Effective longitudinal shear moduli of periodic fibre-reinforced composites with functionally-graded fibre coatings

This paper presents a homogenization method for unidirectional periodic composite materials reinforced by circular fibres with functionally graded coating layers. The asymptotic homogenization method is adopted, and the relevant cell problem is addressed. Periodicity is enforced by resorting to the theory of Weierstrass elliptic functions. The equilibrium equation in the coating domain is solved in closed form by applying the theory of hypergeometric functions, for different choices of grading profiles. The effectiveness of the present analytical procedure is proved by convergence analysis and comparison with finite element solutions. The influence of microgeometry and grading parameters on the shear stress concentration at the coating/matrix interface is addressed, aimed at the composite optimization in regards to fatigue and debonding phenomena.     

Scattering amplitudes from multivariate polynomial division

We show that the evaluation of scattering amplitudes can be formulated as a problem of multivariate polynomial division, with the components of the integration-momenta as indeterminates. We present a recurrence relation which, independently of the number of loops, leads to the multi-particle pole decomposition of the integrands of the scattering amplitudes. The recursive algorithm is based on the weak Nullstellensatz theorem and on the division modulo the Gröbner basis associated to all possible multi-particle cuts. We apply it to dimensionally regulated one-loop amplitudes, recovering the well-known integrand-decomposition formula. Finally, we focus on the maximum-cut, defined as a system of on-shell conditions constraining the components of all the integration-momenta. By means of the Finiteness Theorem and of the Shape Lemma, we prove that the residue at the maximum-cut is parametrized by a number of coefficients equal to the number of solutions of the cut itself.     

CoAPO5 as a water oxidation catalyst and a light sensitizer

We report the first use of cobalt aluminophosphate (CoAPO5) as a water oxidation catalyst. A decrease in the overvoltage by about 0.2 V with respect to catalyst free FTO has been observed. Additionally, we show that CoAPO5, deposited on ITO or Pt, can also act as a photo-electro-catalyst, as it generates enhanced oxidation currents in the presence of light starting from a bias of +0.8 V vs. Ag/AgCl.     

Thermoanalytical investigations on the solid-state synthesis of Sr-doped praseodymium alkaline-earth cobalt oxides

In this study, the formation and characteristics of Sr-doped praseodymium alkaline-earth cobalt oxide were studied as a function of the strontium content (x). PrBa_1?x Sr _x Co₂O_5+d ceramics with x?=?0.0, 1/16, 1/8, 1/4, and 1/2.5 were prepared by solid-state reaction method from Pr₆O₁₁, BaCO₃, SrCO₃, and Co₃O₄. The solid-state reaction mechanisms were analyzed by differential thermal analysis (DTA) and thermogravimetry (TG) techniques to characterize properly the distinct thermal events occurring during synthesis of layered perovskite-type PrBa_1?x Sr _x Co₂O_5+d oxides. The X-ray diffraction (XRD) results were used to assist the interpretation of DTA?CTG analyses. The TG, DTA, and XRD results for the mixtures showed that the solid-state reaction between precursors was completed in a temperature range between 800 and 1000?°C. The strong influence of strontium contents (x) on the solid-state reaction temperatures and PrBa_1?x Sr _x Co₂O_5+d structure was found.     

Implementation of the multireference Brillouin-Wigner and Mukherjee's coupled cluster methods with non-iterative triple excitations utilizing reference-level parallelism

In this paper we discuss the performance of the non-iterative state-specific multireference coupled cluster (SS-MRCC) methods accounting for the effect of triply excited cluster amplitudes. The corrections to the Brillouin-Wigner and Mukherjee's MRCC models based on the manifold of singly and doubly excited cluster amplitudes (BW-MRCCSD and Mk-MRCCSD, respectively) are tested and compared with exact full configuration interaction results for small systems (H(2)O, N(2), and Be(3)). For the larger systems (naphthyne isomers) the BW-MRCC and Mk-MRCC methods with iterative singles, doubles, and non-iterative triples (BW-MRCCSD(T) and Mk-MRCCSD(T)) are compared against the results obtained with single reference coupled cluster methods. We also report on the parallel performance of the non-iterative implementations based on the use of processor groups.     

Inductive Construction of the Loop Transform for Abelian Gauge Theories

We construct the loop transform in the case of Abelian gauge theories as a unitary operator given by the inductive limit of Fourier transforms on tori. We also show that its range, i.e. the space of kinematical states of the quantum loop representation, is the Hilbert space of square integrable complex valued functions on the group of hoops.     

Vector bundles on a three-dimensional neighborhood of a ruled surface

Let S be a ruled surface inside a smooth threefold W and let E be a vector bundle on a formal neighborhood of S. We find minimal conditions under which the local moduli space of E is finite dimensional and smooth. Moreover, we show that E is a flat limit of a flat family of vector bundles whose general element we describe explicitly.     

A brill - noether theory for<Emphasis Type="Italic">κ</Emphasis>-gonal nodal curves

LetV(g, x, k, y) be the set of all pairs (X, F), whereX is an integral projective nodal curve withp _a(X)=g and card(Sing(X))=x andF is a rank 1 torsion free sheaf onX with deg(F)=k, card(Sing(F))=y andh ⁰(X, F)≥2. Here we study a general (X, F) εV(g, x, k, y) and in particular the Brill-Noether theory ofX and the scrollar invariants ofF.