Analytical 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. 

Analytical models can be classified into deterministic and stochastic. The former formulates the relationship between the known and unknown factors in the form of equations, the solution of which often requires application of numerical methods. By following prescribed rules the same result can always be obtained from the same starting conditions and initial values of known factors. In the latter, the model contains a degree of uncertainty caused by random events or variations in the values of factors, thus leading to potentially different results even when starting from the same initial conditions. 

This is because modem analytical measurements indicate the existence of the order of 10 (0(10 )) unique molecules in petroleum feedstocks. In modeling terms, each species corresponds to one differential equation in a deterministic modeling approach. Therefore not only the solution but also the formulation of the implied model is formidable. This motivated the... 

Thus, the question of central concern raised in our contribution has been the macroscopic formulation of EET and its relation to the experimental observable of excimer fluorescence in a time-resolved experiment. EET has been discussed, hers, as a dispersive, i.e., time-depen-dent process in deterministic monomer-excimer models which had been the subject of a detailed kinetic analysis in recent work (3 8, 4.S.). With the use of rate function k(t) (Equation 4) it is natural to yield typical non-exponential intensity-time profiles, either in form of an asymptotic approach (Equations 5,6), or in closed form analytical solutions (Equations 7,8). The physios emer-... 

---