PHYS 235 - Nonlinear Plasma Theory - Diamond [SP22]

Course Modules

Introduction

Introduction Introduction

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Read the syllabus and other course handouts Read the syllabus and other course handouts 1

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Phys 235 Topics Spring 2022 Phys 235 Topics Spring 2022 2

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Phys235_Syllabus_S2022 Phys235_Syllabus_S2022 3

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Context Module Sub Header

Student Lecture Summaries-Spring 2022 4

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Attachment

Mean Field/ Quasilinear Theory Basics: S. Molesworth Mean Field/ Quasilinear Theory Basics: S. Molesworth 5

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Transport by Stochastic Magnetic Fields-A Case Study for Ku <1 : F. Ramirez Transport by Stochastic Magnetic Fields-A Case Study for Ku <1 : F. Ramirez 6

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Attachment

Ku> 1, Cellular Flows and Percolation : M. Cao Ku> 1, Cellular Flows and Percolation : M. Cao 7

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Intermittency and its Modeling : Y. Yakusevich Intermittency and its Modeling : Y. Yakusevich 8

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Motion Beyond Brownian-From Random Walks to Flights: S. Molesworth Motion Beyond Brownian-From Random Walks to Flights: S. Molesworth 9

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Avalanches and SOC : R. Masline Avalanches and SOC : R. Masline 10

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Page

Check your Notification Settings Check your Notification Settings 11

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Context Module Sub Header

Helpful Links 12

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External Url

Important Dates: UCSD Academic and Administrative Calendar, 2021-2022 Important Dates: UCSD Academic and Administrative Calendar, 2021-2022 13

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Lecture Videos

Lecture Videos Lecture Videos

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Registered students 1

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Context Module Sub Header

Log in to Canvas and view under Media Gallery 2

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Context Module Sub Header

Non-registered students 3

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Context Module Sub Header

View on UC San Diego MediaSpace: 4

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External Url

MediaSpace video playlist for PHYS 235 MediaSpace video playlist for PHYS 235 5

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or copy URL: https://mediaspace.ucsd.edu/playlist/dedicated/232710043/1_7oftgobs/ 6

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Seminars

Seminars Seminars

External Url

SoCal Plasma Zoom seminar recordings SoCal Plasma Zoom seminar recordings 4

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Transport in Stochastic Magnetic Fields and related Hamiltonian Systems-Ku<1

Transport in Stochastic Magnetic Fields and related Hamiltonian Systems-Ku<1 Transport in Stochastic Magnetic Fields and related Hamiltonian Systems-Ku<1

Attachment

Chandrasekhar: Stochastic Problems Chandrasekhar: Stochastic Problems 1

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Notes 1: Overview and Stochastic Fields 1 Notes 1: Overview and Stochastic Fields 1 2

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Magnetic Field Lines-Dynamical System Magnetic Field Lines-Dynamical System 3

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Quasilinear Lectures-TheoryApplications Quasilinear Lectures-TheoryApplications 4

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Attachment

Notes 2: Stochastic Fields 2 – Heat Transport Notes 2: Stochastic Fields 2 – Heat Transport 5

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Attachment

Collisional Stochastic B Heat Transport.pdf Collisional Stochastic B Heat Transport.pdf 6

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Attachment

Diffusion in stochastic magnetic fields-Summary Diffusion in stochastic magnetic fields-Summary 7

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Notes 3 : Momentum and Particle Transport-Stresses Notes 3 : Momentum and Particle Transport-Stresses 8

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Attachment

Particle and momentum transport in stochastic-fields-Summary Particle and momentum transport in stochastic-fields-Summary 9

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Attachment

Chaos in Hamiltonian Systems-Ott Chaos in Hamiltonian Systems-Ott 10

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Attachment

Electron Heat Transport in a Tokamak with Destroyed Magnetic Surfaces - A.B. Rechester and M.N. Rosenbluth Electron Heat Transport in a Tokamak with Destroyed Magnetic Surfaces - A.B. Rechester and M.N. Rosenbluth 11

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Attachment

Electron Heat Conductivity of the Plasma Across a "Braided" Magnetic Field - B.B. Kadomtsev and O.P. Pogutse Electron Heat Conductivity of the Plasma Across a "Braided" Magnetic Field - B.B. Kadomtsev and O.P. Pogutse 12

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Narayan and Medvedev 2001, Thermal Conduction in Cooling Flows Narayan and Medvedev 2001, Thermal Conduction in Cooling Flows 13

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Attachment

Particle Transport and Rotation Damping due to Stochastic Magnetic Field Lines Particle Transport and Rotation Damping due to Stochastic Magnetic Field Lines 14

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Transport at Large Kubo Number; Percolation Models

Transport at Large Kubo Number; Percolation Models Transport at Large Kubo Number; Percolation Models

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Linear Response and Kubo Formalism Linear Response and Kubo Formalism 1

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Percolation, statistical topography and transport in random media - M.B. Isichenko Percolation, statistical topography and transport in random media - M.B. Isichenko 2

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Attachment

Notes 4: To Large Kubo Number – 2-D, Diffusion, Contours, Percolation Notes 4: To Large Kubo Number – 2-D, Diffusion, Contours, Percolation 3

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Effective Plasma Heat Conductivity in "Braided" Magnetic Field-II. Percolation Limit Effective Plasma Heat Conductivity in "Braided" Magnetic Field-II. Percolation Limit 4

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Notes 5: Taylor Problem, Shear Dispersion, Percolation I Notes 5: Taylor Problem, Shear Dispersion, Percolation I 5

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Shear Dispersion Notes Shear Dispersion Notes 6

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Taylor Dispersion Notes Taylor Dispersion Notes 7

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Diffusion in shear flows made easy: the Taylor limit - Ronald Smith Diffusion in shear flows made easy: the Taylor limit - Ronald Smith 8

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Shear dispersion - W.R. Young and Scott Jones Shear dispersion - W.R. Young and Scott Jones 9

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Notes 6: Percolation Theory 1 Notes 6: Percolation Theory 1 10

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Zeldovich, et al. - Percolation and Random Barriers Zeldovich, et al. - Percolation and Random Barriers 11

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Zeldovich 1983, Stationary, Random 2-D Fields Zeldovich 1983, Stationary, Random 2-D Fields 12

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Vorticity Percolation Clusters-Boffetta,et al Vorticity Percolation Clusters-Boffetta,et al 13

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Notes 7 :Percolation Theory 2 Notes 7 :Percolation Theory 2 14

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Taylor and McNamara on GC Plasma Taylor and McNamara on GC Plasma 15

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Rosenbluth, et al. on Effective Diffusion in Cellular Convective Flows Rosenbluth, et al. on Effective Diffusion in Cellular Convective Flows 16

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Broadbent and Hammersley on Percolation Theory Broadbent and Hammersley on Percolation Theory 17

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Kirkpatrick on "Percolation and Conduction" Kirkpatrick on "Percolation and Conduction" 18

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Stauffer on "Scaling Theory of Percolation Clusters" Stauffer on "Scaling Theory of Percolation Clusters" 19

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Zeldovich on Percolation of Stationary Magnetic Fields Zeldovich on Percolation of Stationary Magnetic Fields 20

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Dykhne on Conduction in Random Media Dykhne on Conduction in Random Media 21

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Intermittency and Transport: From Diffusion to Flights

Intermittency and Transport: From Diffusion to Flights Intermittency and Transport: From Diffusion to Flights

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Zeldovich et al on Basic Concepts in Intermittency Zeldovich et al on Basic Concepts in Intermittency 1

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Notes 8: Intermittency 1 Notes 8: Intermittency 1 2

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Supplement 1: Kinetics 1 Supplement 1: Kinetics 1 3

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Supplement 2: Kinetics 2 Supplement 2: Kinetics 2 4

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Notes 8 : Addendum: Diffusion on Random Potential Notes 8 : Addendum: Diffusion on Random Potential 5

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Zeldovich, et al-Intermittency in Random Media Zeldovich, et al-Intermittency in Random Media 6

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Supplement 4: Basic OV Lecture on Turbulence Supplement 4: Basic OV Lecture on Turbulence 7

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Notes 9: Intermittency 2 Notes 9: Intermittency 2 8

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Kolmogorov 41 Kolmogorov 41 9

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Kolmogorov 61-Enter Intermittency Kolmogorov 61-Enter Intermittency 10

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Frisch, Sulem, and Nelkin (1978) on Beta Model Frisch, Sulem, and Nelkin (1978) on Beta Model 11

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Mandelbrot OV of Self-Affine Processes Mandelbrot OV of Self-Affine Processes 12

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Notes 9: Addendum: Multifractality in Turbulence Notes 9: Addendum: Multifractality in Turbulence 13

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Frisch on Scaling and Multifractals Frisch on Scaling and Multifractals 14

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Notes 10: Fractional Brownian Motion, Hurst Parameter, 1/f Noise Notes 10: Fractional Brownian Motion, Hurst Parameter, 1/f Noise 15

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Gardiner: Stochastic Methods Gardiner: Stochastic Methods 16

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Mandelbrot and Wallis 1968: Noah, Joseph Effects and Operational Hydrology Mandelbrot and Wallis 1968: Noah, Joseph Effects and Operational Hydrology 17

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Mandelbrot on Models of Price Changes Mandelbrot on Models of Price Changes 18

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On 1/f Processes-Montroll and Shlesinger On 1/f Processes-Montroll and Shlesinger 19

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Notes 11 : L-Stable Distributions,Levy Walks ,etc Notes 11 : L-Stable Distributions,Levy Walks ,etc 20

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Zaslavsky on Levy Flights Zaslavsky on Levy Flights 21

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Levy Stable Distributions-Mainardi Levy Stable Distributions-Mainardi 22

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Weierstass Walk: Hughes, Shlesinger,Montroll Weierstass Walk: Hughes, Shlesinger,Montroll 23

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Notes 12: Physics of Levy Flights, CTRW and Fractional Kinetics I Notes 12: Physics of Levy Flights, CTRW and Fractional Kinetics I 24

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Vlahos, et al.: Elementary Tutorial on Normal and Anomalous Diffusions Vlahos, et al.: Elementary Tutorial on Normal and Anomalous Diffusions 25

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Zaslavsky on General Aspects of Kinetics Zaslavsky on General Aspects of Kinetics 26

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Mandelbrot 1960: Pareto-Levy Law Mandelbrot 1960: Pareto-Levy Law 27

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Klafter: Anomalous Diffusion Klafter: Anomalous Diffusion 28

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Levy Flights in Rotating Flows-Swinney Group Levy Flights in Rotating Flows-Swinney Group 29

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Summary by Chang-Chun Chen: Fractal Brownian Motion,Levy Flights.pdf Summary by Chang-Chun Chen: Fractal Brownian Motion,Levy Flights.pdf 30

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Supplement 3: Another Look at Fokker Planck Supplement 3: Another Look at Fokker Planck 31

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Notes 13 : Introduction to Fractional Kinetics Notes 13 : Introduction to Fractional Kinetics 32

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Mandelbrot on Fractional Random Walks Mandelbrot on Fractional Random Walks 33

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Zaslavsky: Fractional Kinetics and Anomalous Transport Zaslavsky: Fractional Kinetics and Anomalous Transport 34

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Zaslavsky on Fractional Kinetics Zaslavsky on Fractional Kinetics 35

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Notes 14: More on CTRW and FK; Montroll–Weiss Equation Notes 14: More on CTRW and FK; Montroll–Weiss Equation 36

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Avalanches and SOC ; Directed Percolation and Spreading

Avalanches and SOC ; Directed Percolation and Spreading Avalanches and SOC ; Directed Percolation and Spreading

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Notes 15: Self-organized Criticality and Avalanches I Notes 15: Self-organized Criticality and Avalanches I 1

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Bak, Tang, Wisenfeld - Pile PRL Bak, Tang, Wisenfeld - Pile PRL 2

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Bak, Tang, Wiesenfled-Extended Bak, Tang, Wiesenfled-Extended 3

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Kadanoff on SOC Kadanoff on SOC 4

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Turcotte-Review of SOC Turcotte-Review of SOC 5

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Notes 16: SOC II — Hydrodynamic Models of Avalanche Turbulence Notes 16: SOC II — Hydrodynamic Models of Avalanche Turbulence 6

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Hwa and Kardar-Hydrodynamic Model Hwa and Kardar-Hydrodynamic Model 7

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Sornette and Sornette-SOC and Earthquakes Sornette and Sornette-SOC and Earthquakes 8

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Schelling Automata Model of Segregation Schelling Automata Model of Segregation 9

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Notes 17: "Noisy Burgulence" and Turbulence Closures Notes 17: "Noisy Burgulence" and Turbulence Closures 10

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Notes 18: Avalanching and SOC Phenomena in MFE Plasmas Notes 18: Avalanching and SOC Phenomena in MFE Plasmas 11

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Hahm and Diamond 2018, "Mesoscopic Transport Events and the Breakdown of Fick’s Law for Turbulent Fluxes" Hahm and Diamond 2018, "Mesoscopic Transport Events and the Breakdown of Fick’s Law for Turbulent Fluxes" 12

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Diamond, Hahm 95: Avalanches in Confined Plasmas Diamond, Hahm 95: Avalanches in Confined Plasmas 13

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Newman 96: Pile Models of Transport Newman 96: Pile Models of Transport 14

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Avalanching in Flux-Driven G-mode Simulations Avalanching in Flux-Driven G-mode Simulations 15

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Idomura 09-Avalanching in Flux Driven GK ITG Sims Idomura 09-Avalanching in Flux Driven GK ITG Sims 16

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Sheared Sand Pile Sheared Sand Pile 17

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SOC OV SOC OV 18

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Attachment

Carreras, et al. on H Exponent for Edge Turbulence Carreras, et al. on H Exponent for Edge Turbulence 19

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Wildfire Models-Stat Phys Meets Reality Wildfire Models-Stat Phys Meets Reality 20

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Attachment

Notes 19: New Directions-ExB Staircase Notes 19: New Directions-ExB Staircase 21

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Attachment

Notes 19: A Look at Other Directions Notes 19: A Look at Other Directions 22

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Diamond, et al., Zonal Flows-Eikonal Approach Diamond, et al., Zonal Flows-Eikonal Approach 23

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Attachment

Gurcan, Diamond: Zonal Flows-Envelope Approach Gurcan, Diamond: Zonal Flows-Envelope Approach 24

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ExB Staircases ExB Staircases 25

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Jams in Avalanche Gas Jams in Avalanche Gas 26

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Lecture Notes -- Supplementary

Lecture Notes -- Supplementary Lecture Notes -- Supplementary

Attachment

Supplement – MHD Turbulence 1 Supplement – MHD Turbulence 1 3

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Supplement – MHD Turbulence 2 Supplement – MHD Turbulence 2 4

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Supplement 1: Basics of Turbulence Supplement 1: Basics of Turbulence 16

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Attachment

Supplement 2: Notes on Turbulence Supplement 2: Notes on Turbulence 17

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Attachment

Supplement 3: Fluids in Flatland (2D) Supplement 3: Fluids in Flatland (2D) 18

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Supplementary Materials

Supplementary Materials Supplementary Materials

Context Module Sub Header

Zonal Flows and Pattern Formation 1

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Itoh, et al., Supplement Itoh, et al., Supplement 3

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Context Module Sub Header

Percolation Theory 5

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Attachment

Boffetta et al. on "Clusters in Conformally Invariant 2-D Turbulence" Boffetta et al. on "Clusters in Conformally Invariant 2-D Turbulence" 7

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Attachment

Gruzinov, et al. on "Two Dimensional Turbulent Diffusion" Gruzinov, et al. on "Two Dimensional Turbulent Diffusion" 9

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Context Module Sub Header

Traffic Flow and Flocking 14

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Attachment

D. Helbing: Review of Traffic Flow. See also Whitham. D. Helbing: Review of Traffic Flow. See also Whitham. 15

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Toner and Tu: Hydrodynamic Theory of Flocking Toner and Tu: Hydrodynamic Theory of Flocking 16

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Marchetti et al: Review of Hydrodynamics of Soft Active Matter Marchetti et al: Review of Hydrodynamics of Soft Active Matter 17

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Context Module Sub Header

Long Correlation Time and Random Media 18

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Context Module Sub Header

Background on Stochasticity and Chaos 22

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Destruction of Magnetic Surfaces by Magnetic Field Irregularities Destruction of Magnetic Surfaces by Magnetic Field Irregularities 24

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Calculating in the Chaotic Regime Calculating in the Chaotic Regime 26

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FAQ's re Calculation in Chaotic Regime FAQ's re Calculation in Chaotic Regime 27

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Context Module Sub Header

Transport in Stochastic Fields 28

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Attachment

Chandran et al. 1998, Thermal Conduction in Tangle Chandran et al. 1998, Thermal Conduction in Tangle 30

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Context Module Sub Header

Transport and Shear Dispersion 37

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Dispersion of soluble matter in solvent flowing slowly through a tube Dispersion of soluble matter in solvent flowing slowly through a tube 40

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Attachment

The dispersion of matter in turbulent flow thorugh a pipe - Sir Geoffrey Taylor, F.R.S. The dispersion of matter in turbulent flow thorugh a pipe - Sir Geoffrey Taylor, F.R.S. 41

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Context Module Sub Header

Hamiltonian Chaos 44

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Ford on FPU Problem Ford on FPU Problem 45

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Context Module Sub Header

Intermittency and Fractal Models 46

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Touchette: Review of Large Deviation Theory Touchette: Review of Large Deviation Theory 47

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Attachment

R. S. Ellis: Large Deviations – from Boltzmann to 2-D Turbulence R. S. Ellis: Large Deviations – from Boltzmann to 2-D Turbulence 48

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Boffetta et al. on Multifractals Boffetta et al. on Multifractals 50

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Mandelbrot on Distributions Mandelbrot on Distributions 56

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Context Module Sub Header

Phase Dynamics and Synchronization 58

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Strogatz - From Kuramoto to Crawford - Exploring the Onset of Synchronization in Populations of Coupled Oscillators Strogatz - From Kuramoto to Crawford - Exploring the Onset of Synchronization in Populations of Coupled Oscillators 59

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Kuramoto - Chemical Oscillations, Waes and Turbulence - Volume 19 Kuramoto - Chemical Oscillations, Waes and Turbulence - Volume 19 60

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Context Module Sub Header

Intermittency II: Characterization: Hurst Exponent, R/S Analysis, Levy-Pareto Distributions 61

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Context Module Sub Header

Anomalous Diffusion and Fractional Kinetics 69

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Context Module Sub Header

Self-Organized Criticality, Sandpiles, Relaxation 79

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Context Module Sub Header

Application of SOC Concepts in Confinement Physics 87

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PHYS 235 - Nonlinear Plasma Theory - Diamond [SP22]

Course Modules

Introduction

Student Lecture Summaries-Spring 2022 4

Helpful Links 12

Lecture Videos

Registered students 1

Log in to Canvas and view under Media Gallery 2

Non-registered students 3

View on UC San Diego MediaSpace: 4

or copy URL: https://mediaspace.ucsd.edu/playlist/dedicated/232710043/1_7oftgobs/ 6

Seminars

Transport in Stochastic Magnetic Fields and related Hamiltonian Systems-Ku<1

Transport at Large Kubo Number; Percolation Models

Intermittency and Transport: From Diffusion to Flights

Avalanches and SOC ; Directed Percolation and Spreading

Lecture Notes -- Supplementary

Supplementary Materials

Zonal Flows and Pattern Formation 1

Percolation Theory 5

Traffic Flow and Flocking 14

Long Correlation Time and Random Media 18

Background on Stochasticity and Chaos 22

Transport in Stochastic Fields 28

Transport and Shear Dispersion 37

Hamiltonian Chaos 44

Intermittency and Fractal Models 46

Phase Dynamics and Synchronization 58

Intermittency II: Characterization: Hurst Exponent, R/S Analysis, Levy-Pareto Distributions 61

Anomalous Diffusion and Fractional Kinetics 69

Self-Organized Criticality, Sandpiles, Relaxation 79

Application of SOC Concepts in Confinement Physics 87