Polymer science applications of path-integration, integral equations, and fractional calculus. (Q2773690)

In the study of microscopic and macroscopic dynamical behavior of macromolecular systems, fractional expressions occur naturally. A well-motivated treatment is presented for a path-integral description of flexible polymer chains and the relation between the parameters in this model and the familiar Brownian motion model.NEWLINENEWLINE Next, a number of methods for developing the solutions of path integral equations are discussed including the one based on fractional integrals and derivatives. Translational friction of polymer chains is described in detail. Further it is clarified as to how and why fractional order differential equations appear in the solution of transport problems involving fractal surfaces, such as polymer chains.NEWLINENEWLINE Subordination in a physical context is described through the probabilistic calculation of the charge density of a conducting disc of unit radius. Next, an account of various interior-type boundary value problems based on fractal objects is provided.NEWLINENEWLINE Finally, it is pointed out that the general theory of relaxation involving the Erdélyi-Kober fractional order operators is relevant for describing long wavelength relaxation processes in condensed materials such as polymers.NEWLINENEWLINEFor the entire collection see [Zbl 0998.26002].