Browsing by Subject "Branch following and bifurcation"

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    Equilibrium Maps: Characterizing the complex and stochastic behavior of nanosystems subjected to proportional loading
    (2016-11) Pattamatta, A. S. L. Subrahmanyam
    Modeling systems subjected to proportional loading, such as a nanotube being pulled, tem- perature programmed desorption of chemical species on a surface etc, is of significant technological importance. A particularly challenging task when dealing with nanoscale systems is that the thermal fluctuations are on par with the applied stimulus owing to the small system size. Such fluctuations in conjunction with the extreme nonconvexity of the underlying potential energy hyper-surface (PES) means that there are mutually compet- ing pathways the system can take and the evolution of the system is stochastic. Often the evolution is affected by the rate at which the system is loaded. In the current work, we develop a novel solution strategy for simulating nanosystems sub- jected to proportional loading using branch following and bifurcation techniques. To this end, the concepts of the PES, the equilibrium points (ex. stable and transition states), and the transition networks connecting the stable states have been extended to the context of driven systems where the PES morphs in response to the external loading. We introduce the concept of the Equilibrium Map (EM), that is a distillation of the equilibrium and kinetic features of the evolving PES. The EM is then used to construct trajectories of the system for representative scenarios that span a spectrum of loading regimes and boundary conditions. We have developed efficient and highly scalable parallel codes to construct and handle the EM data. As a part of modeling the evolution of the system as a state to state dynamics, we have also addressed the issue of superbasins, arising due to clusters of stable states connected by low energy barriers relative to the barriers for transitions of the system to states out of the superbasin, in the context of an evolving PES. The proposed method is able to accelerate the system trapped in these superbasins and simulate the behavior of the system over long time scales. Finally we apply the EM method to a nanoslab under displacement controlled loading and show that the method qualitatively reproduces experimental observations on similar systems.