Fractional Brownian motion and dynamic approach to complexity.

Fractional Brownian motion and dynamic approach to complexity.

Date: August 2007
Creator: Cakir, Rasit
Description: The dynamic approach to fractional Brownian motion (FBM) establishes a link between non-Poisson renewal process with abrupt jumps resetting to zero the system's memory and correlated dynamic processes, whose individual trajectories keep a non-vanishing memory of their past time evolution. It is well known that the recrossing times of the origin by an ordinary 1D diffusion trajectory generates a distribution of time distances between two consecutive origin recrossing times with an inverse power law with index m=1.5. However, with theoretical and numerical arguments, it is proved that this is the special case of a more general condition, insofar as the recrossing times produced by the dynamic FBM generates process with m=2-H. Later, the model of ballistic deposition is studied, which is as a simple way to establish cooperation among the columns of a growing surface, to show that cooperation generates memory properties and, at same time, non-Poisson renewal events. Finally, the connection between trajectory and density memory is discussed, showing that the trajectory memory does not necessarily yields density memory, and density memory might be compatible with the existence of abrupt jumps resetting to zero the system's memory.
Contributing Partner: UNT Libraries
Renewal and memory properties in the random growth of surfaces

Renewal and memory properties in the random growth of surfaces

Date: February 4, 2008
Creator: Cakir, Rasit; Grigolini, Paolo & Ignaccolo, Massimiliano
Description: Article discussing the renewal and memory properties in the random growth of surfaces.
Contributing Partner: UNT College of Arts and Sciences
Dynamical Origin of Memory and Renewal

Dynamical Origin of Memory and Renewal

Date: August 8, 2006
Creator: Cakir, Rasit; Grigolini, Paolo & Krokhin, Arkadii A.
Description: This article discusses a dynamical origin of memory and renewal.
Contributing Partner: UNT College of Arts and Sciences