A Nonlinear Analysis of the Averaged Euler Equations

This paper develops the geometry and analysis of the averaged Euler equations for ideal incompressible flow in domains in Euclidean space and on Riemannian manifolds, possibly with boundary. The averaged Euler equations involve a parameter $\alpha$; one interpretation is that they are obtained by ensemble averaging the Euler equations in Lagrangian representation over rapid fluctuations whose amplitudes are of order $\alpha$. The particle flows associated with these equations are shown to be geodesics on a suitable group of volume preserving diffeomorphisms, just as with the Euler equations themselves (according to Arnold's theorem), but with respect to a right invariant $H^1$ metric instead of the $L^2$ metric. The equations are also equivalent to those for a certain second grade fluid. Additional properties of the Euler equations, such as smoothness of the geodesic spray (the Ebin-Marsden theorem) are also shown to hold. Using this nonlinear analysis framework, the limit of zero viscosity for the corresponding viscous equations is shown to be a regular limit, {\it even in the presence of boundaries}.Comment: 25 pages, no figures, Dedicated to Vladimir Arnold on the occasion of his 60th birthday, Arnold Festschrift Volume 2 (in press

Comparative analysis of magnetic resonance in the polaron pair recombination and the triplet exciton-polaron quenching models

We present a comparative theoretical study of magnetic resonance within the polaron pair recombination (PPR) and the triplet exciton-polaron quenching (TPQ) models. Both models have been invoked to interpret the photoluminescence detected magnetic resonance (PLDMR) results in π -conjugated materials and devices. We show that resonance line shapes calculated within the two models differ dramatically in several regards. First, in the PPR model, the line shape exhibits unusual behavior upon increasing the microwave power: it evolves from fully positive at weak power to fully negative at strong power. In contrast, in the TPQ model, the PLDMR is completely positive, showing a monotonic saturation. Second, the two models predict different dependencies of the resonance signal on the photoexcitation power, P L . At low P L , the resonance amplitude Δ I / I is ∝ P L within the PPR model, while it is ∝ P 2 L crossing over to P 3 L within the TPQ model. On the physical level, the differences stem from different underlying spin dynamics. Most prominently, a negative resonance within the PPR model has its origin in the microwave-induced spin-Dicke effect, leading to the resonant quenching of photoluminescence. The spin-Dicke effect results from the spin-selective recombination, leading to a highly correlated precession of the on-resonance pair partners under the strong microwave power. This effect is not relevant for TPQ mechanism, where the strong zero-field splitting renders the majority of triplets off resonance. On the technical level, the analytical evaluation of the line shapes for the two models is enabled by the fact that these shapes can be expressed via the eigenvalues of a complex Hamiltonian. This bypasses the necessity of solving the much larger complex linear system of the stochastic Liouville equations. Our findings pave the way towards a reliable discrimination between the two mechanisms via cw PLDMR

Tunable perovskite-based photodetectors in optical sensing

Broad- and narrow-band, tunable perovskite photodetectors (PPDs) with size-dependent fast response times are demonstrated for the first time in optical sensing of analytes, including gas-phase and dissolved oxygen (DO), as well as glucose. The sensors included a LED excitation source and a polystyrene film with embedded oxygen-sensitive dyes, PtOEP or PdOEP. The analyte's dose-dependent photoluminescence (PL) intensity I and decay time τ were measured. Using the PPDs enabled monitoring gas-phase O2 at levels of 0 %–100 % with a sensitivity comparable to that of a Si photodiode. A broad dynamic range was similarly observed for DO monitoring and the limit of detection for glucose monitoring was ∼0.02 mM at an initial level of ∼0.26 mM DO. Importantly, the size-dependent fast response time of the PPDs enabled analyte monitoring via the preferred measurement of τ, rather than I, over a broad dynamic range, which was unattainable with organic photodetectors. The use of the narrow-band PPDs eliminated the need for optical filters, which leads to more compact device designs

Practice characteristics of Emergency Department extracorporeal cardiopulmonary resuscitation (eCPR) programs in the United States: The current state of the art of Emergency Department extracorporeal membrane oxygenation (ED ECMO).

PURPOSE: To characterize the current scope and practices of centers performing extracorporeal cardiopulmonary resuscitation (eCPR) on the undifferentiated patient with cardiac arrest in the emergency department. METHODS: We contacted all US centers in January 2016 that had submitted adult eCPR cases to the Extracorporeal Life Support Organization (ELSO) registry and surveyed them, querying for programs that had performed eCPR in the Emergency Department (ED ECMO). Our objective was to characterize the following domains of ED ECMO practice: program characteristics, patient selection, devices and techniques, and personnel. RESULTS: Among 99 centers queried, 70 responded. Among these, 36 centers performed ED ECMO. Nearly 93% of programs are based at academic/teaching hospitals. 65% of programs are less than 5 years old, and 60% of programs perform ≤3 cases per year. Most programs (90%) had inpatient eCPR or salvage ECMO programs prior to starting ED ECMO programs. The majority of programs do not have formal inclusion and exclusion criteria. Most programs preferentially obtain vascular access via the percutaneous route (70%) and many (40%) use mechanical CPR during cannulation. The most commonly used console is the Maquet Rotaflow(®). Cannulation is most often performed by cardiothoracic (CT) surgery, and nearly all programs (\u3e85%) involve CT surgeons, perfusionists, and pharmacists. CONCLUSIONS: Over a third of centers that submitted adult eCPR cases to ELSO have performed ED ECMO. These programs are largely based at academic hospitals, new, and have low volumes. They do not have many formal inclusion or exclusion criteria, and devices and techniques are variable

Rules for biological regulation based on error minimization

The control of gene expression involves complex mechanisms that show large variation in design. For example, genes can be turned on either by the binding of an activator (positive control) or the unbinding of a repressor (negative control). What determines the choice of mode of control for each gene? This study proposes rules for gene regulation based on the assumption that free regulatory sites are exposed to nonspecific binding errors, whereas sites bound to their cognate regulators are protected from errors. Hence, the selected mechanisms keep the sites bound to their designated regulators for most of the time, thus minimizing fitness-reducing errors. This offers an explanation of the empirically demonstrated Savageau demand rule: Genes that are needed often in the natural environment tend to be regulated by activators, and rarely needed genes tend to be regulated by repressors; in both cases, sites are bound for most of the time, and errors are minimized. The fitness advantage of error minimization appears to be readily selectable. The present approach can also generate rules for multi-regulator systems. The error-minimization framework raises several experimentally testable hypotheses. It may also apply to other biological regulation systems, such as those involving protein-protein interactions.Comment: biological physics, complex networks, systems biology, transcriptional regulation http://www.weizmann.ac.il/complex/tlusty/papers/PNAS2006.pdf http://www.pnas.org/content/103/11/3999.ful

Electronic Structure of Lanthanum Hydrides with Switchable Optical Properties

Recent dramatic changes in the optical properties of LaH_{2+x} and YH_{2+x} films discovered by Huiberts et al. suggest their electronic structure is described best by a local model. Electron correlation is important in H^- -centers and in explaining the transparent insulating behavior of LaH_3. The metal-insulator transition at $x\sim 0.8$ takes place in a band of highly localized states centered on the $H$-vacancies in the LaH_3 structure.Comment: plain tex, 3 figure

Robust Signal Processing in Living Cells

Cellular signaling networks have evolved an astonishing ability to function reliably and with high fidelity in uncertain environments. A crucial prerequisite for the high precision exhibited by many signaling circuits is their ability to keep the concentrations of active signaling compounds within tightly defined bounds, despite strong stochastic fluctuations in copy numbers and other detrimental influences. Based on a simple mathematical formalism, we identify topological organizing principles that facilitate such robust control of intracellular concentrations in the face of multifarious perturbations. Our framework allows us to judge whether a multiple-input-multiple-output reaction network is robust against large perturbations of network parameters and enables the predictive design of perfectly robust synthetic network architectures. Utilizing the Escherichia coli chemotaxis pathway as a hallmark example, we provide experimental evidence that our framework indeed allows us to unravel the topological organization of robust signaling. We demonstrate that the specific organization of the pathway allows the system to maintain global concentration robustness of the diffusible response regulator CheY with respect to several dominant perturbations. Our framework provides a counterpoint to the hypothesis that cellular function relies on an extensive machinery to fine-tune or control intracellular parameters. Rather, we suggest that for a large class of perturbations, there exists an appropriate topology that renders the network output invariant to the respective perturbations

Robustness in Glyoxylate Bypass Regulation

The glyoxylate bypass allows Escherichia coli to grow on carbon sources with only two carbons by bypassing the loss of carbons as CO2 in the tricarboxylic acid cycle. The flux toward this bypass is regulated by the phosphorylation of the enzyme isocitrate dehydrogenase (IDH) by a bifunctional kinase–phosphatase called IDHKP. In this system, IDH activity has been found to be remarkably robust with respect to wide variations in the total IDH protein concentration. Here, we examine possible mechanisms to explain this robustness. Explanations in which IDHKP works simultaneously as a first-order kinase and as a zero-order phosphatase with a single IDH binding site are found to be inconsistent with robustness. Instead, we suggest a robust mechanism where both substrates bind the bifunctional enzyme to form a ternary complex