Dynamical simulation methods minimization algorithms

The predictor/corrector algorithm in Diva includes a stepsize control in order to minimize the number of predictor and corrector steps. Finally, the continuation package contains methods for the computation of the dominating eigenvalues of DAEs. This allows a stability analysis of the steady state solutions and a detection of local bifurcations for large sparse systems. As the continuation method is embedded into a dynamic simulator, the user has the opportunity to switch interactively from continuation to time integration. This allows additional investigations of transient behaviour or domains of attraction with the same simulation tool[2]. 

The simulation is performed in a grand canonical ensemble (GCE) where all microstates have the same volume (V), temperature and chemical potential under the periodic boundary condition to minimize a finite size effect [30, 31]. For thermal equilibrium at a fixed pu, a standard Metropolis algorithm is repetitively employed with single spin-flip dynamics [30, 31]. When equilibrium has been achieved, the lithium content (1 — 5) in the Li, 3 11204 electrode at a given pu is determined from the fraction of occupied sites. The thermodynamic partial molar quantities oflithium ions are theoretically obtained by fluctuation method [32]. The partial molar internal energy Uu at constant Vand T in the GCE is readily given by [32, 33]... 

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