Probing the dynamic scaling hypothesis in 1-D coarsening particle systems.
MSc(R) thesis, University of Glasgow.
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Hopefully this thesis will provide the reader with an idea of what coarsening is and when and where it may occur. The concise definition of coarsening that we employ is that characteristic length scales grow in time. The Dynamic Scaling Hypothesis which asserts that upon suitable scaling of space, features of latetime structures are indistinguishable is the main consideration in this thesis and we will investigate two 1-D coarsening dynamical systems, one for which The Dynamic Scaling Hypothesis holds and one for which it does not. This thesis studies, in particular, the coarsening-ballistic particle CBP* model and
the coarsening reverse-parabolic CRP** model. We utilize an in-house code developed by Watson et al. to generate the morphometric data and we show that The Dynamic Scaling Hypothesis holds for the CBP* model but does not hold for the CRP** model. We also identify the existence of power law scaling and a scaling state in the CBP* model which are not present in the CRP** model. It is found in the CRP** model however, that the distributions have a length scale dependence.
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