Abstract
One aim of the equal load sharing fiber bundle model is to describe the critical behavior of failure events. One way of accomplishing this, is through a discrete recursive dynamics. We introduce a continuous mesoscopic equation catching the critical behavior found through recursive dynamics. It allows us to link the model with the unifying framework of absorbing phase transitions traditionally used in the study of non-equilibrium phase transitions. Moreover, it highlights the analogy between equal load sharing and spinodal nucleation. Consequently, this work is a first step towards the quest of a field theory for fiber bundle models.
Highlights
While equilibrium phase transitions are today well understood, a general framework to study the nonequilibrium counterpart is still lacking
Major efforts have been invested into identifying the universality classes related to nonequilibrium phase transitions
The theory of absorbing phase transitions (APTs) is emerging as a unifying framework [1,2]
Summary
While equilibrium phase transitions are today well understood, a general framework to study the nonequilibrium counterpart is still lacking. The most prominent and generic nonequilibrium universality class is directed percolation, which is believed to describe the phase transition toward a unique absorbing state of systems that is not characterized by any special symmetry (except, effectively, the rapidity reversal symmetry) or conservation law. This is known as the Janssen-Grassberger directed percolation conjecture [6,7]. Fiber bundle models (FBMs) describe rupture phenomena as irreversible fiber breaking processes through discrete breaking rules [8,9]. On the dynamical description of the equal-load-sharing (ELS) model, which is the mean-field (MF) limit of the fiber bundle models [10].
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