Monte Carlo simulations. See

A multitude of different variants of this model has been investigated using Monte Carlo simulations (see, for example [M])- The studies aim at correlating the phase behaviour with the molecular architecture and revealing the local structure of the aggregates. This type of model has also proven useful for studying rather complex structures (e.g., vesicles or pores in bilayers). 

At high coverages, adsorbate interactions will always be present, implying that preexponential factors and activation energies are dependent on coverage. In the following we shall assume that the mean-field approximation is valid, but one should be aware that it may be a source of error. The alternative to this approximation is to perform Monte Carlo simulations (see Chapter 7). 

The Monte-Carlo principle uses random numbers in the region 0 < random < 1. The main randomized values in the Monte-Carlo simulation, see Figure 1, of a gas-phase adsorption process for radioactive species are ... 

Multiple-ionizations model is one of the most probable models because the huge energy deposited in the medium is considerably greater than the total energy needed to ionize the total number of water molecules along the ion track. This has been recently exploited in Monte Carlo simulations (see Fig. This model... 

Another method is to model the statistical distribution of the price (or margin), as illustrated in Figure 6.4e. At its simplest, this method involves taking the average price, adjusted for inflation, over a recent period. This method can miss long-term trends in the data, and few prices follow any of the more commonly used distributions. It is useful, however, in combination with sensitivity analysis methods such as Monte Carlo Simulation (see Section 6.8). 

Efficiency calibration requires a sample of defined shape and volume placed at a defined location relative to the detector. A sample frame may be needed for reproducible placement. Calibration can be performed with a radioactivity standard or by Monte Carlo simulation (see Sections 8.2 and 10.5). 

Beyond the above computation, and with the help of a Monte Carlo simulation (see, also, Section 3), the degree to which the individual component contributes to a system failure was determined. The above method also permits taking into account specific maintenance strategies. The life histories of the individual components are created over a period of time from 5 x 10 h and thereby it is also determined whether the system failure can be traced to corresponding component failures at any specific point in time. Here the failure-prone components are recorded in connection with each individual failure. Results demonstrate that position transmission (2) is involved in 100% of all system failures, which is natural because of the system s logical structure (Figure 5.23). The mechanical system of the valve is involved in 12%, the hydraulic control element in 29%, and the control pulse in 59% of all cases of system failure. 

Monte-Carlo simulations (see Section 10.7) can be done with the results of the regression however, present process simulators are not equipped to perform these direcdy. A sinpler approach is to perform the simulation with a few different values of the BIPs for the equation of state. These values are typically 0.01 to 0.10. Larger values are rare, except in highly asymmetric systems. However, the difference between results calculated with values of, say, 0.01 and 0.02 can be large. 

The thus specified Hamiltonians are then used in a dynamic Monte Carlo simulation (see Chapter 1) that is a numerical realization of the discrete time master equation... 

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