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Modeling Dynamic Force using Stochastic Differential Equations

This research project was motivated by the need to develop stochastic process models to understand the dynamics of the accumulation of damage to a road surface. The factors which cause this degradation are the forces exerted by the vehicles, weather conditions and the materials used to construct the road. The extent of degradation at a given point in time also varies spatially. Eventually, given a road surface, it would be desired to be able to predict the distribution of its time to failure. Further it is also hoped that resulting statistical modeling will provide a better understanding of the uncertainties involved at various stages and thus will eventually also help in building better roads.