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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.

Introduction to Vortex Filaments in Equilibrium

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.