Dynamical Monte Carlo simulations

K. A. Fichthorn, W. H. Weinberg. Theoretical foundations of dynamical Monte Carlo simulations. J Chem Phys 95 1090-1096, 1991. 

R. B. Pandey, A. Milchev, K. Binder. Semidilute and concentrated polymer solutions near attractive walls Dynamic Monte Carlo simulation of density and pressure profiles of a coarse-grained model. Macromolecules 50 1194-1204, 1997. 

Enzyme reactions, like all chemical events, are dynamic. Information coming to us from experiments is not dynamic even though the intervals of time separating observations may be quite small. In addition, much information is denied to us because of technological limitations in the detection of chemical changes. Our models would be improved if we could observe and record all concentrations at very small intervals of time. One approach to this information lies in the creation of a model in which we know all of the concentrations at any time and know something of the structural attributes of each ingredient. A class of models based on computer simulations, such as molecular dynamics, Monte Carlo simulations, and cellular automata, offer such a possibility. 

Korzeniewski C, Kardash D. 2001. Use of a dynamic Monte Carlo simulation in the study of nucleation-and-growth models for CO electrochemical oxidation. J Phys Chem B 105 8663-8671. 

A quantitative analysis [34], based on the adsorption isotherms and the intercrystalline porosity, yielded the remarkable result that a satisfactory fit between the experimental data and the estimates of Aong-range = Pinter Anter following Eqs. (3.1.11) and (3.1.12) only lead to coinciding results for tortuosity factors a differing under the conditions of Knudsen diffusion (low temperatures) and bulk-diffusion (high temperatures) by a factor of at least 3. Similar results have recently been obtained by dynamic Monte Carlo simulations [39—41]. 

A Dynamic Monte Carlo Simulations of Lattice Polymers. 27... 

In the dynamic Monte Carlo simulations described earlier, we used a crystalline template to suppress supercooling (Sect. A.3). If this template is not present, there will be a kinetic interplay between polymer crystallization and liquid-liquid demixing during simulations of a cooling run. In this context, it is of particular interest to know how the crystallization process is affected by the vicinity of a region in the phase diagram where liquid-liquid demixing can occur. 

FaUer, R. and de Pablo, J.J., Constant pressure hybrid molecular dynamics-Monte Carlo simulations, J. Chem. Phys., 116, 55, 2002. 

Molecular dynamics, Monte Carlo simulations (Haile, 1992), and very recently applications of cellular automata to drug research (Kier and Cheng,... 

As stated in Sec. 3.1, only ideal systems will be considered in this section. This definition implies that there is no intramolecular reaction, a condition which is satisfied in practice for very low concentrations of Af monomers (f >2), in the A2 + Af chainwise polymerization. To take into account intramolecular reactions it would be necessary to introduce more advanced methods to describe network formation, such as dynamic Monte Carlo simulations. 

Dynamic Monte Carlo simulations were first used by Verdier and Stockmayer (5) for lattice polymers. An alternative dynamical Monte Carlo method has been developed by Ceperley, Kalos and Lebowitz (6) and applied to the study of single, three dimensional polymers. In addition to the dynamic Monte Carlo studies, molecular dynamics methods have been used. Ryckaert and Bellemans (7) and Weber (8) have studied liquid n-butane. Solvent effects have been probed by Bishop, Kalos and Frisch (9), Rapaport (10), and Rebertus, Berne and Chandler (11). Multichain systems have been simulated by Curro (12), De Vos and Bellemans (13), Wall et al (14), Okamoto (15), Kranbu ehl and Schardt (16), and Mandel (17). Curro s study was the only one without a lattice but no dynamic properties were calculated because the standard Metropolis method was employed. De Vos and Belleman, Okamoto, and Kranbuehl and Schardt studies included dynamics by using the technique of Verdier and Stockmayer. Wall et al and Mandel introduced a novel mechanism for speeding relaxation to equilibrium but no dynamical properties were studied. These investigations indicated that the chain contracted and the chain dynamic processes slowed down in the presence of other polymers. 

Skolnick, J, Kolinski, A Dynamics monte carlo simulations of a new lattice model of globular protein folding, structure and dynamics J. Mol. Biol. 1991 221, 499-531. 

Chapter 18. Dynamic Monte Carlo simulations of oscillatory... 

The usual approach to dynamic Monte Carlo simulations is not based on the master equation, but starts with the definition of some algorithm. This generally starts, not with the computation of a time, but with a selection of a site and a reaction that is to occur at that site. We will show here that this can be extended to a method that also leads to a solution of the master equation, which we call the random-selection method (RSM). [31]... 

K. A. Fichthorn and W. H. Weinberg,/. Chem. Phys., 95,1090 (1991). Theoretical Foundations of Dynamical Monte Carlo Simulations. 

Dynamic Monte Carlo simulations have been employed to study the effect of the bimetallic catalyst structure and CO mobility in a simple model for the electrochemical oxidation of CO on Pt-Ru alloy electrodes. The Pt-Ru surface was modeled as a square lattice of surface sites, which can either be covered by CO or OH, or be empty. The important reactions taken into account in the model reflect the generally accepted bifunctional model, in which the OH with which CO is... 

Figure 17 CO stripping voltammetry from Dynamic Monte Carlo simulations, for pure Pt ( Ru = 0), various Pt-Ru alloy surfaces, and pure Ru. Details of the kinetic rate constants can be found in the original publication. CO surface diffusion is very fast, hopping rate D from site to site of 1000s . (Adapted from Ref. [49].)...

Figure 18 CO stripping peak potential Ep from dynamic Monte Carlo simulations as a function of the Ru fraction on the Pt-Ru model surface, for three different surface diffusion rates Z) = 0, 1, and 1000 s and for a mean-field model. (Adapted from Ref. [49].)...

Finally, dynamic Monte Carlo simulations are very useful in assessing the overall reactivity of a catalytic surface, which must include the effects of lateral interactions between adsorbates and the mobility of adsorbates on the surface in reaching the active sites. The importance of treating lateral interactions was demonstrated in detailed ab initio-based dynamic Monte Carlo simulations of ethylene hydrogenation on palladium and PdAu alloys. Surface diffusion of CO on PtRu alloy surfaces was shown to be essential to explain the qualititative features of the experimental CO stripping voltammetry. Without adsorbate mobility, these bifunctional surfaces do not show any catalytic enhancement with respect to the pure metals. 

Chern, S.-S., Cardenas, A.E., Coalson, R.D. Three-dimensional dynamic Monte Carlo simulations of driven polymer transport through a hole in a wall. J. Chem. Phys. 2001,115, 7772-82. 

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