A systematic formula for the asymptotic expansion of singular integrals

Asymptotic theories like the lifting-line, the slender body or the slender ship lead to lineintegrals with singular kernels. Sometimes these integrals are improper, that is to say that they are defined only by their Finite Part. To find asymptotic expansions of these integrals, the Matched Asymptotic Expansion Method is widely used along with other more specific methods depending on the kernel type. The first method is laborious and not systematic, and the other methods are sometimes too much specific to treat general cases. Moreover, all of them are not well adapted to deal with Finite Part integrals.Here, a new method is proposed to avoid the previous difficulties. This method is systematic for homogeneous kernels and gives approximations up to any order, as long as the derivative of the weight function exists at this given order. Moreover the occurrence of logarithmic terms in the expansion is explained and easily predictable. An elliptic integral and the classical lifting-line theory are treated to illustrate the ease of this method.

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Résumé Les théories asymptotiques telles que la ligne portante, le corps élancé ou le navire de grand allongement conduisent à des intégrales curvilignes à noyaux singuliers. Parfois, ces intégrales sont impropres c'est à dire qu'elles sont définies en Parties Finies. Différentes méthodes ont été mises au point pour trouver les développements asymptotiques de ces intégrales. Généralement elles dépendent fortement de la nature du noyau, et c'est finalement la méthode des développements raccordés qui est utilisées quand le noyau est trop compliqué. Cependant, cette méthode est laborieuse et comme les précèdentes non adaptée aux intégrales défines par leur Partie Finie.Une nouvelle méthode est proposée pour surmonter ces difficultés. Cette méthode est systématique pour les noyaux homogènes et donne les approximations à tout ordre pourvu que les dérivées de la fonction poids existent jusqu'à cet ordre. De plus la présence de termes logarithmiques dans le développement est expliquée et aisément prédictible.Une intégrale elliptique, ainsi que la fameuse théorie de la ligne portante sont traités pour illustrer les possibilités de la méthode.

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Nomenclature D domain of integration - f(x) weight function - FP Finite Part - h(x) weight function - I ,I _o bounded intervals - j, J integers - K(x, ) singular kernel - L, L integers - M integer defining the approximation order - P _k (x) Legendre polynomial - R set of real numbers - R(ß) equals 1 if is an integer and 0 if not - R _{f, J} ,R _{K, L} remainders of Taylor developments - S () equals either 1 or the sign function:sgn() - t, u, v, x variable of integration - , real numbers - homogeneity order of the kernel - F () Euler's integral (gamma function) - small parameter - [.] integer part of     

Preliminary report on detection of papillomaviruses types 6, 11, 16, and 18 in laryngeal benign and malignant lesions

Recently, clinicians have observed an increase in the incidence of laryngeal papilloma coincident with the rising incidence of venereal warts. The lesions occur in young adults of professional singing age. Different types of human papillomavirus (HPV) are presented. Gynecologic exam revealed cervical tumors, involving 18 HPV in benign and malignant lesions. Thirty patients with the following pathologic conditions were studied: 10 papillomas, 10 severe dysplasias, and 10 invasive cancers. All the lesions were located on the free edge of the vocal folds or the anterior commissure involving the epithelium. The results are as follows: 11 patients (33%) had virus infection, of which four had HPV 6 or HPV 11 on laryngeal papilloma, three had HPV 16 or HPV 18 on severe dysplasia, four had HPV 16 or HPV 18 on carcinoma; and 19 (66%) had no virus infection. Gynecologic research in this field is more advanced. However, this preliminary report raises interesting research questions in laryngology.     

Overview of finite elements simulation of temperature profile to estimate properties of materials 3D-printed by laser powder-bed fusion

Laser powder bed fusion(LPBF),like many other additive manufacturing techniques,offers flexibility in design expected to become a disruption to the manufacturing industry.The current cost of LPBF process does not favor a try-anderror way of research,which makes modelling and simulation a field of superior importance in that area of engineering.In this work,various methods used to overcome challenges in modeling at different levels of approximation of LPBF process are reviewed.Recent efforts made towards a reliable and computationally effective model to simulate LPBF process using finite element(FE)codes are presented.A combination of ray-tracing technique,the solution of the radiation transfer equation and absorption measurements has been used to establish an analytical equation,which gives a more accurate approximation of laser energy deposition in powder-substrate configuration.When this new analytical energy deposition model is used in in FE simulation,with other physics carefully set,it enables us to get reliable cooling curves and melt track morphology that agree well with experimental observations.The use of more computationally effective approximation,without explicit topological changes,allows to simulate wider geometries and longer scanning time leading to many applications in real engineering world.Different applications are herein presented including:prediction of printing quality through the simulated overlapping of consecutive melt tracks,simulation of LPBF of a mixture of materials and estimation of martensite inclusion in printed steel.     

Cytotoxicity and inflammation in human alveolar epithelial cells following exposure to occupational levels of gold and silver nanoparticles

This study explores the viability of rare earth-doped zirconia nanophosphors as probable candidates for white light emission. Undoped ZrO₂ and single- and double-doped ZrO₂:M (where M?=?Tb³⁺ and Eu³⁺) nanophosphors have been synthesized using a simple sonochemical process. The products were characterized using X-ray diffraction, scanning electron microscopy (SEM), transmission electron microscopy (TEM), high-resolution transmission electron microscopy (HRTEM), energy dispersive X-ray spectroscopy (EDS), and photoluminescence spectrophotometry. The SEM micrographs show that resultant nanoparticles have dendritic shape. TEM and HRTEM studies showed that the size of the majority of the nanoparticles were around 28?±?5?nm. Characteristic blue and green emission from Tb³⁺ ions and red from Eu³⁺ dopant ions were observed. The CIE coordinates of the double-doped ZrO₂:Tb³⁺ (1.2?%):Eu³⁺ (0.8?%) nanophosphor lie in the white light region of the chromaticity diagram and show promise as good phosphor materials for new lighting devices.     

Etude par RMN de la relaxation spin réseau d'un syst`eme AB de noyaux en interconversion lente

Nuclear Overhauser effects allow us to determine all transition probabilities in a two-spin AB system, using a triple resonance apparatus we have constructed. Theoretical and experimental studies of the relaxation in the special case where the nuclei belong to a molecule interconverting slowly between two different conformations have been made, and the exchange ratio has been deduced.     

Spaces of Tilings, Finite Telescopic Approximations and Gap-Labeling

The continuous Hull of a repetitive tiling T in ℝ^d with the Finite Pattern Condition (FPC) inherits a minimal ℝ^d-lamination structure with flat leaves and a transversal which is a Cantor set. This class of tiling includes the Penrose & the Amman Benkker ones in 2D, as well as the icosahedral tilings in 3D. We show that the continuous Hull, with its canonical ℝ^d-action, can be seen as the projective limit of a suitable sequence of branched, oriented and flat compact d-manifolds. As a consequence, the longitudinal cohomology and the K-theory of the corresponding C*-algebra are obtained as direct limits of cohomology and K-theory of ordinary manifolds. Moreover, the space of invariant finite positive measures can be identified with a cone in the d^th homology group canonically associated with the orientation of ℝ^d. At last, the gap labeling theorem holds: given an invariant ergodic probability measure μ on the Hull the corresponding Integrated Density of States (IDS) of any selfadjoint operators affiliated to takes on values on spectral gaps in the ℤ-module generated by the occurrence probabilities of finite patches in the tiling. Accepted in Revised Form: 7 May 2005     

X-ray absorption study of Cu,Zn SOD under high pressure

Abstract

We have investigated Cu, Zn Superoxide Dismutase (Cu, Zn SOD) metal sites at high pressure using X-ray absorption. XAS (X-ray Absorption Spectroscopy) gives information on local structure and it is particularly suited to metal site investigation. To the best of our knowledge, this is the first time that protein conformational states have been investigated using the high pressure XAS technique. Cu, Zn SOD catalyses the dismutation of toxic oxygen radicals produced in cells; this reaction occurs at the copper metal site. Structural changes around the copper, induced by pressure, can be directly related to protein substates. Their characterisation is thus important in the understanding of protein activity.

The high-pressure device was a Paris-Edinburgh large volume cell.

Experiments were performed on lyophilised Cu, Zn SOD between 0 and 48 kbar at the copper and zinc K-edges. The two metal local atomic environments have a different behaviour as pressure increases: copper exhibits a more flexible environment; on the contrary, zinc shows small structural modifications. We have identified a state, formed between 3 and 8 kbar, which is stable up to 48 kbar.     

The modelling of desk screens by a combined BEM – Source image approach

An original BEM approach is proposed to study the efficiency of desk screens in open plan offices. For large offices the volume geometry can be approximated by two horizontal planes – for floor and ceiling – and the source image approach is used to compute an approximated room Green function. When used in combination with the BEM approach, this allows reducing the discretised boundary to the desks only. The computation of the room Green functions is based on the modelling of the floor and ceiling response by means of the image source approach. The proposed approach is validated both numerically and experimentally. Very significant reductions of computation times have been obtained. The approach is used in an attempt to design efficient desk screens.     

Electron irradiation-enhanced core/shell organization of Al(Cr,Fe, Mn)Si dispersoids in Al–Mg–Si alloys

The age hardening 6061-T6 aluminium alloy has been chosen as structural material for the core vessel of the material testing Jules Horowitz nuclear reactor. The alloy contains incoherent Al(Cr, Fe, Mn)Si dispersoids whose characterization by energy-filtered transmission electron microscopy (EFTEM) analysis shows a core/shell organization tendency where the core is (Mn, Fe) rich, and the shell is Cr rich. The present work studies the stability of this organization under irradiation. TEM characterization on the same particles, before and after 1 MeV electron irradiation, reveals that the core/shell organization is enhanced after irradiation. It is proposed that the high level of point defects, created by irradiation, ensures a radiation-enhanced diffusion process favourable to the unmixing forces between (Fe, Mn) and Cr. Shell formation may result in the low-energy interface segregation of Cr atoms within the (Fe, Mn) system combined with the unmixing of Cr, Fe and Mn components.