Dynamic Crossover in Polymers , Role of Molecular Weight
One of the most characteristic features of glass-forming liquids is the sharp slowing down of relaxation times, τ, upon cooling. In these materials relaxation dynamics exhibit a non-Arrhenius temperature dependence usually described by Vogel-Fulcher-Tamman (VFT) relation [1]. However, for majority of glassforming liquids it is impossible to fit data in the entire temperature range with a single set of VFT parameters. Above some characteristic temperature it is necessary to use another set of VFT parameters. Existence of this dynamic crossover was predicted by the mode-coupling theory (MCT) [2]. The theory predicts a transition from a liquidlike to a solidlike dynamics on a molecular time and length scale at some specific temperature, TC, above the glass transition temperature Tg. The dynamic crossover becomes even more evident with the use of derivative analysis proposed by Stickel et al [3] 2 , where x is the relaxation time or frequency. If
Relaxation in complex systems
The phenomenon of slow relaxation is discussed with emphasis on finding a general explanation of its ubiquity. After a review of the phenomenon, possible causes are considered both at the microscopic level and from a configuration space viewpoint. Quenched randomness and strongly constrained dynamics appear most important microscopically. In configuration space the central requirement seems to be the existence of many valleys connected sparsely in a hierarchical way. Recent toy models are shown to fit into this overall picture.
Mathematical Modeling of Scour and Deposition
Electronic computers are opening up the field of sedimentation engineering by permitting the analysis of problems which heretofore have required too much time and effort. Movable stream bed profiles are being calculated in addition to water surface profiles. The initial gradation of sediment material in the stream bed may be prescribed to facilitate the calculation of an armor layer. This gradation is continually changed by the computer program in response to sediment particles being deposited on the stream bed and material on the stream bed being removed to satisfy transport capacity. Hydraulic sorting of sediment by grain size is accomodated. The stream bed does not have to be represented by a single grain size. Retardance of motion because of armor layer is calculated.