Simulation models, deterministic model formulations

In summary, models can be classified in general into deterministic, which describe the system as cause/effect relationships and stochastic, which incorporate the concept of risk, probability or other measures of uncertainty. Deterministic and stochastic models may be developed from observation, semi-empirical approaches, and theoretical approaches. In developing a model, scientists attempt to reach an optimal compromise among the above approaches, given the level of detail justified by both the data availability and the study objectives. Deterministic model formulations can be further classified into simulation models which employ a well accepted empirical equation, that is forced via calibration coefficients, to describe a system and analytic models in which the derived equation describes the physics/chemistry of a system. 

The developed optimization is solved with genetic algorithm as the previous study based on deterministic optimization techniques showed that it is often trapped in local optima, due to highly non-linear nature of formulations in the model. The simulation model and genetic algorithm is interacted to produce high quality optimal solution(s), although computational time is relatively expensive. 

The WATS model is formulated in deterministic terms. However, an extension to include simple Monte-Carlo stochastic simulation is possible, taking into consideration a measured variability of the process parameters. 

In MD, time is a clearly singled out variable in a deterministic simulation based on a postulated force field and on the classical equations of motion. For the simulation of an evolving crystal aggregate, MD has the obvious advantage that the kinetics of the process is transparent, as accretion rates can be immediately described as a function of computational time, although the rate of any molecular process is obviously dependent on the postulated force model. In contrast, there is no apparent time variable in an MC simulation, because evolution steps are random and may randomly affect molecular evolutions which in reality happen on different timescales. If, as is often the case, time in MC is taken as proportional to the number of moves, one is implicitly assuming that all molecular moves occur on the same timescale, perhaps not a very severe approximation in studies of molecular aggregates bound by nearly isotropic van der Waals forces. In a variant of the MC formulation, called kinetic Monte Carlo (KMC)... 

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