{"id":5051,"date":"2017-04-03T06:08:00","date_gmt":"2017-04-03T06:08:00","guid":{"rendered":"http:\/\/thales.mit.edu\/bush\/?p=5051"},"modified":"2021-04-15T02:08:35","modified_gmt":"2021-04-15T02:08:35","slug":"simulations-of-pilot-wave-dynamics-in-a-simple-harmonic-potential","status":"publish","type":"post","link":"https:\/\/thales.mit.edu\/bush\/index.php\/2017\/04\/03\/simulations-of-pilot-wave-dynamics-in-a-simple-harmonic-potential\/","title":{"rendered":"Walker motion in a spring force"},"content":{"rendered":"\n
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The simulated form of pilot-wave hydrodynamics arising when a walker is confined by a central spring force, leading to orbits quantized in both radius (energy) and angular momentum.<\/figcaption><\/figure>\n\n\n\n

We present the results of a numerical investigation of droplets walking in a harmonic potential on a vibrating fluid bath. The droplet\u2019s trajectory is described by an integro-differential equation, which is simulated numerically in various parameter regimes. We produce a regime diagram that summarizes the dependence of the walker\u2019s behavior on the system parameters for a droplet of fixed size. At relatively low vibrational forcing, a number of periodic and quasiperiodic trajectories emerge. In the limit of large vibrational forcing, the walker\u2019s trajectory becomes chaotic, but the resulting trajectories can be decomposed into portions of unstable quasiperiodic states.<\/p>\n\n\n\n

See paper: Kurianski, K.M., Oza, A.U. and Bush, J.W.M., Physical Review Fluids<\/em> (2017)<\/a>.<\/p>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":5,"featured_media":5053,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[15,3],"tags":[],"class_list":["post-5051","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-hydrodynamic-quantum-analogues","category-pilot-wave-hydrodynamics","entry"],"yoast_head":"\nWalker motion in a spring force - John W. M. Bush<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/thales.mit.edu\/bush\/index.php\/2017\/04\/03\/simulations-of-pilot-wave-dynamics-in-a-simple-harmonic-potential\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Walker motion in a spring force - John W. M. Bush\" \/>\n<meta property=\"og:url\" content=\"https:\/\/thales.mit.edu\/bush\/index.php\/2017\/04\/03\/simulations-of-pilot-wave-dynamics-in-a-simple-harmonic-potential\/\" \/>\n<meta property=\"og:site_name\" content=\"John W. M. 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