Mathematical simulations, experimental

Topaz was used to calculate the time response of the model to step changes in the heater output values. One of the advantages of mathematical simulation over experimentation is the ease of starting the experiment from an initial steady state. The parameter estimation routines to follow require a value for the initial state of the system, and it is often difficult to hold the extruder conditions constant long enough to approach steady state and be assured that the temperature gradients within the barrel are known. The values from the Topaz simulation, were used as data for fitting a reduced order model of the dynamic system. 

Under this electrochemical configuration, it is commonly accepted that the system can be expressed by the Randles-type equivalent circuit (Fig. 6, inset) [23]. For reactions on the bare Au electrode, mathematical simsulations based on the equivalent circuit satisfactorily reproduced the experimental data. The parameters used for the simulation are as follows solution resistance, = 40 kS2 cm double-layer capacitance, C = 28 /xF cm equivalent resistance of Warburg element, W — R = 1.1 x 10 cm equivalent capacitance of Warburg element, IF—7 =l.lxl0 F cm (

charge-transfer resistance, R = 80 kf2 cm. Note that these equivalent parameters are normalized to the electrode geometrical area. On the other hand, results of the mathematical simulation were unsatisfactory due to the nonideal impedance behavior of the DNA adlayer. This should... 

In this paper an overview of the developments in liquid membrane extraction of cephalosporin antibiotics has been presented. The principle of reactive extraction via the so-called liquid-liquid ion exchange extraction mechanism can be exploited to develop liquid membrane processes for extraction of cephalosporin antibiotics. The mathematical models that have been used to simulate experimental data have been discussed. Emulsion liquid membrane and supported liquid membrane could provide high extraction flux for cephalosporins, but stability problems need to be fully resolved for process application. Non-dispersive extraction in hollow fib er membrane is likely to offer an attractive alternative in this respect. The applicability of the liquid membrane process has been discussed from process engineering and design considerations. 

The emerging concept of developing experimental mini-ecosystems — focused on controlled-exposure environments for testing and for developing mathematical simulations of ecosystem impact based on limited, specific tests—should be supported. 

Figure 6. Experimentally observed and mathematically simulated regression lines of foam capacity of different percentages of glandless cottonseed flour in suspensions at various pH values. Experimental 4%, 10%, and 16% suspensions were run at pH 3.5, 6.5, and 9.5 to test the reliability of the multiple linear regression analysis. Quantitative data used in this analysis are in Figures 2 and 4.

Figure 7. Experimentally observed and mathematically simulated regression lines of foam stability at different percentages of glandless cottonseed flour in suspensions at various pH values. See Figure 6 for further explanation of the data.

Thus, the only way to study the early radiolysis stages is to study them theoretically, especially with mathematical simulation. The correctness of our theoretical conceptions is determined by how well all the consequences of the theory agree with the available experimental data... 

Because mold filling is a complex process, flow visualization studies have been useful and necessary, both for the actual mold design and for the mathematical simulation of the process. The first important experimental contributions were made by Gilmore and Spencer (8,9) whose work forms the basis of a review chapter by Beyer and Spencer (10). Ballman et al. (11-13) conducted mold filling experiments in the early 1960s. A decade later, a time that marks the beginning of serious efforts to solve... 

For the purpose of estimating conformational parameters of silaiylene carboorganocyclosiloxanes of the structure XV, two approaches were used [117] computerized mathematical simulation using the Monte-Carlo method and experimental estimation of the flexibility parameters in solution under natural conditions. In the first case, mathematical simulation has determined the skeletal flexibility of the molecule in the absence of substituting agents at atoms forming the backbone. In the second case, all fragments of the chain, possible interactions with the solvent and temperature effect have been taken into account in the flexibility estimation. 

MATHEMATICAL SIMULATION OF TRANSFER OF DIOCTYL PHTHALATE(DOP) BETWEEN SAMPLES OF PLASTICISED PVC SUBMERGED IN OLIVE OIL COMPARISON OF CALCULATED AND EXPERIMENTAL PROFILES Messadi D Djilani S E Annaba,Universite Mokhtar Badji... 

One of the answers to the question Why modelling could therefore be the establishment of a set of simulation process analyses. In addition to the mathematical simulation of processes described above, we have the simulation of a physical process, which, in fact, is a small-scale experimental process investigation. In other words, to simulate a process at laboratory-scale, we use the analysis of a more affordable process which is similar to experimental investigation. 

Fig. 6.12 and 6.13 show two examples of the mathematical simulation of time sequences. They show the time course of the experimentally determined and calculated integral distribution as a function of the dimensionless droplet mass /z = Cx = — I. The initial experimental distribution functions are taken as the start distribution in the integration process. 

Recent progress in computer technology and methods for rapid experimental determination of molecular weight distributions (MWD) has encouraged the development of mathematical simulations of polymer synthesis processes in various types of batch and continuous reactors. 

Another typical process involving branched radical polymerization is the production of poly(vinyl acetate). In the experiments of Stein105,106, the method of mathematical simulation has been used to evaluate the effect of longchain branches on the width of MWD. The reactions of chain transfer to the polymer and polymerization by the terminal double bonds of the polymer were examined separately. A comparison of the calculated and experimental Pw/Pn - f ( ) dependencies yielded the values of Cp = kf/kp and K = k p/kp. 

Figure 15 shows the mathematically simulated amplitude ratio data. This data would be experimentally obtained directly along with phase angle 9 if direct frequency response measurements had been made. 

Engineers are well suited to combine theoretical prediction with experimental measurement. Previous investigators (2, 3, 4, 5, 6, 7) have had considerable success by first mathematically simulating complex biological systems and then conducting well-planned, experimental programs to combine theory with experimental results. 

BGtoshmanesh, Kh. "Mathematical Simulation and Experimental Measurements of a Glass Melting Furnace." MS thesis, Amirkabir University of Technology, Tehran, Iran, 2000. 

Fujita T., Kobayashi A. and Borgesson L. 1996. Experimental investigation and mathematical simulation on coupled T-H-M processes of the engineered buffer materials, the TC3 problem. In Stephansson O, Jing L, Tsang C-F editors. Coupled thermo-hydro-mechanical processes of fractured media. Developments in Geotechnical Engineering, No.79, Amsterdam Elsevier, pp.369-392. 

Rutqvist, J., Follin, S., Khair, K., Nguyen, S. and Wilcock, P. 1996. Experimental investigation and mathematical simulation of a borehole injection test in deformable rocks. In Coupled Thermo-Hydro-Mechanical Processes of Fractured Media,... 

As can be seen in Figure 4-9, when the individual steps are put together, recycling streams are created (in this case one gas and one solvent recycling path). These recycling streams or feedbacks are an economic necessity, but they raise new process engineering problems. Thus, material recycled to the reactor may drastically affect the performance of the catalyst, especially its activity and service life. In addition, the solvent circuit may become enriched in byproducts and this may lower product purity. In principle, these problems can only be solved by mathematical simulation, but since many of the quantities that are required for a mathematical description are unknown, an experimental approach must be adopted. Therefore, it is important to know at as early a stage as possible, the influence of the most important reycle streams on the overall behavior of the plant (reactor with catalyst, separation behavior) and to thus achieve further discrimination between process variants. An economical and fast solution here is a microplant. 

Mathematical simulation of Cpc, E curves shows that the shape of the diffuse-layer capacitance minimum depends on the difference of Ea=o for individual faces, exposed on the PC electrode surface, and their fractions, as well as on the shape of partial Cj, E curves (Fig. 3). The results of experimental capacitance studies at two-plane model PC Bi electrodes were in agreement with these conclusions [5, 15, 16]. Thus it has been shown that the potential of the diffuse-layer capacitance minimum for a PC electrode with noticeable difference in Eu=o values for various planes does not correspond to the PZC of the whole surface and JZy 0 at... 

Two alternative methods of Raman imaging via global illumination and via point illumination in combination with confocal light collection were applied to the study of heterogeneous polymer systems. The spectral and spatial resolving power of the different techniques was estimated experimentally. The influence of the depth resolution on the Raman image of a defined sample structure was demonstrated in a mathematical simulation. Data are given for PE, PS, polyacrylate, and epoxy resins. 23 refs. 

The analysis of fast polymerisation reactions has shown that the effects, revealed during the mathematical simulation (diffusion model), are identical to the experimental effects of the cationic polymerisation of isobutylene (as an example). The important consequence of process nonisothermicity is its adverse effect on polymer quality, while the external thermostating is not effective enough in this case [52],... 

Eq.3 explains the observed independence of the reaction rate from partial pressure of CO (Fig.3(b)) and the tendency of the NO conversion rate to stabilize at high partial pressure of NO (Fig.3(a)). The fitting of Eq.3 on the experimental results is satisfactory as shown by the RSQ values of Table 3. In Table 3 the calculated from the mathematical simulation procedure values of ks and Knonio are shown. The problem of the above kinetic analysis is that the calculated values of the adsorption equilibrium constant Knoni seems to be unvariant with temperature. To avoid this problem a new approach was applied according to which both NO adsorption and reaction 3 are in nonequilibrium conditions [8]. According to this approach the conversion rate of NO is given by ... 

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