Brownian Particles Interacting via Synchronizations
We consider a system x(t) = (x 1(t),…, x N (t)) consisting of N Brownian particles with synchronizing interaction between them occurring at random time moments . Under assumption that the free Brownian motions and the sequence are independent we study asymptotic properties of the system when both the dimension N and the time t go to infinity. We find three time scales t = t(N) of qualitatively different behavior of the system.
Abstract The influence of different post-fermentation treatments intended to afford protection against non-enzymatic browning was studied in a series of varietal wines produced on an industrial scale using a sequential association of yeasts. In view of the complexity of the browning reactions and the difficulty in elucidating the reaction mechanism and in deriving a single precise kinetic equation describing that mechanism, three simple models for approximating the browning reactions have been proposed based on experimental data. An equation which combined both zero order and first order kinetics provided a satisfactory description of non-enzymatic browning in the wines tested. All other factors being equal, the values of the two rate constants depend upon wine variety and temperature.