{"id":285796,"date":"2016-09-28T02:00:00","date_gmt":"2016-09-27T23:00:00","guid":{"rendered":"http:\/\/www.fyysika.ee\/?guid=c15c4e29aef70bf0888ae81ae11b462e"},"modified":"2016-09-28T02:00:00","modified_gmt":"2016-09-27T23:00:00","slug":"random-walk-with-nonuniform-angular-distribution-biased-by-an-external-periodic-pulse","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=285796","title":{"rendered":"Random walk with nonuniform angular distribution biased by an external periodic pulse"},"content":{"rendered":"<p>We studied the motion of a random walker in two dimensions with nonuniform angular distribution<br \/>\nbiased by an external periodic pulse. Here, we analytically calculated the mean square displacement<br \/>\n(end-to-end distance of a walk after n time steps), without bias and with bias. We determined the<br \/>\naverage x -component of the final displacement of the walker. Interestingly, we noted that for a<br \/>\nparticular periodicity of the bias, this average x -component of the final displacement becomes<br \/>\napproximately zero. The average y -component of the final displacement is found to be zero for any<br \/>\nperodicity of the bias, and its reason can be attributed to the nature of the probability density<br \/>\nfunction of the angle (subtended by the displacement vector with the x -axis). These analytical<br \/>\nresults are also supported by computer simulations. The present study may be thought of as a model<br \/>\nfor arresting the bacterial motion (along a preferred direction) by an external per&#8230;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>We studied the motion of a random walker in two dimensions with nonuniform angular distribution<br \/>\nbiased by an external periodic pulse. Here, we analytically calculated the mean square displacement<br \/>\n(end-to-end distance of a walk after n time steps), wi&#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-285796","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\/285796","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=285796"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/285796\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=285796"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=285796"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=285796"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}