1,592 research outputs found
Modeling grain boundaries in solids using a combined nonlinear and geometrical method
The complex arrangements of atoms near grain boundaries are difficult to
understand theoretically. We propose a phenomenological (Ginzburg-Landau-like)
description of crystalline phases based on symmetries and fairly general
stability arguments. This method allows a very detailed description of defects
at the lattice scale with virtually no tunning parameters, unlike usual
phase-field methods. The model equations are directly inspired from those used
in a very different physical context, namely, the formation of periodic
patterns in systems out-of-equilibrium ({\it e.g.} Rayleigh-B\'enard
convection, Turing patterns). We apply the formalism to the study of symmetric
tilt boundaries. Our results are in quantitative agreement with those predicted
by a recent crystallographic theory of grain boundaries based on a geometrical
quasicrystal-like construction. These results suggest that frustration and
competition effects near defects in crystalline arrangements have some
universal features, of interest in solids or other periodic phases.Comment: 10 pages, 3 figure
Slow L\'evy flights
Among Markovian processes, the hallmark of L\'evy flights is superdiffusion,
or faster-than-Brownian dynamics. Here we show that L\'evy laws, as well as
Gaussians, can also be the limit distributions of processes with long range
memory that exhibit very slow diffusion, logarithmic in time. These processes
are path-dependent and anomalous motion emerges from frequent relocations to
already visited sites. We show how the Central Limit Theorem is modified in
this context, keeping the usual distinction between analytic and non-analytic
characteristic functions. A fluctuation-dissipation relation is also derived.
Our results may have important applications in the study of animal and human
displacements.Comment: 6 pages, 2 figure
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