Models of self-organized criticality which can be described by stochastic partial differential equations with noncoercive mono- tone diffusivity function and multiplicative Wiener forcing term (as e.g. the Bak/Tang/Wiesenfeld- and Zhang-models) are analyzed. Existence and uniqueness of nonnegative strong solutions are proved. Previously numerically predicted transition to the critical state in 1-D is confirmed by a rigorous proof that this indeed happens in finite time with high probability.

We derive equations of motion for the dynamical folding of
biological molecules (such as DNA), that are modeled as continuous
filamentary distributions of interacting rigid charge conformations.
The equations of motion for the dynamics of such a system are
nonlocal when the screened Coulomb interactions, or Lennard-Jones
potentials between pairs of charges are included. These nonlocal
dynamical equations are derived using Euler-Poincar'e variational
formulations, extending earlier work for exact geometric rods. In the
absence of nonlocal interactions, the equations reduce to the
Kirchhoff theory of elastic rods. An elegant change of variables
separates the dynamics geometrically into "horizontal" and "vertical"
components.

This is joint work with Francois Gay-Balmaz(EPFL), David Ellis (Imperial),
Darryl D. Holm (Imperial), and Tudor Ratiu (EPFL).