Diffusion, deterministic-chaotic

There are situations for which the deterministic, macroscopic, reaction-diffusion equations may not provide a correct description of the dynamics. Internal noise or molecular fluctuations can give rise to nucleation events that itjduce transitions between stable states. Fluctuations can be amplified near bifurcation points and in the vicinity of deterministic chaotic dynamics. In such cases the validity of mean-field descriptions must be examined. In addition, if the system size is very small, fluctuations can play an important role since their amplitude is a function of the system size. These considerations prompt one to seek descriptions of non-equilibrium reaction dynamics that incorporate the effects of internal noise and allow one to study the system at a level that is finer than that given by the reaction-diffusion equations. 

The results of a full automaton simulation of a small (Af = (100) ) system are shown in Figure 3 (left panel) for K2 = 1.572, corresponding to the deterministic chaotic attractor in the right panel. Diffusion is ble to smooth the concentration fluctuations arising from reactions occurring on the time scale Tchem over a length L = For this automaton simulation... 

The kicked rotor (or the standard map) is one of famous models in chaotic dynamical systems, and it has been studied in various situations [17]. One feature of its chaotic dynamics is the deterministic diffusion along the momentum direction. It is also well known that if we quantize this system, this diffusion is... 

Gaspard, R, Klages, R. Chaotic and fractal properties of deterministic diffusion-reaction processes. Chaos 8(2), 409—423 (1998). http //link.aip.Org/link/7CHA/8/409/l... 

Gaspard, P. Klages, R. Chaotic and Fractal Properties of Deterministic Diffusion-Reaction Processes. Cftaor 1998,8 (2), 409-423. 

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