Calculation of displacement correlation tensor indicating vortical cooperative motion in two-dimensional colloidal liquids

Ooshida Takeshi (大信田 丈志), Susumu Goto (後藤 晋), Takeshi Matsumoto (松本 剛), and Michio Otsuki (大槻 道夫)
Phys. Rev. E 94, 022125 – Published 18 August 2016

Abstract

As an indicator of cooperative motion in a system of Brownian particles that models two-dimensional colloidal liquids, a displacement correlation tensor is calculated analytically and compared with numerical results. The key idea for the analytical calculation is to relate the displacement correlation tensor, which is a kind of four-point space-time correlation, to the Lagrangian two-time correlation of the deformation gradient tensor. Tensorial treatment of the statistical quantities, including the displacement correlation itself, allows capturing the vortical structure of the cooperative motion. The calculated displacement correlation also implies a negative long-time tail in the velocity autocorrelation, which is a manifestation of the cage effect. Both the longitudinal and transverse components of the displacement correlation are found to be expressible in terms of a similarity variable, suggesting that the cages are nested to form a self-similar structure in the space-time.

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  • Received 12 April 2016
  • Revised 22 July 2016

DOI:https://doi.org/10.1103/PhysRevE.94.022125

©2016 American Physical Society

Physics Subject Headings (PhySH)

  1. Physical Systems
Polymers & Soft MatterStatistical Physics & Thermodynamics

Authors & Affiliations

Ooshida Takeshi (大信田 丈志)*

  • Department of Mechanical and Aerospace Engineering, Tottori University, Tottori 680-8552, Japan

Susumu Goto (後藤 晋)

  • Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan

Takeshi Matsumoto (松本 剛)

  • Division of Physics and Astronomy, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan

Michio Otsuki (大槻 道夫)

  • Department of Materials Science, Shimane University, Matsue 690-8504, Japan

  • *ooshida@damp.tottori-u.ac.jp

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Issue

Vol. 94, Iss. 2 — August 2016

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