(110f) Kinematrix Theory and Universalities in Self-Prolpellers, Swimmers and Nanomotors

Authors: 
Nourhani, A., The Pennsylvania State University
Lammert, P. E., The Pennsylvania State University
Borhan, A., The Pennsylvania State University
Crespi, V. H., The Pennsylvania State University

We present an elegant and efficient matrix-based theory for modeling systems within the emerging field of self-propellers, autonomous movers, and active swimmers as an alternative to traditional differential-equation-based Fokker-Planck and Langevin formalisms for the class of stochastic processes with negligible correlation time. Such self-propellers range from micron and submicron biological and artificial motors to macroscale animals, swimmers and pedestrians. The motions of self-propellers naturally decompose into elementary processes such as deterministic linear and rotational motion, stochastic orientational diffusion, flipping, and tumbling. While traditional differential-equation based formalisms become cumbersome as the number of elementary processes in a model increases, our theory treats all the elementary processes on the same footing. A matrix, called kinematrix, is produced from inspection of the elementary processes and from it many ensemble properties of a self-propeller such as autocorrelations of linear and angular velocities, mean-square displacement, and effective diffusion are derived by simple matrix algebra. We examine four different classes of self-propellers and show that the kinematrix formalism can explain the behavior of these systems in a way that reveals underlying universalities previously unrecognized within the more cumbersome traditional treatments.
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