Micro and nanoscale materials have remarkable mechanical properties, such as enhanced strength and toughness, but usually display sample-to-sample fluctuations and non-trivial size effects, a nuisance for engineering applications and an intriguing problem for science. Our understanding of size-effects in small-scale materials has progressed considerably in the past few years thanks to a growing number of experimental measurements on carbon based nanomaterials, such as graphene carbon nanotubes, and on crystalline and amorphous micro/nanopillars and micro/nanowires. At the same time, increased computational power allowed atomistic simulations to reach experimentally relevant sample sizes. From the theoretical point of view, the standard analysis and interpretation of experimental and computational data relies on traditional extreme value theories developed decades ago for macroscopic samples, with recent work extending some of the limiting assumptions of the original theories. In this review, we discuss the recent experimental and numerical literature on micro and nanoscale fracture size effects, illustrate existing theories pointing out their advantages and limitations and finally provide a tutorial for analyzing fracture data from micro and nanoscale samples. We discuss a broad spectrum of materials but provide at the same time a unifying theoretical framework that should be helpful for materials scientists working on micro and nanoscale mechanics.

We provide an economically sound micro-foundation to linear price impact models, by deriving them as the equilibrium of a suitable agent-based system. In particular, we retrieve the so-called propagator model as the high-frequency limit of a generalized Kyle model, in which the assumption of a terminal time at which fundamental information is revealed is dropped. This allows to describe a stationary market populated by asymmetrically-informed rational agents. We investigate the stationary equilibrium of the model, and show that the setup is compatible with universal price diffusion at small times, and non-universal mean-reversion at time scales at which fluctuations in fundamentals decay. Our model suggests that at high frequency one should observe a quasi-permanent impact component, driven by slow fluctuations of fundamentals, and a faster transient one, whose timescale should be set by the persistence of the order flow.

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