Two-Phase Problems for Linear Elliptic Operators with Variable Coefficients: Lipschitz Free Boundaries are <Emphasis Type="Italic">C</Emphasis><Superscript><Emphasis Type="Italic">1,γ</Emphasis></Superscript>

We prove C ^1, regularity of Lipschitz free boundaries of two-phase problems for linear elliptic operators with Hölder continuous coefficients.     

The effects of air bubbles on ultrasound velocity measurements

We report on experiments on the effects of air bubbles on ultrasound velocity measurements in fluids. We used an acoustic Doppler velocimeter system for measuring the three velocity components in a single point and an acoustic Doppler velocimetry profiler system for measuring axial velocity in several points along the beam. The results suggest that both systems essentially measure the velocity of the bubbles, independent of the low air-volume concentration and of bubble radii in the flow field.     

Solutions of vectorial Hamilton-Jacobi equations and minimizers of nonquasiconvex functionals

We provide a unified approach to prove existence results for the Dirichlet problem for Hamilton-Jacobi equations and for the minimum problem for nonquasiconvex functionals of the Calculus of Variations with affine boundary data. The idea relies on the definition of integro-extremal solutions introduced in the study of nonconvex scalar variational problem.     

Sets of type (0,n) in Steiner systems and in finite projective planes

In this paper we study the sets of type (0,n)₁ in a finite projective plane and the inclusion relations between them.     

Tuning oxygen packing in silica by nonhydrostatic pressure

The transformation of SiO2 from low pressure tetrahedral phases into denser octahedral phases takes place via the collapse of the oxygen sublattice into a close-packed arrangement. The transition paths and the resulting products are known to be affected by the presence of anisotropic stresses, which are difficult to control, so interpretation of the experimental results is problematic. Based on nonhydrostatic molecular dynamics simulations, we show that the collapse of the oxygen sublattice in the specific case of cristobalite is concomitant with the disappearance of tetrahedral units and that non hydrostatic stresses can be tuned to yield phases with different oxygen close-packed sublattices, including the alpha-PbO2-like phase, for which we provide a microscopic formation path, and phases with a cubic close packing, like anatase, not seen in experiments yet.     

Dynamic pressure and response factors for progressive gravity waves to third order approximation

Summary This paper proposes expressions of the dynamic pressure and of the transfer functions (response factors) between the dynamic pressure amplitude and the wave amplitude and between the dynamic pressure and the vertical displacement of the wave profile, for irrotational progressive gravity waves to third order approximation (non-linear theory).Some characteristic behaviours of the dynamic pressure and of the response factors are examined and compared with those of waves to first order approximation (linear theory).

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Sommario Si ricavano le espressioni della pressione dinamica per onde irrotazionali progressive di gravità al terzo ordine di approssimazione (modello non lineare).Si individuano le funzioni di trasferimento (fattori di risposta) sia tra l'ampiezza della pressione dinamica e l'ampiezza d'onda, sia tra la pressione dinamica e lo spostamento verticale della superficie di ondulazione.Si esaminano comportamenti caratteristici della pressione dinamica e dei fattori di risposta e si confrontano tali comportamenti con quelli relativi alle onde al primo ordine di approssimazione (modello lineare).

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Nitridosilicates and oxonitridosilicates: from ceramic materials to structural and functional diversity

Silicates are one of the most important classes of compounds on this planet, and more than 1000 silicates have been identified in the mineral kingdom. Additionally, several hundreds of artificial silicates have been synthesized. The substitution of oxygen by nitrogen leads to the structurally diverse and manifold class of nitridosilicates. Silicon nitride, one of the most important non-oxidic ceramic materials, is the binary parent compound of nitridosilicates, and it symbolizes the inherent material properties of these refractory compounds. However, prior to the last decades, a broad systematic investigation of nitridosilicates had not been accomplished. In the meantime, these and related compounds have reached a remarkable level of industrial application. This review illustrates recent progress in synthesis and structure-property relationships and also applications of nitridosilicates, oxonitridosilicates, and related SiAlONs.