Аннотация:
Lobe dynamics and escape from a potential well are general frameworks introduced
to study phase space transport in chaotic dynamical systems.While the former approach studies
how regions of phase space get transported by reducing the flow to a two-dimensional map, the
latter approach studies the phase space structures that lead to critical events by crossing certain
barriers. Lobe dynamics describes global transport in terms of lobes, parcels of phase space
bounded by stable and unstable invariant manifolds associated to hyperbolic fixed points of the
system. Escape from a potential well describes how the critical events occur and quantifies the
rate of escape using the flux across the barriers. Both of these frameworks require computation
of curves, intersection points, and the area bounded by the curves. We present a theory for
classification of intersection points to compute the area bounded between the segments of the
curves. This involves the partition of the intersection points into equivalence classes to apply
the discrete form of Green’s theorem. We present numerical implementation of the theory, and
an alternate method for curves with nontransverse intersections is also presented along with a
method to insert points in the curve for densification.
Образец цитирования:
Shibabrat Naik, Francois Lekien, Shane D. Ross, “Computational Method for Phase Space Transport with Applications to Lobe Dynamics and Rate of Escape”, Regul. Chaotic Dyn., 22:3 (2017), 272–297
\RBibitem{NaiLekRos17}
\by Shibabrat Naik, Francois Lekien, Shane D. Ross
\paper Computational Method for Phase Space Transport with Applications to Lobe Dynamics and Rate of Escape
\jour Regul. Chaotic Dyn.
\yr 2017
\vol 22
\issue 3
\pages 272--297
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\crossref{https://doi.org/10.1134/S1560354717030078}
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Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd257
https://www.mathnet.ru/rus/rcd/v22/i3/p272
Эта публикация цитируется в следующих 6 статьяx:
Naoki Hiraiwa, Mai Bando, Isaia Nisoli, Yuzuru Sato, “Designing robust trajectories by lobe dynamics in low-dimensional Hamiltonian systems”, Phys. Rev. Research, 6:2 (2024)
Albert Jarvis, Ali Hossein Mardi, Hosein Foroutan, Shane D. Ross, “Atmospheric transport structures shaping the “Godzilla” dust plume”, Atmospheric Environment, 333 (2024), 120638
Priyanka Pandey, Shibabrat Naik, Srihari Keshavamurthy, “Classical and Quantum Dynamical Manifestations of Index-2
Saddles: Concerted Versus Sequential Reaction Mechanisms”, Regul. Chaotic Dyn., 26:2 (2021), 165–182
M. Wang, J. M. Ottino, R. M. Lueptow, P. B. Umbanhowar, “Particle capture in a model chaotic flow”, Phys. Rev. E, 104:6 (2021), 064203
Sh. Naik, S. Wiggins, “Detecting reactive islands in a system-bath model of isomerization”, Phys. Chem. Chem. Phys., 22:32 (2020), 17890–17912
J. Zhong, Sh. D. Ross, “Geometry of escape and transition dynamics in the presence of dissipative and gyroscopic forces in two degree of freedom systems”, Commun. Nonlinear Sci. Numer. Simul., 82 (2020), 105033