Nonlinear Axisymmetric Deformation Model for Structures of Revolution

An axisymmetric formulation for modeling three-dimensional deformation of structures of revolution is presented. The axisymmetric deformation model is described using the cylindrical coordinate system. Large displacement effects and material nonlinearities and anisotropy are accommodated by the formulation. Mathematical derivation of the formulation is given, and an example is presented to demonstrate the capabilities and efficiency of the technique compared to the full three-dimensional model.     

Baire generic histograms of wavelet coefficients and large deviation formalism in Besov and Sobolev spaces

Histograms of wavelet coefficients are expressed in terms of the wavelet profile and the wavelet density. The large deviation multifractal formalism states that if a function f has a minimal uniform Hölder regularity then its Hölder spectrum is equal to the wavelet density. The purpose of this paper is twofold. Firstly, we compute generically (in the sense of Baire's categories) these histograms in Besov and Lp,s(T) spaces, where T is the torus Rd/Zd (resp. in the Baire's vector space where s:q?s(q) is a C¹ and concave function on R⁺ satisfying 0?s^′?d and s(0)>0). Secondly, as an application, we deduce some extra generic properties for the histograms in these spaces, and study the generic validity of the large deviation multifractal formalism in Besov and Lp,s spaces for s>d/p (resp. in the above space V).     

Network strength games: the core and the nucleolus

Mathematical Programming - The maximum number of edge-disjoint spanning trees in a network has been used as a measure of the strength of a network. It gives the number of disjoint ways that the...     

Synthesis of fullerodendrons with an ammonium unit at the focal point and their cooperative self-assembly on a fluorescent ditopic crown ether receptor

Dendritic branches with 1, 2, or 4 peripheral fullerene subunits and an ammonium function at the focal point have been prepared. Their ability to form self-assembled dendritic structures with oligophenylenevinylene receptors bearing one or two crown ether moieties has been evidenced by ES-MS studies for the first time. These supramolecular complexes are multicomponent photoactive devices in which the emission of the central receptor is dramatically quenched by the fullerene units. This new property resulting from the association of the different molecular subunits allowed detailed investigations of the self-assembly process by means of fluorescence titrations. The binding studies have revealed positive cooperative effects for the assembly of the fullerodendrimers with the ditopic receptor. Interestingly, the stability of the supramolecular 2:1 structures increases as the size of the dendritic unit increases. This positive dendritic effect has been explained by the larger number of possible intramolecular fullerene-fullerene interactions between the two dendritic guests when the number of fullerene subunits is increased.     

Completely monotonic functions involving the gamma and -gamma functions

We give an infinite family of functions involving the gamma function whose logarithmic derivatives are completely monotonic. Each such function gives rise to an infinitely divisible probability distribution. Other similar results are also obtained for specific combinations of the gamma and -gamma functions.

     

A moment problem and a family of integral evaluations

We study the Al-Salam-Chihara polynomials when . Several solutions of the associated moment problem are found, and the orthogonality relations lead to explicit evaluations of several integrals. The polynomials are shown to have raising and lowering operators and a second order operator equation of Sturm-Liouville type whose eigenvalues are found explicitly. We also derive new measures with respect to which the Ismail-Masson system of rational functions is biorthogonal. An integral representation of the right inverse of a divided difference operator is also obtained.

     

The No Response Test for the reconstruction of polyhedral objects in electromagnetics

We develop a No Response Test for the reconstruction of a polyhedral obstacle from two or few time-harmonic electromagnetic incident waves in electromagnetics. The basic idea of the test is to probe some region in space with waves which are small on some test domain and, thus, do not generate a response when the scatterer is inside of this test domain. We will prove that the No Response Test checks analytic continuability of a time-harmonic field from the far field pattern into the domain for a non-vibrating test domain B.We show that two incident waves, defined by one incident direction and two appropriately chosen directions of polarization, are enough to recover the convex hull of polyhedrals. Based on this uniqueness result, we build up the No Response Test and we prove convergence in the sense that it fully reconstructs a convex polyhedral scatterer D or the convex hull of an arbitrary polyhedral scatterer.Further, we will describe the algorithmic realization of the No Response Test and show the feasibility of the method by reconstruction of convex polyhedral objects in three dimensions. This is the first formulation of the No Response Test for electromagnetics.     

Flutter analysis of a viscoelastic tapered wing under bending–torsion loading

The dynamic stability of a tapered viscoelastic wing subjected to unsteady aerodynamic forces is investigated. The wing is considered as a cantilever tapered Euler–Bernoulli beam. The beam is made of a linear viscoelastic material where Kelvin–Voigt model is assumed to represent the viscoelastic behavior of the material. The governing equations of motion are derived through the extended Hamilton’s principle. The resulting partial differential equations are solved via Galerkin’s method along with the classical flutter investigation approach. The developed model is validated against the well-known Goland wing and HALE wing and good agreement is obtained. Different solution methods, namely; the k method, the p-k method, and the flutter determinant method are compared for the case of elastic wing. However, when the viscoelastic damping is introduced, the k and p-k methods become less effective. The flutter determinant method is modified and employed to carry out non-dimensional parametric study on the Goland wing. The study includes the effects of parameters such as the taper ratio, the density ratio, the viscoelastic damping of wing structure and many other parameters on the flutter speed and flutter frequency. The study reveals that a tapered wing would be more dynamically stable than a uniform wing. It is also observed that the viscoelastic damping provides wider stability region for the wing. The investigation shows that the density ratio, bending-to-torsion frequency ratio, and the radius of gyration have significant effects on the dynamic stability of the wing. Based on the obtained results, a wing with an elastic center and inertial center that are located closer to the mid-chord would be more dynamically stable.     

The layered iron phosphate KMgFe(PO4)2: Crystal structure,Mössbauer spectroscopy and ionic conductivity

A new iron phosphate, KMgFe(PO₄)₂ has been synthesized and investigated by X-ray diffraction, Mössbauer spectroscopy and ionic conductivity. This compound crystallizes in the monoclinic space group C2/c with the parameters a = 18.529(7) Å, b = 5.402(3) Å, c = 9.374(9) Å, β = 120.64(5)° and Z = 4. Its original structure can be described as the stacking along the [101] direction of [MgFe(PO₄)^?₂]_∞ layers of corner-sharing MO₄ (M = 0.5 Fe + 0.5 Mg) and PO₄ tetrahedra. The K⁺ ions are occupying the inter-layer space. The Mössbauer spectroscopy confirms the occurrence of only tetrahedral Fe³⁺ ions and gives a definitive proof of the disordered character of their distribution. Ionic conductivity results obtained by the impedance spectroscopy technique show that this material is a two-dimensional ionic conductor, with low activation energy, 0.51 eV, that is interpreted on the basis of two-dimensional pathways.     

A Shack–Hartmann measuring head for the two‐dimensional characterization of X‐ray mirrors

The recent development of short‐wavelength optics (X/EUV, synchrotrons) requires improved metrology techniques in terms of accuracy and curvature dynamic range. In this article a stitching Shack–Hartmann head dedicated to be mounted on translation stages for the characterization of X‐ray mirrors is presented. The principle of the instrument is described and experimental results for an X‐ray toroidal mirror are presented. Submicroradian performances can be achieved and systematic comparison with a classical long‐trace profiler is presented. The accuracy and wide dynamic range of the Shack–Hartmann long‐trace‐profiler head allow two‐dimensional characterizations of surface figure and curvature with a submillimeter spatial resolution.