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

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

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Elementa physiologiae corporis humani / auctore Alberto v. Haller... ; tomus secundus, sanguis, ejus motus, humorum separatio

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Operum anatomici argumenti minorum

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Index septem voluminum disputationum anatomicarum quas collegit et edidit Albertus v. Haller

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