{"id":750,"date":"2021-03-22T12:39:12","date_gmt":"2021-03-22T12:39:12","guid":{"rendered":"https:\/\/casm.lums.edu.pk\/?p=750"},"modified":"2021-03-22T12:39:14","modified_gmt":"2021-03-22T12:39:14","slug":"simulating-nonlinear-faraday-waves-on-a-cylinder","status":"publish","type":"post","link":"https:\/\/casm.lums.edu.pk\/index.php\/2021\/03\/22\/simulating-nonlinear-faraday-waves-on-a-cylinder\/","title":{"rendered":"Simulating Nonlinear Faraday Waves on a Cylinder"},"content":{"rendered":"\n

By Dr.\u00a0Saad Qadeer\u00a0<\/strong><\/p>\n\n\n\n

Time: 3.00 pm –\u00a0 4:00\u00a0pm.<\/strong><\/p>\n\n\n\n

Day: Wednesday ,\u00a0December\u00a012\u00a0,\u00a02018.<\/strong><\/p>\n\n\n\n

Venue: A2- Academic Block, LUMS<\/strong><\/p>\n\n\n\n

 Abstract<\/strong><\/p>\n\n\n\n

In 1831, Faraday observed the formation of standing waves on the surface of a vibrating fluid body. Subsequent experiments have revealed the existence of a rich tapestry of patterned states that can be accessed by varying the frequency and amplitude of the vibration and have spurredvast research in hydrodynamics and pattern formation. These include linear analyses to determine the conditions for the onset of the patterns, weakly nonlinear studies to understand pattern selection and dynamical systems approaches to study mode competition and chaos. Recently, there has been some work towards numerical simulations in various three-dimensional geometries. These methods however possess low orders of accuracy, making them unsuitable for nonlinear regimes.<\/p>\n\n\n\n

We present a technique for fast and accurate simulations of\u00a0nonlinear\u00a0Faraday waves in a cylinder. Beginning from the viscous\u00a0potential flow model of Dias et al, we generalize the Transformed Field Expansion to this geometry for finding the highly non-local Dirichlet-to-Neumann map for the Laplace equation. A spectral method relying on Zernike polynomials is developed to rapidly and\u00a0accurately compute the bulk potential. The free surface evolution equations are solved in time using fourth-order Runge-Kutta and refined to a high order by Picard iterations. The results are in perfect agreement with the instability thresholds and surface\u00a0patterns predicted for the linearized problem. The\u00a0nonlinear\u00a0simulations reproduce several qualitative features observed experimentally. In addition, by enabling one to switch between various\u00a0nonlinear\u00a0regimes, the technique allows a precise determination of\u00a0the mechanisms triggering various experimental observations.\u00a0<\/p>\n\n\n\n

About the Speaker<\/em><\/strong><\/p>\n\n\n\n

Saad Qadeer is a postdoctoral researcher at UNC Chapel Hill working with Greg Forest and Boyce Griffith. He obtained his PhD in Applied Mathematics from UC Berkeley in 2018 under the supervision of Jon Wilkening. Prior to that, he did his undergraduate work at LUMS and received his BS Mathematics with high honors in 2013.<\/p>\n","protected":false},"excerpt":{"rendered":"

By Dr.\u00a0Saad Qadeer\u00a0 Time: 3.00 pm –\u00a0 4:00\u00a0pm. Day: Wednesday ,\u00a0December\u00a012\u00a0,\u00a02018. Venue: A2- Academic Block, LUMS  Abstract In 1831, Faraday observed the formation of standing waves on the surface of a vibrating fluid body. Subsequent experiments have revealed the existence of a rich tapestry of patterned states that can be accessed by varying the frequency and amplitude …<\/p>\n

Simulating Nonlinear Faraday Waves on a Cylinder<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[10],"tags":[],"_links":{"self":[{"href":"https:\/\/casm.lums.edu.pk\/index.php\/wp-json\/wp\/v2\/posts\/750"}],"collection":[{"href":"https:\/\/casm.lums.edu.pk\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/casm.lums.edu.pk\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/casm.lums.edu.pk\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/casm.lums.edu.pk\/index.php\/wp-json\/wp\/v2\/comments?post=750"}],"version-history":[{"count":1,"href":"https:\/\/casm.lums.edu.pk\/index.php\/wp-json\/wp\/v2\/posts\/750\/revisions"}],"predecessor-version":[{"id":751,"href":"https:\/\/casm.lums.edu.pk\/index.php\/wp-json\/wp\/v2\/posts\/750\/revisions\/751"}],"wp:attachment":[{"href":"https:\/\/casm.lums.edu.pk\/index.php\/wp-json\/wp\/v2\/media?parent=750"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/casm.lums.edu.pk\/index.php\/wp-json\/wp\/v2\/categories?post=750"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/casm.lums.edu.pk\/index.php\/wp-json\/wp\/v2\/tags?post=750"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}