(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
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
Scientific results categorised by research area and listed in inverse chronological order (numbered item and date refers to the publication list page). (i) Classical vortex dynamics and fluid knots (ii) Quantum defects in superfluids and condensates (iii) Energy-complexity relations for magnetic fields (iv) Geometric and topological aspects of space curve kinematics (v) Topological dynamics of … Continue reading
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
My work concerns the following thematic areas: Classical vortex dynamics and fluid knots; Quantum defects in condensates and topological phases; Energy-complexity relations for magnetic fields; Topological transitions of critical energy surfaces; Hydrodynamic analogue models in black hole theory. (i) Classical vortex dynamics and fluid knots Study of dynamical properties of three-dimensional vortex fields, and of … Continue reading