2010/05/30 by Christian Gollwitzer, C Gollwitzer, Ingo Rehberg +3
Computer Science · Engineering · Physics and Astronomy · #Amplitude #Characterization and Applications of Magnetic Nanoparticles #Dynamics (music) #Neighbourhood (mathematics) #Nonlinear Dynamics and Pattern Formation #Nonlinear system #Phase (matter) #Phase space #Relaxation (psychology) #Theoretical and Computational Physics #nlin.PS #physics.flu-dyn
paper · pdf · doi:10.1088/1367-2630/12/9/093037
20 pages, 12 figures
arxiv created 2010/05/30 · openalex publication_date 2010/09/23 · arxiv updated 2015/05/19 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We describe and demonstrate a method to reconstruct an amplitude equation from the nonlinear relaxation dynamics in the neighbourhood of the Rosensweig instability. A flat layer of a ferrofluid is cooled such that the liquid has a relatively high viscosity. Consequently, the dynamics of the formation of the Rosensweig pattern becomes very slow. By a sudden switching of the magnetic induction, the system is pushed to an arbitrary point in the phase space spanned by the pattern amplitude and magnetic induction. Afterwards, it is allowed to relax to its equilibrium point. From the dynamics of this relaxation, we reconstruct the underlying fully nonlinear equation of motion of the pattern amplitude. The measured nonlinear dynamics helps us to select the best weakly nonlinear expansion that describes this hysteretic transition.