This award supports theoretical research on fundamental aspects of collective stochastic processes with many degrees of freedom. The focus is on building novel interrelations between such phenomena and enhancing existing ones. The principal investigator typically formulates specific models that address specific issues and allow for a detailed study combining numerical and analytical tools. Examples include:
(1) Reconstructed rough phases exist in equilibrium, but during KPZ-type surface growth, the reconstruction order fluctuates critically at short length-scales because domain walls become trapped to the ridge lines. These types of coupling can now be tailored to serve as tools for investigating the statistics of specific topological surface aspects, and thus to improve our fundamental understanding of staionary growing states.
(2) The avalanche dynamics in an unloading sandbox model maps exactly onto KPZ-type surface growth. This new example of self-organized criticality can now serve as a benchmark to explore a unifying picture for absorbing-state criticality, surface growth, and avalanche phenomena.
(3) Dissociative dimer surface dynamics gives rise to anomalous equilibrium surface roughness and maps exactly to polymers on random lattices. The role of non-local deposition and extremal statistics needs further investigation.
(4) Driven stochastic flow through narrow channels with an obstruction leads to macroscopic queueing, but only above a critical strength of the slow bond. Below this dynamic phase transition the queue takes a power law shape with a novel scaling exponent. This has intriguing links to other driven phenomena.
This research ties together a number of fields of study. The principal investigator also has close connections with related experimental groups. Graduate students will be trained and the PI also teaches regularly on this research at various schools. %%% This theoretical research focuses on statistical phenomena on surfaces (two-dimensions) with strong connections to both applied mathematics and experiments. The PI is able to work at the intersection between fields and make unique connections between phenomena and models. This research program provides an excellent training for students. ***
