Modeling Crystallization Dynamics when the Avrami Model Fails

On the validity of Avrami formalism in primary crystallization

Distribution kinetics of polymer crystallization and the Avrami equation.

Cluster distribution kinetics is adopted to explore the kinetics of polymer crystallization. Population balance equations based on crystal size distribution and concentration of amorphous polymer segments are solved numerically and the related dynamic moment equations are also solved. The model accounts for heterogeneous or homogeneous nucleation and crystal growth. Homogeneous nucleation rates...

Chemical reaction dynamics when the Born – Oppenheimer approximation fails

Whether a reaction is occurring in the gas phase or condensed phase, electronically nonadiabatic e†ects can become important if the adiabatic reaction coordinate requires a considerable change in the electronic wavefunction. The experiments and analysis presented here seek to make progress on a difficult and important problem, that of developing a back-ofthe-envelope method to predict which ene...

When the Decreasing Sequence Fails

The classical method for program analysis by abstract interpretation consists in computing a increasing sequence with widening, which converges towards a correct solution, then computing a decreasing sequence of correct solutions without widening. It is generally admitted that, when the decreasing sequence reaches a fixpoint, it cannot be improved further. As a consequence, all efforts for impr...

When the greedy algorithm fails

We provide a characterization of the cases when the greedy algorithm may produce the unique worst possible solution for the problem of finding a minimum weight base in an independence system when the weights are taken from a finite range. We apply this theorem to TSP and the minimum bisection problem. The practical message of this paper is that the greedy algorithm should be used with great car...