{"id":442,"date":"2013-12-01T14:48:23","date_gmt":"2013-12-01T14:48:23","guid":{"rendered":"http:\/\/toschi.phys.tue.nl\/wordpress\/?p=442"},"modified":"2013-12-01T14:52:12","modified_gmt":"2013-12-01T14:52:12","slug":"chaos","status":"publish","type":"post","link":"https:\/\/toschi.phys.tue.nl\/wordpress\/chaos\/","title":{"rendered":"3T350 - Chaos"},"content":{"rendered":"
\n

This course is the continuation of 3T220 (Chaos), but now with a greater emphasis on the application of Chaos concepts to fluids. Chaos is the seemingly erratic behavior of simple deterministic, but nonlinear dynamical systems. We will first discuss the route to chaos, where we will already encounter the scaling concepts that will return in the description of chaotic fluid flow and turbulence. After a discussion of basic concepts, such as the sensitivity to variation in initial conditions, and the multifractal organization of phase space, we will introduce chaotic behavior and synchronization in coupled systems. These scaling ideas will then be carried over to the description of turbulence, the erratic flow of a fluid. We will do this in both the Eulerian and Lagrangian frame, where we move with the flow. While turbulence is wild chaos, also stirred viscous fluids may be chaotic, which may help to efficiently stir tracers. Also this case will be analyzed with the tools introduced in this course, such as local sensitivity to perturbations, and scaling of the concentration field of the stirred material. Central to the course is the exposure to the modern literature, in particular papers which appeared in Physical Review Letters (the most famous Physics journal). These papers can serve as inspiration for student presentations. Of course, adequate coaching is offered here.<\/p>\n<\/div>\n<\/div> ","protected":false},"excerpt":{"rendered":"

This course is the continuation of 3T220 (Chaos), but now with a greater emphasis on the application of Chaos concepts to fluids. Chaos is the seemingly erratic behavior of simple deterministic, but nonlinear dynamical systems. We will first discuss the route to chaos, where we will already encounter the scaling concepts that will return in […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_exactmetrics_skip_tracking":false,"_exactmetrics_sitenote_active":false,"_exactmetrics_sitenote_note":"","_exactmetrics_sitenote_category":0,"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[38],"tags":[],"class_list":["post-442","post","type-post","status-publish","format-standard","hentry","category-master"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/s6tiMI-chaos","jetpack_likes_enabled":true,"jetpack-related-posts":[{"id":805,"url":"https:\/\/toschi.phys.tue.nl\/wordpress\/3mt100-chaos\/","url_meta":{"origin":442,"position":0},"title":"3MT100 - Chaos","author":"toschi","date":"February 3, 2016","format":false,"excerpt":"Chaos is the erratic behavior of simple nonlinear dynamical systems. This course covers the basic fundamentals of chaos theory, including the concept of scaling and universal route to chaos, and its connection to these non-linear, deterministic but unpredictable dynamical systems. From simple chaotic maps, to the physics of fractals and\u2026","rel":"","context":"In "master"","block_context":{"text":"master","link":"https:\/\/toschi.phys.tue.nl\/wordpress\/category\/teaching\/master\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":297,"url":"https:\/\/toschi.phys.tue.nl\/wordpress\/population-dynamics-under-flow-2\/","url_meta":{"origin":442,"position":1},"title":"Population dynamics under flow","author":"toschi","date":"June 6, 2013","format":false,"excerpt":"Various recent studies have revealed amazing phenomena in the dynamics of bacterial colonies where biology meets physics, in particular statistical physics, fluid dynamics, and (soft) con- densed matter. 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Depending on the microscopic interactions, an assembly of molecules or of mesoscopic particles can flow like a simple Newtonian fluid, deform elastically like a solid or behave in a complex manner. When the internal constituents\u2026","rel":"","context":"In "projects"","block_context":{"text":"projects","link":"https:\/\/toschi.phys.tue.nl\/wordpress\/category\/research\/projects\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":85,"url":"https:\/\/toschi.phys.tue.nl\/wordpress\/new-directions-in-turbulence-2012\/","url_meta":{"origin":442,"position":3},"title":"New Directions in Turbulence 2012","author":"toschi","date":"February 9, 2012","format":false,"excerpt":"SCIENTIFIC CONTENT This six-week program (12 March 2012 to 20 April 2012) will focus on recent development in the understanding of fluid dynamics turbulence\u00a0with the goal to identify promising breakthrough directions. From the point of view of theoretical physics, turbulence is a classical field theory, out of equilibrium and in\u2026","rel":"","context":"In "conferences"","block_context":{"text":"conferences","link":"https:\/\/toschi.phys.tue.nl\/wordpress\/category\/conferences\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":104,"url":"https:\/\/toschi.phys.tue.nl\/wordpress\/fluids-flowing-across-the-scales\/","url_meta":{"origin":442,"position":4},"title":"fluids, flowing across the scales","author":"toschi","date":"February 9, 2012","format":false,"excerpt":"fluids, flowing across the scales\u00a0 Friday, June 24, at 4 p.m. Fluids are everywhere and still many of their fundamental properties are not understood. The apparent simplicity of the equations describing the motion of simple fluids contrasts with the beautiful complexity of turbulence. Fluid dynamics is clearly important to our\u2026","rel":"","context":"In "research"","block_context":{"text":"research","link":"https:\/\/toschi.phys.tue.nl\/wordpress\/category\/research\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":208,"url":"https:\/\/toschi.phys.tue.nl\/wordpress\/advanced-computational-fluid-dynamics\/","url_meta":{"origin":442,"position":5},"title":"3T380 - Advanced Computational Fluid Dynamics","author":"toschi","date":"February 8, 2012","format":false,"excerpt":"Quick links:\u00a0[Link to course schedule]\u00a0[Link to lecture notes]\u00a0[Link to additional books and material]\u00a0[Link to exercises]\u00a0[Link to possible individual assignments] The\u00a03T380\u00a0course provides an introduction to advanced computational methods useful to investigate fluid flows from the micro to the macro-scales under laminar and turbulent flow regime. 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