title: Calculation of displacement correlation tensor indicating vortical cooperative motion in two-dimensional colloidal liquids.
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.
authors.affiliation: Department of Mechanical and Aerospace Engineering, Tottori University, Tottori 680-8552, Japan.
authors.forename: Takeshi
authors.initials: T
authors.lastname: Ooshida
authors.affiliation: Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan.
authors.forename: Susumu
authors.initials: S
authors.lastname: Goto
authors.affiliation: Division of Physics and Astronomy, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan.
authors.forename: Takeshi
authors.initials: T
authors.lastname: Matsumoto
authors.affiliation: Department of Materials Science, Shimane University, Matsue 690-8504, Japan.
authors.forename: Michio
authors.initials: M
authors.lastname: Otsuki