NDT of Specimen of Complex Geometry Using Ultrasonic Adaptive Techniques - The F.A.U.S.T. System

Phased array techniques, providing an electronic control of the beam, are widely used in ultrasonic imaging. Such techniques, making use of array transducers with delayed transmission pulse on each element, allow to steer and focus the beam, enabling various testing configurations and imaging procedures : sector scanning and tomography, tracking echoes, depth focusing. In nuclear industry, various configurations of geometry and materials are encountered, which require many different testing configurations. The CEA (French Atomic Energy Commission) has developed an adaptive system based on phased array techniques dynamically controlled by a multi-channel acquisition system: theF.A.U.S.T. (Focusing Adaptive UltraSonic Tomography) system. This system aims at improving the performances of nondestructive testing, particularly for what concerns the adaptability to different control configurations and defect characterization. Previous works have described this system, its performances for beam forming and also its specific abilities for defect characterization using beam steering or spatial amplitude distribution at reception [1, 2]

Serre's "formule de masse" in prime degree

For a local field F with finite residue field of characteristic p, we describe completely the structure of the filtered F_p[G]-module K^*/K^*p in characteristic 0 and $K^+/\wp(K^+) in characteristic p, where K=F(\root{p-1}\of F^*) and G=\Gal(K|F). As an application, we give an elementary proof of Serre's mass formula in degree p. We also determine the compositum C of all degree p separable extensions with solvable galoisian closure over an arbitrary base field, and show that C is K(\root p\of K^*) or K(\wp^{-1}(K)) respectively, in the case of the local field F. Our method allows us to compute the contribution of each character G\to\F_p^* to the degree p mass formula, and, for any given group \Gamma, the contribution of those degree p separable extensions of F whose galoisian closure has group \Gamma.Comment: 36 pages; most of the new material has been moved to the new Section

Rank one discrete valuations of power series fields

In this paper we study the rank one discrete valuations of the field $k((X_1,..., X_n))$ whose center in k\lcor\X\rcor is the maximal ideal. In sections 2 to 6 we give a construction of a system of parametric equations describing such valuations. This amounts to finding a parameter and a field of coefficients. We devote section 2 to finding an element of value 1, that is, a parameter. The field of coefficients is the residue field of the valuation, and it is given in section 5. The constructions given in these sections are not effective in the general case, because we need either to use the Zorn's lemma or to know explicitly a section $\sigma$ of the natural homomorphism R_v\to\d between the ring and the residue field of the valuation $v$. However, as a consequence of this construction, in section 7, we prove that k((\X)) can be embedded into a field L((\Y)), where $L$ is an algebraic extension of $k$ and the {\em ``extended valuation'' is as close as possible to the usual order function}

Stability and asymptotic behavior of periodic traveling wave solutions of viscous conservation laws in several dimensions

Under natural spectral stability assumptions motivated by previous investigations of the associated spectral stability problem, we determine sharp $L^p$ estimates on the linearized solution operator about a multidimensional planar periodic wave of a system of conservation laws with viscosity, yielding linearized $L^1\cap L^p\to L^p$ stability for all $p \ge 2$ and dimensions $d \ge 1$ and nonlinear $L^1\cap H^s\to L^p\cap H^s$ stability and $L^2$-asymptotic behavior for $p\ge 2$ and $d\ge 3$. The behavior can in general be rather complicated, involving both convective (i.e., wave-like) and diffusive effects

Complete intersections: Moduli, Torelli, and good reduction

We study the arithmetic of complete intersections in projective space over number fields. Our main results include arithmetic Torelli theorems and versions of the Shafarevich conjecture, as proved for curves and abelian varieties by Faltings. For example, we prove an analogue of the Shafarevich conjecture for cubic and quartic threefolds and intersections of two quadrics.Comment: 37 pages. Typo's fixed. Expanded Section 2.

Coating of conducting and insulating threads with porous mof particles through langmuir-blodgett technique

The Langmuir-Blodgett (LB) method is a well-known deposition technique for the fabrication of ordered monolayer and multilayer thin films of nanomaterials onto different substrates that plays a critical role in the development of functional devices for various applications. This paper describes detailed studies about the best coating configuration for nanoparticles of a porous metal-organic framework (MOF) onto both insulating or conductive threads and nylon fiber. We design and fabricate customized polymethylmethacrylate sheets (PMMA) holders to deposit MOF layers onto the threads or fiber using the LB technique. Two different orientations, namely, horizontal and vertical, are used to deposit MIL-96(Al) monolayer films onto five different types of threads and nylon fiber. These studies show that LB film formation strongly depends on deposition orientation and the type of threads or fiber. Among all the samples tested, cotton thread and nylon fiber with vertical deposition show more homogenous monolayer coverage. In the case of conductive threads, the MOF particles tend to aggregate between the conductive thread’s fibers instead of forming a continuous monolayer coating. Our results show a significant contribution in terms of MOF monolayer deposition onto single fiber and threads that will contribute to the fabrication of single fiber or thread-based devices in the future

Conformal Transformations of the Wigner Function and Solutions of the Quantum Corrected Vlasov Equation

We study conformal properties of the quantum kinetic equations in curved spacetime. A transformation law for the covariant Wigner function under conformal transformations of a spacetime is derived by using the formalism of tangent bundles. The conformal invariance of the quantum corrected Vlasov equation is proven. This provides a basis for generating new solutions of the quantum kinetic equations in the presence of gravitational and other external fields. We use our method to find explicit quantum corrections to the class of locally isotropic distributions, to which equilibrium distributions belong. We show that the quantum corrected stress--energy tensor for such distributions has, in general, a non--equilibrium structure. Local thermal equilibrium is possible in quantum systems only if an underlying spacetime is conformally static (not stationary). Possible applications of our results are discussed.Comment: 30 page

A fast neural-dynamical approach to scale-invariant object detection

We present a biologically-inspired method for object detection which is capable of online and one-shot learning of object appearance. We use a computationally efficient model of V1 keypoints to select object parts with the highest information content and model their surroundings by a simple binary descriptor based on responses of cortical cells. We feed these features into a dynamical neural network which binds compatible features together by employing a Bayesian criterion and a set of previously observed object views. We demonstrate the feasibility of our algorithm for cognitive robotic scenarios by evaluating detection performance on a dataset of common household items. © Springer International Publishing Switzerland 2014

Ramification theory for varieties over a local field

We define generalizations of classical invariants of wild ramification for coverings on a variety of arbitrary dimension over a local field. For an l-adic sheaf, we define its Swan class as a 0-cycle class supported on the wild ramification locus. We prove a formula of Riemann-Roch type for the Swan conductor of cohomology together with its relative version, assuming that the local field is of mixed characteristic. We also prove the integrality of the Swan class for curves over a local field as a generalization of the Hasse-Arf theorem. We derive a proof of a conjecture of Serre on the Artin character for a group action with an isolated fixed point on a regular local ring, assuming the dimension is 2.Comment: 159 pages, some corrections are mad

Blowup Criterion for the Compressible Flows with Vacuum States

We prove that the maximum norm of the deformation tensor of velocity gradients controls the possible breakdown of smooth(strong) solutions for the 3-dimensional compressible Navier-Stokes equations, which will happen, for example, if the initial density is compactly supported \cite{X1}. More precisely, if a solution of the compressible Navier-Stokes equations is initially regular and loses its regularity at some later time, then the loss of regularity implies the growth without bound of the deformation tensor as the critical time approaches. Our result is the same as Ponce's criterion for 3-dimensional incompressible Euler equations (\cite{po}). Moreover, our method can be generalized to the full Compressible Navier-Stokes system which improve the previous results. In addition, initial vacuum states are allowed in our cases.Comment: 17 page