Randomized Rounding for the Largest Simplex Problem

The maximum volume $j$-simplex problem asks to compute the $j$-dimensional simplex of maximum volume inside the convex hull of a given set of $n$ points in $\mathbb{Q}^d$. We give a deterministic approximation algorithm for this problem which achieves an approximation ratio of $e^{j/2 + o(j)}$. The problem is known to be $\mathrm{NP}$-hard to approximate within a factor of $c^{j}$ for some constant $c > 1$. Our algorithm also gives a factor $e^{j + o(j)}$ approximation for the problem of finding the principal $j\times j$ submatrix of a rank $d$ positive semidefinite matrix with the largest determinant. We achieve our approximation by rounding solutions to a generalization of the $D$-optimal design problem, or, equivalently, the dual of an appropriate smallest enclosing ellipsoid problem. Our arguments give a short and simple proof of a restricted invertibility principle for determinants

MEMS calorimetric transducers for flow separation detection and control

International audienceRobust micro machined high temperature gradient calorimetric (HTGC) transducers were developed for flow separation control. Based on thermal principle, the transducers measure the mean and fluctuating bidirectional shear stress that is particularly useful for flow separation detection. More than a hundred micro-sensors were simultaneously micro-machined using MEMS technology. A flexible array of calorimetric micro-sensors was implemented with miniaturized electronics on a flap model also equipped with pulsed jet actuators. Flow control experiments were successfully conducted as the natural separation occurring on the model was detected the HTGC micro sensors and controlled by pulsed jet actuation

A note on some embedding problems for oriented graphs

We conjecture that every oriented graph G on n vertices with δ+(G), δ−(G)≥5n/12 contains the square of a Hamilton cycle. We also give a conjectural bound on the minimum semidegree which ensures a perfect packing of transitive triangles in an oriented graph. A link between Ramsey numbers and perfect packings of transitive tournaments is also considere

Original MEMS wall shear stress sensors developed for separation detection and active flow control on a flap model

Active flow control systems are developed to promote air safety, reduce energetic consumption or increase airplanes efficiency. Sensors are needed to measure flow parameters at high frequencies with a high spatial resolution and micro-electro-mechanical system (MEMS) sensors are potential candidates for precise and located measurements. We present an original MEMS thermal flow sensor designed for flow control and separation detection. The general aim of the work is to run active flow control experiments integrating several MEMS sensors into a motorized deflectable flap model where the actuation is provided by pulsed jets, following previous work performed by Chabert et al. [1].   The micro-sensor is sensitive to the wall shear stress and flow direction [2]. It can be flush mounted to the wall for separation detection and flow control applications. The micro-fabrication process is CMOS-compatible meaning that it allows on-chip integration for designing very small devices. The micro-sensor structure combines suspended wires, free from the substrate, and micro-bridges used as mechanical supports. Designed to be set perpendicularly to the flow, the sensor presents three parallel heated wires. The central wire is structured with multiple layers with a heater, made of gold, and a sensing wire, placed under the heater and made of Ni/Pt multilayer. This central sensing wire is designed to measure the wall shear stress. The other two sensing wires, placed on both side of the central wire, allow flow direction sensing when considering the temperature variation between them as the wire upstream is more cooled than the wire downstream. The micro-wires dimensions, 3 µm width for 1 mm length, and the fact that they are suspended over a 20-µm-deep cavity, allow a high gradient of temperature for low power consumption (8 °C/mW for the central wire and 5 °C/mW for the lateral wires). The micro-sensor was characterized in a turbulent boundary layer wind tunnel by measuring the resistance variations, simultaneously with the wall shear stress fluctuations, measured by near wall hot-wire anemometry. The sensor demonstrates a resistance variation up to 0.3 % for 2.4 Pa for the central wire. The flow direction measurements were performed using the resistance difference between the two lateral wires. The purpose is to provide a way to detect the presence of a flow separation since in such a situation, the velocity field near the wall is reversed. The sensor setup in the wind tunnel enables to rotate it from 0° to 180°, considering that, at 90°, the wires are parallel to the flow. The results demonstrate the sensor ability to detect the flow direction: the resistance difference is +0.25 ? for 0°, 0 for 90° and -0.25 ? for 180°, all for a wall shear stress of 1 Pa. A second set of experiments were performed by adding an obstacle on the wind tunnel wall, upstream of the MEMS sensor, to cause flow separation at the sensor location. The central wire of the sensor, designed for wall shear stress measurements, present an expected behavior: the sensor detects the decrease of wall shear stress in a separated flow. And the lateral wires detect the flow direction inversion, providing an additional information compared to conventional hot-film sensors.  The results demonstrate the sensor ability to measure the wall shear stress and to detect flow separation. Currently, the sensors integration in the flap model is in progress and open-loop active flow control experiments will begin at ONERA Lille. The first results will be presented in the full paper. References: [1] T. Chabert, Thèse, Université Pierre et Marie Curie - Paris VI, 2014. [2] C. Ghouila-Houri et al., Appl. Phys. Lett., vol. 109, no. 24, p. 241905, Dec. 2016

On graphs associated to sets of rankings

In this paper we analyze families of rankings by studying structural properties of graphs. Given a finite number of elements and a set of rankings of those elements, two elements compete when they exchange their relative positions in at least two rankings, and we can associate an undirected graph to a set of rankings by connecting elements that compete. We call this graph a competitivity graph. Competitivity graphs have already appeared in the literature as co-comparability graphs, f-graphs or intersection graphs associated to a concatenation of permutation diagrams. We introduce certain important sets of nodes in a competitivity graph. For example, nodes that compete among them form a competitivity set and nodes connected by chains of competitors form a set of eventual competitors. These sets are analyzed and a method to obtain sets of eventual competitors directly from a set of rankings is shown. © 2015 Elsevier B.V.This paper was partially supported by Spanish MICINN Funds and FEDER Funds MTM2009-13848, MTM2010-16153 and MTM2010-18674, and Junta de Andalucia Funds FQM-264. The authors would like to thank an anonymous referee for the valuable comments and remarks.Criado Herrero, R.; García, E.; Pedroche Sánchez, F.; Romance, M. (2016). On graphs associated to sets of rankings. Journal of Computational and Applied Mathematics. 291:497-508. doi:10.1016/j.cam.2015.03.009S49750829

Nanogap Pirani Sensor Operating in Constant Temperature Mode for Near Atmospheric Pressure Measurements

This paper presents a high sensitive micro-sensor designed for pressure measurements in a wide range around atmospheric pressure, for application in aerodynamics. The sensor is a temperature-resistance transducer operating with the Pirani effect, which states that below a certain pressure limit, the thermal conductivity of a gas is pressure-dependent. The sensor presents a wide measurement range between 10 kPa and about 800 kPa, in both constant current and constant temperature mode. The last mode enables high-sensitive measurements with a maximum of sensitivity around atmospheric pressure, enabling the use of the sensor for applications in aerodynamics and fluid dynamics, such as active flow control