Arnold maps with noise: Differentiability and non-monotonicity of the rotation number

Arnold's standard circle maps are widely used to study the quasi-periodic route to chaos and other phenomena associated with nonlinear dynamics in the presence of two rationally unrelated periodicities. In particular, the El Nino-Southern Oscillation (ENSO) phenomenon is a crucial component of climate variability on interannual time scales and it is dominated by the seasonal cycle, on the one hand, and an intrinsic oscillatory instability with a period of a few years, on the other. The role of meteorological phenomena on much shorter time scales, such as westerly wind bursts, has also been recognized and modeled as additive noise. We consider herein Arnold maps with additive, uniformly distributed noise. When the map's nonlinear term, scaled by the parameter $\epsilon$, is sufficiently small, i.e. $\epsilon < 1$, the map is known to be a diffeomorphism and the rotation number $\rho_{\omega}$ is a differentiable function of the driving frequency $\omega$. We concentrate on the rotation number's behavior as the nonlinearity becomes large, and show rigorously that $\rho _{\omega }$ is a differentiable function of $\omega$, even for $\epsilon \geq 1$, at every point at which the noise-perturbed map is mixing. We also provide a formula for the derivative of the rotation number. The reasoning relies on linear-response theory and a computer-aided proof. In the diffeomorphism case of $\epsilon <1$, the rotation number $\rho_{\omega }$ behaves monotonically with respect to $\omega$. We show, using again a computer-aided proof, that this is not the case when $\epsilon \geq 1$ and the map is not a diffeomorphism.Comment: Electronic copy of final peer-reviewed manuscript accepted for publication in the Journal of Statistical Physic

A Model of Intra-seasonal Oscillations in the Earth atmosphere

We suggest a way of rationalizing an intra-seasonal oscillations (IOs) of the Earth atmospheric flow as four meteorological relevant triads of interacting planetary waves, isolated from the system of all the rest planetary waves. Our model is independent of the topography (mountains, etc.) and gives a natural explanation of IOs both in the North and South Hemispheres. Spherical planetary waves are an example of a wave mesoscopic system obeying discrete resonances that also appears in other areas of physics.Comment: 4 pages, 2 figs, Submitted to PR

Boolean delay equations on networks: An application to economic damage propagation

We introduce economic models based on Boolean Delay Equations: this formalism makes easier to take into account the complexity of the interactions between firms and is particularly appropriate for studying the propagation of an initial damage due to a catastrophe. Here we concentrate on simple cases, which allow to understand the effects of multiple concurrent production paths as well as the presence of stochasticity in the path time lengths or in the network structure. In absence of flexibility, the shortening of production of a single firm in an isolated network with multiple connections usually ends up by attaining a finite fraction of the firms or the whole economy, whereas the interactions with the outside allow a partial recovering of the activity, giving rise to periodic solutions with waves of damage which propagate across the structure. The damage propagation speed is strongly dependent upon the topology. The existence of multiple concurrent production paths does not necessarily imply a slowing down of the propagation, which can be as fast as the shortest path.Comment: Latex, 52 pages with 22 eps figure

Octet, decuplet and antidecuplet magnetic moments in the chiral quark soliton model revisited

We reanalyse the magnetic moments of the baryon octet, decuplet, and antidecuplet within the framework of the chiral quark-soliton model, with SU(3) symmetry breaking taken into account. We consider the contributions of the mixing of higher representations to the magnetic moment operator arising from the SU(3) symmetry breaking. Dynamical parameters of the model are fixed by experimental data for the magnetic moments of the baryon octet and from the masses of the octet, decuplet and of $\Theta^{+}$. The magnetic moment of $\Theta^{+}$ depends rather strongly on the pion-nucleon sigma term and reads $-1.19 {\rm n.m.}$ to $-0.33 {\rm n.m.}$ for $\Sigma_{\pi N} = 45$ and 75 MeV respectively. The recently reported mass of $\Xi^{--}_{\bar{10}}(1862)$ is compatible with $\Sigma_{\pi N} = 73$ MeV. As a byproduct the strange magnetic moment of the nucleon is obtained with a value of $\mu^{(s)}_N =+0.39$ n.m.Comment: RevTeX is used. 12 pages, 3 figures, final version for publication in Phys. Rev.

Exotic and nonexotic magnetic transitions in the context of the SELEX and GRAAL experiments

We calculate magnetic transition moments in the chiral quark-soliton model, with explicit SU(3)-symmetry breaking taken into account. The dynamical model parameters are fixed by experimental data for the magnetic moments of the baryon octet and from the recent measurements of $\Theta^{+}$ mass. Known magnetic transition moments $\mu_{\Lambda\Sigma}$, $\mu_{N\Delta}$ are reproduced and predictions for other octet-decuplet and octet-antidecuplet transitions are given. In particular $\mu_{\Sigma\Sigma^{\ast}}$ recently constrained by SELEX is shown to be below $0.82 \mu_N$. The recent GRAAL data on $\eta$ photoproduction off the nucleon are explained in terms of a new narrow antidecuplet neutron-like resonance.Comment: 14 pages, 9 figures. Final version accepted for publication in Phys.Rev.

On quantifying the climate of the nonautonomous lorenz-63 model

The Lorenz-63 model has been frequently used to inform our understanding of the Earth's climate and provide insight for numerical weather and climate prediction. Most studies have focused on the autonomous (time invariant) model behaviour in which the model's parameters are constants. Here we investigate the properties of the model under time-varying parameters, providing a closer parallel to the challenges of climate prediction, in which climate forcing varies with time. Initial condition (IC) ensembles are used to construct frequency distributions of model variables and we interpret these distributions as the time-dependent climate of the model. Results are presented that demonstrate the impact of ICs on the transient behaviour of the model climate. The location in state space from which an IC ensemble is initiated is shown to significantly impact the time it takes for ensembles to converge. The implication for climate prediction is that the climate may, in parallel with weather forecasting, have states from which its future behaviour is more, or less, predictable in distribution. Evidence of resonant behaviour and path dependence is found in model distributions under time varying parameters, demonstrating that prediction in nonautonomous nonlinear systems can be sensitive to the details of time-dependent forcing/parameter variations. Single model realisations are shown to be unable to reliably represent the model's climate; a result which has implications for how real-world climatic timeseries from observation are interpreted. The results have significant implications for the design and interpretation of Global Climate Model experiments. Over the past 50 years, insight from research exploring the behaviour of simple nonlinear systems has been fundamental in developing approaches to weather and climate prediction. The analysis herein utilises the much studied Lorenz-63 model to understand the potential behaviour of nonlinear systems, such as the 5 climate, when subject to time-varying external forcing, such as variations in atmospheric greenhouse gases or solar output. Our primary aim is to provide insight which can guide new approaches to climate model experimental design and thereby better address the uncertainties associated with climate change prediction. We use ensembles of simulations to generate distributions which 10 we refer to as the \climate" of the time-variant Lorenz-63 model. In these ensemble experiments a model parameter is varied in a number of ways which can be seen as paralleling both idealised and realistic variations in external forcing of the real climate system. Our results demonstrate that predictability of climate distributions under time varying forcing can be highly sensitive to 15 the specification of initial states in ensemble simulations. This is a result which at a superficial level is similar to the well-known initial condition sensitivity in weather forecasting, but with different origins and different implications for ensemble design. We also demonstrate the existence of resonant behaviour and a dependence on the details of the \forcing" trajectory, thereby highlighting 20 further aspects of nonlinear system behaviour with important implications for climate prediction. Taken together, our results imply that current approaches to climate modeling may be at risk of under-sampling key uncertainties likely to be significant in predicting future climate

On Sub-ENSO Variability

Multichannel singular spectrum analysis (MSSA) of surface zonal wind, sea surface temperature (SST), 20° isotherm depth, and surface zonal current observations (between 1990 and 2004) identifies three coupled ocean–atmosphere modes of variability in the tropical Pacific: the El Niño–Southern Oscillation (ENSO), the annual cycle, and a mode with a 14–18-month period, which is referred to as sub-ENSO in this study. The sub-ENSO mode accounts for the near 18-month (near annual) variability prior to (following) the 1997/98 El Niño event. It was strongest during this El Niño event, with SST anomalies exceeding 1°C. Sub-ENSO peak SST anomalies are ENSO-like in structure and are associated with eastward propagating heat content variations. However, the SST anomalies are preceded by and in near quadrature with relatively strong remotely forced westward propagating zonal current variations, suggesting the sub-ENSO mode arises from the zonal-advective feedback. The sub-ENSO mode is found to exist also in an intermediate complexity model (ICM) of the tropical Pacific. A heat budget analysis of the model’s sub-ENSO mode shows it indeed arises from the zonal-advective feedback. In the model, both ENSO and sub-ENSO modes coexist, but there is a weak nonlinear interaction between them. Experiments also show that the observed changes in sub-ENSO’s characteristics may be explained by changes in the relative importance of zonal and vertical advection SST tendencies

The chromosphere: gateway to the corona, or the purgatory of solar physics?

I argue that one should attempt to understand the solar chromosphere not only for its own sake, but also if one is interested in the physics of: the corona; astrophysical dynamos; space weather; partially ionized plasmas; heliospheric UV radiation; the transition region. I outline curious observations which I personally find puzzling and deserving of attention.Comment: To appear in the proceedings of the 25th NSO Workshop "Chromospheric Structure and Dynamics. From Old Wisdom to New Insights", Memorie della Societa' Astronomica Italiana, Eds. Tritschler et a

Modeling the dynamics of glacial cycles

This article is concerned with the dynamics of glacial cycles observed in the geological record of the Pleistocene Epoch. It focuses on a conceptual model proposed by Maasch and Saltzman [J. Geophys. Res.,95, D2 (1990), pp. 1955-1963], which is based on physical arguments and emphasizes the role of atmospheric CO2 in the generation and persistence of periodic orbits (limit cycles). The model consists of three ordinary differential equations with four parameters for the anomalies of the total global ice mass, the atmospheric CO2 concentration, and the volume of the North Atlantic Deep Water (NADW). In this article, it is shown that a simplified two-dimensional symmetric version displays many of the essential features of the full model, including equilibrium states, limit cycles, their basic bifurcations, and a Bogdanov-Takens point that serves as an organizing center for the local and global dynamics. Also, symmetry breaking splits the Bogdanov-Takens point into two, with different local dynamics in their neighborhoods

Decreasing intensity of open-ocean convection in the Greenland and Iceland seas

The air–sea transfer of heat and fresh water plays a critical role in the global climate system. This is particularly true for the Greenland and Iceland seas, where these fluxes drive ocean convection that contributes to Denmark Strait overflow water, the densest component of the lower limb of the Atlantic Meridional Overturning Circulation (AMOC). Here we show that the wintertime retreat of sea ice in the region, combined with different rates of warming for the atmosphere and sea surface of the Greenland and Iceland seas, has resulted in statistically significant reductions of approximately 20% in the magnitude of the winter air–sea heat fluxes since 1979. We also show that modes of climate variability other than the North Atlantic Oscillation (NAO) are required to fully characterize the regional air–sea interaction. Mixed-layer model simulations imply that further decreases in atmospheric forcing will exceed a threshold for the Greenland Sea whereby convection will become depth limited, reducing the ventilation of mid-depth waters in the Nordic seas. In the Iceland Sea, further reductions have the potential to decrease the supply of the densest overflow waters to the AMOC