On the regularization of impact without collision: the Painlevé paradox and compliance

We consider the problem of a rigid body, subject to a unilateral constraint, in the presence of Coulomb friction. We regularize the problem by assuming compliance (with both stiffness and damping) at the point of contact, for a general class of normal reaction forces. Using a rigorous mathematical approach, we recover impact without collision (IWC) in both the inconsistent and indeterminate Painlev\'e paradoxes, in the latter case giving an exact formula for conditions that separate IWC and lift-off. We solve the problem for arbitrary values of the compliance damping and give explicit asymptotic expressions in the limiting cases of small and large damping, all for a large class of rigid bodies.Comment: Compared to previous version of the paper, we have: (a) Added a new theorem 2, (b) added a new discussion section with numerical computations, and (c) changed the overall exposition of the manuscrip

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

K2 Variable Catalogue II: Machine Learning Classification of Variable Stars and Eclipsing Binaries in K2 Fields 0-4

We are entering an era of unprecedented quantities of data from current and planned survey telescopes. To maximise the potential of such surveys, automated data analysis techniques are required. Here we implement a new methodology for variable star classification, through the combination of Kohonen Self Organising Maps (SOM, an unsupervised machine learning algorithm) and the more common Random Forest (RF) supervised machine learning technique. We apply this method to data from the K2 mission fields 0-4, finding 154 ab-type RR Lyraes (10 newly discovered), 377 Delta Scuti pulsators, 133 Gamma Doradus pulsators, 183 detached eclipsing binaries, 290 semi-detached or contact eclipsing binaries and 9399 other periodic (mostly spot-modulated) sources, once class significance cuts are taken into account. We present lightcurve features for all K2 stellar targets, including their three strongest detected frequencies, which can be used to study stellar rotation periods where the observed variability arises from spot modulation. The resulting catalogue of variable stars, classes, and associated data features are made available online. We publish our SOM code in Python as part of the open source PyMVPA package, which in combination with already available RF modules can be easily used to recreate the method.Comment: Accepted for publication in MNRAS, 16 pages, 13 figures. Updated with proof corrections. Full catalogue tables available at https://www2.warwick.ac.uk/fac/sci/physics/research/astro/people/armstrong/ or at the CD

Exotoxin-encoding gene content in community-acquired and hospital-acquired methicillin-resistant Staphylococcus aureus

AbstractReports of community-acquired methicillin-resistant Staphylococcus aureus (CA-MRSA) causing hospital infections are increasing, and it is questionable whether the existing molecular definition of CA-MRSA is suitable for the characterization of all strains involved. The 821 methicillin-resistant S. aureus (MRSA) isolates recovered from patients in Health Region East, Norway during the period 1991—2006 were characterized by multilocus sequence typing (MLST), staphylococcal cassette chromosome mec (SCCmec) typing, staphylococcal protein A (spa) gene typing, and their content of exotoxin-encoding genes. Cluster analysis based on exotoxin-encoding gene content was performed to separate the MRSA isolates into valid clusters with respect to microbiological characteristics. The analysis gave a four-cluster structure, and the four toxin clusters differed in the genetic lineages they included and in the diversity of the genetic lineages. A few genetic lineages were present in several toxin clusters. These results support the theory that mobile genetic elements encoding virulence genes do not move randomly among genetic lineages, but are restricted by the clonal lineages’ genetic background. Using the molecular criteria, MLST type, SCCmec type and the presence of the lucS/F-Panton–Valentine leukocidin (PVL) gene to define a CA-MRSA isolate, it was found that the CA-MRSA isolates mainly grouped together in two toxin clusters with a low prevalence of exotoxin-encoding genes. Statistical analyses supported the conclusion that toxin clusters with CA-MRSA genetic lineages were characterized by a low prevalence of exotoxin-encoding genes, whereas toxin clusters with hospital-acquired MRSA genetic lineages were characterized by a higher prevalence of exotoxin-encoding genes

The Certification of the Mass Concentrations of Aluminium, Selenium and Zinc in Human Serum, BCR-637, BCR-638, BCR-639.

Abstract not availableJRC.D-Institute for Reference Materials and Measurements (Geel

Computation of saddle type slow manifolds using iterative methods

This paper presents an alternative approach for the computation of trajectory segments on slow manifolds of saddle type. This approach is based on iterative methods rather than collocation-type methods. Compared to collocation methods, that require mesh refinements to ensure uniform convergence with respect to $\epsilon$, appropriate estimates are directly attainable using the method of this paper. The method is applied to several examples including: A model for a pair of neurons coupled by reciprocal inhibition with two slow and two fast variables and to the computation of homoclinic connections in the FitzHugh-Nagumo system.Comment: To appear in SIAM Journal of Applied Dynamical System