A model is presented which describes the geometrical effects in the radiolysis of water as a result of the diffusion of free radicals. The motion of secondary electrons immediately following the passage of the ionizing particle is discussed in an appendix, and it is concluded that radicals are most likely formed in pairs at the approximate sites of the original ionizations. Models for the diffusion of these radicals are shown to result in a definite fraction of radicals which undergo initial recombination for gamma- and fast beta-rays, for which the spurs are considered as diffusing independently. For alpha-rays a connected-track model is used. For the intermediate case of tritium beta-rays, a two-stage model is constructed. In each case the comparative yields of the ``forward'' and ``radical'' reactions (GF and GR) are calculated. Subsequent chemical effects in pure water and solutions are also considered briefly.

The chemical reactions which occur in particle tracks are diffusion-controlled. In this paper a set of partial differential equations is presented which describes the dissipation of a track composed of N particles. These equations involve functions which can be interpreted as correlation functions for the relative distribution of the particles. A superposition approximation is introduced which greatly simplifies the equations and a method for obtaining the correlation functions is presented. As an example of application of these equations a model for the action of ionizing radiation on water is discussed. It is shown that the radiation chemistry of water is adequately described for reasonable values of the parameters of the model.

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This paper reports a number of mathematical models and experiments that have been designed for the analysis and evaluation of delays of first-class letter mail in a post office. The flow pattern of mail consists of a number of serial and parallel processing stages. A letter takes a particular path through this flow network, which depends on its final destination, consequently, the delay of letter mail depends on its address as well as the inventories of other mail and the processing rates met enroute. While mail flow into a post office may contain many random elements, it is generally the case that input rates are predictable and strongly time-dependent. Scheduling policies must take into account the peak flows that temporarily exceed available processing rates and, in addition, must observe certain specified restrictions on the cost of processing, sorting, and storage operations. The effect of various transportation facilities between processing stages and from one post office to another must also be considered. The mathematical analysis deals with the minimization of letter delay through a network of processing and storage stages where there are capacity restrictions on individual and/or serial and parallel stage combinations. Analytical and graphical procedures are developed and numerical results are reported. The paper also reports a series of full-scale experiments performed at one of the larger United States Post Offices where theoretical procedures and decision rules were applied and tested. Delay reductions for first-class letter mail are believed to be of the order of 25 per cent.

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