KINETIC ROUGHENING PHENOMENA, STOCHASTIC GROWTH DIRECTED POLYMERS ANDALL THAT - ASPECTS OF MULTIDISCIPLINARY STATISTICAL-MECHANICS

Kinetic interfaces form the basis of a fascinating, interdisciplinary branch of statistical mechanics. Diverse stochastic growth processes c an be unified via an intriguing nonlinear stochastic partial different ial equation whose consequences and generalizations have mobilized a s izeable community of physicists concerned with a statistical descripti on of kinetically roughened surfaces. Substantial analytical, experime ntal and numerical effort has already been expended. Despite impressiv e successes, however, there remain many open questions, with much rich ness and subtlety still to be revealed. In this review, we give an uno rthodox account of this rapidly growing field, concentrating on two ma in lines - the interface growth equations themselves, and their direct ed polymer counterparts. We emphasize the intrinsic links among the to pics discussed, as well as the relationships to other branches of natu ral science. Our aim is to persuade the reader that multidisciplinary statistical mechanics can be challenging, enjoyable pursuit of surpris ing depth.