A Kohlrausch Type Equation Based on a Simplified Cooperative Model

Abstract

The differential equation \({\text{d(}}\dot n/n{\text{)/d}}t{\text{ = - }}a{\text{(}}\dot n/n{\text{) + }}b{\text{(}}\left| {\dot n} \right|/n{\text{)}}^s \)is analysed, with n denoting the relaxing quantity, n = dn/dt(tis time), and a, band sconstants. Equations of this type have previously been shown to describe a large variety of relaxational patterns. Especially interesting is the close relationship with Bose–Einstein (B–E) like distributions and the underlying induction mechanisms. Here, the focus is on the special case of a= 0 which yields a generalised stretched exponential and, for certain variable ranges, the Kohlrausch (KWW) function in its usual form. The relaxation time τ is shown to depend strongly on the parameters entering the underlying differential equation. Conditions for constant τ are given.