The L-L estimates of solutions to one-dimensional damped wave equations and their application to the compressible flow through porous media

We first obtain the L^p-L^q estimates of solutions to the Cauchy problem for one-dimensional damped wave equation

     

Relaxation dynamics in tert-butylpyridine/tristyrene mixture investigated by broadband dielectric spectroscopy

We investigated, by means of dielectric spectroscopy, the relaxation dynamics of glass forming binary mixtures composed by the quite rigid polar molecules tert-butylpyridine dissolved in the apolar solvent tristyrene. By changing the relative concentration of the components we observed a transition from a relaxation scenario with a structural process and an excess wing to that with a structural process and a well resolved secondary process. Another relaxation process, slower than the latter, was observed, well below Tg. Our detailed analysis evidenced that the secondary relaxation with shorter relaxation time can be identified as the Johari-Goldstein relaxation for all the mixtures, whereas the new relaxation process was attributed to a different type of motion of tert-butylpyridine needing a larger amount of free volume for the molecular rotation.     

Influence of a reduced mobility layer on the structural relaxation dynamics of aluminum capped ultrathin films of poly(ethylene terephthalate)

The structural dynamics of ultrathin polymer films of poly(ethylene terephthalate) capped between aluminum electrodes have been investigated by dielectric relaxation spectroscopy. A deviation from bulk behavior, appearing as an increase of the relaxation time at a fixed temperature, is observed for films of thickness below 35 nm. The slowing down acts as a constant shift factor independent from the temperature, and the fragility is constant. The interfacial energy between aluminum and poly(ethylene terephthalate) is calculated to be 3 mJ/m2, confirming a strong interaction between polymer and substrate, which leads to the presence of a layer characterized by a reduced mobility at their interfaces. We proposed a mathematical schematization of a multylayer model that allowed qualitative reproduction of the observed thickness dependences of the static and dynamic properties. In terms of such a model, the upper limit for the thickness of the reduced mobility layer was estimated as 20 nm. The conditions to extend the proposed model to different observables are finally suggested.     

Evolution of hypersurfaces in $ {\Bbb R}^N$ by Gaussian curvature

In this paper we first prove short time existence of a classical solution for the problem which describes the evolution by Gaussian curvature of a strictly convex hypersurface in . Then we give a proof of the existence of a viscosity solution for this problem in such a way as to define a generalized motion existing for each time. Received November 24, 1997     

The combined relaxation and vanishing Debye length limit in the hydrodynamic model for semiconductors

The combined relaxation and vanishing Debye length limit for the hydrodynamic model for semiconductors is considered in both the unipolar and the bipolar case. The resulting limit problems are non‐linear drift driven hyperbolic equations. We make use of non‐standard entropy functions and the related entropy productions in order to obtain uniform estimates. In the bipolar case additional time‐dependent L^∞‐type estimates, available from the existence theory, are needed in order to control the entropy production terms. Finally, strong convergence of the electric field allows the limit towards the limiting problem. Copyright © 2001 John Wiley & Sons, Ltd.     

Impact of rock fabric,thermal behavior,and carbonate decomposition kinetics on quicklime industrial production and slaking reactivity

This paper deals with thermal analyses, burning trials and reactivity tests on 15 carbonate rocks, i.e., pure and impure carbonates, mud-supported and grain-supported limestones, crystalline marbles, and dolomites, used for the production of different lime products in industrial vertical shaft kilns worldwide. In particular, thermogravimetric and differential thermogravimetric analysis (TG–DTG) on massive (80–120 g) fine-grained (< 3.35 mm) samples allowed the extrapolation of the Arrhenius kinetic parameters, i.e., the (apparent) activation energy (E_a) and the pre-exponential or frequency factor (A). Other calcination parameters, i.e., the duration time, starting and ending calcination times and temperatures, and peaks of maximum calcination rate were also extrapolated in order to enhance their relationships with quicklime reactivity. Moreover, thermal analyses (TG–DTG–DTA) were repeated on powders (90 mg) using a more accurate analyzer to compare results. The study is completed by a thorough chemical–physical and mineralogical–petrographic characterization of carbonate rocks and derived burnt products. Results pointed out that medium-to-coarse crystalline materials, i.e., grain-supported limestones, diagenetic dolomites, and granoblastic marbles presented the highest activation energy, burnability and slaking reactivity. Conversely, microcrystalline carbonates with the highest micrite-to-sparite ratio, i.e., mud-supported limestones, and impure carbonates, enriched in quartz, clay minerals, and other subordinated non-carbonate impurities, presented the lowest activation energy, burnability, and slaking reactivity. This study also investigated the effect of BET-specific surface area and real density, depending on specific sintering tendency, on quicklime reactivity. Results from this multidisciplinary research activity put further constraints on carbonate rocks calcination kinetics and their suitability in the lime industry.

     

The syntheses and electrochemical studies of a ferrocene substituted diiminopyridine ligand and its p, s, se, and te complexes

A new reversible, redox active diiminopyridine ligand (1Fc) containing pendant ferrocene functionalities was isolated and fully characterized. The reaction of 1Fc with chalcogen pseudohalides of sulfur, selenium, and tellurium yielded the respective N,N',N″-chelated chalcogen dications. Phosphorus chemistry proceeded in a related manner but, in this case, by the direct addition of 1Fc with PI(3) to yield the N,N',N″-chelated P(I) cation. These species represent the first synthesized main group complexes involving a redox active diiminopyridine ligand containing pendant ferrocenes. Electrochemical studies of the free ligand shows a reversible two-electron process. The chelated phosphorus cation, however, displayed three events, the first being a quasi-reversible two-electron process, involving the oxidation at the P(I) center, resulting in a P(III) cation. The subsequent reversible one- and two-electron processes arise from the ligand framework and pendant ferrocenes, respectively.     

A multichromophoric dendrimer: from synthesis to energy up-conversion in a rigid matrix

A dendrimer with a [Ru(bpy)(3)](2+) (bpy = 2,2'-bipyridine) complex as a core and four diphenylanthracene units at the periphery was prepared from a scaffold based on a bipyridyl ligand bearing four terminal alkyne groups. Upon green light excitation, the dendrimer shows blue luminescence even in a rigid matrix at 77 K thanks to the dendritic multichromophoric structure.