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The Omori-Utsu law shows the temporal power-law-like decrease of the frequency of earthquake aftershocks and, interestingly, is found in a variety of complex systems/phenomena exhibiting catastrophes. Now, it may be interpreted as a characteristic response of such systems to large events. Here, hierarchical dynamics with the fast and slow degrees of freedom is studied on the basis of the Fokker-Planck theory for the load-state distribution to formulate the law as a relaxation process, in which diffusion coefficient in the space of the load state is treated as a fluctuating slow variable. The evolution equation reduced from the full Fokker-Planck equation and its Green's function are analyzed for the subdynamics governing the load state as the fast degree of freedom. It is shown that the subsystem has the temporal translational invariance in the logarithmic time, not in the conventional time, and consequently the aging phenomenon appears. [ABSTRACT FROM AUTHOR]

A mononuclear Co(II) complex of a Schiff base ligand derived from 5-Bromo-vanillin and 4-aminoantipyrine, that has a compressed tetragonal bipyramidal geometry and exhibiting field-induced slow magnetic relaxation, has been synthesized and characterized by single crystal X-ray diffraction, elemental analysis and molecular spectroscopy. In the crystal packing, a hydrogen-bonded dimer structural topology has been observed with two distinct metal centers having slightly different bond parameters. The complex has been further investigated for its magnetic nature on a SQUID magnetometer. The DC magnetic data confirm that the complex behaves as a typical S = 3/2 spin system with a sizable axial zero-field splitting parameter D/hc = 38 cm−1. The AC susceptibility data reveal that the relaxation time for the single-mode relaxation process is τ = 0.16(1) ms at T = 2.0 K and BDC = 0.12 T. [ABSTRACT FROM AUTHOR]