Avalanche dynamics in driven materials

Phase transitions in equilibrium have traditionally been classified as first-order or second-order (critical). The essential difference between the two is whether the order parameter exhibits a discontinuous or a continuous behavior at the transition point. In the second half of the last century, second-order phase transitions were extensively studied. Concepts such as the lack of characteristic scales, divergence of correlation length, criticality, critical exponents, and universality were established. Very powerful techniques, such as the renormalization group approach, were developed as well. In the last 20 years, the focus has been on first-order phase transitions (FOPTs). Theoretically, systems slowly driven across a FOPT exhibit an equilibrium behavior with a single discontinuity of the order parameter. However, even when driven very slowly, they often evolve following a non-equilibrium metastable trajectory. This trajectory, instead of consisting of a single macroscopic discontinuity, exhibits many small discontinuities, or “avalanches,” with sizes ranging from the microscopic to the macroscopic. This behavior is an example of the “avalanche dynamics” discussed herein. The essential difference that distinguishes this behavior from other non-equilibrium intermittent dynamics is the lack of characteristic scales. This is why the term “critical” is applied to these systems, despite the fact that they undergo a FOPT. For this phenomenon to occur, two ingredients are needed: quenched-in disorder and athermal behavior, a consequence of low thermal fluctuations. However, “avalanche dynamics” is not limited to systems with FOPTs but may also occur in heterogeneous systems irreversibly driven by an instability. A second example discussed in this article is the case of the mechanical failure of porous materials under compression, for which disorder and athermal behavior play crucial roles. [Contrib Sci 11(2): 153-162 (2015)]Keywords: non-equilibrium first-order phase transitions · metastable behavior · hysteresis · avalanche dynamics · compression of porous material