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Fractional Brownian motion and dynam...

Cakir, Rasit.

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Fractional Brownian motion and dynamic approach to complexity.

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Fractional Brownian motion and dynamic approach to complexity./
作者:	Cakir, Rasit.
面頁冊數:	111 p.
附註:	Adviser: Paolo Grigolini.
Contained By:	Dissertation Abstracts International68-11B.
標題:	Physics, Theory. -
電子資源:	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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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.
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