{"id":608065,"date":"2017-10-24T02:00:00","date_gmt":"2017-10-23T23:00:00","guid":{"rendered":"http:\/\/www.fyysika.ee\/?guid=35087138c89117ccad6dd7dac0cf9533"},"modified":"2017-10-24T02:00:00","modified_gmt":"2017-10-23T23:00:00","slug":"langevin-equation-with-time-dependent-linear-force-and-periodic-load-force-stochastic-resonance","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=608065","title":{"rendered":"Langevin equation with time dependent linear force and periodic load force: stochastic resonance"},"content":{"rendered":"<p>The motion of a particle described by the Langevin equation with constant diffusion coefficient,<br \/>\ntime dependent linear force ( ##IMG##<br \/>\n[http:\/\/ej.iop.org\/images\/0143-0807\/38\/6\/065104\/ejpaa8d54ieqn1.gif] {$\\omega (1+\\alpha \\cos ({\\omega<br \/>\n}_{1}t))x$} ) and periodic load force ( ##IMG##<br \/>\n[http:\/\/ej.iop.org\/images\/0143-0807\/38\/6\/065104\/ejpaa8d54ieqn2.gif] {${A}_{0}\\cos ({\\rm{\\Omega<br \/>\n}}t)$} ) is investigated. Analytical solutions for the probability density function (PDF) and n<br \/>\n-moment are obtained and analysed. For ##IMG##<br \/>\n[http:\/\/ej.iop.org\/images\/0143-0807\/38\/6\/065104\/ejpaa8d54ieqn3.gif] {${\\omega }_{1}\\gg \\alpha \\omega<br \/>\n$} the influence of the periodic term ##IMG##<br \/>\n[http:\/\/ej.iop.org\/images\/0143-0807\/38\/6\/065104\/ejpaa8d54ieqn4.gif] {$\\alpha \\cos ({\\omega }_{1}t)$}<br \/>\nis negligible to the PDF and n -moment for any time; this result shows that the statistical averages<br \/>\nsuch as n -moments a&#8230;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The motion of a particle described by the Langevin equation with constant diffusion coefficient,<br \/>\ntime dependent linear force ( ##IMG##<br \/>\n[http:\/\/ej.iop.org\/images\/0143-0807\/38\/6\/065104\/ejpaa8d54ieqn1.gif] {$\\omega (1+\\alpha \\cos ({\\omega<br \/>\n}_{1}t))x$} )&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[178],"tags":[],"class_list":{"0":"post-608065","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-rss-fuusikaharidus","7":"entry"},"_links":{"self":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/608065","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=608065"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/608065\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=608065"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=608065"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=608065"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}