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The main point of this paper is to show how the first and third key steps, as described above, can be accurately replaced by analytical equations. This will aid in further applications of the multi-scale model to other concrete mixtures, by making the multi-scale model usable by those without access to large amounts of computing power. This replacement will also make the model easier to use for parameter studies, as run times for the random walker step, step (3), can take weeks of clock time.