Magnetic Helicity, Ampère’s Theorem and Emergence of Linking
(2 lectures; 2025) Lecture 1: Magnetic Helicity in Ideal MHD: Definition and Conservation Lecture 2: Ampère’s theorem, Solid Angle and Emergence of Linking number… Continue reading
Riemann, Topology and Physics
(2 lectures; 2024) Lecture 1: Riemann’s Cuts and Green’s First Identity Lecture 2: Green’s First Identity, AB Effect and Helicity in Multiconnected Domains… Continue reading
Gallery of Fluid Motion
Gallery of Fluid Motion • Topological collapse of a Möbius soap film Topological transition of a Möbius soap film that develops rapidly a twist fold singularity as changes from a one-sided film surface to a two-sided film surface. • Topological dynamics of quantum vortex knots and links Direct numerical simulation of the interaction and reconnection … Continue reading
Topological collapse of a Möbius soap film
Topological transition of a Möbius soap film developing a twist fold singularity Twist fold singularity from a Möbius soap film collaps… Continue reading
Topological dynamics of quantum vortex knots and links
Reconnection of two vortex ring defects Flight of a vortex loop from the reconnection of two vortex ring defects Topological cascade of a Hopf link of vortex defects to unlinked loops Topological cascade of the minimal surface of a link of vortex defects Head-on collision of two anti-parallel vortex ring defects Topological collapse of a … Continue reading
Advanced Courses Video Lectures
School Courses • Magnetic Helicity, Ampère’s Theorem and Emergence of Linking Two lectures given for the Master course “Interdisciplinary Frontiers in Theoretical Physics” held at the Beijing University of Technology (BJUT). • Riemann, Topology and Physics (2 lectures; 2024) Two lectures given for the Master course “Interdisciplinary Frontiers in Theoretical Physics” held at the Beijing … Continue reading
Elements of Topological Vortex Dynamics
(5 lectures; 2023) Lecture 1: Kelvin’s Topological Vortex Dynamics Lecture 2: Helicity and Linking Numbers Lecture 3: From Linking Numbers to Vortex Torus Knots Lecture 4: De-Singularisation of the Biot-Savart Law and Vortex Reconnection Lecture 5: On Vortex Reconnection and Topological Cascade of Vortex Knots… Continue reading
Keynote Lectures and Webinars
Review Talks, Webinars and Short Communications • Keynote lectures and webinars Keynote presentations and webinars on new advancements and progress in the field. • Seminars at international meetings and conferences Short communications of new results at special thematic sessions. Click on to visit and subscribe to my YouTube Channel!… Continue reading
Recent Progress in Topological Fluid Dynamics
Slides from the Ravello School on Mathematical Physics (2017) Topological interpretation of helicity Coherent structures and topological fluid mechanics Diffeomorphisms and topological equivalence Kinetic and magnetic helicity of flux tubes Gauss linking number Călugăreanu invariant and geometric decomposition Vortex knots dynamics and momenta of a tangle Localized Induction Approximation (LIA) and Non-Linear Schroedinger (NLS) equation … Continue reading