transform then gives the desired solution. The general theory underlying such solution of boundary value problems in two and three independent variables is advanced in detail. Use of this theory is illustrated by solution of two specific problems.

Calculation of the Capacitance of a Circular Annulus by the Method of Subareas

1. The basic theory of approximate calculation by the use of subareas of the capacitance of a plane area and of the distribution of charge density over it is outlined. 2. The method of subareas is employed to obtain an accurate value for the capacitance of an annulus of ratio of outer to inner radius of ro/ri=1.5. 3. The fourth approximation to the capacitance of a specified circular disk, as calculated by the method of subareas, is found to be in good agreement with the known exact value. As a circular disk is an annulus of ratio of radii ro/ri=∞, it is to be concluded that the fourth approximation for the much narrower annulus of ratio 1.5 is very nearly the exact value. This conjecture is substantiated by the curve of Figure 3. 4. Comparison in Figure 6 of the charge distribution on a circular disk as determined both from the known equation and by the method of subareas indicates that calculation of charge distribution by use of subareas affords a good approximation to the actual distribution. Accordingly, the charge distribution of Figure 7 for the much narrower annulus is to be considered as a close approximation to the actual distribution. 5. The universal curve of Figure 8 yields the capacitance of an annulus of any stated ratio of external to internal radii.

Cut‐Off Frequency in Two‐Dielectric Layered Rectangular Wave Guides

Equations for the modes and eigenvalues of two‐dielectric layered rectangular wave guides with cross sections as in Fig. 1(a), (b), and (c) are derived. From these equations are plotted graphs of cut‐off frequency over a range of geometric and dielectric parameters sufficiently wide to cover most requirements of design.

Minicomputers in Industrial Control

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History of the operational calculus as used in electric circuit analysis

Called one of the most important mathematical advances of the last quarter of the 19th century, operational calculus has become a very useful and powerful tool in modern circuit theory, servo-mechanisms, and transient analysis. This summary survey gives the development and cites the present status of the subject, pointing out the fundamental differences between the more common types of operational calculi currently in use.

New Formulas for Calculating Short‐Circuit Stresses in Bus Supports for Rectangular Tubular Conductors

New and simple formulas are derived for calculating short‐circuit stress in bus supports for rectangular tubular conductors. A numerical example illustrates their use and advantages.

Formulas for the Inductance of Rectangular Tubular Conductors

Authors closure of paper 41–168 by Thomas James Higgins, presented at the AIEE Southern District meeting, New Orleans, La., December 3–5, 1941, and published in AIEE TRANSACTIONS, 1941 (December section), pages 1046–50.

Analiza Nodala a Sistemelor Electroenergetice (Nodal Analysis of Power Systems)

The content of this very interesting book (Bucharest, Romania: Editura Academiei Republica Socialiste Romania, 1968, 627 pp.) by Paul Dimo is developed in 26 chapters and one appendix. The scope is very broad: the author advances an exhaustive treatment of the nodal analysis of power systems, as considered and developed for the past two decades by the writer and others in research institutes in Romania. This book is of prime interest and value for all engineers-in-practice and engineering college teachers concerned with power-systems operation and/or instruction because of the following reasons. All important aspects are discussed in depth; the particular method of analysis detailed in the text is powerful in manner and facile in use; the content is developed in a systematic lucid fashion; and the implementation of theory in practice is well illuminated by many detailed illustrative numerical examples, which well exemplify the advantages stemming from modern computer oriented techniques. Again, many details of theory, calculation, and practice are advanced which either are not to be found in English-language books in power-systems analysis or are further advanced in the detailed treatments given herein. In consequence this volume certainly should be in all college engineering libraries and on the personal reference shelves of all individuals concerned with modern power systems analysis and operation as teachers or engineers-in-practice.

Fixed-time fuel-optimal control of linear state-constrained systems by use of linear programming techniques

Abstract : A procedure is developed for obtaining a numerical approximation to the fixed-time fuel-optimal control for a state-constrained linear system. The constraints on both the state variable and the control variable are given by systems of linear inequalities describing convex polygonal sets which are allowed to be time-varying. The initial state and the final state can be explicitly given or specified as members of certain convex polygonal sets. The numerical approximation is obtained by reformulating the control problem into a form that is solvable by linear programming techniques. (Author)