Fractional Stochastic Field Theory

Abstract

Abstract. Models describing evolution of physical, chemical, biological, social and financial processes are often formulated as differential equations with the understanding that they are large-scale equations for averages of quantities describing intrinsically random processes. Explicit account of randomness may lead to significant changes in the asymptotic behaviour (anomalous scaling) in such models especially in low spatial dimensions, which in many cases may be captured with the use of the renormalization group. Anomalous scaling and memory effects may also be introduced with the use of fractional derivatives and fractional noise. Construction of renormalized stochastic field theory with fractional derivatives and fractional noise in the underlying stochastic differential equations and master equations and the interplay between fluctuation-induced and built-in anomalous scaling behaviour is reviewed and discussed.

Universality in Incompressible Active Fluid: Effect of Non-local Shear Stress

“…In fact, superdifussive Lévy walks have been reported in several recent experiments [42][43][44][45]. Furthermore, our minimal extension of the original model is the most convenient for practical calculations, since it leads to the appearance of the fractional Laplace operator, whose renormalization is well understood in field theories [46][47][48].…”

The puzzling persistence of the intellectual property right/climate change relationship

“…According to Honkonen, 'intellectual property rights form a big part of the answer as to why technology transfer has not been as successful as it was expected to be'. 72 This is a potentially important finding, chiming as it does with the argument made by IP lawyers, as will be discussed further in the section below. Unfortunately however, Honkonen's response is rather under-argued, providing little basis either for the proposition that TT has been unsuccessful or that IPRs are to blame.…”