title: Kinematic matrix theory and universalities in self-propellers and active swimmers.
abstract: We describe an efficient and parsimonious matrix-based theory for studying the ensemble behavior of self-propellers and active swimmers, such as nanomotors or motile bacteria, that are typically studied by differential-equation-based Langevin or Fokker-Planck formalisms. The kinematic effects for elementary processes of motion are incorporated into a matrix, called the "kinematrix," from which we immediately obtain correlators and the mean and variance of angular and position variables (and thus effective diffusivity) by simple matrix algebra. The kinematrix formalism enables us recast the behaviors of a diverse range of self-propellers into a unified form, revealing universalities in their ensemble behavior in terms of new emergent time scales. Active fluctuations and hydrodynamic interactions can be expressed as an additive composition of separate self-propellers.
authors.affiliation: Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA.
authors.forename: Amir
authors.initials: A
authors.lastname: Nourhani
authors.affiliation: Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA.
authors.forename: Paul E
authors.initials: PE
authors.lastname: Lammert
authors.affiliation: Department of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, USA.
authors.forename: Ali
authors.initials: A
authors.lastname: Borhan
authors.affiliation: Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA and Department of Materials Science and Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, USA and Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802, USA.
authors.forename: Vincent H
authors.initials: VH
authors.lastname: Crespi
mesh_terms: D000818:Animals; D018407:Bacterial Physiological Phenomena; D001696:Biomechanical Phenomena; D003621:Daphnia / Q000502:physiology; D004058:Diffusion; D057446:Hydrodynamics; D060526:Magnetic Fields; D008962:Models, Theoretical; D009038:Motion; D049329:Nanostructures / Q000737:chemistry; D013995:Time