71 research outputs found
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
for intermediate and with exponent
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
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