Correlation simulation

Hussey, J. R., Myers, R. H., and Houck, E. C. (1987a), Correlated Simulation Experiments in First-Order Response SiuTace Design, Operations Research, Vol. 35, pp. 744-758. 

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Furthermore, a phenomenological engineering model was developed to correlate simulation data. This phenomenological model was parameterized initially to gas diffusion in pure n-alkanes and further extended to n-alkane mixtures. 

Table 4. Compare of relative volatility in correlative simulation and experiment.

It is seen from Table 4 that the relative volatility of correlative simulation and experiment were basically the same, and the relative error were much less than 5%. Therefore, the results of experiment were accurate and reliable. 

There are a lot of indane, 1,2,4-Trimethylbenzene, endo-Tetrahydrodicyclopentadiene in the hydrogenated C9 arenes, which were valuable resources for the development of fine chemicals. The article preliminary selected three kinds of representative solvents sulfolane, glycerol and dioctyl phthalate. First of all, the VLB date were obtained by the single stage gas-liquid equilibrium still as well as the Aspen Plus, and the relative errors between experiment and correlative simulation were much less than 5%, which proved the vapor-liquid equilibrium experiments were accurate and reliable. 

The kinetic contributions to the transport coefficients presented in Table 1 have all been derived under the assumption of molecular chaos, i.e., that particle velocities are not correlated. Simulation results for the shear viscosity and thermal diffusivity have generally been found to be in good agreement with these results. However, it is known that there are correlation effects for A/a smaller than unity [15,55]. They arise from correlated collisions between particles that are in the same collision cell for more than one time step. 

An example of the good correlation between TBP and simulated distillation is given in Figure 2.4, where it is shown that 71% of a Kuwait crude distils below 535T. 

Under certain conditions of temperature and pressure, and in the presence of free water, hydrocarbon gases can form hydrates, which are a solid formed by the combination of water molecules and the methane, ethane, propane or butane. Hydrates look like compacted snow, and can form blockages in pipelines and other vessels. Process engineers use correlation techniques and process simulation to predict the possibility of hydrate formation, and prevent its formation by either drying the gas or adding a chemical (such as tri-ethylene glycol), or a combination of both. This is further discussed in SectionlO.1. 

If two variables are dependent, the value chosen in the simulation for the dependent variable can be linked to the randomly selected value of the first variable using the defined correlation. 

A Monte Carlo simulation is fast to perform on a computer, and the presentation of the results is attractive. However, one cannot guarantee that the outcome of a Monte Carlo simulation run twice with the same input variables will yield exactly the same output, making the result less auditable. The more simulation runs performed, the less of a problem this becomes. The simulation as described does not indicate which of the input variables the result is most sensitive to, but one of the routines in Crystal Ball and Risk does allow a sensitivity analysis to be performed as the simulation is run.This is done by calculating the correlation coefficient of each input variable with the outcome (for example between area and UR). The higher the coefficient, the stronger the dependence between the input variable and the outcome. 

The investigations show that the microfocus high speed radioscopy system is suitable for monitoring the hard particle transport during laser beam dispersing. It is possible to observe and analyse the processes inside the molten bath with the presented test equipment. As a consequence a basis for correlation with the results of a simulation is available. 

We used the concept of sound velocity dispersion for explanation of the shift of pulse energy spectrum maximum, transmitted through the medium, and correlation of the shift value with function of medium heterogeneity. This approach gives the possibility of mathematical simulation of the influence of both medium parameters and ultrasonic field parameters on the nature of acoustic waves propagation in a given medium. 

Progress in the theoretical description of reaction rates in solution of course correlates strongly with that in other theoretical disciplines, in particular those which have profited most from the enonnous advances in computing power such as quantum chemistry and equilibrium as well as non-equilibrium statistical mechanics of liquid solutions where Monte Carlo and molecular dynamics simulations in many cases have taken on the traditional role of experunents, as they allow the detailed investigation of the influence of intra- and intemiolecular potential parameters on the microscopic dynamics not accessible to measurements in the laboratory. No attempt, however, will be made here to address these areas in more than a cursory way, and the interested reader is referred to the corresponding chapters of the encyclopedia. 

Predicting the solvent or density dependence of rate constants by equation (A3.6.29) or equation (A3.6.31) requires the same ingredients as the calculation of TST rate constants plus an estimate of and a suitable model for the friction coefficient y and its density dependence. While in the framework of molecular dynamics simulations it may be worthwhile to numerically calculate friction coefficients from the average of the relevant time correlation fiinctions, for practical purposes in the analysis of kinetic data it is much more convenient and instructive to use experimentally detemiined macroscopic solvent parameters. 

How large a simulation do we need Once more this depends on the system and properties of interest. From a spatial correlation fiinction (x(O)x(r) relating values computed at different points r apart, we may define a characteristic distance over which the correlation decays. The sumdation box size L should be significantly larger than in order not to influence the results. 

Near critical points, special care must be taken, because the inequality L will almost certainly not be satisfied also, cridcal slowing down will be observed. In these circumstances a quantitative investigation of finite size effects and correlation times, with some consideration of the appropriate scaling laws, must be undertaken. Examples of this will be seen later one of the most encouraging developments of recent years has been the establishment of reliable and systematic methods of studying critical phenomena by simulation. 

Flere we discuss only briefly the simulation of continuous transitions (see [132. 135] and references therein). Suppose that tire transition is characterized by a non-vanishing order parameter X and a corresponding divergent correlation length We shall be interested in the block average value where the L... 

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). 

Equation (C3.5.3) shows tire VER lifetime can be detennined if tire quantum mechanical force-correlation Emotion is computed. However, it is at present impossible to compute tliis Emotion accurately for complex systems. It is straightforward to compute tire classical force-correlation Emotion using classical molecular dynamics (MD) simulations. Witli tire classical force-correlation function, a quantum correction factor Q is needed 5,... 

VER in liquid O 2 is far too slow to be studied directly by nonequilibrium simulations. The force-correlation function, equation (C3.5.2), was computed from an equilibrium simulation of rigid O2. The VER rate constant given in equation (C3.5.3) is proportional to the Fourier transfonn of the force-correlation function at the Oj frequency. Fiowever, there are two significant practical difficulties. First, the Fourier transfonn, denoted [Pg.3041]

However, in many applications the essential space cannot be reduced to only one degree of freedom, and the statistics of the force fluctuation or of the spatial distribution may appear to be too poor to allow for an accurate determination of a multidimensional potential of mean force. An example is the potential of mean force between two ions in aqueous solution the momentaneous forces are two orders of magnitude larger than their average which means that an error of 1% in the average requires a simulation length of 10 times the correlation time of the fluctuating force. This is in practice prohibitive. The errors do not result from incorrect force fields, but they are of a statistical nature even an exact force field would not suffice. 

The second application of the CFTI approach described here involves calculations of the free energy differences between conformers of the linear form of the opioid pentapeptide DPDPE in aqueous solution [9, 10]. DPDPE (Tyr-D-Pen-Gly-Phe-D-Pen, where D-Pen is the D isomer of /3,/3-dimethylcysteine) and other opioids are an interesting class of biologically active peptides which exhibit a strong correlation between conformation and affinity and selectivity for different receptors. The cyclic form of DPDPE contains a disulfide bond constraint, and is a highly specific S opioid [llj. Our simulations provide information on the cost of pre-organizing the linear peptide from its stable solution structure to a cyclic-like precursor for disulfide bond formation. Such... 

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