### 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.

Original language | English (US) |
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Article number | 062304 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 89 |

Issue number | 6 |

DOIs | |

State | Published - Jun 12 2014 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics

### Cite this

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**Kinematic matrix theory and universalities in self-propellers and active swimmers.** / Nourhani, Amir; Lammert, Paul E.; Borhan, Ali; Crespi, Vincent H.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Kinematic matrix theory and universalities in self-propellers and active swimmers

AU - Nourhani, Amir

AU - Lammert, Paul E.

AU - Borhan, Ali

AU - Crespi, Vincent H.

PY - 2014/6/12

Y1 - 2014/6/12

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84902478366&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84902478366&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.89.062304

DO - 10.1103/PhysRevE.89.062304

M3 - Article

C2 - 25019773

AN - SCOPUS:84902478366

VL - 89

JO - Physical Review E

JF - Physical Review E

SN - 2470-0045

IS - 6

M1 - 062304

ER -