Levy flight

Do we expect this model to be accurate for a dynamics dictated by Tsallis statistics A jump diffusion process that randomly samples the equilibrium canonical Tsallis distribution has been shown to lead to anomalous diffusion and Levy flights in the 5/3 < q < 3 regime. [3] Due to the delocalized nature of the equilibrium distributions, we might find that the microstates of our master equation are not well defined. Even at low temperatures, it may be difficult to identify distinct microstates of the system. The same delocalization can lead to large transition probabilities for states that are not adjacent ill configuration space. This would be a violation of the assumptions of the transition state theory - that once the system crosses the transition state from the reactant microstate it will be deactivated and equilibrated in the product state. Concerted transitions between spatially far-separated states may be common. This would lead to a highly connected master equation where each state is connected to a significant fraction of all other microstates of the system. [9, 10]... [Pg.211]

B. Bergersen, Z. Racz. Dynamical generation of long-range interactions Random Levy flights in the kinetic Ising and spherical models. Phys Rev Lett 67 3047-3050, 1991. [Pg.436]

E. V. Albano. Branching annihilating Levy flights Irreversible phase transitions with long-range exchanges. Europhys Lett 54 97-102, 1996. [Pg.437]

J. P. Bouchaud, A. Ott, D. Langevin, W. Urbach. Anomalous diffusion in elongated micelles and its Levy flight interpretation. J Phys II (Erance) 2 1465-1482, 1991. [Pg.551]

The data of figure 2 demonstrate, that at the present choice (3=0,25 in reesterification reaction course only antipersistent (subdiffusive) transport processes are possible (a=l is achieved for low-molecular substances with Df= 0 only), i.e., active time is always smaller than real time. This indicates on the important role of Levy flights in strange diffusion type definition. [Pg.246]

The characteristic changes brought about by fractional dynamics in comparison to the Brownian case include the temporal nonlocality of the approach manifest in the convolution character of the fractional Riemann-Liouville operator. Initial conditions relax slowly, and thus they influence the evolution of the system even for long times [62, 116] furthermore, the Mittag-Leffler behavior replaces the exponential relaxation patterns of Brownian systems. Still, the associated fractional equations are linear and thus extensive, and the limit solution equilibrates toward the classical Gibbs-B oltzmann and Maxwell distributions, and thus the processes are close to equilibrium, in contrast to the Levy flight or generalised thermostatistics models under discussion. [Pg.255]

The type of monomer attached to the growth center during the simulation under kinetic control (at large tr values, see Eq. 3) is determined by the conformation and primary structure of the growing chain as a whole, not only by the local concentration of reactive monomers near the active end of the macroradical. As a result of such cooperativity, the formation of sequences with specific LRCs of the Levy-flight type was observed [76-78]. [Pg.35]

Shlesinger MF, Zaslavskii GM, Frisch U (1996) Levy flights and related topics in physics. Springer, Berlin Heidelberg New York... [Pg.96]

The Levy walk is physically more plausible than the Levy flight. How to derive the Levy walk from a Liouville approach of the kind described in Section III Here, we illustrate a path explored some years ago, to establish a connection between GME and this kind of superdiffusion [49,50]. We assume that there exists a waiting time distribution v /(x), prescribed, for instance, by the dynamic model illustrated in Section V. This function corresponds to a distribution of uncorrelated times. We can imagine the ideal experiment of creating the sequence x,, by drawing in succession the numbers of this distribution. Then we create the fluctuating velocity E,(f), according to the procedure illustrated in Section V. [Pg.389]

In Section VI we have seen that the Levy walk is physically more attractive than the Levy flight. It is therefore reasonable to address the issue of the derivation of noncanonical equilibrium by using the Levy walk perspective. On the other... [Pg.410]

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