Topology optimization of composite hyperelastic material using SPIMFO-method

Meccanica - Fiber reinforced materials are used in assorted engineering application and for this reason, new additive manufacturing technologies have been developed for this type of materials. With...     

Resonances and Gamow States in Non-Local Potentials

For a large class of non-local, non separable potentials with non-compact support, the solution of the radial integrodifferential equation may be reduced to the solution of a homogeneous linear integral equation of Fredholm type with a quadratically integrable kernel. In this way we derive expansions of the wave functions and the Green's function of the Schrödinger equation with a non-local potential in terms of bound states, resonant states and a continuum of scattering functions with complex wave number. The rules of normalization, orthogonality and completeness satisfied by the eigenstates of the Schrödinger equation belonging to complex eigenvalues with Im E_n < 0, (Gamow or resonant states) are also derived. Finally, by means of a realistic example, it is shown how to use these expansions to exhibit the resonant behaviour of the differential cross section. Explicit expressions for the transition amplitudes and the partial widths in terms of expectation values of operators computed with Gamow functions are given.     

Corrosion products on steel 20 in aerated hydrazine solutions: Mössbauer study

Composition of corrosion layers on steel 20 in aerated solutions with hydrazine concentrations less than 11 ppm was studied at 50, 60, and 80°C in dynamic conditions by transmission Mössbauer spectroscopy and X-ray diffraction as supplementary technique. Corrosion rates were determined by gravimetric method. A comparison with corrosion in water at 80°C was made. The observed layers have not any protective character. For 0.1 m/s linear velocity, they are composed by nonstoichiometric magnetite, (Fe_3?x O₄,x=0.02–0.04) with lepidocrocite (γ-FeOOH) as secondary phase at 50°C. Haematite (α-Fe₂O₃) is observed at 60 and 80°C with a 19 nm particle size. It becomes smaller for higher velocity (0.7 m/s).     

Banach-stone theorems and separating maps

LetC(X,E) andC(Y,F) denote the spaces of continuous functions on the Tihonov spacesX andY, taking values in the Banach spacesE andF, respectively. A linear mapH:C(X,E)→C(Y,F) isseparating iff(x)g(x)=0 for allx inX impliesHf(y)Hg(y)=0 for ally inY. Some automatic continuity properties and Banach-Stone type theorems (i.e., asserting that isometries must be of a certain form) for separating mapsH between spaces of real- and complex-valued functions have already been developed. The extension of such results to spaces of vector-valued functions is the general subject of this paper. We prove in Theorem 4.1, for example, for compactX andY, that a linear isometryH betweenC(X,E) andC(Y,F) is a “Banach-Stone” map if and only ifH is “biseparating (i.e,H andH ⁻¹ are separating). The Banach-Stone theorems of Jerison and Lau for vector-valued functions are then deduced in Corollaries 4.3 and 4.4 for the cases whenE andF or their topological duals, respectively, are strictly convex. Research supported by the Fundació Caixa Castelló, MI/25.043/92     

Extended X-ray absorption fine structure studies of thulium doped GaN epilayers

The local structure of Tm³⁺ ions incorporated into GaN epilayers was studied by means of Extended X-ray Absorption Fine Structure. The samples were doped either in situ during growth by Molecular Beam Epitaxy or by ion implantation of layers grown by Metal Organic Chemical Vapour Deposition. The implantation was done at ion energy of 300 keV and different nominal fluences of 3×10¹⁵, 4×10¹⁵ cm⁻² and 5×10¹⁵ cm⁻². The concentration of Tm in the samples studied was measured by Wavelength Dispersive X-ray analysis. For the in situ doped sample with concentration of 0.5%, and for all of the implanted samples, Tm was found on the Ga site in GaN. The ion implanted sample and an in situ doped sample with a similar concentration of Tm showed the same local structure, which suggests that the lattice site occupied by Tm does not depend on the doping method. When the average Tm concentration for in situ doped samples is increased to 1.2% and 2.0%, Tm is found to occupy the Ga substitutional site and the presence of a substantial number of Tm ions in the second coordination sphere indicates dopant clustering in the films. The formation of pure TmN clusters was found in an in situ doped sample with a dopant concentration of 3.4%.     

Alloy model for high-temperature superconductors

An alloy model is proposed for the electronic structure of high-temperature superconductors. It is based on the assumption that holes and extra electrons are localized in small copper-oxygen clusters, that would be the components of such an alloy. This model, when used together with quantum chemical calculations on small clusters, can explain the structure observed in the experimental densities of states of both hole and electron superconductors close to the Fermi energy. The main point is the strong dependence of the energy level distribution and composition on the number of electrons in a cluster. The alloy model also suggests a way to correlate T_c with the number of holes, or extra electrons, and the number of adequate clusters to locate them.     

A multivalued version of Sharkovskiĭ’s theorem holds with at most two exceptions

A multivalued version of Sharkovskiĭ’s theorem is formulated for M-maps on linear continua and, more generally, for triangular M-maps on a Cartesian product of linear continua. This improves the main result of [AP1] in the sense that our multivalued analogue holds with at most two exceptions. A further specification requires some additional restrictions. For instance, 3- orbits of m-maps imply the existence of k-orbits for all k ? \mathbbNk \in {\mathbb{N}} , except possibly for k ?k \in {4, 6}. It is also shown that, on every connected linearly ordered topological space, an M-map with orbits of all periods can always be constructed. This demonstrates that Baldwin’s classification of linear continua in terms of admissible periods [Ba] is useless for multivalued maps.