Computer programming steps

The formulas are really not too difficult to use. In fact, with these handy formulas, you can compute the volume for a 6-D sphere just as easily as for a 4-D one. Code 2 in Appendix F lists some of the computer program steps used to evaluate this formula. 

Step 11. At this point a computer program refines the atomic parameters of the atoms that were assigned labels. The atomic parameters consist of the three position parameters x,j, and for each atom. Also one or six atomic displacement parameters that describe how the atom is "smeared" (due to thermal motion or disorder) are refined for each atom. The atomic parameters are varied so that the calculated reflection intensities are made to be as nearly equal as possible to the observed intensities. During this process, estimated phase angles are obtained for all of the reflections whose intensities were measured. A new three-dimensional electron density map is calculated using these calculated phase angles and the observed intensities. There is less false detail in this map than in the first map. 

Fault Tree Solution. Solving the fault tree means obtaining the minimal cut sets. The minimal cut sets are all the combinations of equipment failures that can result in the fault tree TOP event. Computer programs are requked to determine the minimal cut sets for large fault trees (72). The solution method has four steps ... 

Power system stability studies can provide some insight into the effects of power failure. The calculations can become tedious if performed manually because of the iterative steps required to obtain satisfactory answers. Therefore, a computer program is used to supply the iterative answers in a short time and with comparable accuracy. 

However, some companies consider that they have sufficient experience of their requirements to use computer programs to provide economic assessments of candidate protective systems. The following summarizes typical steps to be taken. 

An important step toward the understanding and theoretical description of microwave conductivity was made between 1989 and 1993, during the doctoral work of G. Schlichthorl, who used silicon wafers in contact with solutions containing different concentrations of ammonium fluoride.9 The analytical formula obtained for potential-dependent, photoin-duced microwave conductivity (PMC) could explain the experimental results. The still puzzling and controversial observation of dammed-up charge carriers in semiconductor surfaces motivated the collaboration with a researcher (L. Elstner) on silicon devices. A sophisticated computation program was used to calculate microwave conductivity from basic transport equations for a Schottky barrier. The experimental curves could be matched and it was confirmed for silicon interfaces that the analytically derived formulas for potential-dependent microwave conductivity were identical with the numerically derived nonsimplified functions within 10%.10... 

Normally, we stop the step-size determination here and we proceed to perform another iteration of Gauss-Newton method. This is what has been implemented in the computer programs accompanying this book. 

The following steps, implemented by a computer program written in C, generate the smoothed, recommended values. Input to the program consists of the set of observed density values, temperatures, estimated uncertainties, critical constants and values of certain parameters used by the program. 

First of all, the hourly heat load of building is calculated. This step is crucial for deciding the volume of storage tank. The heat load can be calculated by manual calculation or computer program, such as TRNSYS or EnergyPlus. 

The next two steps after the development of a mathematical process model and before its implementation to "real life" applications, are to handle the numerical solution of the model s ode s and to estimate some unknown parameters. The computer program which handles the numerical solution of the present model has been written in a very general way. After inputing concentrations, flowrate data and reaction operating conditions, the user has the options to select from a variety of different modes of reactor operation (batch, semi-batch, single continuous, continuous train, CSTR-tube) or reactor startup conditions (seeded, unseeded, full or half-full of water or emulsion recipe and empty). Then, IMSL subroutine DCEAR handles the numerical integration of the ode s. Parameter estimation of the only two unknown parameters e and Dw has been described and is further discussed in (32). 

From experimental SAXS data of isotropic materials Q is determined by means of Eq. (7.25) (cf. p. 91). An interactive computer program (e.g., TOPAS) is very helpful, because several manual steps are involved. 

STEP 2. Determine for each possible pairing of like-signed charges the values of the functions %(/) and E9(j(I) of I by numerical integration or approximation (for details, see Pitzer, 1987, pp. 130-132 Harvie and Weare, 1980). A computer program for this purpose is listed in Appendix 2. The functions are zero for like charges and symmetrical about zero, so only the positive unlike pairings (e.g., 2-1, 3-1, 3-2) need be evaluated. 

Many extensive models of the high-temperature oxidation process of methane have been published [20, 20a, 20b, 21], Such models are quite complex and include hundreds of reactions. The availability of sophisticated computers and computer programs such as those described in Appendix I permits the development of these models, which can be used to predict flow-reactor results, flame speeds, emissions, etc., and to compare these predictions with appropriate experimental data. Differences between model and experiment are used to modify the mechanisms and rate constants that are not firmly established. The purpose here is to point out the dominant reaction steps in these complex... 

Table 4.4 gives a computer program and results for the ODE of Eq. (4.52) using fourth-order Runge-Kutta with a step size of 0.2. Figure 4.9 shows the effect of... 

Write a digital computer program that will calculate G,i j from step test data. 

The schemes considered are only a few of the variety of combinations of consecutive first-order and second-order reactions possible including reversible and irreversible steps. Exact integrated rate expressions for systems of linked equilibria may be solved with computer programs. Examples other than those we have considered are rarely encountered however except in specific areas such as oscillating reactions or enzyme chemistry, and such complexity is to be avoided if at all possible. 

Although computer programs are now used to perform speciation calculations, examining how these calculations are performed provides important insights into the limitations of the model predictions. Thus, we will step through a small part of the calculation used to generate the results presented in Figure 5.4, which represents the iron... 

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