Algorithm of Calculation

We use the simplest method (Eyler method, with the step of integration h) to write the algorithm for numerical solution of equations (3.52) 

Calculating the dispersions of the random processes Aff s) and A/ (s), one has to take into account that relations (3.50) and (3.51) for the random forces are written for the continuous time, so that in the discrete approach one has 

It is easy to see that, the expressions for the random forces have to be similar to relations (3.53) and (3.54), that is 

To solve the system of equations (3.55), initial values of co-ordinates and an extra random force have to be chosen. We accept that 

Note that steady-state situations are investigated, so that the end-to-end distance (R2) and the mean gyration radius 

---

Comparison of the measurements with the microdensitometers and the algorithms of calculation inclusive the filter function and the accuracy of measurement of all project partners. 

The algorithm of calculating crack depth is realized in electropotential device Zond IGT-97 for measuring cracks depth. Its structure diagram is shown in Fig. 8 Using quasi-direct current is the device particular feature that made it possible to reduce its dimensions and weight. 

Suppose we want to develop a module that represents the chemical structure of compounds. A structure is the signature of a compound that, in most cases, uniquely defines all chemical properties of the compound such as mol-weight, molformula, stereo chemistry, pKa, and logP. Suppose a structure can be represented in many different formats—Molfile, Chime, Smiles. The algorithms of calculating the chemical properties are different depending on the structure format, and our application has to support all of them. A naive solution is to develop a class for each structure format and repeat every common attribute and method in all of them. 

Before developing the algorithm of calculation, we have to deduce the mixture h/H... 

Algorithm of calculation of resistivity of soil using a defined petrophysical model of soil (clay content, sahnity of pore moisture and radiuses of sand and clay capillaries, ion exchange capacity of... 

The algorithm of calculation of minimum reflux mode at tangential pinch has some peculiarities. At tangential pinch in top section (L/y) = =... 

As far as the second assumption is concerned, as was mentioned in Section 5.5, it does not influence the compositions in the stationary points. Therefore, it does not influence the first two stages of the described algorithms of calculation of minimumreflux mode. This assumption could have some influence only at the third stage of the algorithms, when curvature of separatrix trajectory bundles should be taken into consideration. Therefore, the assumption about equilibrium plates at calculation of minimum reflux mode is even more justified than at calculation of finite columns. 

Therefore, the stated algorithm of calculation of minimum reflux mode, based on the geometry of the trajectory bundles in concentration space, are potentially as one likes precise and most general, because they embrace any spUts on mixtures with any components number and any degree of nonideahty. 

In Chapter 5, to develop a general algorithm of calculation of minimum reflux mode for columns with one feed, we had to understand the location of reversible distillation trajectories and the structure of top and bottom section trajectory bundles. 

General Algorithm of Calculation of Minimum Reflux Mode... 

This develops the general algorithm of calculation of minimum reflux mode for the columns with two feed inputs at distillation of nonideal zeotropic and azeotropic mixtures with any number of components. The same way as for the columns with one feed, the coordinates of stationary points of three-section trajectory bundles are defined at the beginning at different values of the parameter (L/V)r. Besides that, for the intermediate section proper values of the system of distillation differential equations are determined for both stationary points from the values of phase equihbrium coefficients. From these proper values, one finds which of the stationary points is the saddle one Sm, and states the direction of proper vectors for the saddle point. The directions of the proper vectors obtain linear equations describing linearized boundary elements of the working trajectory bundle of the intermediate section. We note that, for sharp separation in the top and bottom sections, there is no necessity to determine the proper vectors of stationary points in order to obtain linear equations describing boundary elements of their trajectory bundles, because to obtain these linear equations it is sufficient to have... 

The general algorithm of calculation of the minimum reflux mode for columns of extractive distillation with two feeds requires the check-up of the conditions of trajectories joining for the cases of bottom and top control feed and requires the determination of the values of (E/E) bigger of these two... 

In particular, for the most widespread spht with one-component entrainer and one-component top product nim = 2, wzr = 1), the joining of intermediate section trajectories with the trajectories of the top and the bottom sections goes on the way it is at direct split in two-section colunms. This uses the simplest modification of the algorithm of calculation of the minimum reflux mode. 

We now discuss the general algorithm of calculation of minimum reflux mode for the column with several side withdrawals located above and below feed cross-section at sharp separation in each section and at the best separation between products. 

The main purpose of design calculation is to determine necessary tray numbers for all sections at fixed values of mode parameters. At design calculation, one takes into consideration the equality of compositions at the tray of output of the side product obtained at the calculation of the second and third columns. Each two-section column entering into a Petlyuk column is calculated with the help of algorithms described before for two-section columns. The algorithm of calculation for splits with a distributed component is used for the first column, the algorithms for the direct and the indirect sphts are used for the second, and the third columns at separation of a three-component mixture, respectively. At separation of multicomponent mixtures, the algorithms for intermediate separation are used. 

According to this model, the equations of traffic written for each phase, dare in common. The algorithm of calculation of such currents has been offered, in particular, in-process (Menter, 1994), and realized in Ansys CFX. The given model is the most exacting to computing resources of the computer—and to an online storage size, and to speed of the processor. 

---