Rotation Prevents Finite-Time Breakdown

We consider a two-dimensional convection model augmented with the rotational Coriolis forcing, $U_t + U\cdot\nabla_x U = 2k U^\perp$, with a fixed $2k$ being the inverse Rossby number. We ask whether the action of dispersive rotational forcing alone, $U^\perp$, prevents the generic finite time breakdown of the free nonlinear convection. The answer provided in this work is a conditional yes. Namely, we show that the rotating Euler equations admit global smooth solutions for a subset of generic initial configurations. With other configurations, however, finite time breakdown of solutions may and actually does occur. Thus, global regularity depends on whether the initial configuration crosses an intrinsic, ${\mathcal O}(1)$ critical threshold, which is quantified in terms of the initial vorticity, $\omega_0=\nabla \times U_0$, and the initial spectral gap associated with the $2\times 2$ initial velocity gradient, $\eta_0:=\lambda_2(0)-\lambda_1(0), \lambda_j(0)= \lambda_j(\nabla U_0)$. Specifically, global regularity of the rotational Euler equation is ensured if and only if $4k \omega_0(\alpha) +\eta^2_0(\alpha) <4k^2, \forall \alpha \in \R^2$ . We also prove that the velocity field remains smooth if and only if it is periodic. We observe yet another remarkable periodic behavior exhibited by the {\em gradient} of the velocity field. The spectral dynamics of the Eulerian formulation reveals that the vorticity and the eigenvalues (and hence the divergence) of the flow evolve with their own path-dependent period. We conclude with a kinetic formulation of the rotating Euler equation

Dampening prey cycle overrides the impact of climate change on predator population dynamics : a long-term demographic study on tawny owls

Funded by ERA-Net BiodivERsA NERC. Grant Numbers: NE/E010660/1, NE/F021402/1, NE/G002045/1Peer reviewedPublisher PD

Low-lying bifurcations in cavity quantum electrodynamics

The interplay of quantum fluctuations with nonlinear dynamics is a central topic in the study of open quantum systems, connected to fundamental issues (such as decoherence and the quantum-classical transition) and practical applications (such as coherent information processing and the development of mesoscopic sensors/amplifiers). With this context in mind, we here present a computational study of some elementary bifurcations that occur in a driven and damped cavity quantum electrodynamics (cavity QED) model at low intracavity photon number. In particular, we utilize the single-atom cavity QED Master Equation and associated Stochastic Schrodinger Equations to characterize the equilibrium distribution and dynamical behavior of the quantized intracavity optical field in parameter regimes near points in the semiclassical (mean-field, Maxwell-Bloch) bifurcation set. Our numerical results show that the semiclassical limit sets are qualitatively preserved in the quantum stationary states, although quantum fluctuations apparently induce phase diffusion within periodic orbits and stochastic transitions between attractors. We restrict our attention to an experimentally realistic parameter regime.Comment: 13 pages, 10 figures, submitted to PR

Mixed LICORS: A Nonparametric Algorithm for Predictive State Reconstruction

We introduce 'mixed LICORS', an algorithm for learning nonlinear, high-dimensional dynamics from spatio-temporal data, suitable for both prediction and simulation. Mixed LICORS extends the recent LICORS algorithm (Goerg and Shalizi, 2012) from hard clustering of predictive distributions to a non-parametric, EM-like soft clustering. This retains the asymptotic predictive optimality of LICORS, but, as we show in simulations, greatly improves out-of-sample forecasts with limited data. The new method is implemented in the publicly-available R package "LICORS" (http://cran.r-project.org/web/packages/LICORS/).Comment: 11 pages; AISTATS 201