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Modeling granularity
Computers and Mathematics with Applications 55 (2008) 131 www.elsevier.com/locate/camwa
Editorial
Modeling granularity When bodies are probed at a minute scale, a very complex and surprisingly manifold morphology is revealed. Heterogeneity appears ever more prominent, due to entanglement of macromolecules, contact among irregularly arranged grains or crystallites, contrast between different phases. Granular assemblies are a paradigm for evidencing how prominently lower scale events influence gross behaviour. Challenging theoretical and practical problems emerge, even of fundamental nature. They can be tackled from different perspectives, the approaches often converging towards, or arising from, a possibly overlooked unique framework. Solutions of particular problems may suggest indirectly the path toward unifying theoretical structures. In a Meeting/Summer School organized at the Mediterranean University at Reggio Calabria in 2005 (“Granular Matter: Mathematical Models and Physical Instances”), we invited a group of scholars to discuss problems dealing with the description of substructural morphology and their changes in condensed matter, by focusing attention mainly on the modeling of granular assemblies. Specific research contributions, additional to the general lectures presented at the Summer School, are collected here. They deal primarily with granular matter from its minute structure to very large effects (such as those occurring during earthquakes). Germane phenomena are also discussed (e.g., events occurring during frying), always with the intent of suggesting possible, though uncommon, avenues of advance or clues to so far lacking but potentially crucial concepts. Gianfranco Capriz Accademia dei Lincei, University of Pisa, Italy Pasquale Giovine Mediterranean University of Reggio Calabria, Italy Paolo Maria Mariano ∗ University of Florence, via Santa Marta 3, I-50139 Firenze, Italy E-mail address: [email protected]. 8 November 2006
∗
Corresponding editor.
c 2007 Elsevier Ltd. All rights reserved. 0898-1221/$ - see front matter doi:10.1016/j.camwa.2007.04.002
Editorial
Modeling granularity When bodies are probed at a minute scale, a very complex and surprisingly manifold morphology is revealed. Heterogeneity appears ever more prominent, due to entanglement of macromolecules, contact among irregularly arranged grains or crystallites, contrast between different phases. Granular assemblies are a paradigm for evidencing how prominently lower scale events influence gross behaviour. Challenging theoretical and practical problems emerge, even of fundamental nature. They can be tackled from different perspectives, the approaches often converging towards, or arising from, a possibly overlooked unique framework. Solutions of particular problems may suggest indirectly the path toward unifying theoretical structures. In a Meeting/Summer School organized at the Mediterranean University at Reggio Calabria in 2005 (“Granular Matter: Mathematical Models and Physical Instances”), we invited a group of scholars to discuss problems dealing with the description of substructural morphology and their changes in condensed matter, by focusing attention mainly on the modeling of granular assemblies. Specific research contributions, additional to the general lectures presented at the Summer School, are collected here. They deal primarily with granular matter from its minute structure to very large effects (such as those occurring during earthquakes). Germane phenomena are also discussed (e.g., events occurring during frying), always with the intent of suggesting possible, though uncommon, avenues of advance or clues to so far lacking but potentially crucial concepts. Gianfranco Capriz Accademia dei Lincei, University of Pisa, Italy Pasquale Giovine Mediterranean University of Reggio Calabria, Italy Paolo Maria Mariano ∗ University of Florence, via Santa Marta 3, I-50139 Firenze, Italy E-mail address: [email protected]. 8 November 2006
∗
Corresponding editor.
c 2007 Elsevier Ltd. All rights reserved. 0898-1221/$ - see front matter doi:10.1016/j.camwa.2007.04.002