Collective dynamics of colloids at fluid interfaces

The evolution of an initially prepared distribution of micron sized colloidal particles, trapped at a fluid interface and under the action of their mutual capillary attraction, is analyzed by using Brownian dynamics simulations. At a separation \lambda\ given by the capillary length of typically 1 mm, the distance dependence of this attraction exhibits a crossover from a logarithmic decay, formally analogous to two-dimensional gravity, to an exponential decay. We discuss in detail the adaption of a particle-mesh algorithm, as used in cosmological simulations to study structure formation due to gravitational collapse, to the present colloidal problem. These simulations confirm the predictions, as far as available, of a mean-field theory developed previously for this problem. The evolution is monitored by quantitative characteristics which are particularly sensitive to the formation of highly inhomogeneous structures. Upon increasing \lambda\ the dynamics show a smooth transition from the spinodal decomposition expected for a simple fluid with short-ranged attraction to the self-gravitational collapse scenario.Comment: 13 pages, 12 figures, revised, matches version accepted for publication in the European Physical Journal

Equilibrium and nonequilibrium properties of systems with long-range interactions

We briefly review some equilibrium and nonequilibrium properties of systems with long-range interactions. Such systems, which are characterized by a potential that weakly decays at large distances, have striking properties at equilibrium, like negative specific heat in the microcanonical ensemble, temperature jumps at first order phase transitions, broken ergodicity. Here, we mainly restrict our analysis to mean-field models, where particles globally interact with the same strength. We show that relaxation to equilibrium proceeds through quasi-stationary states whose duration increases with system size. We propose a theoretical explanation, based on Lynden-Bell's entropy, of this intriguing relaxation process. This allows to address problems related to nonequilibrium using an extension of standard equilibrium statistical mechanics. We discuss in some detail the example of the dynamics of the free electron laser, where the existence and features of quasi-stationary states is likely to be tested experimentally in the future. We conclude with some perspectives to study open problems and to find applications of these ideas to dipolar media.Comment: 8 pages, 14 figures, Procs. of STATPHYS23, to be published on EPJ