MC approach

Short-time Brownian motion was simulated and compared with experiments [108]. The structural evolution and dynamics [109] and the translational and bond-orientational order [110] were simulated with Brownian dynamics (BD) for dense binary colloidal mixtures. The short-time dynamics was investigated through the velocity autocorrelation function [111] and an algebraic decay of velocity fluctuation in a confined liquid was found [112]. Dissipative particle dynamics [113] is an attempt to bridge the gap between atomistic and mesoscopic simulation. Colloidal adsorption was simulated with BD [114]. The hydrodynamic forces, usually friction forces, are found to be able to enhance the self-diffusion of colloidal particles [115]. A novel MC approach to the dynamics of fluids was proposed in Ref. 116. Spinodal decomposition [117] in binary fluids was simulated. BD simulations for hard spherocylinders in the isotropic [118] and in the nematic phase [119] were done. A two-site Yukawa system [120] was studied with... 

This approach was successfully used in modeling the CVD of silicon nitride (Si3N4) films [18, 19, 22, 23]. Alternatively, molecular dynamics (MD) simulations can be used instead of or in combination with the MC approach to simulate kinetic steps of film evolution during the growth process (see, for example, a study of Zr02 deposition on the Si(100) surface [24]). Finally, the results of these simulations (overall reaction constants and film characteristics) can be used in the subsequent reactor modeling and the detailed calculations of film structure and properties, including defects and impurities. 

The MC method is a powerful technique for investigating complicated phenomena that are difficult to solve by the conventional differential equation approach. In the MC approach, all one needs are the individual probabilities of various kinetic events. It is easy to understand the advantages of applying the MC method to emulsion polymerization if we note that it is possible to simulate the formation processes of all polymer molecules in each polymer particle directly because the volume of the reaction locus is very small. One... 

The easy availability of computers of increasing power has greatly encouraged the two approaches described in this section. In the Monte Carlo (MC) approach. 

One should note that in the MF approach no second order phase transition is present. Contrary to this, MC simulations with diffusion [45,46,54-56] do show this transition, even when the results are extrapolated to infinitely fast diffusion. This means that, at least in this case, MC simulations with fast diffusion do not show the same results as MF calculations. This is remarkable since it is generally assumed that in the fast diffusion limit, both approaches should be equivalent. The MC method is certainly correct, and we believe that the discrepancies show that the MF approach is not always valid. This is the reason why we have chosen the MC approach to study CO oxidation on Pt(lOO) surfaces, as will be discussed in the next section. 

The three papers by Rice and co-workers involve differences of elaboration. Figure 3.22 compares a mean field with a MC approach, between which not much difference is found. Density profiles are typical results from this type of analysis. The quantitative outcome depends of course on the choice of peiriuneters, which is analyzed in some detail by the authors the reader is referred to their papers for further information. As expected, the layer becomes thicker at higher surface occup-cmcy it is also seen that at low occupancy some segments close to the head group are in contact with the solvent. 

Next are methods based on zeroth-order wave functions that are linear combinations of Slater determinants that again may or may not include a treatment of residual electron correlation effects. In these multiconfigurational (MC) approaches, the starting wave function is presupposed to be given by a determinantal expansion... 

The large number of contemporary MC approaches for dealing with the problem of phase behaviour can usefully be categorized in terms of the the interphase path they utilize to connect the phases and the sampling strategy adopted to traverse this path. We have exemplified some of the principal concepts within the limited context of the phase behaviour of simple particle... 

The completion of an organic structure is a challenging task, since the electron density maps resulting from the application of DM usually contain partial and distorted molecular fragments. Tanahashi et al. ° accomplished it by combining DM with a MC approach borrowed from the procedure described in Harris et al. The positions of three missing atoms were found by varying their coordinates in each MC move. 

Bartkowiak, W., Lipifiski, J. Solvent effect on the nonlinear optical properties of para-nitroaniline studied by Langevin dipoles-Monte Carlo (LD/MC) approach. Computers Chem. 22, 31-37 (1998)... 

It can be seen that implementing the power spectrum of fluctuations for the calculation of bending rigidity requires an efficient sampling on large spatial scales of the membrane (low q values). In this scope, casting the recently reported [142] Mode Excitation MC approach in context of the presented model could be very promising. 

Mapping Pharmacophores in Ligands. Relaxed MCS approach. A rigid alignment, based on clique detection and genetic algorithm. (141)... 

Then, by comparing the MC approach with the lEE technique, we find that the approximation errors coming from the simulation smdy are up to 10 times higher than the equivalent figures for the lEE approach (figures (5.2.S1, S3 and S5) vs. (5.2.S2, S4 and S6)). Furthermore, it has to be pointed out that the series expansion of the probabilities is almost everywhere in between the 97.5% confidence interval of the MC simulation (figure (5.2.S3 and S4)). 

Overall, we find a difference between the simulated and approximated swaption prices of up to 1.3% for out-of-the-money options (see figure ( 5.3.SI)). Nevertheless, based on our results of the last section, where the lEE performed up to 10 times more accurate than the corresponding MC simulation study, we expect that the difference between the simulated and the approximated option prices is mainly linked to the impreciseness of the MC approach (figure (5.3.SI)). The lEE approach performs very efficient and accurate, even if we compute the price of a 1x20 swaption (see table 5.1). Again, all 21 single probabilities TlJ iEEm for i = 0,. ..,20 are in between the 97.5% confidence coming from the simulation approach. ... 

As a simple example of possible MC strategies that an organometallic chemist may wish to employ, consider a four-orbital, four-electron system such as a metal-carbon double bond in an alkylidene. The most expensive MC approach is the brute-force approach, generating all possible combinations among the four orbitals and four electrons... 

Combined RISM-MC approach for predicting peptide conformations... 

Mass spectrometry, 147 MC approach. See Monte Carlo approach (MC approach)... 

The increased current tailing at longer times along with a shift of the current peak to longer times found in kMC simulations with low CO surface mobility, cf. Figure 2.4a, is characteristic for experimental transients on small nanoparticles ( 1.8 nm). Overall, the simulated transients capture all the essential features of experimental current transients. Analogous as for large nanoparticles, the model fits chronoamperometric current transients for various potentials and, thereby, explore effects of particle size and surface structure on rate constants, Tafel parameters (transfer coefficients), and equilibrium potentials. Due to the stochastic nature of the MC approach, systematic optimization of the fits is a much more delicate task. 

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