Model Monte Carlo, dependencies

Once it is decided that an assumption of independence is not supported, there are a number of approaches for building dependencies into the probabilistic model (Monte Carlo per se does not assume independence) ... 

Both the Rouse theory and the Rouse-model Monte Carlo simulation are a mean-field representation, meaning that the stress relaxation is the sum of contributions from all the chains in a unit volume, each represented by its statistically averaged time dependence (Chapters 6 and 7). Thus, simulations as explained above are performed on a singe chain. 

Molecular dynamics calculations are more time-consuming than Monte Carlo calculations. This is because energy derivatives must be computed and used to solve the equations of motion. Molecular dynamics simulations are capable of yielding all the same properties as are obtained from Monte Carlo calculations. The advantage of molecular dynamics is that it is capable of modeling time-dependent properties, which can not be computed with Monte Carlo simulations. This is how diffusion coefficients must be computed. It is also possible to use shearing boundaries in order to obtain a viscosity. Molec-... 

Figure 6 shows the field dependence of hole mobiUty for TAPC-doped bisphenol A polycarbonate at various temperatures (37). The mobilities decrease with increasing field at low fields. At high fields, a log oc relationship is observed. The experimental results can be reproduced by Monte Carlo simulation, shown by soHd lines in Figure 6. The model predicts that the high field mobiUty follows the following equation (37) where d = a/kT (p is the width of the Gaussian distribution density of states), Z is a parameter that characterizes the degree of positional disorder, E is the electric field, is a prefactor mobihty, and Cis an empirical constant given as 2.9 X lO " (cm/V). ...

Another interesting version of the MM model considers a variable excluded-volume interaction between same species particles [92]. In the absence of interactions the system is mapped on the standard MM model which has a first-order IPT between A- and B-saturated phases. On increasing the strength of the interaction the first-order transition line, observed for weak interactions, terminates at a tricritical point where two second-order transitions meet. These transitions, which separate the A-saturated, reactive, and B-saturated phases, belong to the same universality class as directed percolation, as follows from the value of critical exponents calculated by means of time-dependent Monte Carlo simulations and series expansions [92]. 

The model in either its analytic or Monte Carlo form is dependent upon four reactivity ratios defined by ... 

Both the molecular dynamics and the Monte Carlo approaches have great strengths and often lead to quite similar results for the properties of the systems investigated [10]. However, these methods depend on rather elaborate models for the molecular interactions. As a result, as noted above, both methods are... 

As described in Section 9.4, the determination and refinement of molecular conformations comprehends three main methods DG, MD and SA. Other techniques like Monte Carlo calculations have only a limited applicability in the field of structure elucidation. In principle, it is possible to exclusively make use of DG, MD or SA, but normally it is strongly suggested to combine these methods in order to obtain robust and reliable structural models. Only when the results of different methods match a 3D structure should be presented. There are various ways of combining the described techniques and the procedural methods may differ depending on what kind of molecules are investigated. However, with the flowchart in Fig. 9.13 we give an instruction on how to obtain a reliable structural model. 

Third, a further simplification of the Boltzmann equation is the use of the two-term spherical harmonic expansion [231 ] for the EEDF (also known as the Lorentz approximation), both in the calculations and in the analysis in the literature of experimental data. This two-term approximation has also been used by Kurachi and Nakamura [212] to determine the cross section for vibrational excitation of SiHj (see Table II). Due to the magnitude of the vibrational cross section at certain electron energies relative to the elastic cross sections and the steep dependence of the vibrational cross section, the use of this two-term approximation is of variable accuracy [240]. A Monte Carlo calculation is in principle more accurate, because in such a model the spatial and temporal behavior of the EEDF can be included. However, a Monte Carlo calculation has its own problems, such as the large computational effort needed to reduce statistical fluctuations. 

Huber et al. [12] investigated the same model by Monte Carlo simulations however, they focused on a different aspect the dependence of the interfacial capacity on the nature of the ions, which in this model is characterized by the interaction constant u. Samec et al. [13] have observed the following experimental trend the wider the potential window in which no reactions take place, the lower the interfacial capacity. Since the width of the window is determined by the free energy of transfer of the ions, which is 2mu in this model, the capacity should be lower, the higher u. ... 

The original proposal of the approach, supported by a Monte Carlo simulation study [36], has been further validated with both pre-clinical [38, 39] and clinical studies [40]. It has been shown to be robust and accurate, and is not highly dependent on the models used to fit the data. The method can give poor estimates of absorption or bioavailability in two sets of circumstances (i) when the compound shows nonlinear pharmacokinetics, which may happen when the plasma protein binding is nonlinear, or when the compound has cardiovascular activity that changes blood flow in a concentration-dependent manner or (ii) when the rate of absorption is slow, and hence flip-flop kinetics are observed, i.e., when the apparent terminal half-life is governed by the rate of drug input. 

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