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Teachers open the door,
but you must enter by yourself.
Current courses  Old courses 
More details in the Syllabi coming soon
Osher classes 

What is:  
1) Dynamics and Control of SOC Systems (Sandpiles, Plasmas)
Motivated by the complicated dynamics observed in simulations and experiments of gradient driven turbulent transport, a simple paradigmatic transport model based on the ideas of self organized criticality (SOC) has been developed and investigated . In many cases a strong coupling exists between the turbulence and bulk flows in the system. If the bulk flows are uniform the turbulence imbedded in the flow is simply advected and the dynamics are usually not changed. Often however, such flows are spatially dependent (sheared) and therefore can have an impact on the dynamics of the system. SOC systems have been the focus of much investigation recently due to the broad relevance of many of the characteristics of these systems. For example, 1/f noise is a ubiquitous feature in many diverse physical systems from starlight flicker through river flows to stock market data. Additionally many of these systems (and others) exhibit a remarkable spatial and temporal selfsimilar structure. The physical and dynamical selfsimilarity that is exhibited by these systems is very robust to perturbations and is not necessarily close to any "linearly marginal" state such as the angle of repose for a sandpile. It is this selfsimilarity and non linear self organization that leads to the term "SelfOrganized Criticality". In many systems (magnetically confined plasmas for example) the transport of constituents down their ambient gradient is thought to be dominated by turbulent transport. That is a turbulent relaxation of the gradient. The turbulence itself is often driven by the freeenergy in the gradient . It is this combination of turbulent relaxation removing the source of free energy thereby turning off the turbulence which then allows the gradient to build back up which allows the development of robust (albeit fluctuating) profiles. The dynamics of such systems can be computationally investigated with a cellular automata model of a running sand pile. This model allows us to investigate the major dynamical scales and the effect of an applied sheared flow on these dominant scales. In addition to allowing the paradigmatic investigation of turbulent transport, the introduction of sheared flow (wind) and the determination of transport coefficients in sandpiles, both of which naturally arise in the context of magnetically confined plasmas, act as a novel and important extension to the chaotic dynamics of SOC systems.Recent papers in this area (in PDF format)
Basic SOC systems
Avalanche structure of a running sandpile (2002), A Transition in the Dynamics of a Diffusive Running Sandpile(2002,) Quiettime statistics: a tool to probe SOC dynamics from within the strong overlapping regime(2002), Waitingtime statistics of selforganized critical systems(2002)
Plasmas
2) The Dynamics of Complex Infrastucture Systems (Power Transmission, Communications, Traffic, etc)
Note (16 Aug 2003): If you are interested in papers relating to the dynamics of blackouts like the 2003 blackout you might want to read the following papers
Blackout Dynamics in Power Transmission Systems (HICSS2001 Data analysis paper 1 , HICSS2001 Modeling paper 1 , HICSS2001 Modeling paper 2 , HICSS2002 modeling paper 1 , HICSS2002 modeling paper 2 )Communications systems ( HICSS2002 Modeling paper 1)
3) The Interaction Between Sheared Flows and Turbulence
4) Basic Plasma and Fluid Turbulence
Investigations of the basic dynamics of the turbulent systems can shed light on both interesting nonlinear dynamics and applications of these dynamics in relevent physical systems.
5) Modeling Transitions in Plasma Transport
Transitions to enhanced confinement regimes are very important for the success of the fusion energy program.
6) Dynamics of Atomistic Flows in Carbon Nanotubes
In nature the interaction between fluid flows and surfaces and the resultant transport due to the flows is both ubiquitous and of fundamental importance. One of the flow regimes of particular interest is that in which the fluid transitions to a turbulent flow. In this case, the transport characteristics and flow dynamics change dramatically. In addition to an enormous amount of attention given to these systems, much progress has been made in recent years on modeling and understanding the dynamics of these continuous fluid flows (CFD) using the NavierStokes equations. However, with the everincreasing interest in smaller size devices (for example, in MicroElectroMechanicalSystems  MEMS applications) an interesting new regime is encountered. This is the regime in which the distance between surfaces becomes comparable to the atomic or molecular sizes of the flowing material. While the highly "viscous" flow through irregular microporous materials has been extensively studied the basic underlying physics of the "fluid" dynamics of flows through "smooth" regular structures on this scale have yet to be characterized. In particular, the demonstration and characterization of transitions in flows on these scales will have a profound impact on the development of the new blossoming capabilities in building micro and nano scale devices and structured materials.A relevant yet simple realization of such a flow is that given by atoms flowing through carbon nanotubes. Typically, in nano scale systems, the effective viscosity is expected to be high unless, perhaps, the flow "channel" is very regular and smooth such as that found inside a carbon nanotube, for example. Investigation of these "atomistic" flows is of interest for the obvious reason that one must understand how material flows in these nanotubes if one wishes to use them. More importantly the demonstration of new flow dynamics with transitions within the tube could lead to altogether new uses. In addition, basic understanding of flows on these scales may be of relevance in the extreme boundary layer of continuous (NavierStokes) flows and may help in the design of special coatings, for example, to decrease (or increase) drag. It should be stressed that the novel aspect of this is not simply the nanoscales in the system, but rather the interaction between the atomistic flow and the very regular surface created by the nanotubes etc. This research project, which is on the cutting edge of the burgeoning field of nanotechnology, can at the same time make fundamental contributions to the underlying basic physics.
7) The Effect of Noise on Propagation in ReactionDiffusion Equations
8) Verification and Validationof Computational Codes
Support from DOE under grants DEFG0399ER54551 and DEFG0300ER54599 (a young investigator award) and NSF under grant ECS0085647 are gratefully acknowledged
Many of the papers found on these pages are in pdf format. To find out more about pdf viewing or to get a free viewer for pdf documents see Adobes Acrobat Reader (for Macintosh(R), IBM AIX, Windows(R), Sun(TM) SPARC(R), HP/UX(TM), Silicon Graphics(R) and others) or Xpdf (for x86  Linux 2.0 ELF , PowerPC  AIX 4.1 , SPARC  SunOS 4.1.3 , MIPS, Ultrix 4.4 , Alpha  OSF/1 3.2 , HPPA, HPUX 9.05 , and others).
Last changed on 3 January, 2020
This page is maintained by David Newman