Search results for "Geometric progression"
showing 3 items of 3 documents
A model for planktic foraminiferal shell growth
1993
In this paper we analyze the laws of growth that control planktic foraminiferal shell morphology. We assume that isometry is the key toward the understanding of their ontogeny. Hence, our null hypothesis is that these organisms construct isometric shells. To test this hypothesis, geometric models of their shells have been generated with a personal computer. It is demonstrated that early chambers in log-spirally coiled structures cannot follow a strict isometric arrangement. In the real world, the centers of juvenile chambers deviate from the logarithmic growth curve. Juvenile stages are generally more planispiral and contain more chambers per whorl than adult stages. These traits are shown …
MUTUAL INDUCTANCE FOR AN EXPLICITLY FINITE NUMBER OF TURNS
2011
Non coaxial mutual inductance calculations, based on a Bessel function formulation, are presented for coils modelled by an explicitly flnite number of circular turns. The mutual inductance of two such turns can be expressed as an integral of a product of three Bessel functions and an exponential factor, and it is shown that the exponential factors can be analytically summed as a simple geometric progression, or other related sums. This allows the mutual inductance of two thin solenoids to be expressed as an integral of a single analytical expression. Sample numerical results are given for some representative cases and the approach to the limit where the turns are considered to be smeared ou…
Mutual inductance for an explicitly finite number of turns
2011
Published version of an article published in Progress In Electromagnetics Research B, 28, 273-287. Also available from the publisher at http://www.jpier.org/pierb/pier.php?paper=10110103 Non coaxial mutual inductance calculations, based on a Bessel function formulation, are presented for coils modelled by an explicitly finite number of circular turns. The mutual inductance of two such turns can be expressed as an integral of a product of three Bessel functions and an exponential factor, and it is shown that the exponential factors can be analytically summed as a simple geometric progression, or other related sums. This allows the mutual inductance of two thin solenoids to be expressed as an…