Controlling chaos

Brownian motors: noisy transport far from equilibrium

A comprehensive review of zonal flow phenomena in plasmas is presented. While the emphasis is on zonal flows in laboratory plasmas, planetary zonal flows are discussed as well. The review presents the status of theory, numerical simulation and experiments relevant to zonal flows. The emphasis is on developing an integrated understanding of the dynamics of drift wave–zonal flow turbulence by combining detailed studies of the generation of zonal flows by drift waves, the back-interaction of zonal flows on the drift waves, and the various feedback loops by which the system regulates and organizes itself. The implications of zonal flow phenomena for confinement in, and the phenomena of fusion devices are discussed. Special attention is given to the comparison of experiment with theory and to identifying directions for progress in future research.

/pdf/zonal-flows-in-plasma-a-review-3byloag115.pdf

Zonal flows in plasma—a review

We formalize a notion of topological simplification within the framework of a filtration, which is the history of a growing complex. We classify a topological change that happens during growth as either a feature or noise depending on its lifetime or persistence within the filtration. We give fast algorithms for computing persistence and experimental evidence for their speed and utility.

https://link.springer.com/content/pdf/10.1007%2Fs00454-002-2885-2.pdf

Topological Persistence and Simplification

Chaos, fractional kinetics, and anomalous transport

Symplectic maps are the discrete-time analog of Hamiltonian motion. They arise in many applications including accelerator, chemical, condensed-matter, plasma, and fluid physics. Twist maps correspond to Hamiltonians for which the velocity is a monotonic function of the canonical momentum. Twist maps have a Lagrangian variational formulation. One-parameter families of twist maps typically exhibit the full range of possible dynamics-from simple or integrable motion to complex or chaotic motion. One class of orbits, the minimizing orbits, can be found throughout this transition; the properties of the minimizing orbits are discussed in detail. Among these orbits are the periodic and quasiperiodic orbits, which form a scaffold in the phase space and constrain the motion of the remaining orbits. The theory of transport deals with the motion of ensembles of trajectories. The variational principle provides an efficient technique for computing the flux escaping from regions bounded by partial barriers formed from minimizing orbits. Unsolved problems in the theory of transport include the explanation for algebraic tails in correlation functions, and its extension to maps of more than two dimensions.

Symplectic maps, variational principles, and transport

Transport in Hamiltonian systems

Preface List of figures List of tables 1. Introduction 2. Linear systems 3. Existence and uniqueness 4. Dynamical systems 5. Invariant manifolds 6. The phase plane 7. Chaotic dynamics 8. Bifurcation theory 9. Hamiltonian dynamics A. Mathematical software Bibliography Index.

Differential dynamical systems

/pdf/stochastic-dynamical-systems-4hz2b4xdib.pdf

James D. Meiss

Papers

Symplectic maps, variational principles, and transport

Transport in Hamiltonian systems

Differential dynamical systems

Stochastic dynamical systems

Markov tree model of transport in area-preserving maps