This book presents fundamental concepts and seminal results to the study of vortex filaments in equilibrium. It also presents new discoveries in quasi-2D vortex structures with applications to geophysical fluid dynamics and magnetohydrodynamics in plasmas. It fills a gap in the vortex statistics literature by simplifying the mathematical introduction to this complex topic, covering numerical methods, and exploring a wide range of applications with numerous examples. The authors have produced an introduction that is clear and easy to read, leading the reader step-by-step into this topical area. Alongside the theoretical concepts and mathematical formulations, interesting applications are discussed. This combination makes the text useful for students and researchers in mathematics and physics.

Includes discussion topics and questions Informal survey-style benefits, survey courses, and seminar classes focused on discussion and independent projects Gradual increase in depth as the book progresses - refocuses students and learners on topics covered in earlier chapters Focuses on particular kind of feature, vortex filaments, in numerous areas of physics rather than a particular area of physics Includes supplementary material: sn.pub/extras

Autorentext
Timothy D. Andersen received his Ph.D. in Mathematics in 2007. His research interests include Feynman-Kac path integral approaches to vortex filaments, plasmas, and biochemical electrostatics, quantum interpretation problem and the arrow of time, and dark matter and the Dirac equation. Chjan Lim, Ph.D., is a professor of Mathematical Sciences at Rensselaer Polytechnic Institute. His research areas include statistical physics and turbulence, computational science and vortex dynamics, symmetric dynamical systems, and combinational matrix theory.

Inhalt

Introduction.- Vortex Filaments and Where to Find Them.- Statistical Mechanics.- Parallel Filaments.- Curved Filaments.- Quantum Fluids.- Plasmas.- Computational Methods.- Quasi 2-D Monte Carlo in Deep Ocean Convection.- Conclusion.