IMA Threads

IMA programs proceed on many time-scales, ranging from a highly focused workshop of a couple of days, through workshops and clusters of related workshops, through quarters of concentration and annual thematic years, to longer threads which carry over from year to year as a subject develops. These threads are an important mechanism, by which the IMA builds on earlier experiences. One program may suggest ideas for another. Communities and individuals which have become familiar to the IMA in an earlier program become a resource in developing another.

One such thread concerns Material science, and we will elaborate on that below. We plan to discuss other threads in future issues of Update.

Materials science. The IMA has been credited as having been responsible for the creation and nurturing of the field of mathematical material science, a role it continues to assume. The 1999 NRC report on US Research Institute of Mathematical Sciences highlighted as one of a few "Noteworthy Impacts of US Mathematical Institutes", Advances in Materials Science, with the accompanying description "The IMA recognized early that materials science, a critical technology area for the nation, also represented an important opportunity in this area for mathematical sciences. The IMA helped build a mathematical research community in this area more than five times the size of the community 10 years earlier." The many outcomes of this effort -- ranging from tremendous advances in the calculus of variations and links between topology and analysis to concrete new materials and devices, are documented elsewhere. Here we describe the chief programs that have contributed to the materials science thread at the IMA.

• 1982-1983 Continuum and Statistical Approaches to Phase Transition. Winter quarter dedicated to applications of statistical and continuum mechanics to properties of materials.
• 1984-1985 Continuum Physics and Partial Differential Equations. Fall quarter workshop on continuum physics, effective medium theory; Winter quarter dedicated to polymers and liquid crystals.
• 1985-1986 Stochastic Differential Equations and their Application. Fall quarter workshop in random media.
• 1986-1987 Scientific Computation. Winter quarter concentration period in structural mechanics and properties of material. Spring: Workshop on atomic and molecular structure dynamics.
• 1988-1989 Nonlinear Waves. Winter quarter minisymposium in plasticity.
• 1990-1991 Phase Transition and Free Boundaries. Fall workshop in microstructure and phase transition. Spring workshop in polymer configurations.
• 1994-1995 Waves and Scattering. Fall workshop in random and complex media.
• 1995-1996 Mathematical Methods in Material Science. Year long program.
• 2001-2002 Mathematics in the Geosciences. Winter workshop in nonlinear continuum mechanics.
• 2004-2005 Mathematics of Materials and Macromolecules: Multiple Scales, Disorder and Singularities.Year long program.