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

Rádio Escola no Ar: a Palavra (en)cantada na Educação Literária Antirracista

Nesta investigação qualitativa, pretendemos descrever e analisar as práticas de educação literária realizadas durante o curso de extensão Escola no Ar (2015 e 2016), com adolescentes da Escola Municipal de Ensino Fundamental Prezideu Amorim localizada no bairro Bonfim, Vitória ES. Nosso objetivo é discutir as práticas ler e dizer à luz da função humanizadora da literatura (CANDIDO, 1997) como possível contribuição à tomada de consciência da humanidade de quem tem a humanidade negada, formando leitores críticos aos racismos no Brasil a partir de poemas e palavra cantada que dialoguem não somente com a realidade socioeconômica e cultural dos estudantes, mas que também permitam problematizar a condição racial à qual estão submetidos os negros no país. Para tanto, serão consideradas as noções de racismos (dADESKY, 2005), ler e dizer (BAJARD, 2014) e educação literária (LEAHY-DIOS, 2013). Palavras-chave: Educação literária. Leitura. Dizer. Racismos

Final Technical Report for "Collaborative Research: Regional climate-change projections through next-generation empirical and dynamical models"

This project was a continuation of previous work under DOE CCPP funding in which we developed a twin approach of non-homogeneous hidden Markov models (NHMMs) and coupled ocean-atmosphere (O-A) intermediate-complexity models (ICMs) to identify the potentially predictable modes of climate variability, and to investigate their impacts on the regional-scale. We have developed a family of latent-variable NHMMs to simulate historical records of daily rainfall, and used them to downscale seasonal predictions. We have also developed empirical mode reduction (EMR) models for gaining insight into the underlying dynamics in observational data and general circulation model (GCM) simulations. Using coupled O-A ICMs, we have identified a new mechanism of interdecadal climate variability, involving the midlatitude oceans mesoscale eddy field and nonlinear, persistent atmospheric response to the oceanic anomalies. A related decadal mode is also identified, associated with the oceans thermohaline circulation. The goal of the continuation was to build on these ICM results and NHMM/EMR model developments and software to strengthen two key pillars of support for the development and application of climate models for climate change projections on time scales of decades to centuries, namely: (a) dynamical and theoretical understanding of decadal-to-interdecadal oscillations and their predictability; and (b) an interface from climate models to applications, in order to inform societal adaptation strategies to climate change at the regional scale, including model calibration, correction, downscaling and, most importantly, assessment and interpretation of spread and uncertainties in multi-model ensembles. Our main results from the grant consist of extensive further development of the hidden Markov models for rainfall simulation and downscaling specifically within the non-stationary climate change context together with the development of parallelized software; application of NHMMs to downscaling of rainfall projections over India; identification and analysis of decadal climate signals in data and models; and, studies of climate variability in terms of the dynamics of atmospheric flow regimes. Each of these project components is elaborated on below, followed by a list of publications resulting from the grant

Variational assimilation of Lagrangian data in oceanography

We consider the assimilation of Lagrangian data into a primitive equations circulation model of the ocean at basin scale. The Lagrangian data are positions of floats drifting at fixed depth. We aim at reconstructing the four-dimensional space-time circulation of the ocean. This problem is solved using the four-dimensional variational technique and the adjoint method. In this problem the control vector is chosen as being the initial state of the dynamical system. The observed variables, namely the positions of the floats, are expressed as a function of the control vector via a nonlinear observation operator. This method has been implemented and has the ability to reconstruct the main patterns of the oceanic circulation. Moreover it is very robust with respect to increase of time-sampling period of observations. We have run many twin experiments in order to analyze the sensitivity of our method to the number of floats, the time-sampling period and the vertical drift level. We compare also the performances of the Lagrangian method to that of the classical Eulerian one. Finally we study the impact of errors on observations.Comment: 31 page

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

Cluster Analysis of Typhoon Tracks. Part II: Large-Scale Circulation and ENSO

A new probabilistic clustering method, based on a regression mixture model, is used to describe tropical cyclone (TC) propagation in the western North Pacific (WNP). Seven clusters were obtained and described in Part I of this two-part study. In Part II, the present paper, the large-scale patterns of atmospheric circulation and sea surface temperature associated with each of the clusters are investigated, as well as associations with the phase of the El Niño–Southern Oscillation (ENSO). Composite wind field maps over the WNP provide a physically consistent picture of each TC type, and of its seasonality. Anomalous vorticity and outgoing longwave radiation indicate changes in the monsoon trough associated with different types of TC genesis and trajectory. The steering winds at 500 hPa are more zonal in the straight-moving clusters, with larger meridional components in the recurving ones. Higher values of vertical wind shear in the midlatitudes also accompany the straight-moving tracks, compared to the recurving ones. The influence of ENSO on TC activity over the WNP is clearly discerned in specific clusters. Two of the seven clusters are typical of El Niño events; their genesis locations are shifted southeastward and they are more intense. The largest cluster is recurving, located northwestward, and occurs more often during La Niña events. Two types of recurving and one of straight-moving tracks occur preferentially when the Madden–Julian oscillation is active over the WNP region

Clustering of eastern North Pacific tropical cyclone tracks: ENSO and MJO effects

A probabilistic clustering technique is used to describe tropical cyclone tracks in the eastern North Pacific, on the basis of their shape and location. The best track data set is decomposed in terms of three clusters; these clusters are analyzed in terms of genesis location, trajectory, landfall, intensity, seasonality, and their relationships with the El Niño–Southern Oscillation (ENSO) and Madden-Julian Oscillation (MJO). Longitudinal track location plays a strong discriminating role in the regression mixture model's solution, with the average track orientation becoming more zonal toward the west. This progression encapsulates well the relationship between tropical cyclones over the eastern tropical Pacific and the MJO or ENSO. Two of the clusters describe tropical cyclones (TCs) with tracks that lie near the coast of Mexico and Central America. The most frequent cluster contains tracks that trend west-northwestward, while the second most frequent one has genesis locations that lie slightly to the southeast of those in the most frequent cluster and tracks that run typically parallel to the Central American coast. This second cluster is shown to be significantly associated with the westerly phase of the MJO. The third, least frequent cluster contains TCs with westward trajectories over the central and eastern equatorial Pacific; some of these TCs have an impact on Hawaii and other islands, as far as the central and western North Pacific regions. The least frequent cluster is strongly related to ENSO, while the others are not; it occurs significantly more frequently during El Niño conditions. Examination of the large-scale patterns of atmospheric circulation and sea surface temperature associated with each of our three clusters are consistent with previous studies. Anomalous low-level westerly zonal winds from the monsoon trough and MJO meet anomalous easterlies near the region of genesis in each cluster

Evidence of coupling in ocean-atmosphere dynamics over the North Atlantic

Coupling between the ocean and the atmosphere is investigated in reanalysis data sets. Projecting the data sets onto a dynamically defined subspace allows one to isolate the dominant modes of variability of the coupled system. This coupled projection is then analyzed using multichannel singular spectrum analysis. The results suggest that a dominant low-frequency signal with a 25-30 year period already mentioned in the literature is a common mode of variability of the atmosphere and the ocean. A new score for evaluating the internal nature of the common variability is then introduced, and it confirms the presence of coupled dynamics in the ocean-atmosphere system that impacts the atmosphere at large scale. The physical nature of this coupled dynamics is then discussed