- Ref: cds.cern.ch/record/2700089
- This monograph emphasizes the main role differential geometry and convex analysis play in the understanding of physical, chemical, and mechanical notions. Providing a thorough overview of mathematical modeling of physical systems, this book is a useful resource for graduate students and researchers.
This course examines electric and magnetic quasistatic forms of Maxwell's equations applied to dielectric, conduction, and magnetization boundary value problems. Topics covered include: electromagnetic forces, force densities, and stress tensors, including magnetization and polarization; thermodynamics of electromagnetic fields, equations of motion, and energy conservation; applications to synchronous, induction, and commutator machines; sensors and transducers; microelectromechanical systems; propagation and stability of electromechanical waves; and charge transport phenomena. Acknowledgments The instructor would like to thank Thomas Larsen and Matthew Pegler for transcribing into LaTeX the homework problems, homework solutions, and exam solutions.
This course explores electromagnetic phenomena in modern applications, including wireless and optical communications, circuits, computer interconnects and peripherals, microwave communications and radar, antennas, sensors, micro-electromechanical systems, and power generation and transmission. Fundamentals include quasistatic and dynamic solutions to Maxwell's equations; waves, radiation, and diffraction; coupling to media and structures; guided waves; resonance; acoustic analogs; and forces, power, and energy.
. Abstract: The golden ratio is found to be related to the fine-structure constant, which determines the strength of the electromagnetic interaction. The golden ratio and classical harmonic proportions with quartic equations give an approximate value for the inverse fine-structure constant the same as that discovered previously in the geometry of the hydrogen atom. With…
Cours gratuits de physique chimie pour le collège (cinquième, quatrième, troisième), le lycée (seconde, première S, terminale S), la licence (1ère année), le capes de physique-chimie et l'agrégation de physique.
The fine-structure constant, which determines the strength of the electromagnetic interaction, is briefly reviewed beginning with its introduction by Arnold Sommerfeld and also includes the interest of Wolfgang Pauli, Paul Dirac, Richard Feynman and others. Sommerfeld was very much a Pythagorean and sometimes compared to Johannes Kepler. The archetypal Pythagorean triangle has long been known as a hiding place for the golden ratio. More recently, the quartic polynomial has also been found as a hiding place for the golden ratio. The Kepler triangle, with its golden ratio proportions, is also a Pythagorean triangle. Combining classical harmonic proportions derived from Kepler’s triangle with quartic equations determine an approximate value for the fine-structure constant that is the same as that found in our previous work with the golden ratio geometry of the hydrogen atom. These results make further progress toward an understanding of the golden ratio as the basis for the fine-structure constant.
A. Dulny, A. Hotho, and A. Krause. KI 2022: Advances in Artificial Intelligence - 45th German Conference on AI, Trier, Germany, September 19-23, 2022, Proceedings, volume 13404 of Lecture Notes in Computer Science, page 75--89. Springer, (2022)