Aging and Rejuvenation with Fractional Derivatives

Description:

Article on aging and rejuvenation with fractional derivatives.

Creator(s):
Creation Date: February 2, 2008
Partner(s):
UNT College of Arts and Sciences
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UNT Scholarly Works
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Creator (Author):
Aquino, Gerardo

University of North Texas

Creator (Author):
Bologna, Mauro

University of North Texas

Creator (Author):
Grigolini, Paolo

University of North Texas; Università di Pisa; Istituto dei Processi Chimico Fisici del Consiglio Nazionale delle Ricerche

Creator (Author):
West, Bruce J.

United States. Army Research Office

Date(s):
  • Creation: February 2, 2008
Description:

Article on aging and rejuvenation with fractional derivatives.

Degree:
Department: Physics
Note:

This is the author manuscript version of an article published in Physical Review E.

Note:

Abstract: We discuss a dynamic procedure that makes the fractional derivative emerge in the time asymptotic limit of non-Poisson processes. We find that two-state fluctuations, with an inverse power-law distribution of waiting times, finite first moment and divergent second moment, namely with the power index μ in the interval 2 < μ < 3, yields a generalized master equation equivalent to the sum of an ordinary Markov contribution and of a fractional derivative term. We show that the order of the fractional derivative depends on the age of the process under study. If the system is infinitely old, the order of the fractional derivative, ord = μ - 2. If the system is prepared at time -tₐ < 0 and the observation begins at time t = 0, we derive the following scenario. For times 0 < t << tₐ the system is satisfactorily described by the fractional derivative with ord = 3 - μ. Upon time increase the system undergoes a rejuvenation process that in the time limit t >> tₐ yields ord = μ - 2. The intermediate time regime is probably incompatible with a picture based on fractional derivatives, or, at least, with a mono-order fractional derivative.

Physical Description:

11 p.: ill.

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Subject(s):
Keyword(s): aging order | fractional derivatives | Onsager principle | fractional operators
Source: arXiv: cond-mat/0311314
Partner:
UNT College of Arts and Sciences
Collection:
UNT Scholarly Works
Identifier:
  • ARK: ark:/67531/metadc174699
Resource Type: Paper
Format: Text
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Access: Public