MATHEMATICAL TOOLS FOR SOLVING NEW, MORE REALISTIC MODELS OF POLYMER MELTS

Stochastic processes play an important role in the kinetic theory of polymeric liquids. Various concepts, such as "configurational distribution functions", "diffusion equations", "Brownian motion", "white noise", "generalized Langevin equations"..., are indispensable in the theory of polymer dynamics. We review the mathematical description of various types of stochastic processes in order to provide (i) a sound basis for the formulation of new kinetic theory models, (ii) recipes for the development of computer simulation algorithms and (iii) a feeling for the possible pitfalls in the naive use of stochastic calculus. Various possible applications of the mathematical background presented here are discussed in connection with particular models of polymer melts.