# Bistability of Nanopropellers in low Reynolds numbers in Magnetic Fields

Ferromagnetic helical nanopropellers are driven by rotating magnetic fields and they have two modes, tumbling (rotating about one position), or precession (moving like a screw in response to the magnetic field). It turns out which mode is stable depends on the applied frequency of rotation of the magnetic field, and moreover for a certain range of magnetic fields, both modes are stable and the system randomly switches from one mode to another. The transition into bistability and the point of bistability are not well understood. I studied this as a problem of rigid body rotation. I tried to solve for the stability of the solutions by linearizing the equations using perturbation analysis, but the results were inconclusive. I further did a numerical study of the equations and showed that the linearization approach was not valid- one of the Euler angles changes by a large amount before returning to its mean position, even for small perturbations. I tried to analyze the problem by plotting the trajectory in phase-space, but it was not illuminating. This project taught me some techniques of stability analysis like

• Perturbative analysis by linearizing equations
• Lyapunov functions for stability criterion
• Numerically simulating stability criterion
• Plotting phase space trajectories to visualize stability

I also took experimental data on nanopropellers, to find the points of bistability, and construct a statistical distribution of how likely a propeller was to be in a certain mode, given a certain frequency of rotation of the magnetic field.

I learnt a lot of laboratory techniques like

• preparing, cleaning and sonicating slides
• creating and using a microfluidic cell
• providing magnetic field input to the cell
• recognizing various sorts of problems and noise and deal with them effectively
• writing and using MATLAB scripts to do video analysis frame by frame
• extracting usable data from raw microscope video.

[Reference: Ambarish Ghosh, https://doi.org/10.1103/PhysRevE.86.031401
https://journals.aps.org/pre/abstract/10.1103/PhysRevE.86.031401 ]