Journal
EUROPEAN PHYSICAL JOURNAL E
Volume 9, Issue 3, Pages 287-291Publisher
SPRINGER-VERLAG
DOI: 10.1140/epje/i2002-10075-3
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We compute the dynamical structure factor S(q, tau) of an elastic medium where force dipoles appear at random in space and in time, due to micro-collapses of the structure. Various regimes are found, depending on the wave vector q and the collapse time theta. In an early time regime, the logarithm of the structure factor behaves as (qtau)(3/2), as predicted in (L. Cipelletti et al., Phys. Rev Lett. 84, 2275 (2000)) using heuristic arguments. However, in an intermediate-time regime we rather obtain a (qtau)(5/4) behaviour. Finally, the asymptotic long-time regime is found to behave as q(3/2)tau. We also give a plausible scenario for aging, in terms of a strain-dependent energy barrier for micro-collapses. The relaxation time is found to grow with the age t(w), quasi-exponentially at first, and then as t(w)(4/5) with logarithmic corrections.
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