The Kohlrausch function: properties and applications

Abstract

In a wide variety of applications, including the modelling of the glassy state of dense matter, non-exponential correlation functions in nuclear magnetic resonance, polymer dynamics, and bone and muscle rheology, Kohlrausch functions have proved to be more appropriate in modelling the associated relaxation and decay processes than the standard exponential function. However, mathematical results about this function, important for both computational and modelling endeavours, are spread over publications in several quite different areas of mathematics and science. The purpose of this paper is to review the key properties of Kohlrausch functions in a unified manner, which motivates its use in the modelling of molecular processes. Some representative applications and related computational issues are discussed.