| Summary: | The objective of this thesis is to propose modeling techniques that enable the design and optimization of material systems which require descriptions via molecular simulations. These kinds of systems are quite common in materials and engineering research. The first step in performing design and optimization tasks on such systems is the development of accurate simulation models from experimental data. In the first part of this thesis, we present a novel simulation model for the hyperbranched polymerization process of difunctional A2 oligomers, and B3 monomers. Unlike the previous models developed by other groups, our model is able to simulate the evolution of the polymer structure development under a wide range of synthesis routes, and in the presence of cyclization and endcapping reactions. Furthermore, our results are in agreement with the experimental data, and add insight into the underlying kinetic mechanisms of this polymerization process. The second major step in our work is the development of reduced order process models that are suitable for design and optimization tasks, using simulation data. We illustrate our approach on a stochastic simulation model of epitaxial thin film deposition process. Compared to the widely used approach called equation-free modeling, our method requires fewer assumptions about the dynamic system. The assumptions required in equation-free modeling include a wide separation between the time scales of low and high order moments describing the system state, and the accuracy of the time derivatives of system properties computed from molecular simulation data, despite the potentially large amount of fluctuations in stochastic simulations. Unlike the recent similar studies, our study also includes the analysis of prediction error which is important to evaluate the predictions of the reduced order model, compared to the high dimensional molecular simulations. Hence, we address two major issues in this thesis: development of simulation models from molecular experimental data, and derivation of reduced order models from molecular simulation data. These two aspects of modeling are both necessary to design and optimize processing conditions of materials for which continuum level descriptions are not available or accurate enough.
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