Probabilistic models and computer simulations

There are nine and sixty ways of constructing tribal lays, and-every-single-one-of-them-is-right. 

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Such stochastic modelling was advanced by Klein and Virk Q) as a probabilistic, model compound-based prediction of lignin pyrolysis. Lignin structure was not considered explicitly. Their approach was extended by Petrocelli (4) to include Kraft lignins and catalysis. Squire and coworkers ( ) introduced the Monte Carlo computational technique as a means of following and predicting coal pyrolysis routes. Recently, McDermott ( used model compound reaction pathways and kinetics to determine Markov Chain states and transition probabilities, respectively, in a rigorous, kinetics-oriented Monte Carlo simulation of the reactions of a linear polymer. Herein we extend the Monte Carlo... 

Dembo et al. [1988] developed a model based on the ideas of Evans [1985] and Bell [1978]. In this model, a piece of membrane is attached to the wall, and a pulling force is exerted on one end while the other end is held fixed. The cell membrane is modeled as a thin inextensible membrane. The model of Dembo et al. [1988] was subsequentlyextended via a probabilistic approach for the formation of bonds by Coezens-Roberts et al. [1990]. Other authors used the probabilistic approach and Monte Carlo simulation to study the adhesion process as reviewed by Zhu [ 2000]. Dembo s model has also been extended to account for the distribution of microvilli on the surface of the cell and to simulate the rolling and the adhesion of a cell on a surface under shear flow. Hammer and Apte [1992] modeled the cell as a microvilli-coated hard sphere covered with adhesive springs. The binding and breakage of bonds and the distribution of the receptors on the tips of the microvilli are computed using a probabilistic approach. 

Figure 9.4 Risk assessment for an aquatic environment based on a probabilistic procedure into which the concept of varying sensitivity in multispecies communities is incorporated (Nendza, Volmer and Klein, 1990). Exposure and effects are determined separately from experimental or, if not available, QSAR data. Physico-chemical data and information on bioaccumulation and biotransformation are the input for computer simulations of transport and distribution processes that estimate the concentrations of a potential contaminant in a selected river scenario, using, for example, the EXAMS model (Bums, Cline and Lassiter, 1982). For the effects assessment, the log-normal sensitivity distribution is calculated from ecotoxicological data and the effective concentrations for the most sensitive species are determined. The exposure concentrations and toxicity data are then compared by analysis of variance to give a measure of risk for the environment. Modified from Nendza, Volmer and Klein (1990) with kind permission from Kluwer Academic Publishers, Dordrecht.

However, all the referenced procedures are based on simulations which are performed at the level of a MDOF model. Recently, an approximate procedure utilizing a deterministic MDOF model and uncertainty analysis at the level of a SDOF model was proposed (Kosic et al. 2014). It can be classified as being somewhere in between the aforementioned procedures for the determination of fragility parameters on the basis of pushover methods, both in terms of computational time and in terms of accuracy. Such an approach is computationally less demanding, since all the simulations are performed at the level of the so-called probabilistic SDOF model. It can therefore be attractive for the fragility analysis of more extensive building stock. 

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