(7 lectures; 2018) Lecture 1: Fundamentals of Fluid Flows and Kinematic Transport Theorem Lecture 2: Conservation of Linear Momentum and Decomposition of Fluid Flows Lecture 3: Circulation and Vorticity Transport Equation September 26, 2018 Click on to watch this video Duration: 1:31:26 Summary of the talk Lecture 4: Helmholtz’s Conservation Laws and Kinetic Helicity September … Continue reading
On Quantum Vortex Knots and Links Defect Production by Phase Twist Injection as Aharonov-Bohm Effect Minimal Unlinking Pathways as Geodesics in Polynomial Space Quantum Vortex Dynamics by Seifert Surface Information Vortex knots cascade by HOMFLYPT polynomial On the Energy Spectrum of Magnetic Knots and Links Impulse of Vortex Knots from Diagram Projections On Călugăreanu’s Theorem… Continue reading
A Topological Approach to Turbulence Cascade February 2, 2025Talk given at the “1st Online International Knot Theory Congress”. Click on to watch this video Duration: 0:39:36 Summary of the talk Quantum Versus Classical Vortex Dynamics Quantum Vortex Knots and Links under Zero Helicity Condition A Topological Route to Superfluid Turbulence On the Energy and Helicity … Continue reading
(i) Structural complexity and dynamical systems Relationships between dynamical features and evolution of complex fluid systems such as vortex tangles and magnetic fields in terms of geometric, algebraic and topological information. Aims: to establish relations between dynamical aspects and morphological information by analytical means. (ii) Energy lower bounds on magnetic knots and links Identification of … Continue reading