Theoretical papers, mathematical derivations

Since the Murday-Cotts paper in 1968 much progress has been made toward the theoretical description of the spin-echo intensity E g, A) for spins diffusing in well-defined geometries. Tanner and Stejskal derived already in 1968 the exact expression of ii(g. A) for spins diffusing in a rectangular box. The derivation of an exact expression for E g, A) for diffusion in a sphere with reflecting walls is not a trivial mathematical problem and it took between 1992 and 1994 when three expressions were published. All three expressions are only valid in the short-gradient-pulse approximation (see below). 

The derivation of a consistent mixed quantum-classical dynamics discussed in this paper was first proposed in Ref. [15] and commented and clarified in Ref. [1], This derivation is based on a group-theoretical formulation of quantum and classical mechanics, which introduces a very elegant and formally rigorous mathematical apparatus and allows to directly obtain classical mechanics as the limit for h —> 0 of quantum mechanics, in the Heisenberg representation of quantum dynamics. 

A recent paper describes a mathematical model for the chlorination of polyethylene in a bubble column reactor, the model was used to optimize product quality in the continuous chlorination of polyethylene. Another theoretical treatment deals with the change in polymer reactivity during the course of a macromolecular reactions in solution or in the melt. The reactivity of a transforming unit in the polymer depends on its microenvironment, including nearest neighbours on the same chain and on other chains, as well as small molecules in the reacting system. The equations derived describe the kinetic curve, the distribution of units, and the compositional heterogeneity of the products. 

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