scholarly journals An Adaptive Phase-Amplitude Reduction Framework without $\mathcal{O}(\epsilon)$ Constraints on Inputs

2022 ◽  
Vol 21 (1) ◽  
pp. 204-230
Author(s):  
Dan Wilson
Keyword(s):  
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

scholarly journals Phase-amplitude coupling of ripple activities during seizure evolution with theta phase

2021 ◽  
Author(s):  
Hiroaki Hashimoto ◽  
Hui Ming Khoo ◽  
Takufumi Yanagisawa ◽  
Naoki Tani ◽  
Satoru Oshino ◽  
...  
Keyword(s):  
Theta Phase ◽  
Phase Amplitude

scholarly journals Phase/Amplitude Synchronization of Brain Signals During Motor Imagery BCI Tasks

2021 ◽  
pp. 1-1
Author(s):  
Tiziana Cattai ◽  
Stefania Colonnese ◽  
Marie-Constance Corsi ◽  
Danielle S. Bassett ◽  
Gaetano Scarano ◽  
...  
Keyword(s):  
Motor Imagery ◽  
Brain Signals ◽  
Phase Amplitude
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