High-g accelerometer based on an in-fiber bragg grating sensor

An accelerometer based on an in-fiber Bragg grating sensor has been fabricated and demonstrated. The grating sensor operates linearly up to accelerations of 170,000g_n. The design, testing and performance of the accelerometer are discussed.     

Carbon nanotubes as nanoparticles collector

This communication reports on a new method for the collection of nanoparticles using carbon nanotubes (CNT) as collecting surfaces, by which the problem of agglomeration of nanoparticles can be circumvented. CNT (10–50 nm in diameter, 1–10 μm in length) were grown by thermal CVD at 923 K in a 7 v/v% C₂H₂ in N₂ mixture on electroless nickel-plated copper transmission electron microscopy (TEM) grids and Monel coupons. These samples were then placed downstream of an arc plasma reactor to collect individual copper nanoparticles (5–30 nm in diameter). It was observed that the Cu nanoparticles preferentially adhere onto CNT and that the macro-particles (diameter >1 μm), a usual co-product obtained with metal nanoparticles in the arc plasma synthesis, are not collected. Cu–Ni nanoparticles, a catalyst for CNT growth, were deposited on CNT to grow multibranched CNT. CNT-embedded thin films were produced by re-melting the deposited nanoparticles.     

Control and Stabilization Properties for a Singular Heat Equation with an Inverse-Square Potential

The goal of this article is to analyze control properties of parabolic equations with a singular potential ? μ/|x|², where μ is a real number. When μ ≤ (N ? 2)²/4, it was proved in [19 Vancostenoble , J. , Zuazua , E. ( 2008 ). Null controllability for the heat equation with singular inverse-square potentials . J. Funct. Anal. 254 : 1864 – 1902 .[Crossref], [Web of Science ®] , [Google Scholar]] that the equation can be controlled to zero with a distributed control which surrounds the singularity. In the present work, using Carleman estimates, we will prove that this assumption is not necessary, and that we can control the equation from any open subset as for the heat equation. Then we will study the case μ > (N ? 2)²/4, and prove that the situation changes completely: indeed, we will consider a sequence of regularized potentials μ/(|x|² + ?²), and prove that we cannot stabilize the corresponding systems uniformly with respect to ? > 0, due to the presence of explosive modes which concentrate around the singularity.     

Global Carleman Estimates for Waves and Applications

In this article, we extensively develop Carleman estimates for the wave equation and give some applications. We focus on the case of an observation of the flux on a part of the boundary satisfying the Gamma conditions of Lions. We will then consider two applications. The first one deals with the exact controllability problem for the wave equation with potential. Following the duality method proposed by Fursikov and Imanuvilov in the context of parabolic equations, we propose a constructive method to derive controls that weakly depend on the potentials. The second application concerns an inverse problem for the waves that consists in recovering an unknown time-independent potential from a single measurement of the flux. In that context, our approach does not yield any new stability result, but proposes a constructive algorithm to rebuild the potential. In both cases, the main idea is to introduce weighted functionals that contain the Carleman weights and then to take advantage of the freedom on the Carleman parameters to limit the influences of the potentials.     

Approximations of a Continuous Time Filter. Application to Optimal Allocation Problems in Finance

Abstract

In this article, we study a continuous time optimal filter and its various numerical approximations. This filter arises in an optimal allocation problem in the particular context of a non-stationary economy. We analyse the rates of convergence of the approximations of the filter when the model is misspecified and when the observations can only be made at discrete times. We give bounds that are uniform in time. Numerical results are presented.     

Accessibility and stability of the coalition structure core

This article shows that, for any transferable utility game in coalitional form with a nonempty coalition structure core, the number of steps required to switch from a payoff configuration out of the coalition structure core to a payoff configuration in the coalition structure core is less than or equal to $(n^2+4n)/4$ , where $n$ is the cardinality of the player set. This number improves the upper bounds found so far. We also provide a sufficient condition for the stability of the coalition structure core, i.e. a condition which ensures the accessibility of the coalition structure core in one step. On the class of simple games, this sufficient condition is also necessary and has a meaningful interpretation.     

Relaxation of residual stress and reentanglement of polymers in spin-coated films

Performing detailed studies of viscoelastic dewetting of thin polystyrene films on solid substrates, we demonstrate the existence of residual stress due to strongly out of equilibrium chain conformations and a reduced entanglement density resulting from film preparation by spin coating. The ratio of stress over elastic modulus was found to increase strongly with decreasing film thickness and increasing chain length. Full equilibration of chain conformations required long times comparable to bulk reptation times. However, for chains longer than about 3000 monomers, the residual stress relaxed faster, at a rate independent of chain length.