John Michael McCormick

Bio: John Michael McCormick is an academic researcher. The author has contributed to research in topics: Fortran. The author has an hindex of 1, co-authored 2 publications receiving 100 citations.

An introduction to numerical methods and optimization techniques

Abstract: Although numerical methods and optimization techniques share a common philosophy, both being iterative procedures, they are rarely taught in the same course. This text links the two procedures by treating optimization techniques as a collection of numerical methods which have been linked together in a specific way. Thus, once a student becomes familiar with numerical methods, the extension to optimization techniques is very natural. The author helps the undergraduate to learn to apply a computer to many different types of problems. He covers ways in which a computer can be used for the solution of linear and nonlinear equations, interpolation, differentiation and integration. Daniels then shows how to use these methods in optimization techniques such as simplex, steepest-descent, Fletcher- Powell, least-squares and least p-th. Because the application of many of the algorithms in the text requires the use of a computer, numerous programs are included. Written in a version of timesharing FORTRAN that is similar to (continued on back flap) (continued from front flap) FORTRAN IV, these programs implement the methods described in the text and provide a means for the student to apply the algorithms. The problems at the end of each chapter help to extend the material presented in the text and also to check the reader's knowledge of subtle points. These problems also illustrate the application of the programs or equations, and present the computer as an ally for the reader's future endeavors. • Richard

Two-Dimensional Failure-Free Warranty Policies: Two-Dimensional Point Process Models

Abstract: A two-dimensional warranty policy is characterized by a region in a two-dimensional plane with the horizontal axis representing time and the vertical axis the usage. In this paper, we study two-dimensional failure-free warranty policies for nonrepairable items that require the manufacturer to replace all items which fail under warranty by new ones at no cost to the buyer. We derive expressions for the expected warranty cost per item sold and for the expected life cycle cost for four different warranty regions. We illustrate these by numerical examples and discuss some resulting implications for the consumer and the manufacturer.

Stable three-dimensional action potential circulation in the FitzHugh-Nagumo model

Abstract: Excitable media generally support vortex rings of self-excitation. Depending on the exact nature of the medium, such a ring may expand or contract, possibly to a stable radius. We describe one such case encountered during numerical experiments on a simple model of electrophysiological excitability in nerve and cardiac muscle membrane. The ring's rate of shrinkage depends parabolically on curvature and on proximity to other rings. The vortex period also depends on curvature, so rings of different sizes compete for territory. We associate the stability of the ring with repulsive forces which we show are present between two-dimensional rotors. The observed minimal distance for repulsion agrees with the stable radius of the vortex ring.

Interaction of fatty acids with lipid bilayers

Abstract: We present a method by which it is possible to describe the binding of fatty acids to phospholipid bilayers. Binding constants for oleic acid and a number of fatty acids used as spectroscopic probes are deduced from electrophoresis measurements. There is a large shift in p K value for the fatty acids on binding to the phospholipid bilayers, consistent with stronger binding of the uncharged form of the fatty acid. For dansylundecanoic acid, fluorescence titrations are consistent with the binding constants derived from the electrophoresis experiments. For 12-(9-anthroyloxy)stearic acid, fluorescence and electrophoresis data are inconsistent, and we attribute this to quenching of fluorescence at high molar ratios of 12-anthroylstearic acid to phospholipid in the bilayer.