On nonequilibrium spatial correlations in a model chemical reaction

Spatial correlations in nonequilibrium reaction-diffusion problems by the Gillespie algorithm

“…Therefore, we find it best to perform fittings to the theoretical result of Eq. (21). For these fittings we fix the values of N p and k 1 /k 2 to the ones actually used in the simulations (N p = 3000 and k 1 /k 2 = 1500, for W = 128 cells), and used μ as the only fitting parameter.…”

“…Several mechanisms have been devised and considered in the literature to drive a reaction-diffusion system out of equilibrium. One possibility is to externally impose a flow, by adding and removing particles [21,[32][33][34][35]. Another option, that keeps the system closed, is to consider a complex chain of chemical reactions that effectively break detailed balance, like the Schlögl kinetic mechanism [18] or other variants [20,21,32].…”

“…Furthermore, one can think of Eq. (3) as a limiting case, when the inverse rates go to zero of a more complicated kinetics, kind of the ones adopted by other investigators [18], not to mention many literature examples adopting similar one-directional kinetics [21,32,36].…”

“…Although some authors have presented numerical simulations of nonequilibrium correlations [19][20][21], the number of investigations is still scarce. Our goal here is to contribute to fill this gap by presenting numerical simulations of equilibrium and nonequilibrium reaction-diffusion problems, for which the Gillespie [22,23] algorithm is particularly adequate.…”

“…For instance, Wakou et al [21] analyzed the spatial correlation function of density fluctuations in a model chemical reaction assuming that the monomolecular decay rate is fast enough to consider the motion of the chemicals as ballistic instead of diffusive. They obtained analytical expressions for the spatial correlation functions under this approximation, and simulated them with molecular dynamics.…”