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Equilibria, periodic orbits and computing them

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arxiv 1908.06730 v2 pith:YVM6FPMO submitted 2019-08-09 physics.flu-dyn

classification physics.flu-dyn
keywords codemethodorbitsperiodicappliedequilibriafindflow
verification ladder T0 review T1 audit T2 compute T3 formal
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In this short exposition, we describe equilibria and periodic orbits in terms of the flow map, {\Phi}, and discuss the essentials of the Jacobian-free Newton-Krylov (JFNK) method that can be used to find them. This method requires little more than calls to an existing time stepping code, which {\Phi} can be considered to represent. Fortran90 / MATLAB code is available to try it out for yourself, where, in the template/example the method is applied to the Lorenz system. This code is problem-independent and can be applied to large systems, having initially been developed to find periodic orbits in simulations of pipe flow.

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Cited by 2 Pith papers

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    Using a 3D far-field potential-flow model, the authors show that passive hydrodynamic interactions can keep small swimmer groups together, while large groups break into smaller cohesive subgroups and the circular hydr...

  2. Numerical solutions of fixed points in two-dimensional Kuramoto-Sivashinsky equation expedited by reinforcement learning

    cs.LG 2024-12 conditional novelty 5.0 of 10

    A DRL-assisted Jacobian-Free Newton-Krylov method finds 303 fixed points of the 2D Kuramoto-Sivashinsky equation on a 20x20 periodic domain.

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