CNS Meetings and Journal Club
Fall 2008
All meetings, unless otherwise noted are held
on Tuesdays at 2:00pm in the CNS conference room at
Howey W505.
Tuesday, 2008-09-09, 2:00pm, W505Domenico LippolisHow well can one resolve the state space of a chaotic flow?
All physical systems are affected by some noise that limits the resolution that can be attained in partitioning their state space. For chaotic, locally hyperbolic flows, this resolution depends on the interplay of the local stretching/contraction and the smearing due to noise. Our goal is to determine the finest possible partition of the state space for a given hyperbolic dynamical system and a given weak additive white noise of specified strength. We test these ideas on the ``skew Ulam'' repeller, by computing the local eigenfunctions of the Fokker-Planck evolution operator in the neighborhood of each periodic point, and use their widths to attain an optimal partition of the state space. The Fokker-Planck evolution is then represented by a finite Markov graph, whose determinant is used to evaluate the escape rate of the repeller.
Upcoming talks
Tuesday, 2008-09-30, 2:00pm, W505
John
Gibson
Invariant solutions and state-space dynamics of plane Couette flow
It has recently become possible to compute precise equilibrium, traveling wave, and periodic orbit solutions to pipe and plane Couette flow at moderate Reynolds numbers. These invariant solutions (1) capture the complex dynamics of rolls and streaks (coherent structures) in wall-bounded flows and (2) provide a framework for understanding turbulent flows as dynamical systems. We present a number of weakly unstable equilibria, traveling waves, and periodic orbits of plane Couette flow and a new method of visualizing their state-space dynamics. What emerges is a picture of low-Reynolds turbulence as a walk among a set of weakly unstable invariant solutions.
Tuesday, 2008-10-07, 2:00pm, W505Annalisa BraccoScaling 2d turbulence towards the classical limit of infinite Reynolds number
I use the Navier-Stokes equations for barotropic turbulence as a zero-order approximation of chaotic space-time patterns and equilibrium distributions that mimic turbulence in geophysical flows. In this overly-simplified set-up for which smooth-solutions exist, we investigate if is possible to bound the uncertainty associated with the numerical domain discretization, i.e. with the limitation imposed by the Reynolds number range we can explore. To do so I analyze a series of stationary barotropic turbulence simulations spanning a range of Reynolds number of 105 and run over a three year period for over 300,000 CPU hours. A persistent Reynolds number dependency in the energy power spectra and second order vorticity structure function is found, while distributions of dynamical quantities such as velocity, vorticity, dissipation rates and others are invariant in shape and have variances scaling with the viscosity coefficient according to simple power-laws. The relevance to this work to climate models will be discussed.
Tuesday, 2008-10-14(Fall break) move to Wednesday 15?, 2:00pm, W505
John
Gibson
Introduction to The "Channelflow" software.
Past talks
Tuesday, 2008-09-02, 2:00pm, W505William RayPower combining of fiber lasers
Recent experiments using passively coupled fiber lasers report coherent emission even though members of the laser array are poorly matched in length and operate on thousands of longitudinal modes. I discuss our latest theoretical and experimental contributions to understanding this phenomenon and extending it to larger arrays. Our model predicts - and our experiments confirm - a simple pathway to achieving a robust, synchronized output.
Tuesday, 2008-08-26, 2:00pm, W505Francois MaugerNonsequential double ionization of atoms and molecules
The Helium atom driven by an external pulse exhibits single and double ionizations. Some of the double ionized electrons result from sequential double ionization, others correspond to non-sequential double ionization. The double ionization probability takes the form of a ''knee'' as a function of the intensity of the pulse. Here, we investigate the classical dynamics of this system. Using Lyapunov indicators, periodic orbits, as well as reduced Hamiltonian models, we investigate the mechanisms occurring in phase space which shed light on the single and double ionization mechanisms. We find that although the Helium in the absence of the laser field is extremely chaotic, the mechanisms behind all three kinds of ionization are based on integrable models and explain the ''knee'' observed in experiments and numerical simulations.
Thursday, 2008-08-21, 2:00pm, W505Cristel ChandreHamiltonian framework for the Maxwell-Vlasov equations: Application to the Free Electron Lasers
The Hamiltonian description of the self-consistent interaction between an electromagnetic plane-wave and a co-propagating beam of charged particles is considered. We show how the motion can be reduced to a one-dimensional Hamiltonian model (in a canonical setting) from the Vlasov-Maxwell Poisson brackets. The reduction to this paradigmatic Hamiltonian model is performed using a Lie algebraic formalism which allows us to remain Hamiltonian at each step of the derivation.
R. Bachelard, C. Chandre, M. Vittot, arxiv:0802.2602
Tuesday, 2008-08-19, 2:00pm, Howey N110Xavier LeonciniParticle dynamics in regular and chaotic flows
We will consider the dynamics of passive tracers in a system of
three point vortices and in an array of vortices. These dynamics are all
particular examples of chaotic advection. This phenomenon has fundamental
implication in various physical systems. On large scales one may for instance
think as plasma physics (confinement), geophysical flows (pollution). But
also on a much smaller scale for micro-fluidic devices, for which chaotic
advection seems to be the best candidate in order to trigger mixing wihtout
breaking anything. For the point vortex flow some motivation of the choice
of the flow and the dynamics of vortices will be given. Then transport
properties of the tracers will be discussed and the anomalous effects induced
by the stickiness around regular islands presented.
While for the array of vortices I will present a way to perturb the flow in
order to enhence mixing while limiting transport.