{"id":4869,"date":"2018-06-01T05:35:00","date_gmt":"2018-06-01T05:35:00","guid":{"rendered":"http:\/\/thales.mit.edu\/bush\/?p=4869"},"modified":"2021-04-15T04:11:03","modified_gmt":"2021-04-15T04:11:03","slug":"a-review-of-the-theoretical-modeling-of-walking-droplets-toward-a-generalized-pilot-wave-framework","status":"publish","type":"post","link":"http:\/\/thales.mit.edu\/bush\/index.php\/2018\/06\/01\/a-review-of-the-theoretical-modeling-of-walking-droplets-toward-a-generalized-pilot-wave-framework\/","title":{"rendered":"Toward a generalized pilot-wave theory"},"content":{"rendered":"\n<div class=\"wp-block-cover alignwide has-purple-background-color has-background-dim\"><div class=\"wp-block-cover__inner-container is-layout-flow wp-block-cover-is-layout-flow\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"762\" height=\"370\" src=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2021\/04\/Turton2.png\" alt=\"\" class=\"wp-image-4870\"\/><figcaption>A millimetric drop self-propels across a vibrating fluid bath, propelled by its own wave field.<\/figcaption><\/figure>\n\n\n\n<p class=\"tw-text-wide has-extra-small-font-size\">The walking droplet system has extended the range of classical systems to include several features previously thought to be exclusive to quantum systems. We review the hierarchy of analytic models that have been developed, on the basis of various simplifying assumptions, to describe droplets walking on a vibrating fluid bath. Particular attention is given to detailing their successes and failures in various settings. Finally, we present a theoretical model that may be adopted to explore a more generalized pilot-wave framework capable of further extending the phenomenological range of classical pilot-wave systems beyond that achievable in the laboratory.<\/p>\n\n\n\n<p class=\"tw-text-wide has-small-font-size\">See paper:  <a href=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2021\/04\/Turton-Chaos2018.pdf\" data-type=\"URL\" data-id=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2021\/04\/Turton-Chaos2018.pdf\">Turton, S.E., Couchman, M.M.P. and Bush, J.W.M., <em>Chaos<\/em> (2018)<\/a><\/p>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":5,"featured_media":4871,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[14,3],"tags":[],"class_list":["post-4869","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-pilot-wave-theory","category-pilot-wave-hydrodynamics","entry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v16.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Toward a generalized pilot-wave theory - 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\/2018\/06\/01\/a-review-of-the-theoretical-modeling-of-walking-droplets-toward-a-generalized-pilot-wave-framework\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Toward a generalized pilot-wave theory - John W. M. Bush\" \/>\n<meta property=\"og:url\" content=\"https:\/\/thales.mit.edu\/bush\/index.php\/2018\/06\/01\/a-review-of-the-theoretical-modeling-of-walking-droplets-toward-a-generalized-pilot-wave-framework\/\" \/>\n<meta property=\"og:site_name\" content=\"John W. M. Bush\" \/>\n<meta property=\"article:published_time\" content=\"2018-06-01T05:35:00+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2021-04-15T04:11:03+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2021\/04\/Turton.png\" \/>\n\t<meta property=\"og:image:width\" content=\"586\" \/>\n\t<meta property=\"og:image:height\" content=\"562\" \/>\n<meta name=\"twitter:card\" content=\"summary\" \/>\n<meta name=\"twitter:label1\" content=\"Est. reading time\">\n\t<meta name=\"twitter:data1\" content=\"1 minute\">\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebSite\",\"@id\":\"https:\/\/thales.mit.edu\/bush\/#website\",\"url\":\"https:\/\/thales.mit.edu\/bush\/\",\"name\":\"John W. M. Bush\",\"description\":\"Professor of Applied Mathematics, MIT\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":\"https:\/\/thales.mit.edu\/bush\/?s={search_term_string}\",\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/thales.mit.edu\/bush\/index.php\/2018\/06\/01\/a-review-of-the-theoretical-modeling-of-walking-droplets-toward-a-generalized-pilot-wave-framework\/#primaryimage\",\"inLanguage\":\"en-US\",\"url\":\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2021\/04\/Turton.png\",\"contentUrl\":\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2021\/04\/Turton.png\",\"width\":586,\"height\":562},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/thales.mit.edu\/bush\/index.php\/2018\/06\/01\/a-review-of-the-theoretical-modeling-of-walking-droplets-toward-a-generalized-pilot-wave-framework\/#webpage\",\"url\":\"https:\/\/thales.mit.edu\/bush\/index.php\/2018\/06\/01\/a-review-of-the-theoretical-modeling-of-walking-droplets-toward-a-generalized-pilot-wave-framework\/\",\"name\":\"Toward a generalized pilot-wave theory - John W. M. Bush\",\"isPartOf\":{\"@id\":\"https:\/\/thales.mit.edu\/bush\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/thales.mit.edu\/bush\/index.php\/2018\/06\/01\/a-review-of-the-theoretical-modeling-of-walking-droplets-toward-a-generalized-pilot-wave-framework\/#primaryimage\"},\"datePublished\":\"2018-06-01T05:35:00+00:00\",\"dateModified\":\"2021-04-15T04:11:03+00:00\",\"author\":{\"@id\":\"https:\/\/thales.mit.edu\/bush\/#\/schema\/person\/a9fe68c435ef049a3b089b5bb46446b1\"},\"breadcrumb\":{\"@id\":\"https:\/\/thales.mit.edu\/bush\/index.php\/2018\/06\/01\/a-review-of-the-theoretical-modeling-of-walking-droplets-toward-a-generalized-pilot-wave-framework\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/thales.mit.edu\/bush\/index.php\/2018\/06\/01\/a-review-of-the-theoretical-modeling-of-walking-droplets-toward-a-generalized-pilot-wave-framework\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/thales.mit.edu\/bush\/index.php\/2018\/06\/01\/a-review-of-the-theoretical-modeling-of-walking-droplets-toward-a-generalized-pilot-wave-framework\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"item\":{\"@type\":\"WebPage\",\"@id\":\"https:\/\/thales.mit.edu\/bush\/\",\"url\":\"https:\/\/thales.mit.edu\/bush\/\",\"name\":\"Home\"}},{\"@type\":\"ListItem\",\"position\":2,\"item\":{\"@id\":\"https:\/\/thales.mit.edu\/bush\/index.php\/2018\/06\/01\/a-review-of-the-theoretical-modeling-of-walking-droplets-toward-a-generalized-pilot-wave-framework\/#webpage\"}}]},{\"@type\":\"Person\",\"@id\":\"https:\/\/thales.mit.edu\/bush\/#\/schema\/person\/a9fe68c435ef049a3b089b5bb46446b1\",\"name\":\"John WM Bush\",\"url\":\"http:\/\/thales.mit.edu\/bush\/index.php\/author\/bush\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","_links":{"self":[{"href":"http:\/\/thales.mit.edu\/bush\/index.php\/wp-json\/wp\/v2\/posts\/4869","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/thales.mit.edu\/bush\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/thales.mit.edu\/bush\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/thales.mit.edu\/bush\/index.php\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"http:\/\/thales.mit.edu\/bush\/index.php\/wp-json\/wp\/v2\/comments?post=4869"}],"version-history":[{"count":7,"href":"http:\/\/thales.mit.edu\/bush\/index.php\/wp-json\/wp\/v2\/posts\/4869\/revisions"}],"predecessor-version":[{"id":6856,"href":"http:\/\/thales.mit.edu\/bush\/index.php\/wp-json\/wp\/v2\/posts\/4869\/revisions\/6856"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/thales.mit.edu\/bush\/index.php\/wp-json\/wp\/v2\/media\/4871"}],"wp:attachment":[{"href":"http:\/\/thales.mit.edu\/bush\/index.php\/wp-json\/wp\/v2\/media?parent=4869"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/thales.mit.edu\/bush\/index.php\/wp-json\/wp\/v2\/categories?post=4869"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/thales.mit.edu\/bush\/index.php\/wp-json\/wp\/v2\/tags?post=4869"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}