Examples of Simulation Results

We now present some of the simulation results by the generalized-ensemble algorithms that were described in the previous section. 

The first example is the results of the calculation of the residual entropy of the ordinary ice [126,127], This calculation shows how accurate the density of states can be obtained by multicanonical simulations from the reweighting formula of (4.24). 

In the crystal structure of ordinary ice, each oxygen atom is located at the center of a tetrahedron and straight lines (bonds) through the sites of the tetrahedron point towards four nearest-neighbor oxygen atoms. Hydrogen atoms are distributed according to the ice rules [128]  

There is one hydrogen atom on each bond (then called hydrogen bond). 

There are two hydrogen atoms near each oxygen atom (these three atoms constitute a water molecule). 

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The effects of hydrocarbon partial pressure and residence time distribution are easily incorporated into the reaction model, when the reaction kinetics are mathematically described. Figures 3 and 4 show the examples of simulated results by use of the model. They clearly show that the effect of hydrocarbon partial pressure on the product distribution is larger than generally recognized and low pressure is preferable to obtain high liquid yield and that residence time distribution should be controlled as narrow as possible to reduce coke precursor(Ql) in the residual component. 

Monte Carlo simulation is often used for the calculations of the system availability. In Fig. 2 an example of simulated results for the availability of the system is illustrated. Availability is here defined as the probability that the system is functioning. 

One of the flexibilities of eomputer simulation is that it is possible to define the themiodynamie eonditions eorresponding to one of many statistieal ensembles, eaeh of whieh may be most suitable for the purpose of the study. A knowledge of the underlying statistieal meehanies is essential in the design of eorreet simulation methods, and in the analysis of simulation results. Flere we deseribe two of the most eommoir statistieal ensembles, but examples of the use of other ensembles will appear later in the ehapter. 

Chen et al. [76C02] and Lawrence and Davison [77L01] have placed the fully coupled nonlinear theory of uniaxial piezoelectric response in a form that is convenient for numerical solution of problems and have simulated a number of experiments in terms of this theory. An example of the results obtained is given below. 

Fig. 2 shows examples of the results obtained by the 453-reaction model. The effects of the reaction temperature were investigated by experiments and numerical simulation. It is... 

If a simulation model is used as part of a MES to evaluate production schedules and support daily operation the presentation of simulation results quite often is integrated in the MES environment. The planner might not even see or know the simulation model itself. There might be a feature such as assess order schedule within the MES, which starts a simulation experiment. Details on this and on the other ways of application will be illustrated by the examples in the next section. 

These examples of simulations of the molecular dynamics of carbohydrates show the possibility of predicting their behavior in different solvents. Experimental work has confirmed these findings. While theoretical prediction is becoming more reliable, it is only qualitative and we must consider the theoretical results within the framework of the actual capability of the methods. Current minicomputers allow simulation of large system. Polysaccharides, for instance, are being studied by this technique. However, the description of carbohydrate solutions is still poor, and simple systems can help in the understanding of the problems. 

The worked examples and simulation results in Chapter 14 were, for the most part, obtained with a simulation program known as ChemSep (Kooijman and Taylor, 1992). You will need to obtain this program (or something equivalent) in order to carry out the numerical exercises for this chapter. Contact R. Taylor for more information on the availability of ChemSep. 

Q (r — fb). In this case, and for transfer of one electron, A(R ) = A(R ) is the difference between the electrostatic potentials at the A and B centers that is easily evaluated in numerical simulations. An example of such result, the free energy surfaces for electron transfer within the Fe i /Fe redox pair, is shown in Fig. 16.5. The resulting curves are fitted very well by identical shifted parabolas. Results of such numerical simulations indicate that the origin of the parabolic form of these free energy curves is more fundamental than what is implied by continuum linear dielectric theory. 

In the next section a brief layout of simulation methods will be given. Then, some basic properties of the models used in computer simulations of electrochemical interfaces on the molecular level will be discussed. In the following three large sections, the vast body of simulation results will be reviewed structure and dynamics of the water/metal interface, structure and dynamics of the electrolyte solution/metal interface, and microscopic models for electrode reactions will be analyzed on the basis of examples taken mostly from my own work. A brief account of work on the adsorption of organic molecules at interfaces and of liquid/liquid interfaces complements the material. In the final section, a brief summary together with perspectives on future work will be given. 

The sensitivity to variation of force field parameters of free energy difference results can be used to optimize interaction parameters. Examples include the derivation of accurate parameters for ion—water interactions.A study of the variation of free energy of solvation due to changes in the solute charge, expressed in a form that can be parameterized via simulation results, may be useful in the analysis of the sensitivity of simulation results to the partial charges of solutes. 

In order to maintain a constant surface-to-volume ratio all grains are assumed to have the same radius 7 = 0.015 cm. As an example of the results. Fig. 3.5 shows breakthrough curves (BTCs) at the column outlet obtained from four model test runs (runs 1 ) simulating sorption. The nms can be distinguished by the varying mass fractions fj for each lithological component (Tab. 3.2). 

The visualization of virtual prototypes calls for the processing of the data with dependence on the visualization techniques. Apart from purely realistic visuaUzation, complexity-reducing models and symbolic visualization are used as well. Mixed models of both methods are most widely spread. Metaphors for visualization of simulation results, for example, are used in FEM aneilysis (overlaying of paint leveling) or the representation of paint coat thickness in robot simulation (Brown 1996). 

The field of simulation (mostly FEM and CFD) deals with engineering and the natural sciences, which in many cases are to complex to be discussed exclusively on the basis of numerical values or texts. Multidimensional data sets need adequate visualization and presentation. An interdisciplinary discussion of simulation results is supported by a spatial, multidimensional representation of the data using VR-based techniques. An example of an industrial VR-based postprocessing application can be seen in Figure 6, where the thermal comfort in a car cabin is analyzed by examining the results of a stationary fluid flow simulation (using STAR CD). 

A model was developed to cope with nonstationary behavior observed in Fig. 6.10 see Fig. 6.11 for an example of the resulting simulations/ which shows the effect of rotation rate on the current. While results from the simulation exhibit curves similarly shaped to those found in practice/ there are quite a number of parameters that are not accurately known. Such unknown effects as the layer homogeneity on the rate of electron exchange and the swollen layer thickness... 

For this application example MC simulation results are given and the way of feedback to the design of the operation is outlined. 

Sometimes, despite extensive corrosion testing, some components of the telecommuiucation cable plant may fail in the field. Often these failures are caused by unforeseen field conditions or by the presence of unexpected corrosives. To establish the source and mechanism of corrosion failure, these components are exposed to simulated field conditions, and the results are compared to the field failures. Some examples of simulated field failures are described below. 

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