On the use of blow up to study regularizations of singularities of piecewise smooth dynamical systems in R3\mathbb{R}^3

In this paper we use the blow up method of Dumortier and Roussarie \cite{dumortier_1991,dumortier_1993,dumortier_1996}, in the formulation due to Krupa and Szmolyan \cite{krupa_extending_2001}, to study the regularization of singularities of piecewise smooth dynamical systems \cite{filippov1988differential} in $\mathbb R^3$. Using the regularization method of Sotomayor and Teixeira \cite{Sotomayor96}, first we demonstrate the power of our approach by considering the case of a fold line. We quickly recover a main result of Bonet and Seara \cite{reves_regularization_2014} in a simple manner. Then, for the two-fold singularity, we show that the regularized system only fully retains the features of the singular canards in the piecewise smooth system in the cases when the sliding region does not include a full sector of singular canards. In particular, we show that every locally unique primary singular canard persists the regularizing perturbation. For the case of a sector of primary singular canards, we show that the regularized system contains a canard, provided a certain non-resonance condition holds. Finally, we provide numerical evidence for the existence of secondary canards near resonance.Comment: To appear in SIAM Journal of Applied Dynamical System

The Borexino Thermal Monitoring & Management System and simulations of the fluid-dynamics of the Borexino detector under asymmetrical, changing boundary conditions

A comprehensive monitoring system for the thermal environment inside the Borexino neutrino detector was developed and installed in order to reduce uncertainties in determining temperatures throughout the detector. A complementary thermal management system limits undesirable thermal couplings between the environment and Borexino's active sections. This strategy is bringing improved radioactive background conditions to the region of interest for the physics signal thanks to reduced fluid mixing induced in the liquid scintillator. Although fluid-dynamical equilibrium has not yet been fully reached, and thermal fine-tuning is possible, the system has proven extremely effective at stabilizing the detector's thermal conditions while offering precise insights into its mechanisms of internal thermal transport. Furthermore, a Computational Fluid-Dynamics analysis has been performed, based on the empirical measurements provided by the thermal monitoring system, and providing information into present and future thermal trends. A two-dimensional modeling approach was implemented in order to achieve a proper understanding of the thermal and fluid-dynamics in Borexino. It was optimized for different regions and periods of interest, focusing on the most critical effects that were identified as influencing background concentrations. Literature experimental case studies were reproduced to benchmark the method and settings, and a Borexino-specific benchmark was implemented in order to validate the modeling approach for thermal transport. Finally, fully-convective models were applied to understand general and specific fluid motions impacting the detector's Active Volume.Comment: arXiv admin note: substantial text overlap with arXiv:1705.09078, arXiv:1705.0965

Computing Slow Manifolds of Saddle Type

Slow manifolds are important geometric structures in the state spaces of dynamical systems with multiple time scales. This paper introduces an algorithm for computing trajectories on slow manifolds that are normally hyperbolic with both stable and unstable fast manifolds. We present two examples of bifurcation problems where these manifolds play a key role and a third example in which saddle-type slow manifolds are part of a traveling wave profile of a partial differential equation. Initial value solvers are incapable of computing trajectories on saddle-type slow manifolds, so the slow manifold of saddle type (SMST) algorithm presented here is formulated as a boundary value method. We take an empirical approach here to assessing the accuracy and effectiveness of the algorithm.Comment: preprint version - for final version see journal referenc

AAO Starbugs: software control and associated algorithms

The Australian Astronomical Observatory's TAIPAN instrument deploys 150 Starbug robots to position optical fibres to accuracies of 0.3 arcsec, on a 32 cm glass field plate on the focal plane of the 1.2 m UK-Schmidt telescope. This paper describes the software system developed to control and monitor the Starbugs, with particular emphasis on the automated path-finding algorithms, and the metrology software which keeps track of the position and motion of individual Starbugs as they independently move in a crowded field. The software employs a tiered approach to find a collision-free path for every Starbug, from its current position to its target location. This consists of three path-finding stages of increasing complexity and computational cost. For each Starbug a path is attempted using a simple method. If unsuccessful, subsequently more complex (and expensive) methods are tried until a valid path is found or the target is flagged as unreachable.Comment: 10 pages, to be published in Proc. SPIE 9913, Software and Cyberinfrastructure for Astronomy IV; 201

Vertical structure models of the 1990 equatorial disturbance on Saturn

In September 1990, an atmospheric disturbance in the form of an abnormally high albedo area developed in the equatorial region of Saturn. Events of this nature are exceedingly rare for this planet as they have been detected in the equatorial region on only two other occasions in over a century. In ongoing monitoring of the atmospheres of the outer planets, CCD imaging observations of Saturn by New Mexico State University's Tortugas Mountain Station were made before, during, and after the disturbance's formation through both broad-band filters and narrow-band visible/near-IR filters centered in methane absorption bands. Also, multispectral Hubble Space Telescope observations were made within weeks of the event and later in 1991. These observations were calibrated and scans of reflectivity at constant latitude are being modeled with a vertically inhomogeneous, multiple scattering model previously used to model Jupiter's South Equatorial Belt brightening event in 1989. In addition, the reflectivity of the disturbance as a function of the scattering angles is being obtained so as to model this feature's vertical structure in particular. A preliminary report of the modeling results will be presented

Relative cost-effectiveness of using a liquid human milk fortifier in preterm infants in the US

Objective: To estimate the cost-effectiveness of using a liquid human milk fortifier (LHMF) compared to a powdered human milk fortifier (PHMF) in preterm infants in the US from the perspective of third-party payers and parents. Methods: This was a decision modelling study using patient data obtained from a random- ized controlled trial comparing a LHMF with a PHMF in preterm infants, supplemented with additional data obtained by performing a chart review among 79% of the trial patients. The model estimated the cost-effectiveness of LHMF versus PHMF in US$at 2014/2015 prices. Results: More infants in the LHMF group were discharged home (92$10,497 per infant less in the LHMF group than the PHMF group ($240,928 versus$251,425). Conclusion: Using LHMF instead of PHMF in preterm infants enabled resources to be freed-up for alternative use within the system. There is no health economic reason why LHMF should not be used in preference to PHMF in the NICU

Proteomics reveals distinct mechanisms regulating the release of cytokines and alarmins during pyroptosis

A major pathway for proinflammatory protein release by macrophages is inflammasome-mediated pyroptotic cell death. As conventional secretion, unconventional secretion, and cell death are executed simultaneously, however, the cellular mechanisms regulating this complex paracrine program remain incompletely understood. Here, we devise a quantitative proteomics strategy to define the cellular exit route for each protein by pharmacological and genetic dissection of cellular checkpoints regulating protein release. We report the release of hundreds of proteins during pyroptosis, predominantly due to cell lysis. They comprise constitutively expressed and transcriptionally induced proteins derived from the cytoplasm and specific intracellular organelles. Many low-molecular-weight proteins including the cytokine interleukin-1b, alarmins, and lysosomal-cargo proteins exit cells in the absence of cell lysis. Cytokines and alarmins are released in an endoplasmic reticulum (ER)-Golgi-dependent manner as free proteins rather than by extracellular vesicles. Our work provides an experimental framework for the dissection of cellular exit pathways and a resource for pyroptotic protein release