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We investigate a class of stochastic fragmentation processes involving stable and unstable fragments. We solve analytically for the fragment length density and find that a generic algebraic divergence characterizes its small-size tail. Furthermore, the entire range of acceptable values of decay exponent consistent with the length conservation can be realized. We show that the stochastic fragmentation process is non-self-averaging as moments exhibit significant sample-to-sample fluctuations. Additionally, we find that the distributions of the moments and of extremal characteristics possess an infinite set of progressively weaker singularities.
There has been a considerable amount of interest in recent years on the robustness of networks to failures. Many previous studies have concentrated on the effects of node and edge removals on the connectivity structure of a static network; the networ
We experimentally investigate the response of a sheared granular medium in a Couette geometry. The apparatus exhibits the expected stick-slip motion and we probe it in the very intermittent regime resulting from low driving. Statistical analysis of t
The swap Monte Carlo algorithm allows the preparation of highly stable glassy configurations for a number of glass-formers, but is inefficient for some models, such as the much studied binary Kob-Andersen (KA) mixture. We have recently developed gene
We study the Ising model in a hierarchical small-world network by renormalization group analysis, and find a phase transition between an ordered phase and a critical phase, which is driven by the coupling strength of the shortcut edges. Unlike ordina
Coalescence-fragmentation problems are of great interest across the physical, biological, and recently social sciences. They are typically studied from the perspective of the rate equations, at the heart of such models are the rules used for coalesce