Hyperbolic Principal Subsystems: Entropy Convexity and Subcharacteristic Conditions

We consider a system of N balance laws compatible with an entropy principle and convex entropy density. Using the special symmetric form induced by the main field, we define the concept of principal subsystem associated with the system. We prove that the 2 ^N −2 principal subsystems are also symmetric hyperbolic and satisfy a subentropy law. Moreover we can verify that for each principal subsystem the maximum (minimum) characteristic velocity is not larger (smaller) than the maximum (minimum) characteristic velocity of the full system. These are the subcharacteristic conditions. We present some simple examples in the case of the Euler fluid. Then in the case of dissipative hyperbolic systems we consider an equilibrium principal subsystem and we discuss the consequences in the setting of extended thermodynamics. Finally in the moments approach to the Boltzmann equation we prove, as a consequence of the previous result, that the maximum characteristic velocity evaluated at the equilibrium state does not decrease when the number of moments increases. (Accepted October 6, 1995)     

Analysis of interpolation schemes for image deformation methods in PIV

Abstract   Image deformation methods in particle image velocimetry are becoming more and more accepted by the scientific community but some aspects have not been thoroughly investigated neither theoretically nor with the aid of simulations. A fundamental step in this type of algorithm is reconstruction of the deformed images that requires the use of an interpolation scheme. The aim of this paper is to examine the influence of this aspect on the accuracy of the PIV algorithm. The performance assessment has been conducted using synthetic images and the results show that both the systematic and total errors are strongly influenced by the interpolation scheme used in the reconstruction of the deformed images. Time performances and the influence of particle diameter are also analysed.

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Rationality in families of threefolds

We prove that in a family of projective threefolds defined over an algebraically closed field, the locus of rational fibers is a countable union of closed subsets of the locus of separably rationally connected fibers. When the ground field has characteristic zero, this implies that the locus of rational fibers in a smooth family of projective threefolds is the union of at most countably many closed subfamilies.     

Thermodynamics of the glass transition

A thermodynamic analysis of the glass transition in polymers is presented, which predicts, with a minimum of assumptions, three of the four inequalities which have consistently been observed experimentally: i.e., that specific heat and isothermal compressibility of the glass are lower than those of the rubber, and that the Prigogine-Defay ratio is larger than unity. The analysis cannot predict the fact that the thermal expansion coefficient of the glass is also lower than that of the rubber, and indeed the converse situation is not a thermodynamic impossibility.     

Dendritic structures based on bis(hydroxymethyl)propionic acid as platforms for surface reactions

In this paper we present results related to the self-assembly of different generations of disulfide-cored 2,2-bis(hydroxymethyl)propionic acid-based dendritic structures onto gold surfaces. These molecular architectures, ranging from generation 1 to generation 3, contain removable acetonide protecting groups at their periphery that are accessible for hydrolysis with subsequent formation of OH-terminated surface-attached dendrons. The deprotection has been investigated in detail as a versatile approach to accomplish reactive surface platforms. A special focus has been devoted to the comparison of the properties of the layers formed by hydrolysis of the acetonide moieties directly on the surface and in solution, prior to the layer formation.