scholarly journals Global computation of phase-amplitude reduction for limit-cycle dynamics

2018 ◽  
Vol 28 (7) ◽  
pp. 073108 ◽  
Author(s):  
A. Mauroy ◽  
I. Mezić
Keyword(s):  
Limit Cycle ◽  
Phase Amplitude

Hamilton-Jacobi Theory

2018 ◽  
Author(s):  
Peter Mann
Keyword(s):  
Phase Space ◽  
Bbgky Hierarchy ◽  
Distribution Functions ◽  
Symplectic Integrators ◽  
Partition Functions ◽  
Von Neumann ◽  
Equipartition Theorem ◽  
Recurrence Theorem ◽  
Phase Amplitude ◽  
Canonical Ensembles

This chapter focuses on Liouville’s theorem and classical statistical mechanics, deriving the classical propagator. The terms ‘phase space volume element’ and ‘Liouville operator’ are defined and an n-particle phase space probability density function is constructed to derive the Liouville equation. This is deconstructed into the BBGKY hierarchy, and radial distribution functions are used to develop n-body correlation functions. Koopman–von Neumann theory is investigated as a classical wavefunction approach. The chapter develops an operatorial mechanics based on classical Hilbert space, and discusses the de Broglie–Bohm formulation of quantum mechanics. Partition functions, ensemble averages and the virial theorem of Clausius are defined and Poincaré’s recurrence theorem, the Gibbs H-theorem and the Gibbs paradox are discussed. The chapter also discusses commuting observables, phase–amplitude decoupling, microcanonical ensembles, canonical ensembles, grand canonical ensembles, the Boltzmann factor, Mayer–Montroll cluster expansion and the equipartition theorem and investigates symplectic integrators, focusing on molecular dynamics.

scholarly journals Dissociating harmonic and non-harmonic phase-amplitude coupling in the human brain

NeuroImage ◽  
2021 ◽  
Vol 227 ◽  
pp. 117648
Author(s):  
Janet Giehl ◽  
Nima Noury ◽  
Markus Siegel
Keyword(s):  
Human Brain ◽  
Harmonic Phase ◽  
Phase Amplitude
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