A Formulation of Anisotropic Elastic Damage Using Compact Tensor Formalism

An anisotropic elastic-damage model for initially-isotropic materials is presented. The model is based on a pseudo-logarithmic second-order damage tensor rate. To derive the complete expression of the tangent stiffness entering the rate constitutive law, various tensor operations and derivatives of tensor functions must be developed. Such derivations have been performed in compact form. Some useful tensor derivatives and a table of tensor algebra operations are given in Appendix. This note should interest engineering researchers involved in the development of constitutive models through tensor formalism. This revised version was published online in July 2006 with corrections to the Cover Date.     

The Sagnac Phase Shift Suggested by the Aharonov-Bohm Effect for Relativistic Matter Beams

The phase shift due to the Sagnac Effect, for relativistic matter beams counter-propagating in a rotating interferometer, is deduced on the bases of a formal analogy with the Aharonov-Bohm effect. A procedure outlined by Sakurai, in which non relativistic quantum mechanics and Newtonian physics appear together with some intrinsically relativistic elements, is generalized to a fully relativistic context, using the Cattaneo's splitting technique. This approach leads to an exact derivation, in a self-consistently relativistic way, of the Sagnac effect. Sakurai's result is recovered in the first order approximation.     

A polynomial case of the parsimony haplotyping problem

The parsimony haplotyping problem was shown to be NP-hard when each genotype had k?3ambiguous positions, while the case for k?2 was open. In this paper, we show that the case for k?2 is polynomial, and we give approximation and FPT algorithms for the general case of k?0 ambiguous positions.     

Navier–Stokes computation of transonic vortices over a round leading edge delta wing

A 3D Navier–Stokes solver has been developed to simulate laminar compressible flow over quadrilateral wings. The finite volume technique is employed for spatial discretization with a novel variant for the viscous fluxes. An explicit three-stage Runge–Kutta scheme is used for time integration, taking local time steps according to the linear stability condition derived for application to the Navier–Stokes equations. The code is applied to compute primary and secondary separation vortices at transonic speeds over a 65° swept delta wing with round leading edges and cropped tips. The results are compared with experimental data and Euler solutions, and Reynolds number effects are investigated.     

Masonry as structured continuum

A structured continuum model is formulated to describe the behaviour of block masonry modelled as distinct rigid body systems with elastic interfaces. A correspondence between the two motions is obtained by postulating a relationship between the displacement fields of the continuum and the discrete models. The constitutive functions for the dynamic actions of the continuum are derived by equating the power of the two models.A preliminary version was presented at AIMETA '92, congress held at Trento, Italy, on 28 September – 2 October 1992.     

Synthesis,X-ray powder structure,and magnetic properties of the new,weak ferromagnet iron(II) phenylphosphonate

A new molecule-based weak ferromagnet of formula Fe[C6H5PO3].H2O was synthesized. It was characterized by thermogravimetric analysis and UV-visible and infrared spectroscopy, and the magnetic properties were studied using a superconducting quantum interference device magnetometer. The crystal structure of the compound was determined "ab initio" from X-ray powder diffraction data and refined by the Rietveld method. The crystals of Fe[C6H5PO3].H2O are orthorhombic, space group Pmn2(1), with a = 5.668(8) A, b = 14.453(2) A, c = 4.893(7) A, and Z = 2. The title compound is isostructural with the previously reported lamellar M[C6H5PO3].H2O, M = Mn(II), Zn(II), and Cd(II). The inorganic layers are made of Fe(II) ions octahedrally coordinated by five phosphonate oxygen atoms and one from oxygen of the water molecule. These layers are then separated by bilayers of the phenyl groups, and van der Waals contacts are established between them. The refinement has shown that the phenyl rings are disordered in the lattice. The oxidation state of the metal ion is +2, and the electronic configuration is d6 (S = 2) high-spin, as determined from dc magnetic susceptibility measurements from 150 K to room temperature. Below 100 K, the magnetic moment of Fe[C6H5PO3].H2O rises rapidly to a maximum at TN = 21.5 K, and then it decreases again. The peak at TN is associated with the 3D antiferromagnetic long-range ordering. Below the critical temperature, the title compound behaves as a "weak" ferromagnet, which represents the third type of magnetic materials characterized by having a finite zero-field magnetization, ferromagnets and ferrimagnets being the other two types. The large coercive field (i.e., 6400 G) observed in the hysteresis loop at T = 10 K is rare in molecule-based materials; it can be ascribed to a pronounced spin-orbit coupling for the 5T2g ground state of the Fe(II) ion in the octahedral environment.     

Structural, MALDI-TOF-MS, magnetic and spectroscopic studies of new dinuclear copper(II), cobalt(II) and zinc(II) complexes containing a biomimicking μ-OH bridge

The Py(2)N(4)S(2) octadentate coordinating ligand afforded dinuclear cobalt, copper and zinc complexes and the corresponding mixed metal compounds. The overall geometry and bonding modes have been deduced on the basis of elemental analysis data, MALDI-TOF-MS, IR, UV-vis and EPR spectroscopies, single-crystal X-Ray diffraction, conductivity and magnetic susceptibility measurements. In the copper and zinc complexes, a μ-hydroxo bridge links the two metal ions. In both cases, the coordination geometry is distorted octahedral. Magnetic and EPR data reveal weakly antiferromagnetic high spin Co(II) ions, compatible with a dinuclear structure. The magnetic characterization of the dinuclear Cu(II) compound indicates a ferromagnetically coupled dimer with weak antiferromagnetic intermolecular interactions. The intra-dimer ferromagnetic behaviour was unexpected for a Cu(II) dimer with such μ-hydroxo bridging topology. We discuss the influence on the magnetic properties of non-covalent interactions between the bridging moiety and the lattice free water molecules.     

Quantum cascade laser-based photoacoustic spectroscopy of volatile chemicals: application to hexamethyldisilazane

The use of photoacoustic spectroscopy and mid-infrared quantum-cascade lasers (QCLs) for the detection of hexamethyldisilazane (HMDS) is reported. A detection limit of 200 parts in 10(9) is found using a Fabry-Perot QCL operated at 8.4 microm in pulsed mode and a photoacoustic cell equipped with four electret microphones. The laser multimode spectrum matches the range of the N-H bending absorption band of HMDS. Further improvements to reach lower detection limits are discussed.     

On the Essential Self-Adjointness of Singular Sub-Laplacians

Potential Analysis - We prove a general essential self-adjointness criterion for sub-Laplacians on complete sub-Riemannian manifolds, defined with respect to singular measures. We also show that,...