Self-similar aftershock rates

In many important systems exhibiting crackling noise --- intermittent avalanche-like relaxation response with power-law and, thus, self-similar distributed event sizes --- the "laws" for the rate of activity after large events are not consistent with the overall self-similar behavior expected on theoretical grounds. This is in particular true for the case of seismicity and a satisfying solution to this paradox has remained outstanding. Here, we propose a generalized description of the aftershock rates which is both self-similar and consistent with all other known self-similar features. Comparing our theoretical predictions with high resolution earthquake data from Southern California we find excellent agreement, providing in particular clear evidence for a unified description of aftershocks and foreshocks. This may offer an improved way of time-dependent seismic hazard assessment and earthquake forecasting

Self-organization and time-stability of social hierarchies

The formation and stability of social hierarchies is a question of general relevance. Here, we propose a simple generalized theoretical model for establishing social hierarchy via pair-wise interactions between individuals and investigate its stability. In each interaction or fight, the probability of "winning" depends solely on the relative societal status of the participants, and the winner has a gain of status whereas there is an equal loss to the loser. The interactions are characterized by two parameters. The first parameter represents how much can be lost, and the second parameter represents the degree to which even a small difference of status can guarantee a win for the higher-status individual. Depending on the parameters, the resulting status distributions reach either a continuous unimodal form or lead to a totalitarian end state with one high-status individual and all other individuals having status approaching zero. However, we find that in the latter case long-lived intermediary distributions often exist, which can give the illusion of a stable society. As we show, our model allows us to make predictions consistent with animal interaction data and their evolution over a number of years. Moreover, by implementing a simple, but realistic rule that restricts interactions to sufficiently similar-status individuals, the stable or long-lived distributions acquire high-status structure corresponding to a distinct high-status class. Using household income as a proxy for societal status in human societies, we find agreement over their entire range from the low-to-middle-status parts to the characteristic high-status "tail". We discuss how the model provides a conceptual framework for understanding the origin of social hierarchy and the factors which lead to the preservation or deterioration of the societal structure.Comment: Added sections 4.1 and S2.A about agonistic interactions in animals, added sections 4.2.1 and S2.B regarding potential proxies for societal status in non-human animals, added references to sections 1 and 2. Main text: 34 pages, 11 figures. Supplementary appendices: 36 pages, 24 figure

Are seismic waiting time distributions universal?

We show that seismic waiting time distributions in California and Iceland have many features in common as, for example, a power-law decay with exponent $\alpha \approx 1.1$ for intermediate and with exponent $\gamma \approx 0.6$ for short waiting times. While the transition point between these two regimes scales proportionally with the size of the considered area, the full distribution is not universal and depends in a non-trivial way on the geological area under consideration and its size. This is due to the spatial distribution of epicenters which does \emph{not} form a simple mono-fractal. Yet, the dependence of the waiting time distributions on the threshold magnitude seems to be universal.Comment: 5 pages, 4 figures, accepted for publication in Geophys. Res. Let

Chimera patterns in conservative systems and ultracold atoms with mediated nonlocal hopping

Chimera patterns, characterized by coexisting regions of phase coherence and incoherence, have so far been studied in non-conservative systems with dissipation. Here, we show that the formation of chimera patterns can also be observed in conservative Hamiltonian systems with nonlocal hopping in which both energy and particle number are conserved. Effective nonlocality can be realized in a physical system with only local coupling if different time scales exist, which can be illustrated by a minimal conservative model with an additional mediating channel. Finally, we show that the patterns should be observable in ultracold atomic systems. Nonlocal spatial hopping over up to tens of lattice sites with independently tunable hopping strength and on-site nonlinearity can be implemented in a two-component Bose-Einstein condensate with a spin-dependent optical lattice, where the untrapped component serves as the matter-wave mediating field. The present work highlights the connections between chimera patterns, nonlinear dynamics, condensed matter, and ultracold atoms.Comment: 4 figures with supplementar