Free energy and states of fractional-order hereditariness

Complex materials, often encountered in recent engineering and material sciences applications, show no complete separations between solid and fluid phases. This aspect is reflected in the continuous relaxation time spectra recorded in cyclic load tests. As a consequence the material free energy cannot be defined in a unique manner yielding a significative lack of knowledge of the maximum recoverable work that can extracted from the material. The non-uniqueness of the free energy function is removed in the paper for power-laws relaxation/creep function by using a recently proposed mechanical analogue to fractional-order hereditariness.     

Territorial origin of olive oil: representing georeferenced maps of olive oils by NMR profiling

ABSTRACT Proton NMR profiling is nowadays a consolidated technique for the identification of geographical origin of food samples. The common approach consists in correlating NMR spectra of food samples to their territorial origin by multivariate classification statistical algorithms. In the present work, we illustrate an alternative perspective to exploit territorial information, contained in the NMR spectra, which is based on the implementation of a geographic information system (GIS). Nuclear magnetic resonance spectra are used to build a GIS map permitting the identification of territorial regions having strong similarities in the chemical content of the produced food (terroir units). These terroir units can, in turn, be used as input for labeling samples to be analyzed by traditional classification methods. In this work, we describe the methods and the algorithms that permit to produce GIS maps from NMR profiles and apply the described method to the analysis of the geographical distribution of olive oils in an Italian region. In particular, we analyzed by ¹H NMR up to 98 georeferenced olive oil samples produced in the Abruzzo Italian region. By using the first principal component of the NMR variables selected according to the Moran test, we produced a GIS map, in which we identified two regions incidentally corresponding to the provinces of Teramo and Pescara. We then labeled the samples according to the province of provenience and built an LDA model that provides a classification ability up to 99% . A comparison between the variables selected in the geostatistics and classification steps is finally performed. Copyright © 2016 John Wiley & Sons, Ltd.