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Fracture, and particularly brittle fracture, is a good example of
an instability. For a homogeneous solid, subjected to a uniform
stress field, a crack may appear anywhere in the structure once the
threshold stress is reached. However, once a crack has been
nucleated in some place, further damage in the solid will in most
cases propagate from the initial crack, and not somewhere else in
the solid. In this sense fracture is an unstable process. This
property makes the process extremely sensitive to any heterogeneity
present in the medium, which selects the location of the first
crack nucleated. In particular, fracture appears to be very
sensitive to disorder, which can favor or impede local cracks.
Therefore, in most realistic cases, a good description of fracture
mechanics should include the effect of disorder. Recently this need
has motivated work in this direction starting from the usual
description of fracture mechanics. Parallel with this first trend,
statistical physics underwent a very important development in the
description of disordered systems. In particular, let us mention
the emergence of some "new" concepts (such as fractals, scaling
laws, finite size effects, and so on) in this field. However, many
models considered were rather simple and well adapted to
theoretical or numerical introduction into a complex body of
problems. An example of this can be found in percolation theory.
This area is now rather well understood and accurately described.
CARGESE INSTITUfE ON DISORDER AND MIXING Convection, diffusion and
reaction are the three basic mechanisms in physico-chemical
hydrodynamics and chemical engineering. Both convective and
diffusive processes are strongly influenced by the effect of
disorder of granular matter in porous media, suspensions, fluidized
beds or/and by the randomness caused in turbulent flow field. This
book has been initiated by a NATO summer institute held in Cargese
(Corsica, FRANCE) from June 15 th to 27 th 1987 . Its aim was to
associate statistical physicists, fluid mechanicians and
specialists of chemical engineering on the problems of the relation
between disorder and mixing and, in this respect, this is a "
premiere ." This book is made of chapters based on lectures given
in the meeting. However we have paid a considerable attention to
harmonize the contents and styles of chapters made by scientists
trained in different communities and using different languages and
techniques to describe similar problems. The Prelude by the editors
of the book introduces the different points and is a biased view of
some of the important and most active aspects of the subjects
developed. We wish to thank all contributors and students of the
institute who gave the style of the present interdisciplinary
approach. We also greatly thank Elisabeth Charlaix who has shared
with us the scientific and practical organisation of the institute,
and Marie-France Hanseler for her technical support.
CARGESE INSTITUfE ON DISORDER AND MIXING Convection, diffusion and
reaction are the three basic mechanisms in physico-chemical
hydrodynamics and chemical engineering. Both convective and
diffusive processes are strongly influenced by the effect of
disorder of granular matter in porous media, suspensions, fluidized
beds or/and by the randomness caused in turbulent flow field. This
book has been initiated by a NATO summer institute held in Cargese
(Corsica, FRANCE) from June 15 th to 27 th 1987 . Its aim was to
associate statistical physicists, fluid mechanicians and
specialists of chemical engineering on the problems of the relation
between disorder and mixing and, in this respect, this is a "
premiere ." This book is made of chapters based on lectures given
in the meeting. However we have paid a considerable attention to
harmonize the contents and styles of chapters made by scientists
trained in different communities and using different languages and
techniques to describe similar problems. The Prelude by the editors
of the book introduces the different points and is a biased view of
some of the important and most active aspects of the subjects
developed. We wish to thank all contributors and students of the
institute who gave the style of the present interdisciplinary
approach. We also greatly thank Elisabeth Charlaix who has shared
with us the scientific and practical organisation of the institute,
and Marie-France Hanseler for her technical support.
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