Title: "On Ephemeral Continua"
Dates: May 10th-22nd, 2010
Location: Burnside Hall Building, 1B23
Hours: 9am to 12pm instruction; 2pm-3pm discussion
Instructor: Professor Gianfranco Capriz
Synopsis:
Among the fundamentals of continuum mechanics, a cardinal tenet is the perfect identifiability of material elements. Consequently, the key mathematical tools one summons are bijections between sets in Euclidean space. We explore how one can manage without that tenet and what might ensue from the attendant want. The image one evokes directly is that of a loose shifting throng of minute pebbles, a numerous assembly of streaming motes. Thus, directly, the issues are relevant to fast granular flows; however, most results bear also on the study of complex media generally, even on a deeper analysis of response of standard continua. There are also connections with various recent extensions of fluid dynamics, with old properties known from the kinetic theory, with certain premises in molecular dynamics, with renewed arguments on irreversible thermodynamics, with manifold proposals in hypoelasticity. Therefore the course will begin with a panorama of approaches to many theories of continua.
Tentative program of short course:
- Clockwork versus ephemeral continua.
- The Lagrangean scheme for clockwork continua.
- The microstructure of time.
- Special continua with microstructure: nematics, girocontinua.
- Granular assemblies; corresponding distributions.
- Average and peculiar velocities. Objectivity for peculiarities.
- Ephemeral continua: mean, moment, variance.
- Consequent balance equations.
- Alternative deduction of the balance equations through a Boltzmann equation.
- Noll's holographic lemmas.
- Kinetic energy theorems.
- Extended mechanics in a thermodynamic role.
- Types of velocity distributions; temperature.
- Some elementary flows.
- Hypocontinua.
- Connections with hypoelastic continua and with generalizations of Navier-Stokes fluids.
- Hybrid continua. Structural distributions.
- Temperature associated with a structural distribution.
- Examples: nematics and polycrystals.
- Kinetic and structural disorder.
- Melting of microstructure.
- Continua with microstructure as limits of sequences of ordinary bodies.
- Substructure as a fabric.
- Mutant bodies.
Biographical information on Professor Gianfranco Capriz:
Gianfranco Capriz is presently Emeritus Professor in the Department of Mathematics of the University of Pisa and a National Member of the Italian Accademia dei Lincei.
After the two years' distraction due to war circumstances (one year in a German camp), Professor Capriz resumed studies at the University of Pisa and the Scuola Normale Superiore, from which he also obtained also a PhD in mathematics in 1949. Thereafter, he was on the research staff of the Istituto di Calcolo and assistant for Antonio Signorini in Rome from 1950 to 1956. Professor Capriz then emigrated to England to work in the central research laboratories of English Electric Co Ltd on the pilot model DEUCE of the computer designed by Alan Turing. The problems he studied, proposed by the many operating companies of the group, included high temperature creep, heat generation and flow during supersonic flight, vibrations of turbine blades, cavitation in lubricating films, oil whirl in rotating shafts, flow of ceramic bodies in extruders, and fracture between semiconductor layers. In 1962, Professor Capriz was called back in Pisa to become the director of the Institute for Computer Studies, a position he held for the next 20 years. Professor Capriz also won the chair of Mechanics in the Department of Mathematics at Pisa and established a lively collaboration with Clifford Truesdell and other colleagues within the Society for Natural Philosophy, organizing a number of Italian-American meetings. During a nine year leave of absence from his chair, Professor Capriz was chosen as chairman of a new company Tecsiel (part of a large state-owned group) dedicated to system software and helped to set up three development laboratories (Rome, Pisa, Neapel).
Professor Capriz has been a visiting professor at Johns Hopkins University, the Universities of Minnesota, Manitoba, and Canterbury (New Zealand), Carnegie Mellon University, Herriot Watt University (Scotland), an the Tata Institute (India). He has also held shorter visiting positions at a variety of other universities.
During the last three decades Professor Capriz's research has focused on complex continua, including liquid crystals and granular assemblies. The central goal of his work has been to extend, in a sense, the precise approach and ample view of Classical Field Theory to account for microstructure. Some of his contributions in this area included in the tract "Continua with Microstructure," published by Springer in 1989.