Exchange and persistence times are shown in the trajectory of FA model at . The shaded regions represent parts of space time with excitations, while the white regions represent parts with no excitations.
Exchange and persistence time distributions for FA and East models. Here, , and is similarly related to . Exchange-time distribution from simulation (filled circles), persistence-time distribution from simulation (open circles), and persistence-time distribution predicted from Eq. (18) (solid lines). (a) FA model at , (b) FA model at , (c) East model at , and (d) East model at .
The first (circles), second (squares), and third (diamonds) moments of exchange- (open symbols) and persistence-(shaded symbols) time distributions of , 2, and 3 FA models (left panels) and East models (right panels) as functions of excitation concentration .
Comparison of mean-field approximation, Eq. (25) (dashed line), and simulation results of mean exchange times in , 2, and 3 FA and East models. for FA models and for East models.
Decompositions of exchange-time distributions of FA models (left panels) and East models (right panels) for , 2, and 3 at . Four subdistributions—case 1 (circles), case 2 (squares), case 3 (diamonds), and case 4 (triangles)—add up to the full distribution (solid line). Positions of three peaks in are shown for FA model cases.
Examples of exchange events that belong to each case of Eq. (30) are illustrated in the trajectory of FA model.
Positions of peaks in the exchange-time distributions are shown for various excitation concentrations.
(Color) Distributions of the logarithm of exchange and persistence times of FA model for , 2, and 3 at various temperatures. From left to the right: for case, and for and cases.
(Color) Distributions of the logarithm of exchange and persistence times of East model for , 2, and 3 at various temperatures. From left to the right: 10, 1, 0.6, 0.5, 0.4, and 0.3 for case, , 1, 0.5, 0.4, 0.3, 0.25, and 0.22 for case, and , 1, 0.5, 0.4, 0.3, 0.25, 0.22, and 0.2 for case.
(Color) Exchange-time distributions of FA models (left panels) and East models (right panels) in log scales. Temperatures are the same as those given in the captions to Figs. 8 and 9. A power-law corresponding to or is shown as a dashed line with , and a stretched exponential corresponding to where is shown as a dot-dashed line for FA model. In and 3 FA models, exponential fits, , are given as dashed lines for the lowest temperature of each case.
(Color) Persistence time pair (PDFs) at a high and a low temperature at equilibrium (solid lines) and right after the bleaching (dotted lines). Each dashed line corresponds to the distribution created by bleaching efficiency function, with different values of , given in the inset of Fig. 11. Inset: Bleaching efficiency function used in the simulation, Eq. (32), with . From left to the right, progressively increases from to by a factor of 100.
Mean persistence times right after the bleaching experiment, , are shown for various bleaching depths and temperatures. increases more abruptly as a function of the bleach depth at a lower temperature.
Relaxation dynamics of the distributions of persistence times to equilibrium after the bleaching of East model at . and were chosen in .
Recovery of the nonequilibrium distribution, to equilibrium is shown by the decay of (upper panel) and (lower panel). Time scale of the recovery to equilibrium is on the order of the equilibrium mean persistence time itself. The model parameters are the same as those used in Fig. 13.
Scaling exponents for fitting various moments of exchange and persistence-time distributions to Arrhenius form, are shown for , 2, and 3 FA and East models. The numbers in the parentheses are those for persistence time-distributions. Fitting of the moments to the Arrhenius form was done for data corresponding to .
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