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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.
Inhaltsverzeichnis
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.
Über den Autor / die Autorin
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.
Zusammenfassung
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.
Zusatztext
“This
book is devoted to the study of vortex filaments in equilibrium, quasi-2D
vortex structures with applications to geophysical fluid dynamics and
magnetohydrodynamics in plasmas. … The text is useful for both researchers and
students.” (Maria Christina Mariani, zbMATH 1327.82001, 2016)
“This is a short but excellent research monograph that would be useful for the advanced study of and future research on vortex dynamics and its modern applications. I strongly recommend it to anyone interested in analytical and computational research on vortex filaments as well as quantum vortices and their applications. It would be suitableas a resource book for graduate-level research seminars for advanced graduate students and research professionals.” (L. Debnath, Mathematical Reviews, May, 2015)
Bericht
"This book is devoted to the study of vortex filaments in equilibrium, quasi-2D vortex structures with applications to geophysical fluid dynamics and magnetohydrodynamics in plasmas. ... The text is useful for both researchers and students." (Maria Christina Mariani, zbMATH 1327.82001, 2016)
"This is a short but excellent research monograph that would be useful for the advanced study of and future research on vortex dynamics and its modern applications. I strongly recommend it to anyone interested in analytical and computational research on vortex filaments as well as quantum vortices and their applications. It would be suitableas a resource book for graduate-level research seminars for advanced graduate students and research professionals." (L. Debnath, Mathematical Reviews, May, 2015)
