| Accurate determination of the onset of structural transitions in complex physico-chemical systems is of crucial importance in condensed matter science and materials engineering. As direct access to such responses is typically difficult to attain experimentally, computational techniques such as molecular dynamics (MD) have become powerful tools for probing the underlying atomic-scale dynamics and determining the transition onsets. While the most appealing feature of MD lies in its ability to provide dynamic information with atomistic resolution, integrating all the degrees of freedom over observable length and time scales remains a major challenge in computational materials science. The problem is compounded when the underlying physical processes are governed by rare events. In recent years, a variety of new techniques, such as accelerated dynamics, transition path sampling, metadynamics, and equation-free methods have been proposed to address long-time dynamics issues directly through atomistic simulation.;In this thesis, new equation-free-based (i.e., time-stepper-based) coarse molecular-dynamics (CMD) methods are developed and implemented to analyze and determine the onsets of structural transitions in condensed-matter systems. In CMD, coarse-grained information is estimated on the fly from many short and properly initialized independent replica MD simulations. This information can then be used to predict transition points in the physical behavior of the complex systems under consideration. The method is based on the description of the evolution of the probability density, P (psi, t), as approximated by the Fokker-Planck equation where psi ( t) is an appropriate coarse-grained observable that describes the state of the system. Specific problems that have been analyzed in this thesis include the thermodynamic melting of crystalline materials, the pressure-induced polymorphic transformation of metallic crystals, and the thermally induced order-to-disorder transition of inert-gas layers physisorbed on graphite substrate surfaces. The analysis focuses on the construction of the underlying effective free-energy landscapes and leads to accurate and computationally efficient determination of the corresponding transition onsets. |
