Phase transition in fiber bundle models with recursive dynamics

Bhattacharyya, Pratip ; Pradhan, Srutarshi ; Chakrabarti, Bikas K. (2003) Phase transition in fiber bundle models with recursive dynamics Physical Review E - Statistical, Nonlinear and Soft Matter Physics, 67 (4). 046122_1-046122_9. ISSN 1539-3755

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Official URL: http://pre.aps.org/abstract/PRE/v67/i4/e046122

Related URL: http://dx.doi.org/10.1103/PhysRevE.67.046122

Abstract

We study the phase transition in a class of fiber bundle models in which the fiber strengths are distributed randomly within a finite interval and global load sharing is assumed. The dynamics is expressed as recursion relations for the redistribution of the applied stress and the evolution of the surviving fraction of fibers. We show that an irreversible phase transition of second-order occurs, from a phase of partial failure to a phase of total failure, when the initial applied stress just exceeds a critical value. The phase transition is characterized by static and dynamic critical properties. We calculate exactly the critical value of the initial stress for three models of this kind, each with a different distribution of fiber strengths. We derive exact expressions for the order parameter, the susceptibility to changes in the initial applied stress, and the critical relaxation of the surviving fraction of fibers for all the three models. The static and dynamic critical exponents obtained from these expressions are found to be universal.

Item Type:Article
Source:Copyright of this article belongs to The American Physical Society.
ID Code:44802
Deposited On:23 Jun 2011 07:55
Last Modified:23 Jun 2011 07:55

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