Robert Pego

Carnegie Mellon University

Dynamics and oscillations in models of coagulation and fragmentation

Coaglation-fragmentation equations are rather simple-looking kinetic models for evolution of the size distribution of clusters, appearing widely in science and technology. But few general analytical results characterize their dynamics. Solutions can exhibit self-similar growth, singular mass transport, and weak or slow approach to equilibrium. I will review some recent results in this vein for models that lack detailed balance: For a data-driven model of fish school size, we derive results on equilibration and self-similar spreading from the use of Bernstein transforms and complex function theory for Pick or Herglotz functions. Temporal oscillations are proved to be possible in a closed Becker–Doering-type model including an atomization reaction. Formal modeling of physical Becker–Doering models of nucleation and condensation with small-scale source and large-scale sinks identifies a scaling regime yielding oscillations in first-order phase transitions.