PYL711: Difference between revisions
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| credits = 4 | | credits = 4 | ||
| credit_structure = 3-1-0 | | credit_structure = 3-1-0 | ||
| pre_requisites = PYL127 & PYL121 OR PYL551 & PYL553 | | pre_requisites = [[PYL127]] & [[PYL121]] OR [[PYL551]] & [[PYL553]] | ||
| overlaps = APL340, ESL300, AML836 | | overlaps = [[APL340]], [[ESL300]], [[AML836]] | ||
}} | }} | ||
== pYL711 : Introduction to Nonlinear Dynamics == | == pYL711 : Introduction to Nonlinear Dynamics == | ||
Introduction, phase space, stability analysis, bifurcations, iterative maps. Dissipative Systems; noninvertible maps; period-doubling and universality, intermittency. Hamiltonian Systems; Integrability, Liouville's theorem, action-angle variables, perturbation techniques, KAM theorem, area-preserving maps. Fractals; Self-similarity; fractal dimensions and multifractals. Chaos in plasmas, Generalised hydrodynamic model for strongly coupled plasma medium, connections with visco-elastic and soft matter. Soft and Active matter: Nonlinear Rheology, Rhea-chaos, Oscillatory Chemical Reactions) Wrinkling, Folding. Quantum chaos: Regular versus irregular states. Path Integrals. Random Matrix theory. Streamline and turbulent flows and transport for hydrodynamic and Magnetofluids, Kolmogorov's 5/3 law. Synchrony and phase transitions - Kuramoto model. Chaotic synchronization; the synchronization manifold. | Introduction, phase space, stability analysis, bifurcations, iterative maps. Dissipative Systems; noninvertible maps; period-doubling and universality, intermittency. Hamiltonian Systems; Integrability, Liouville's theorem, action-angle variables, perturbation techniques, KAM theorem, area-preserving maps. Fractals; Self-similarity; fractal dimensions and multifractals. Chaos in plasmas, Generalised hydrodynamic model for strongly coupled plasma medium, connections with visco-elastic and soft matter. Soft and Active matter: Nonlinear Rheology, Rhea-chaos, Oscillatory Chemical Reactions) Wrinkling, Folding. Quantum chaos: Regular versus irregular states. Path Integrals. Random Matrix theory. Streamline and turbulent flows and transport for hydrodynamic and Magnetofluids, Kolmogorov's 5/3 law. Synchrony and phase transitions - Kuramoto model. Chaotic synchronization; the synchronization manifold. | ||
Latest revision as of 16:44, 14 April 2026
| pYL711 | |
|---|---|
| Introduction to Nonlinear Dynamics | |
| Credits | 4 |
| Structure | 3-1-0 |
| Pre-requisites | PYL127 & PYL121 OR PYL551 & PYL553 |
| Overlaps | APL340, ESL300, AML836 |
pYL711 : Introduction to Nonlinear Dynamics
Introduction, phase space, stability analysis, bifurcations, iterative maps. Dissipative Systems; noninvertible maps; period-doubling and universality, intermittency. Hamiltonian Systems; Integrability, Liouville's theorem, action-angle variables, perturbation techniques, KAM theorem, area-preserving maps. Fractals; Self-similarity; fractal dimensions and multifractals. Chaos in plasmas, Generalised hydrodynamic model for strongly coupled plasma medium, connections with visco-elastic and soft matter. Soft and Active matter: Nonlinear Rheology, Rhea-chaos, Oscillatory Chemical Reactions) Wrinkling, Folding. Quantum chaos: Regular versus irregular states. Path Integrals. Random Matrix theory. Streamline and turbulent flows and transport for hydrodynamic and Magnetofluids, Kolmogorov's 5/3 law. Synchrony and phase transitions - Kuramoto model. Chaotic synchronization; the synchronization manifold.