Description:

Title: Nonlinear Dynamics of Magnetic Fluid Interfaces

Speaker: Ivan C. Christov, Assistant Professor of Mechanical Engineering, Purdue University

Abstract: Recently, there has been significant interest in the physics of active and responsive fluids. From Bose-Einstein condensate solitons to microrobots, magnetic fields allow non-invasive manipulation of dynamics. This actuation mechanism is particularly enticing for biological applications (microswimmers, drug delivery) due to the safe operation of magnetic fields in the medical setting. Ferrofluids, which are responsive to external magnetic fields, are a fundamental model for exploring these rich physics. By tuning an external field, we recently demonstrated coherently spinning ferrofluid droplets. Nonlinear periodic interfacial waves drive the dynamics, emerging from the linearly unstable base state upon saturating nonlinearity arresting the instability. Weakly nonlinear theory determines a phase diagram for perturbations that "grow" into stable spinning gears, as well as their rotational speed. To understand these novel interfacial ferrofluid dynamics, we developed the first mathematical theory of long waves on a confined (Hele-Shaw configuration) ferrofluid interface. The resulting long-wave equation is of generalized Kuramoto--Sivashinsky type. Importantly, we find nonlinear, periodic traveling wave solutions, which are shown to be a new class of non-localized 'dissipative solitons'. Further, we discover transitions between nonlinear wave states, which we explain via the spectral stability of the traveling waves. Interestingly, multiperiodic waves, which are a non-integrable analog of the double cnoidal wave of the Korteweg--de Vries equation, are also found. These multiperiodic solutions are investigated numerically, and they are found to be long-lived transients, but ultimately abruptly transition to one of the stable periodic states identified.

**Please note, this event will be held in-person, and will be simultaneously broadcast via Zoom at the following link: https://northwestern.zoom.us/j/93390821569. Masks are required to be worn by all in-person attendees per university guidelines and eating and drinking are prohibited. 

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