Kinetic Monte Carlo simulation Subject

Breant et al. (1996) followed up the work of Al-Banna, Kelman, and Whiting and used Monte Carlo simulation to determine the number of subjects and samples per subject needed to obtain accurate and precise parameter estimates with a drug that showed monoexponential disposition kinetics. They found that for a 1-compartment model, concentration data from 15 to 20 subjects with two samples per subject produced reasonable parameter estimates. Although the authors did not use NONMEM, their results should be applicable to NONMEM analyses. 

Monte Carlo simulations have been used in some cases to study kinetics of clusters. For example, evaporation kinetics lends itself to this method. The method has been used to study kinetics of passage between pairs of adjacent minima, a subject discussed in a bit more detail later. A Monte Carlo study has described how a cluster of CO2 molecules containing a single 12 molecule relaxes when the extra electron is suddenly removed from the foreign molecule. ... 

Chapter 4 starts with some basic equations, which relate the molecular-kinetic picture of gas-solid chromatography and the experimental data. Next come some common mathematical properties of the chromatographic peak profiles. The existing attempts to find analytical formulae for the shapes of TC peaks are subject to analysis. A mathematical model of migration of molecules down the column and its Monte Carlo realization are discussed. The zone position and profile in vacuum thermochromatography are treated as chromatographic, diffusional and simulation problems. 

In microfluid mechanics, the direct simulation Monte Carlo (DSMC) method has been applied to study gas flows in microdevices [2]. DSMC is a simple form of the Monte Carlo method. Bird [3] first applied DSMC to simulate homogeneous gas relaxation problem. The fundamental idea is to track thousands or millions of randomly selected, statistically representative particles and to use their motions and interactions to modify their positions and states appropriately in time. Each simulated particle represents a number of real molecules. Collision pairs of molecule in a small computational cell in physical space are randomly selected based on a probability distribution after each computation time step. In essence, particle motions are modeled deterministically, while collisions are treated statistically. The backbone of DSMC follows directly the classical kinetic theory, and hence the applications of this method are subject to the same limitations as kinetic theory. 

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