Saint-Venant's problem and semi-inverse solutions in nonlinear elasticity

Saint-Venant's problem consists in finding elastic deformations of an infinite prismatic body taking given values for the cross-sectional resultants of force and moment. Using the center manifold approach we show that all deformations having sufficiently small bounded strains lie on a finite-dimensional manifold. In particular, the flow on this manifold is described by a set of equations having exactly the form of the classical rod equations. Moreover, the set of semi-inverse solutions can be analyzed locally.     

Kinetics of the reaction of the heaviest hydrogen atom with H2, the 4Heμ + H2 → 4HeμH + H reaction: experiments, accurate quantal calculations, and variational transition state theory, including kinetic isotope effects for a factor of 36.1 in isotopic mass

The neutral muonic helium atom (4)Heμ, in which one of the electrons of He is replaced by a negative muon, may be effectively regarded as the heaviest isotope of the hydrogen atom, with a mass of 4.115 amu. We report details of the first muon spin rotation (μSR) measurements of the chemical reaction rate constant of (4)Heμ with molecular hydrogen, (4)Heμ + H(2) → (4)HeμH + H, at temperatures of 295.5, 405, and 500 K, as well as a μSR measurement of the hyperfine coupling constant of muonic He at high pressures. The experimental rate constants, k(Heμ), are compared with the predictions of accurate quantum mechanical (QM) dynamics calculations carried out on a well converged Born-Huang (BH) potential energy surface, based on complete configuration interaction calculations and including a Born-Oppenheimer diagonal correction. At the two highest measured temperatures the agreement between the quantum theory and experiment is good to excellent, well within experimental uncertainties that include an estimate of possible systematic error, but at 295.5 K the quantum calculations for k(Heμ) are below the experimental value by 2.1 times the experimental uncertainty estimates. Possible reasons for this discrepancy are discussed. Variational transition state theory calculations with multidimensional tunneling have also been carried out for k(Heμ) on the BH surface, and they agree with the accurate QM rate constants to within 30% over a wider temperature range of 200-1000 K. Comparisons between theory and experiment are also presented for the rate constants for both the D + H(2) and Mu + H(2) reactions in a novel study of kinetic isotope effects for the H + H(2) reactions over a factor of 36.1 in isotopic mass of the atomic reactant.     

Chromium localization in plant tissues of Lycopersicum esculentum Mill using ICP-MS and ion microscopy (SIMS)

High-resolution imaging secondary ion mass spectrometry (HRI-SIMS) in combination with inductively coupled plasma mass spectrometry (ICP-MS) were utilised to determine specific sites of chromium concentration in tomato plant tissues (roots, stems and leaves). The tissues were obtained from plants grown for 2 months in hydroponic conditions with Cr added in a form chromium salt (CrCl₃·6H₂O) to concentrations of 25 and 50 mg/L. The chemical fixation procedure used permit to localize only insoluble or strongly bound Cr components in tomato plant tissue. In this work no quantitative SIMS analysis was made. HRI-SIMS analysis revealed that the transport of chromium is restricted to the vascular system of roots, stems and leaves. No Cr was detected in epidermis, palisade parenchyma and spongy parenchyma cells of the leaves. The SIMS-300 spectra obtained from the tissues confirm the HRI-SIMS observations. The roots, and especially walls of xylem vessels, were determined as the principal site of chromium accumulation in tomato plants.     

Energy release rate for cracks in finite‐strain elasticity

Griffith's fracture criterion describes in a quasistatic setting whether or not a pre‐existing crack in an elastic body is stationary for given external forces. In terms of the energy release rate (ERR), which is the derivative of the deformation energy of the body with respect to a virtual crack extension, this criterion reads: if the ERR is less than a specific constant, then the crack is stationary, otherwise it will grow. In this paper, we consider geometrically nonlinear elastic models with polyconvex energy densities and prove that the ERR is well defined. Moreover, without making any assumption on the smoothness of minimizers, we rigorously derive the well‐known Griffith formula and the J‐integral, from which the ERR can be calculated. The proofs are based on a weak convergence result for Eshelby tensors. Copyright © 2007 John Wiley & Sons, Ltd.     

Structure, spectra and stability of a tetrafluoromethane-water complex

The complex formed between water and tetrafluoromethane has been studied by infrared matrix isolation spectroscopy and ab initio calculations. The geometries of the CF4-H2O complexes were optimized in two steps at the MP2/aug-cc-pVTZ level of theory. The structure found at this level was reoptimized on the CP-corrected potential energy surface. The interaction energy was partitioned according to the SAPT scheme and the topological analysis of the electron density was performed. The optimized structure corresponds to the nonhydrogen bonded complex with an oxygen atom of water oriented toward the carbon atom of CF4. The infrared spectra of CF4-H2O /Ne(Ar) matrices demonstrate the presence of a well defined CF4-H2O structure in accord with theoretical prediction. Two complex vibrations were identified in the spectra of neon matrices and four vibrations were observed in the spectra of argon matrices. The available experimental data are in accord with the CP-corrected calculated data.     

Localized 5f electrons in superconducting PuCoIn?: consequences for superconductivity in PuCoGa?

The physical properties of the first In analog of the PuMGa(5) (M = Co, Rh) family of superconductors, PuCoIn(5), are reported. With its unit cell volume being 28% larger than that of PuCoGa(5), the characteristic spin-fluctuation energy scale of PuCoIn(5) is three to four times smaller than that of PuCoGa(5), which suggests that the Pu 5f electrons are in a more localized state relative to PuCoGa(5). This raises the possibility that the high superconducting transition temperature T(c) = 18.5 K of PuCoGa(5) stems from the proximity to a valence instability, while the superconductivity at T(c) = 2.5 K of PuCoIn(5) is mediated by antiferromagnetic spin fluctuations associated with a quantum critical point.     

Pair Formation of Hard Core Bosons in Flat Band Systems

Hard core bosons in a large class of one or two dimensional flat band systems have an upper critical density, below which the ground states can be described completely. At the critical density, the ground states are Wigner crystals. If one adds a particle to the system at the critical density, the ground state and the low lying multi particle states of the system can be described as a Wigner crystal with an additional pair of particles. The energy band for the pair is separated from the rest of the multi-particle spectrum. The proofs use a Gerschgorin type of argument for block diagonally dominant matrices. In certain one-dimensional or tree-like structures one can show that the pair is localised, for example in the chequerboard chain. For this one-dimensional system with periodic boundary condition the energy band for the pair is flat, the pair is localised.     

Quantum oscillations in the underdoped cuprate YBa2Cu4O8

We report the observation of quantum oscillations in the underdoped cuprate superconductor YBa2Cu4O8 using a tunnel-diode oscillator technique in pulsed magnetic fields up to 85 T. There is a clear signal, periodic in inverse field, with frequency 660+/-15 T and possible evidence for the presence of two components of slightly different frequency. The quasiparticle mass is m(*)=3.0+/-0.3m(e). In conjunction with the results of Doiron-Leyraud et al. for YBa2Cu3O6.5, the present measurements suggest that Fermi surface pockets are a general feature of underdoped copper oxide planes and provide information about the doping dependence of the Fermi surface.     

Axion condensate as a model for dark matter halos

Localized solutions of an axion-like scalar model with a periodic self-interaction are analyzed as a model of dark matter halos. It is shown that such a cold Bose–Einstein type condensate can provide a substantial contribution to the observed rotations curves of galaxies, as well provide a soliton type interpretation of the dark matter ‘bullets’ observed via gravitational lensing in merging clusters.