On the continuous diversity of nature, its modeling and applications to complex systems

In geophysics, the thermodynamics of recrystallization and creep of large polycrystalline rocks is of vital importance. On the other hand, physicists have since long proposed sophisticated theories for the modeling of induced anisotropy and streaming birefringence in polymers and liquid crystals. Likewise, the dynamics of structured populations (viz. populations composed of individuals classified by age or other physiological characteristics) has been a far-reaching research theme for mathematical biologists along the last decades. Evidently, the mechanics of polydisperse granular media has become a stimulating topic in civil engineering, and so do also the theories of polymerization, cracking and other complex reactions in petroleum and atmospheric chemistry. Curiously, in spite of the dissimilitude of all these problems, it happens that their modeling falls into the same mathematical structure. It is the objective of the theory of mixtures with continuous diversity to formalize and explore this common mathematical framework so as to unify the formulation of all these apparently disparate theories and serves as a bridge for the exchange of methods and ideas between distinct disciplines.