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Fractional Brownian motion and dynam...

Cakir, Rasit.

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Fractional Brownian motion and dynamic approach to complexity.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Fractional Brownian motion and dynamic approach to complexity./
Author:	Cakir, Rasit.
Description:	111 p.
Notes:	Adviser: Paolo Grigolini.
Contained By:	Dissertation Abstracts International68-11B.
Subject:	Physics, Theory. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3290149
ISBN:	9780549338192

Fractional Brownian motion and dynamic approach to complexity.
Cakir, Rasit.

Fractional Brownian motion and dynamic approach to complexity. - 111 p.

Adviser: Paolo Grigolini.

Thesis (Ph.D.)--University of North Texas, 2007.

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 mu=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 mu=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.

ISBN: 9780549338192Subjects--Topical Terms:

1019422
Physics, Theory.

Fractional Brownian motion and dynamic approach to complexity.
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020 $a 9780549338192
035 $a (UMI)AAI3290149
035 $a AAI3290149
040 $a UMI $c UMI
100 1 $a Cakir, Rasit. $3 1266266
245 1 0 $a Fractional Brownian motion and dynamic approach to complexity.
300 $a 111 p.
500 $a Adviser: Paolo Grigolini.
500 $a Source: Dissertation Abstracts International, Volume: 68-11, Section: B, page: 7409.
502 $a Thesis (Ph.D.)--University of North Texas, 2007.
520 $a 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 mu=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 mu=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.
590 $a School code: 0158.
650 4 $a Physics, Theory. $3 1019422
650 4 $a Statistics. $3 517247
690 $a 0463
690 $a 0753
710 2 $a University of North Texas. $3 1017396
773 0 $t Dissertation Abstracts International $g 68-11B.
790 $a 0158
790 1 0 $a Grigolini, Paolo, $e advisor
791 $a Ph.D.
792 $a 2007
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3290149