Statistical state dynamics of weak jets in barotropic beta-plane turbulence

Zonal jets in a barotropic setup emerge out of homogeneous turbulence through a flow-forming instability of the homogeneous turbulent state (`zonostrophic instability') which occurs as the turbulence intensity increases. This has been demonstrated using the statistical state dynamics (SSD) framework with a closure at second order. Furthermore, it was shown that for small supercriticality the flow-forming instability follows Ginzburg-Landau (G-L) dynamics. Here, the SSD framework is used to study the equilibration of this flow-forming instability for small supercriticality. First, we compare the predictions of the weakly nonlinear G-L dynamics to the fully nonlinear SSD dynamics closed at second order for a wide ranges of parameters. A new branch of jet equilibria is revealed that is not contiguously connected with the G-L branch. This new branch at weak supercriticalities involves jets with larger amplitude compared to the ones of the G-L branch. Furthermore, this new branch continues even for subcritical values with respect to the linear flow-forming instability. Thus, a new nonlinear flow-forming instability out of homogeneous turbulence is revealed. Second, we investigate how both the linear flow-forming instability and the novel nonlinear flow-forming instability are equilibrated. We identify the physical processes underlying the jet equilibration as well as the types of eddies that contribute in each process. Third, we propose a modification of the diffusion coefficient of the G-L dynamics that is able to capture the asymmetric evolution for weak jets at scales other than the marginal scale (side-band instabilities) for the linear flow-forming instability.Comment: 27 pages, 17 figure

Kinetic energy functional for Fermi vapors in spherical harmonic confinement

Two equations are constructed which reflect, for fermions moving independently in a spherical harmonic potential, a differential virial theorem and a relation between the turning points of kinetic energy and particle densities. These equations are used to derive a differential equation for the particle density and a non-local kinetic energy functional.Comment: 8 pages, 2 figure

Metastable states of a ferromagnet on random thin graphs

We calculate the mean number of metastable states of an Ising ferromagnet on random thin graphs of fixed connectivity c. We find, as for mean field spin glasses that this mean increases exponentially with the number of sites, and is the same as that calculated for the +/- J spin glass on the same graphs. An annealed calculation of the number <N_{MS}(E)> of metastable states of energy E is carried out. For small c, an analytic result is obtained. The result is compared with the one obtained for spin glasses in order to discuss the role played by loops on thin graphs and hence the effect of real frustration on the distribution of metastable states.Comment: 15 pages, 3 figure

High-predation habitats affect the social dynamics of collective exploration in a shoaling fish

Collective decisions play a major role in the benefits that animals gain from living in groups. Although the mechanisms of how groups collectively make decisions have been extensively researched, the response of within-group dynamics to ecological conditions is virtually unknown, despite adaptation to the environment being a cornerstone in biology. We investigate how within-group interactions during exploration of a novel environment are shaped by predation, a major influence on the behavior of prey species. We tested guppies (Poecilia reticulata) from rivers varying in predation risk under controlled laboratory conditions and find the first evidence of differences in group interactions between animals adapted to different levels of predation. Fish from high-predation habitats showed the strongest negative relationship between initiating movements and following others, which resulted in less variability in the total number of movements made between individuals. This relationship between initiating movements and following others was associated with differentiation into initiators and followers, which was only observed in fish from high-predation rivers. The differentiation occurred rapidly, as trials lasted 5 min, and was related to shoal cohesion, where more diverse groups from high-predation habitats were more cohesive. Our results show that even within a single species over a small geographical range, decision-making in a social context can vary with local ecological factors