Mathematical models and methods for smart materials : [papers presented at the Conference on "Mathematical Models and Methods for Smart Materials"], Cortona, Italy, 25 - 26 June 2001

384 Pages·14.788 MB·English

by  eds.: !224524305! Mauro Fabrizio, Barbara Lazzari, !224524313! Angelo Morro.

MATHEMATICAL
MODELS AND
METHODS FOR
SMART MATERIALS
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Series on Advances in Mathematics for Applied Sciences -Vol. 62
MATHEMATICAL
MODELS AND
METHODS FOR
SMART MATERIALS
Cortona, Italy 25 - 29 June 2001
Editors
Mauro Fabrizio
Barbara Lazzari
Department of Mathematics
University of Bologna, Italy
Angelo Morro
DIBE, University of Genoa, Italy
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MATHEMATICAL MODELS AND METHODS FOR SMART MATERIALS
Series on Advances in Mathematics for Applied Sciences — Vol. 62
Copyright © 2002 by World Scientific Publishing Co. Pte. Ltd.
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INdAM MEETING
Mathematical Models and Methods
for Smart Materials
CORTONA - June 25-29, 2001
Scientific Committee
M. Fabrizio, A. Hanyga, A. Mono
Host Organization
Istituto Nazionale di Alta Matematica (INdAM)
"Francesco Severi",
Scuola Normale Superiore - PISA
Supported by
INdAM
COFIN 2000 "Mathematical Models for Material Science" (MIUR)
V

Preface
This book contains the papers presented at the Conference on "Mathematical
Models and Methods for Smart Materials" which was held in Cortona, June 25-29,
2001, organized by M. Fabrizio, G.A. Hanyga e A. Morro in memory of Giorgio
Gentili. The topics of the Conference were much influenced by the research devel
oped by Gentili within the framework of mathematical problems connected with the
modelling of materials.
The Conference was organized within the program of the Italian INdAM. The
Editors are grateful to INdAM for accepting the proposal of the Conference and the
general support. The hospitality at the Palazzone has made the stay an easy, friendly
and stimulating occasion for scientific contacts among the participants. Indeed, it
is worth remarking that similar Conferences on mathematical models and methods
for continuous media were organized at the Palazzone and Gentili was one of the
most active participants. The authors of the present papers witness their friendship
and admiration for the scientific activity of Gentili.
The papers are gathered in four parts. First, "Methods in materials science"
deals mainly with mathematical techniques for the investigation of physical systems
such as liquid crystals, materials with internal variables, amorphous materials, ther-
moelastic materials. Also, techniques are exhibited for the analysis of stability and
controllability of classical models of continuum mechanics and of dynamical systems.
"Modelling of smart materials" is devoted to models of superfluids, supercon
ductors, materials with memory, nonlinear elastic solids, damaged materials. In
the elaboration of the models, thermodynamic aspects play a central role in the
characterization of the constitutive properties.
"Well-posedness in materials with memory" involves existence, uniqueness and
stability for the solution to problems, most often expressed by integro-differential
equations, which involve materials with fading memory. Also, attention is addressed
to exponential decay in viscoelasticity, inverse problems in heat conduction with
memory, automatic control for parabolic equations.
"Analytic problems in phase transitions" deals with nonlinear partial differential
equations associated with phase transitions, hysteresis, possibly involving fading
memory effects. Particular applications are developed for the phase-field model
with memory, the Stefan problem with a Cattaneo-type equation, the hysteresis in
thermo-visco-plasticity, the solid-solid phase transition.
Mauro Fabrizio, Barbara Lazzari, Angelo Morro
VII
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Giorgio Gentili
OBITUARY
It is a deeply sorrow task to trace the activity of a young collaborator at the
University, a community where the time spent is certainly more than that spent in
the family or in any other community. That is why, quite naturally, strict collab
orators are also close friends. This aspect is especially true for Giorgio Gentili, a
very generous and kind man.
He was born on 1961, in Fossombrone. After the "Maturita" from the Liceo
Scientifico of Fermo on 1980, he went to the University of Bologna and received
the degree in Physics on 1985, maximum cum laude. He developed a thesis on "A
macroscopic non-local theory of superfluidity" with G. Turchetti and M. Fabrizio
as supervisors.
I knew him through C. Giorgi. They both were active members of the catholic
movement "Comunione e Liberazione". Next, at the Department of Mathematics,
especially B. Lazzari joined them thus constituting a group of friends both at the
University and in everyday life.
After the degree, Gentili received a fellowship from CNR and next pursued the
doctoral studies in Mathematics at the University of Bologna.
ix
X
He doesn't attained the PhD degree because he got a permanent position as a
researcher of Mathematical Physics on March 1990 and this was incompatible with
the position of PhD student. Since 1990 he was very active in tutoring students of
Rational Mechanics and has given the course of Mechanics of space flight within the
DU of Aerospace Engineering at Forli'.
Since November 1999, he was Associate professor of Rational Mechanics, still at
the Faculty of Engineering at the University of Bologna.
He delivered the course of Rational Mechanics for Environment Engineering and,
in the first semester of 2000/01, Applied Mathematics for Electronic Engineering.
He couldn't complete the semester course because of his sudden death on De
cember 3, 2000, at the age of 39 years.
His teaching was always open to any questions from the students; he was very
handy for interviews and generous during the examinations. The students used
to approach him so frequently for questions about the course and the solution of
problems; he was especially skillful in calculations and in relating results and mod
elling. He was also an efficient member of the governing Counsel (Giunta) of the
Department often performing burdensome tasks.
Since the beginning, I had the impression of a deeply correct and reserved man.
Next I realised that he had a strong character supported by a well-grounded faith.
He used to view his and other people's inconveniences with a remarkable sense
of humour but also to face problems with skill and firmness. That is why he was
able to perform successfully many different tasks with an uncommon efficiency. In
particular, while he was engaged with the academic work and the family (with two
little children) he was much involved in the Centro Manfredini which is renowned,
at least in Bologna, for the organisation of a cultural activity.
After the degree in 1985, he began the scientific research while the mathematical
physics was undergoing a strong development, both qualitative and quantitative,
since the early seventies.
Incidentally, since 1970 to 2000 the number of papers of the Italian commu
nity grew over ten times while the papers on international journals passed from a
few exceptions to almost all. Sure, Gentili took advantage of this rapid positive
evolution.
In 1990 he stayed some months at the Carnegie-Mellon Institute of Pittsburgh,
a well-renowned center for the research on continuum thermomechanics. That stay
allowed him to improve the rigorous approach and the understanding of advanced
topics of research.