A statistical-mechanical theory of self-diffusion in colloidal suspensions — application to colloidal glass transitions

A statistical-mechanical theory of self-diffusion in colloidal suspensions is presented. A renormalized linear Langevin equation is derived from a nonlinear Langevin equation by employing the Tokuyama–Mori projection operator method. The friction constant is thus shown to be renormalized by the many-body correlation effects due to not only the direct interactions between particles, but also due to the hydrodynamic interactions between particles. The equations for the mean-square displacement and the non-Gaussian parameter are then derived. The present theory is applied to colloidal glass transitions to discuss the crossover phenomena in the dynamics of a single particle from a short-time self-diffusion process to a long-time self-diffusion process via a β (caging) stage. The effects of the renormalized friction coefficient on self-diffusion are thus explored with the aid of the analyses of the experimental data and the simulation results by the mean-field theory proposed by the present author. It is thus shown that the relaxation time of the renormalized memory function is given by the β-relaxation time. It is also shown that the non-Gaussian parameter is very small, even near the glass transition, because of the existence of the short-time self-diffusion coefficient caused by the hydrodynamic interactions.     

Comment on “Synchronization in dynamic networks with nonsymmetrical time-delay coupling based on linear feedback controllers” [Physica A 387 (2008) 2111-2119]

In this paper, we point out two problems in synchronization of dynamic networks based on linear feedback controllers presented by Wu and Jiao [J. Wu, L. Jiao, Synchronization in dynamic networks with nonsymmetrical time-delay coupling based on linear feedback controllers, Physica A 387 (2008) 2111-2119]. Furthermore, an amendatory version on global exponential synchronization is given and proved in this paper.     

Erratum and addendum to “A variational theory of hyperbolic Lagrangian coherent structures” [Physica D 240 (2011) 574-598]

This brief note corrects a minor error in the statement of the main result in Haller (2011) [1] on a variational approach to Lagrangian coherent structures. We also show that the corrected formulation leads to a substantial simplification of LCS criteria for two-dimensional flows.