Strength vs. toughness optimization of microstructured composites

Aim of this paper is to present a new fractal approach linking the macroscopic mechanical properties of micro- and nano-structured materials with the main parameters: composition, grain size and structural dimension, as well as contiguity and mean free path. Assuming the key role played by the interfaces, the proposed fractal energy approach unifies the influences of all the above parameters, through the introduction of a fractal structural parameter (FSP), which represents an extension of the Gurland’s structural parameter. This modeling approach is assessed through an extensive comparison with experimental data on poly crystalline diamond (PCD) and WC–Co alloys. The results clearly show that the theoretical fractal predictions are in a fairly good agreement with the experiments on both hardness and toughness. This new synthetic parameter is thus proposed to investigate, design and optimize new micro- and nano-grained materials. Eventually, FSP-based optimization maps are developed, that allow to design new materials with high hardness and toughness.     

3-Quasi-Sasakian manifolds

We correct the results in section 6 of [B. Cappelletti Montano, A. De Nicola, G. Dileo, 3-Quasi-Sasakian manifolds, Ann. Global Anal. Geom. 33 (2008), 397–409], concerning the corrected energy of the Reeb distribution of a compact 3-quasi-Sasakian manifold. The results are slightly different than what was originally claimed and they are obtained by using results in [B. Cappelletti Montano, A. De Nicola, G. Dileo, The geometry of a 3-quasi-Sasakian manifold, Int. J. Math., to appear, arXiv:0801.1818], where the geometry of these manifolds is more deeply investigated. The online version of the original article can be found under doi:.     

On the shape factor of interaction laws for a non-local approximation of the Sobolev norm and the total variation

We consider the family of non-local and non-convex functionals introduced by H. Brézis and H.-M. Nguyen in a recent paper. These functionals Gamma-converge to a multiple of the Sobolev norm or the total variation, depending on a summability exponent, but the exact values of the constants are unknown in many cases.We describe a new approach to the Gamma-convergence result that leads in some special cases to the exact value of the constants, and to the existence of smooth recovery families.     

Paleodiet characterisation of an Etrurian population of Pontecagnano (Italy) by Isotope Ratio Mass Spectrometry (IRMS) and Atomic Absorption Spectrometry (AAS)(#)

Human bones recovered from the archaeological site of Pontecagnano (Salerno, Italy) have been studied to reconstruct the diet of an Etrurian population. Two different areas were investigated, named Library and Sant' Antonio, with a total of 44 tombs containing human skeletal remains, ranging in age from the 8th to the 3rd century B.C. This time span was confirmed by 14C dating obtained using Accelerator Mass Spectrometry (AMS) on one bone sample from each site.Atomic Absorption Spectrometry (AAS) was used to extract information about the concentration of Sr, Zn, Ca elements in the bone inorganic fraction, whilst stable isotope ratio measurements (IRMS) were carried out on bone collagen to obtain the delta13C and delta15N. A reliable technique has been used to extract and separate the inorganic and organic fractions of the bone remains.Both IRMS and AAS results suggest a mixed diet including C3 plant food and herbivore animals, consistent with archaeological indications.     

New properties of convex functions in the Heisenberg group

We prove some new properties of the weakly -convex functions recently introduced by Danielli, Garofalo and Nhieu. As an interesting application of our results we prove a theorem of Busemann-Feller-Alexandrov type in the Heisenberg groups , .

     

Exactly quantized dynamics of classical incommensurate sliders

We report peculiar velocity quantization phenomena in the classical motion of an idealized 1D solid lubricant, consisting of a harmonic chain interposed between two periodic sliders. The ratio upsilon(c.m.)/upsilon(ext) of the chain center-of-mass velocity to the externally imposed relative velocity of the sliders stays pinned to exact "plateau" values for wide ranges of parameters, such as slider corrugation amplitudes, external velocity, chain stiffness, and dissipation, and is strictly determined by the commensurability ratios alone. The phenomenon is explained by one slider rigidly dragging the kinks that the chain forms with the other slider. Possible consequences of these results for some real systems are discussed.     

Density functional theory in transition-metal chemistry: a self-consistent Hubbard U approach

Transition-metal centers are the active sites for a broad variety of biological and inorganic chemical reactions. Notwithstanding this central importance, density-functional theory calculations based on generalized-gradient approximations often fail to describe energetics, multiplet structures, reaction barriers, and geometries around the active sites. We suggest here an alternative approach, derived from the Hubbard U correction to solid-state problems, that provides an excellent agreement with correlated-electron quantum chemistry calculations in test cases that range from the ground state of Fe2 and Fe2- to the addition elimination of molecular hydrogen on FeO+. The Hubbard U is determined with a novel self-consistent procedure based on a linear-response approach.