Geometry of the ergodic quotient reveals coherent structures in flows

Dynamical systems that exhibit diverse behaviors can rarely be completely understood using a single approach. However, by identifying coherent structures in their state spaces, i.e., regions of uniform and simpler behavior, we could hope to study each of the structures separately and then form the understanding of the system as a whole. The method we present in this paper uses trajectory averages of scalar functions on the state space to: (a) identify invariant sets in the state space, (b) form coherent structures by aggregating invariant sets that are similar across multiple spatial scales. First, we construct the ergodic quotient, the object obtained by mapping trajectories to the space of trajectory averages of a function basis on the state space. Second, we endow the ergodic quotient with a metric structure that successfully captures how similar the invariant sets are in the state space. Finally, we parametrize the ergodic quotient using intrinsic diffusion modes on it. By segmenting the ergodic quotient based on the diffusion modes, we extract coherent features in the state space of the dynamical system. The algorithm is validated by analyzing the Arnold-Beltrami-Childress flow, which was the test-bed for alternative approaches: the Ulam's approximation of the transfer operator and the computation of Lagrangian Coherent Structures. Furthermore, we explain how the method extends the Poincar\'e map analysis for periodic flows. As a demonstration, we apply the method to a periodically-driven three-dimensional Hill's vortex flow, discovering unknown coherent structures in its state space. In the end, we discuss differences between the ergodic quotient and alternatives, propose a generalization to analysis of (quasi-)periodic structures, and lay out future research directions.Comment: Submitted to Elsevier Physica D: Nonlinear Phenomen

Precision Measurements of Stretching and Compression in Fluid Mixing

The mixing of an impurity into a flowing fluid is an important process in many areas of science, including geophysical processes, chemical reactors, and microfluidic devices. In some cases, for example periodic flows, the concepts of nonlinear dynamics provide a deep theoretical basis for understanding mixing. Unfortunately, the building blocks of this theory, i.e. the fixed points and invariant manifolds of the associated Poincare map, have remained inaccessible to direct experimental study, thus limiting the insight that could be obtained. Using precision measurements of tracer particle trajectories in a two-dimensional fluid flow producing chaotic mixing, we directly measure the time-dependent stretching and compression fields. These quantities, previously available only numerically, attain local maxima along lines coinciding with the stable and unstable manifolds, thus revealing the dynamical structures that control mixing. Contours or level sets of a passive impurity field are found to be aligned parallel to the lines of large compression (unstable manifolds) at each instant. This connection appears to persist as the onset of turbulence is approached.Comment: 5 pages, 5 figure

Severe Respiratory Insufficiency Complicating Epstein-Barr Virus Infection: Case Report and Review

We report a case involving a young adult who had life-threatening bilateral pneumonitis in the course of an acute Epstein-Barr virus (EBV) infection. Because of severe hypoxemia, the patient required mechanical ventilation and additional oxygenation by an intravascular oxygenator. The patient was treated with corticosteroids and survived without sequelae. Severe pulmonary involvement associated with EBV infection is a rare but potentially fatal complication of infectious mononucleosis. Similar cases reported in the literature are reviewed, and the therapeutic options for this particular complication are discusse

A configuration system for the ATLAS trigger

The ATLAS detector at CERN's Large Hadron Collider will be exposed to proton-proton collisions from beams crossing at 40 MHz that have to be reduced to the few 100 Hz allowed by the storage systems. A three-level trigger system has been designed to achieve this goal. We describe the configuration system under construction for the ATLAS trigger chain. It provides the trigger system with all the parameters required for decision taking and to record its history. The same system configures the event reconstruction, Monte Carlo simulation and data analysis, and provides tools for accessing and manipulating the configuration data in all contexts.Comment: 4 pages, 2 figures, contribution to the Conference on Computing in High Energy and Nuclear Physics (CHEP06), 13.-17. Feb 2006, Mumbai, Indi

Detecting barriers to transport: A review of different techniques

We review and discuss some different techniques for describing local dispersion properties in fluids. A recent Lagrangian diagnostics, based on the Finite Scale Lyapunov Exponent (FSLE), is presented and compared to the Finite Time Lyapunov Exponent (FTLE), and to the Okubo-Weiss (OW) and Hua-Klein (HK) criteria. We show that the OW and HK are a limiting case of the FTLE, and that the FSLE is the most efficient method for detecting the presence of cross-stream barriers. We illustrate our findings by considering two examples of geophysical interest: a kinematic meandering jet model, and Lagrangian tracers advected by stratospheric circulation.Comment: 15 pages, 9 figures, submitted to Physica

Elementa physiologiae corporis humani auctore Alberto v. Haller... : tomus tertius, respiratio vox

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