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In Chapter 3, we mainly focus on the fundamentals of typical mesoscale simulation methods, which can provide a bridge between atomistic structures and macroscopic properties of materials. Among many mesoscale simulation methods, the phase-field and cellular automaton methods are extremely popular and powerful for simulating microstructure evolution. Consequently, we first give a detailed introduction on the fundamentals of the two methods, briefly describing some other mesoscale simulation methods, such as level set and front tracking. After that, application examples using individual mesoscale simulation methods and integrations of the phase-field method with other simulation methods such as atomistic simulation, crystal plasticity, CALPHAD, and machine learning are described in detail. Finally, a case study for design of high-energy-density polymer nanocomposites using the phase-field method is very briefly presented.
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