{"id":5020,"date":"2017-04-03T04:16:00","date_gmt":"2017-04-03T04:16:00","guid":{"rendered":"http:\/\/thales.mit.edu\/bush\/?p=5020"},"modified":"2021-04-15T04:15:23","modified_gmt":"2021-04-15T04:15:23","slug":"tunneling-with-a-hydrodynamic-pilot-wave-model","status":"publish","type":"post","link":"https:\/\/thales.mit.edu\/bush\/index.php\/2017\/04\/03\/tunneling-with-a-hydrodynamic-pilot-wave-model\/","title":{"rendered":"Walkers tunnel: numerics"},"content":{"rendered":"\n
\n
\"\"
Numerical simulation of a drop tunneling across a submerged obstacle.<\/figcaption><\/figure>\n\n\n\n

Eddi et al. (2009) presented experimental results demonstrating the unpredictable tunneling of a classical wave-particle association as may arise when a droplet walking across the surface of a vibrating fluid bath approaches a submerged barrier. We here present a theoretical model that captures the influence of bottom topography on this wave-particle association and so enables us to investigate its interaction with barriers. The coupledwave-droplet dynamics results in unpredictable tunneling events. As reported in the experiments by Eddi et al. and as is the case in quantum tunneling [Gamow, Nature (London) 122, 805 (1928)], the predicted tunneling probability decreases exponentially with increasing barrier width. In the parameter regimes examined, tunneling between two cavities suggests an underlying stationary ergodic process for the droplet\u2019s position.<\/p>\n\n\n\n

See paper: Nachbin, A., Milewski, P.A. 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":5022,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[15,3],"tags":[],"class_list":["post-5020","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-hydrodynamic-quantum-analogues","category-pilot-wave-hydrodynamics","entry"],"yoast_head":"\nWalkers tunnel: numerics - 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\/tunneling-with-a-hydrodynamic-pilot-wave-model\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Walkers tunnel: numerics - John W. M. Bush\" \/>\n<meta property=\"og:url\" content=\"https:\/\/thales.mit.edu\/bush\/index.php\/2017\/04\/03\/tunneling-with-a-hydrodynamic-pilot-wave-model\/\" \/>\n<meta property=\"og:site_name\" content=\"John W. M. Bush\" \/>\n<meta property=\"article:published_time\" content=\"2017-04-03T04:16:00+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2021-04-15T04:15:23+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2021\/04\/TunnelNach-thumb.png\" \/>\n\t<meta property=\"og:image:width\" content=\"456\" \/>\n\t<meta property=\"og:image:height\" content=\"444\" \/>\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\/2017\/04\/03\/tunneling-with-a-hydrodynamic-pilot-wave-model\/#primaryimage\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2021\/04\/TunnelNach-thumb.png\",\"contentUrl\":\"https:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2021\/04\/TunnelNach-thumb.png\",\"width\":456,\"height\":444},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/thales.mit.edu\/bush\/index.php\/2017\/04\/03\/tunneling-with-a-hydrodynamic-pilot-wave-model\/#webpage\",\"url\":\"https:\/\/thales.mit.edu\/bush\/index.php\/2017\/04\/03\/tunneling-with-a-hydrodynamic-pilot-wave-model\/\",\"name\":\"Walkers tunnel: numerics - John W. M. Bush\",\"isPartOf\":{\"@id\":\"https:\/\/thales.mit.edu\/bush\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/thales.mit.edu\/bush\/index.php\/2017\/04\/03\/tunneling-with-a-hydrodynamic-pilot-wave-model\/#primaryimage\"},\"datePublished\":\"2017-04-03T04:16:00+00:00\",\"dateModified\":\"2021-04-15T04:15:23+00:00\",\"author\":{\"@id\":\"https:\/\/thales.mit.edu\/bush\/#\/schema\/person\/a9fe68c435ef049a3b089b5bb46446b1\"},\"breadcrumb\":{\"@id\":\"https:\/\/thales.mit.edu\/bush\/index.php\/2017\/04\/03\/tunneling-with-a-hydrodynamic-pilot-wave-model\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/thales.mit.edu\/bush\/index.php\/2017\/04\/03\/tunneling-with-a-hydrodynamic-pilot-wave-model\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/thales.mit.edu\/bush\/index.php\/2017\/04\/03\/tunneling-with-a-hydrodynamic-pilot-wave-model\/#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\/2017\/04\/03\/tunneling-with-a-hydrodynamic-pilot-wave-model\/#webpage\"}}]},{\"@type\":\"Person\",\"@id\":\"https:\/\/thales.mit.edu\/bush\/#\/schema\/person\/a9fe68c435ef049a3b089b5bb46446b1\",\"name\":\"John WM Bush\",\"url\":\"https:\/\/thales.mit.edu\/bush\/index.php\/author\/bush\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","_links":{"self":[{"href":"https:\/\/thales.mit.edu\/bush\/index.php\/wp-json\/wp\/v2\/posts\/5020","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/thales.mit.edu\/bush\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/thales.mit.edu\/bush\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/thales.mit.edu\/bush\/index.php\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/thales.mit.edu\/bush\/index.php\/wp-json\/wp\/v2\/comments?post=5020"}],"version-history":[{"count":6,"href":"https:\/\/thales.mit.edu\/bush\/index.php\/wp-json\/wp\/v2\/posts\/5020\/revisions"}],"predecessor-version":[{"id":6861,"href":"https:\/\/thales.mit.edu\/bush\/index.php\/wp-json\/wp\/v2\/posts\/5020\/revisions\/6861"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/thales.mit.edu\/bush\/index.php\/wp-json\/wp\/v2\/media\/5022"}],"wp:attachment":[{"href":"https:\/\/thales.mit.edu\/bush\/index.php\/wp-json\/wp\/v2\/media?parent=5020"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/thales.mit.edu\/bush\/index.php\/wp-json\/wp\/v2\/categories?post=5020"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/thales.mit.edu\/bush\/index.php\/wp-json\/wp\/v2\/tags?post=5020"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}