Nonlinear and nonequilibrium dynamics in geomaterials

The transition from linear to nonlinear dynamical elasticity in rocks is of considerable interest in seismic wave propagation as well as in understanding the basic dynamical processes in consolidated granular materials. We have carried out a careful experimental investigation of this transition for Berea and Fontainebleau sandstones. Below a well-characterized strain, the materials behave linearly, transitioning beyond that point to a nonlinear behavior which can be accurately captured by a simple macroscopic dynamical model. At even higher strains, effects due to a driven nonequilibrium state, and relaxation from it, complicate the characterization of the nonlinear behavior.     

Error estimates for the three-field formulation with bubble stabilization

In this paper we prove convergence and error estimates for the so-called 3-field formulation using piecewise linear finite elements stabilized with boundary bubbles. Optimal error bounds are proved in and in the broken norm for the internal variable , and in suitable weighted norms for the other variables and .     

Heterotrimetallic Coordination Polymers: {CuIILnIIIFeIII} Chains and {NiIILnIIIFeIII} Layers: Synthesis,Crystal Structures,and Magnetic Properties

The use of the [Fe^III(AA)(CN)₄]^? complex anion as metalloligand towards the preformed [Cu^II(valpn)Ln^III]³⁺ or [Ni^II(valpn)Ln^III]³⁺ heterometallic complex cations (AA=2,2′‐bipyridine (bipy) and 1,10‐phenathroline (phen); H₂valpn=1,3‐propanediyl‐bis(2‐iminomethylene‐6‐methoxyphenol)) allowed the preparation of two families of heterotrimetallic complexes: three isostructural 1D coordination polymers of general formula {[Cu^II(valpn)Ln^III(H₂O)₃(μ‐NC)₂Fe^III(phen)(CN)₂ {(μ‐NC)Fe^III(phen)(CN)₃}]NO₃ ? 7 H₂O}_n (Ln=Gd ( 1 ), Tb ( 2 ), and Dy ( 3 )) and the trinuclear complex [Cu^II(valpn)La^III(OH₂)₃(O₂NO)(μ‐NC)Fe^III(phen)(CN)₃] ? NO₃ ? H₂O ? CH₃CN ( 4 ) were obtained with the [Cu^II(valpn)Ln^III]³⁺ assembling unit, whereas three isostructural heterotrimetallic 2D networks, {[Ni^II(valpn)Ln^III(ONO₂)₂(H₂O)(μ‐NC)₃Fe^III(bipy)(CN)] ? 2 H₂O ? 2 CH₃CN}_n (Ln=Gd ( 5 ), Tb ( 6 ), and Dy ( 7 )) resulted with the related [Ni^II(valpn)Ln^III]³⁺ precursor. The crystal structure of compound 4 consists of discrete heterotrimetallic complex cations, [Cu^II(valpn)La^III(OH₂)₃(O₂NO)(μ‐NC)Fe^III(phen)(CN)₃]⁺, nitrate counterions, and non‐coordinate water and acetonitrile molecules. The heteroleptic {Fe^III(bipy)(CN)₄} moiety in 5 – 7 acts as a tris‐monodentate ligand towards three {Ni^II(valpn)Ln^III} binuclear nodes leading to heterotrimetallic 2D networks. The ferromagnetic interaction through the diphenoxo bridge in the Cu^II?Ln^III ( 1 – 3 ) and Ni^II?Ln^III ( 5 – 7 ) units, as well as through the single cyanide bridge between the Fe^III and either Ni^II ( 5 – 7 ) or Cu^II ( 4 ) account for the overall ferromagnetic behavior observed in 1 – 7 . DFT‐type calculations were performed to substantiate the magnetic interactions in 1 , 4 , and 5 . Interestingly, compound 6 exhibits slow relaxation of the magnetization with maxima of the out‐of‐phase ac signals below 4.0 K in the lack of a dc field, the values of the pre‐exponential factor (τ_o) and energy barrier (E_a) through the Arrhenius equation being 2.0×10^?12 s and 29.1 cm^?1, respectively. In the case of 7 , the ferromagnetic interactions through the double phenoxo (Ni^II–Dy^III) and single cyanide (Fe^III–Ni^II) pathways are masked by the depopulation of the Stark levels of the Dy^III ion, this feature most likely accounting for the continuous decrease of χ_M T upon cooling observed for this last compound.     

LOW MACH NUMBER LIMIT ON EXTERIOR DOMAINS

This paper is concerned with the low Mach number limit for the compressible Navier-Stokes equations in an exterior domain.We present here an approach based on Strichartz estimate defined on a non trapp...     

On the phase transitions in fluid mixtures

Summary The integral equations of balance for a binary fluid mixture are stated when the mixture presents two phases which are separated by an interface. The equilibrium conditions are derived together with the Gibbs phase rule for plane interfaces. The theory is extended to the mixture with three phases.

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Sommario Si scrivono le equazioni integrali del bilancio per una miscela fluida binaria che una interfaccia separa dalla miscela del suo vapore. Si derivano le condizioni di equilibrio e, nel caso di interfaccia piana, la regola delle fasi di Gibbs. La teoria proposta è poi estesa a sistemi di miscela binaria con tre fasi.

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This paper is made under the auspices of G.N.F.M. of the Italian C.N.R.     

Mean convergence of an extended Lagrange interpolation process on [0,+∞)

We study some extended Lagrange interpolation processes based on the zeros of the generalized Laguerre polynomials. We give necessary and sufficient conditions such that the convergence of these processes, in suitable L _p weighted spaces on the real semiaxis, is assured for 1<p<+∞.