Search

We investigate the non-equilibrium dynamics of spherical spin models with two-spin interactions. For the exactly solvable models of the d-dimensional spherical ferromagnet and the spherical Sherrington-Kirkpatrick model the asymptotic dynamics has for large times and for large waiting times the same formal structure. In the limit of large waiting times we find in both models an intermediate time scale, scaling as a power of the waiting time with an exponent smaller than one, and thus separating the time-translation invariant short-time dynamics from the aging regime. It is this time scale on which the fluctuation-dissipation regime is violated. Aging in these models is similar to that observed in spin glasses at the level of correlation functions, but different at the level of response functions, and thus different at the level of experimentally accessible quantities like the thermoremanent magnetization., Comment: 8 pages, 1 eps figure

Calcium oxalate crystals were observed on facing peridial surfaces of developing basidiocarps of Geastrum minus. Five crystal forms were characterized by their outward shapes and X-ray diffraction patterns: Form One, small bipyramids (COD); Form Two, crystals with split tips (COD); Form Three, crystals with oriented overgrowths (COD); Form Four, large bipyramids (COD); and Form Five, rosettes of plate-like crystals (COM). Forms One and Two were first to appear after peridia separated in unopened basidiocarps, whereas Forms Three, Four and Five were present on exposed peridia of opened basidiocarps. Based on time of appearance during basidiocarp development and crystallography of each form, we believe Form One gives rise to Forms Two, Three and Four. Form Five may arise from dissolution and recrystallization of pre-existing forms. Farinose or asperate basidiocarps of eight other species of Geastrum showed no crystals, indicating that only G. minus forms crystals. Comparison of the five forms with crystals on old basidiocarps indicates Form Four is predominant. The functional value of the crystals is discussed and they are compared with crystal forms found in human and animal urinary tracts.