In applied mathematics, Arnold diffusion is the phenomenon of instability of integrable Hamiltonian systems. The phenomenon is named after Vladimir Arnold who was the first to publish a result in the field in 1964. More precisely, Arnold diffusion refers to results asserting the existence of solutions to nearly integrable Hamiltonian systems that exhibit a significant change in the action variables. Arnold diffusion describes the diffusion of trajectories due to the ergodic theorem in a portion of phase space unbound by any constraints (i.e. unbounded by Lagrangian tori arising from constants of motion) in Hamiltonian systems. It occurs in systems with more than N=2 degrees of freedom, since the N-dimensional invariant tori do not separate the 2N-1 dimensional phase space any more. Thus, an arbitrarily small perturbation may cause a number of trajectories to wander pseudo-randomly through the whole portion of phase space left by the destroyed tori. (Wikipedia).
Some geometric mechanisms for Arnold diffusion - Rafael de la Llave
Emerging Topics Working Group Topic: Some geometric mechanisms for Arnold diffusion Speaker: Rafael de la Llave Affiliation: Georgia Tech Date: April 10, 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Arnold diffusion for `complete' families of perturbations with... - Amadeu Delshams
Emerging Topics Working Group Topic: Arnold diffusion for `complete' families of perturbations with two or three independent harmonics Speaker: Amadeu Delshams Affiliation: UPC Date: April 9, 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
A wave spreading from a vertical strip in the reduced non-oscillatory Edblom-Orban-Epstein model of reaction-diffusion, from equation 8.8 of Robin Engelhardt's master's thesis: http://www.robinengelhardt.info/speciale/ Generated by the open-source program: http://code.google.com/p/reac
From playlist Ready
Arnold Diffusion via Normally Hyperbolic Invariant Cylinders and...Method, Part I - Vadim Kaloshin
Vadim Kaloshin Pennsylvania State University; Member, School of Mathematics March 7, 2012 In 1964 Arnold constructed an example of instabilities for nearly integrable systems and conjectured that generically this phenomenon takes place. There has been big progress attacking this conjecture
From playlist Mathematics
Arnold Diffusion via Normally Hyperbolic Invariant Cylinders... Part II - Ke Zhang
Ke Zhang Institute for Advanced Study March 21, 2012 In 1964 Arnold constructed an example of instabilities for nearly integrable systems and conjectured that generically this phenomenon takes place. There has been big progress attacking this conjecture in the past decade. Jointly with Ke
From playlist Mathematics
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From playlist Biology
Diffusion and Osmosis - Passive and Active Transport With Facilitated Diffusion
This Biology video tutorial discusses diffusion and osmosis. It also mentions the difference between passive and active transport. Diffusion is the movement of any material down the concentration gradient. Osmosis is the diffusion of water. Facilitated diffusion is the movement of mate
From playlist Biology
Arnold Diffusion by Variational Methods - John Mather
John Mather Princeton University; Institute for Advanced Study October 26, 2011 For more videos, visit http://video.ias.edu
From playlist Mathematics
Arnold diffusion and Mather theory - Ke Zhang
Emerging Topics Working Group Topic: Arnold diffusion and Mather theory Speaker: Ke Zhang Affiliation: University of Toronto Date: April 11, 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Some questions around quasi-periodic dynamics – Bassam Fayad & Raphaël Krikorian – ICM2018
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John Mather Princeton University; Institute for Advanced Study November 9, 2011 For more videos, visit http://video.ias.edu
From playlist Mathematics
Jack Xin: "Lagrangian Approximations and Computations of Effective Diffusivities and Front Speed..."
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Stability and Instability of Near-Integrable Hamiltonian Systems - Abed Bounemoura
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From playlist Mathematics
Dynamical Glass by Sergej Flach
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From playlist Engineering
A wave spreading from a gap in the reduced non-oscillatory Edblom-Orban-Epstein model of reaction-diffusion, from equation 8.8 of Robin Engelhardt's master's thesis: http://www.robinengelhardt.info/speciale/ Generated by the open-source program: http://code.google.com/p/reaction-diffus
From playlist Ready