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on which I post my miscellaneous daily activities ===== to-do list===== 2009-07-17 - Produce Poincare section plots for EQ2 unstable manifold and P47p18 - Add functionality to DNS to terminate integration on a Poincare section - Write an ad-hoc program to translate localized solutions so they're s_xyz-symmetric about the center of the box - Center the snaking-bifurcation solutions and compute their eigenspectra - Review a PRE - Read/edit proof of n00bs. - Respond to queries about forcing functions in channelflow howto blog - Figure out why I can't converge past 1e-05 for traveling waves in x. Gotta be a bug. Should be able to get 3,4 done today. 1,2 will take a couple days. 5 will take a day, 6 a half day, 7 some hours. ===== unstable periodic orbits - University College of London ===== 2009-06-30 JFG: This page was world-readable, but I changed it to GTspring09-only. Agreed about Boghosian. I heard him talk about linear algebra algorithms on the Connection Machine when I was at los Alamos. I have the sinking feeling that Jonathan mentioned after reading Smeigel's thesis.... Lattice-Boltzmann is sub-optimal way to simulate Navier-Stokes, I think. Good for parellization, bad for discretization. I wonder if their solutions converge. This would seem to prove you right that is is computationally feasible to compute orbits variationally, in a spatio-temporally discretized search space. I should have been clearer in my earlier protestations that it was not feasible for //me// to do it in a time scale that either of us would be comfortable with. 2009-06-29. PC: this info is confidential, so I am putting it on a password protected page - move it wherever else you see fit, as long as it is not world-readable. Here is a talk that will be presented in Trieste end of July (I remember Boghosian as a smart guy): Author(s): L. Fazendeiro$^1$, B. M. Boghosian$^2$, P. V. Coveney$^1$, J. L{\"{a}}tt$^3$, S. Smith$^2$\\ Affiliation(s): $^1$ Centre for Computational Science, University College of London, 20 Gordon Street, London WC1H 0AJ, UK; $^2$ Department of Mathematics, Tufts University Bromfield-Pearson Hall, Medford, MA 02155, U.S.A.\\ $^3$ Institute of Mechanical Engineering, Ecole Polytechnique Federale de Lausanne CH-1015 Lausanne, Switzerland}\\ Email(s): l.fazendeiro@ucl.ac.uk, bruce.boghosian@tufts.edu, P.V.Coveney@ucl.ac.uk, jonas.latt@gmail.com, Spencer.Smith@tufts.edu\\ Position(s) of author(s)/presenter(s): PhD student (presenter/first author) Abstract text: "We present a novel algorithm for the identification of periodic orbits in differential equations. With this new approach, both space and time are parallelized, and a search procedure minimizes a functional simultaneously towards the trajectory of the orbit in phase space and its period. We discuss in detail the methodology followed for the identification of unstable periodic orbits (UPOs) in the Navier-Stokes equations (NSE) for incompressible viscous fluid flow, simulated using the lattice Boltzmann method. It has been known for quite some time that driven dissipative systems exhibit finite-dimensional attractors which are replete with UPOs. The attractors can be thought of as the closure of the set of all such UPOs. The UPOs in turn provide a countable sequence of trajectories from which dynamical averages can be extracted using the zeta function formalism. Averages thus obtained are not stochastic in nature, i.e., they do not suffer from the problem of having the statistical error decay as the inverse square root of the number of decorrelation times. In this presentation we discuss the numerical difficulties involved in the numerical relaxion procedure for systems with very many dimensions such as the NSE, and describe the application of the conjugate gradient method to the problem. Since this method requires the storage in memory of spacetime trajectories, huge computational resources are required, which places the work firmly in the emerging field of petascale grid computing. We present results obtained on the IBM BlueGene/P at the Argonne National Laboratory and on the Sun Constellation Linux Cluster at the Texas Advanced Computing Centre, two of the world's current largest resources for open science. Results of turbulent flow simulations are presented and discussed and preliminary periodic orbits are presented. The insights that the identification and classification of these UPOs are expected to bring to turbulence theories are discussed. ===== localized eqbs ===== 2009-06-11. PC: You might want to get in touch with [[http://www.mech.kth.se/~duguet/webpage.html|Yohann Duguet, KTH Stockholm]]. He has some interesting spatially localized equilibria for plane Couette. 2009-06-11. I have started examining spatially localized equilibria in collaboration with Tobias Schneider, who found them with Daniel Marinc and Bruno in Marinc's 2008 Master's thesis. Tobias has some interesting plans to continue this work; I am reproducing some continuations from Marinc's thesis, will attempt to continue around bifurcations and produce more solutions with different numbers of roll-streak pairs, upper branch solutions, etc. ===== computer upgrade ===== 2009-06-09. I ended the semester with my PACE account (10 GB) and home computer (180 GB) crammed with thousands of binary flow fields from time integrations and parametric continuations. The time integrations can be recomputed pretty easily, but parametric continuation is not cheap. So I decided to upgrade to larger disks at home, and a faster CPU while at it. After some research I settled on the AMD Phenom II 955 ($245). The Intel Core i7 920 ($280) is a faster chip, at least for single threaded applications (it boosts the clock speed when running just a single core), but according to the few scientific benchmarks I could find the i7 multicore scaling seems to be poorer than the Phenom II. Also, X58 motherboards for Core i7 are all > $200 high-end dual-graphics monsters, whereas for AMD I found a good $85 just-the-basics Gigabyte motherboard for AM3. I also trust AMD to keep putting out chips with good price/performance ratios, compared to Intel. So, here's my new rig 1 x ($245.00) CPU AMD|PH II X4 955 3.2G AM3 R $245.00 1 x ($64.99) MEM 2Gx2|GSK F3-12800CL9D-4GBNQ R $64.99 2 x ($94.99) HD 1T|WD 7K 32M SATA2 WD1001FALS $189.98 1 x ($84.99) MB GIGABYTE | GA-MA770T-UD3P AMD770 $84.99 1 x ($29.99) A64 COOLER |ARCTIC FREEZER 64 PRO R $29.99 totalling some $600. I used my current Lian-Li aluminum case, DVD burner, power supply, graphics card, etc. The new computer is up and running (opensuse-11.1). Each core is about twice as fast as the cores in my old Athlon X2 4200+ and my Core 2 Duo laptop, and it has 4 cores instead of 2. I have the disks on RAID-1 (mirroring) and 870 GB is devoted to my home directory. Backups are onto a 500 GB external USB drive, automated daily/weekly/monthly snapshots with rsnapshot. I will soon have to modify my backup scripts so that data-* directories (time integrations) are left out. My old ASUS motherboard, memory, and Athlon X2 cpu are going to my buddy David Johnston in Chicago.
