Winding number instability in the phase-turbulence regime of the Complex Ginzburg-Landau Equation

We give a statistical characterization of states with nonzero winding number in the Phase Turbulence (PT) regime of the one-dimensional Complex Ginzburg-Landau equation. We find that states with winding number larger than a critical one are unstable, in the sense that they decay to states with smaller winding number. The transition from Phase to Defect Turbulence is interpreted as an ergodicity breaking transition which occurs when the range of stable winding numbers vanishes. Asymptotically stable states which are not spatio-temporally chaotic are described within the PT regime of nonzero winding number.Comment: 4 pages,REVTeX, including 4 Figures. Latex (or postscript) version with figures available at http://formentor.uib.es/~montagne/textos/nupt

The Application of Lagrangian Descriptors to 3D Vector Fields

Since the 1980s, the application of concepts and ideas from Dynamical Systems Theory to analyze phase space structures has provided a fundamental framework to understand long-term evolution of trajectories in many physical systems. In this context, for the study of fluid transport and mixing the development of Lagrangian techniques that can capture the complex and rich dynamics of time dependent flows has been crucial. Many of these applications have been to atmospheric and oceanic flows in two-dimensional (2D) relevant scenarios. However, the geometrical structures that constitute the phase space structures in time dependent three-dimensional (3D) flows require further exploration. In this paper we explore the capability of Lagrangian Descriptors (LDs), a tool that has been successfully applied to time dependent 2D vector fields, to reveal phase space geometrical structures in 3D vector fields. In particular we show how LDs can be used to reveal phase space structures that govern and mediate phase space transport. We especially highlight the identification of Normally Hyperbolic Invariant Manifolds (NHIMs) and tori. We do this by applying this methodology to three specific dynamical systems: a 3D extension of the classical linear saddle system, a 3D extension of the classical Duffing system, and a geophysical fluid dynamics f-plane approximation model which is described by analytical wave solutions of the 3D Euler equations. We show that LDs successfully identify and recover the template of invariant manifolds that define the dynamics in phase space for these examples.S. Wiggins acknowledges the support of ONR Grant No. N00014-01-1-0769 and EPSRC Grant no. EP/P021123/1. A. M. Mancho acknowledges the support of ONR grant N00014-17-1-3003. V. J. Garc�?a-Garrido, J. Curbelo and A. M. Mancho thankfully acknowledge the computer resources provided by ICMAT. C.R. Mechoso was supported by the U.S. NSF grant AGS-1245069

How is the world changing ?: What does it mean for the rural poor ?

Rapport

The autism brain imaging data exchange: towards large-scale evaluation of the intrinsic brain architecture in autism

Autism spectrum disorders (ASDs) represent a formidable challenge for psychiatry and neuroscience because of their high prevalence, lifelong nature, complexity and substantial heterogeneity. Facing these obstacles requires large-scale multidisciplinary efforts. Although the field of genetics has pioneered data sharing for these reasons, neuroimaging had not kept pace. In response, we introduce the Autism Brain Imaging Data Exchange (ABIDE)—a grassroots consortium aggregating and openly sharing 1112 existing resting-state functional magnetic resonance imaging (R-fMRI) data sets with corresponding structural MRI and phenotypic information from 539 individuals with ASDs and 573 age-matched typical controls (TCs; 7–64 years) (http://fcon_1000.projects.nitrc.org/indi/abide/). Here, we present this resource and demonstrate its suitability for advancing knowledge of ASD neurobiology based on analyses of 360 male subjects with ASDs and 403 male age-matched TCs. We focused on whole-brain intrinsic functional connectivity and also survey a range of voxel-wise measures of intrinsic functional brain architecture. Whole-brain analyses reconciled seemingly disparate themes of both hypo- and hyperconnectivity in the ASD literature; both were detected, although hypoconnectivity dominated, particularly for corticocortical and interhemispheric functional connectivity. Exploratory analyses using an array of regional metrics of intrinsic brain function converged on common loci of dysfunction in ASDs (mid- and posterior insula and posterior cingulate cortex), and highlighted less commonly explored regions such as the thalamus. The survey of the ABIDE R-fMRI data sets provides unprecedented demonstrations of both replication and novel discovery. By pooling multiple international data sets, ABIDE is expected to accelerate the pace of discovery setting the stage for the next generation of ASD studies.status: publishe