v1.4.4

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Documentation

An introduction to time-dependent dynamical systems and a brief description of ManGen and its graphical user interface can be found in F. Lekien, Time-Dependent Dynamical Systems and Geophysical Flows, Ph.D. Thesis, California Institute of Technology, March 12, 2003 Recently, Shawn Shadden presented a tutorial about Lagrangian coherent structures that includes step-by-step instructions to compute LCS at the surface of an airfoil with ManGen. In addition, the following papers provide details about some components of ManGen or describe a particular application. The simulations presented in these papers can be reproduced using ManGen 1.4.3: F. Lekien, C. Coulliette, A.J. Mariano, E.H. Ryan, L.K. Shay, G. Haller, J.E. Marsden, Pollution Release Tied to Invariant Manifolds: A case Study for the Coast of Florida, Physica D, 210(1-2), pp 1--20, 2005 S.C. Shadden, F. Lekien, J.E. Marsden, Definition and Properties of Lagrangian Coherent Structures from Finite-Time Lyapunov Exponents in Two-Dimensional Aperiodic Flows, Physica D, 212(3-4), pp 271--304, 2005 M. Dellnitz, O. Junge, W.S. Koon, F. Lekien, M.W. Lo, J.E. Marsden, K. Padberg, R. Preis, S.D. Ross, B. Thiere, Transport in Dynamical Astronomy and Multibody Problems, Intern. J. of Bifurcation and Chaos, 15(3), pp 699--727, 2005 F. Lekien, J.E. Marsden, Tricubic Interpolation in Three Dimensions, International Journal for Numerical Methods in Engineering, 63 (3), pp 455--471, 2005 F. Lekien, N. Leonard, Dynamically Consistent Lagrangian Coherent Structures, in American Inst. of Physics: 8th Experimental Chaos Conference, CP 742, pp 132--139, 2004 F. Lekien, C. Coulliette, J. Marsden, Lagrangian Structures in Very High-Frequency Radar Data and Optimal Pollution Timing, in American Inst. of Physics: 7th Experimental Chaos Conference, CP 676, pp 162--168, 2003 F. Lekien, Time-Dependent Dynamical Systems and Geophysical Flows, Ph.D. Thesis, California Institute of Technology, March 12, 2003 ManGen reads a configuration file (or "mangen.in" file) to determine what has to be computed and what velocity field is provided. If you are experiencing trouble using an existing "*.in" file or creating your own, please contact Francois Lekien

 

Download

All packages contain the source code and information to install ManGen. Version 1.0 contains a Windows installer inside the archive as well as examples. A compiled version 1.4.4 for Windows was provided by Shawn Shadden and is included in the archive. Version Size Format Source Binaries 1.4.4 28 Mb 53 kb ZIP Arch. 1.4.4 28 Mb 9 kb Gzipped Tar 1.4.3d 25 Mb 845 kb ZIP Arch. 1.4.3d 19 Mb 584 kb Gzipped Tar 1.4.3c 19 Mb 584 kb Gzipped Tar 1.0b 156 Mb 1022 kb ZIP Arch. Below are additional downloads to operate ManGen in real-time. The first succesfull real-time operation took place during the AOSN project. The output of a real-time simulations can be tracked on my Caltech web page. Version Size Format Source Binaries Real-Time Server 2.0 580 kb 675 bytes Gzipped Tar Real-Time Client 2.0 5 kb 895 bytes C++ source N/A Below is a bundle containing MANGEN 1.4.6 source code, real-time server and client. The archive also contains data to simulate a real-time LCS computation in Monterey Bay (based on CODAR HF Radar data and HOPS Ocean model). This system was installed at the Jet Propulsion Laboratory. The result of such simulation can be tracked on the MANGEN Real-Time Page. Version Size Format Source Binaries 1.4.6 [JPL] 192 Mb 314 kb Tar.Gz 1.4.6 [JPL] 193 Mb 961 kb Gzipped Tar 1.4.6 [JPL] 196 Mb 282 kb Zip Arch.

 

Examples

Monterey Bay, August 2003 The modes, configuration files and resulting nowcasts for Monterey Bay in August 2003 can be found in the source section of F. Lekien, C. Coulliette, R. Bank, J. Marsden, Open-Boundary Modal Analysis: Interpolation, Extrapolation, and Filtering, J. of Geophysical Research -- Oceans, 109, C12004, 2004 Monterey Bay, California ManGen was originally developped to study the flow field in Monterey Bay, CA. In particular, the time-dependent flow exhibits a strong separation near Point Pinos (Monterey Peninsula). A generalized stable manifold (e.g., a repulsive Lagrangian coherent structure) emanates from the peninsula and separates the bay into two regions: recirculating fluids and oceanic region. An example of such an analysis based on high-frequency radar data can be found in F. Lekien, N. Leonard, Dynamically Consistent Lagrangian Coherent Structures, in American Inst. of Physics: 8th Experimental Chaos Conference, CP 742, pp 132--139, 2004. ManGen is used to interpolate, extrapolate and compute the finite-time Lyapunov exponents and Lagrangian coherent structures. Data and configuration files for Monterey Bay can be found in the Windows Installer of ManGen 1.0b or on the page dedicated to LeLe04. Fort Lauderdale, Florida coastline Arthur Mariano et. al. obtained sub-mesoscale footprints of the currents of the coast of Florida using very high frequency radar stations. ManGen reveals a moving separation structure attached to the coastline between Fort Lauderdale and Hollywood Beach, FL. Details, data and ManGen configuration files can be found on the page dedicated to F. Lekien, C. Coulliette, A.J. Mariano, E.H. Ryan, L.K. Shay, G. Haller, J.E. Marsden, Pollution Release Tied to Invariant Manifolds: A case Study for the Coast of Florida, Physica D, 210(1-2), pp 1--20, 2005. Properties of Lagrangian Coherent Structures (LCS) Lagrangian Coherent Structures (or LCS) are defined as ridges of the finite-time Lyapunov exponent field that ManGen computes. In S.C. Shadden, F. Lekien, J.E. Marsden, Definition and Properties of Lagrangian Coherent Structures from Finite-Time Lyapunov Exponents in Two-Dimensional Aperiodic Flows, Physica D, 212(3-4), pp 271--304, 2005, we show that the LCS are quasi-Lagrangian. In other words, they are not strictly invariant manifolds but behave very much like it. The results are illustrated by the computation of the flux of particles accross some LCS. The configuration file to compute and the high-resolution LCS with ManGen and corresponding sample field can be dowloaded at ShLeMa05. Separation at the surface of an airfoil ManGen is not restricted to geophysical flows and can be used for any fluid flows. Recently, Shawn Shadden posted data and configuration files to study DLE and LCS at the surface of an airfoil. These materials can be downloaded on the page for S.C. Shadden, F. Lekien, J.E. Marsden, Definition and Properties of Lagrangian Coherent Structures from Finite-Time Lyapunov Exponents in Two-Dimensional Aperiodic Flows, Physica D, 212(3-4), pp 271--304, 2005. A tutorial on how to use these files and interpret the results is also available in Shawn's LCS tutorial. Preliminary results on how to control the separation profile by using two actuators can be found in F. Lekien, T. Insperger, G. Stepan, H. Salman, G. Haller, Control of Separation in Two-Dimensional Flows, Automatica, (submitted), 2006. Three-Body Problems and Dynamical Astronomy Mangen and GAIO are combined in M. Dellnitz, O. Junge, W.S. Koon, F. Lekien, M.W. Lo, J.E. Marsden, K. Padberg, R. Preis, S.D. Ross, B. Thiere, Transport in Dynamical Astronomy and Multibody Problems, Intern. J. of Bifurcation and Chaos, 15(3), pp 699--727, 2005 to study transport in the restricted three-body problem. Transport is studied in terms of lobes bringing particles from the planetary realm to the interior realm.

 

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