Numerical simulations and experimental results

3 Numerical simulations and experimental results (a) Numerical simulations 

Duxbury et al (1987) performed the same type of simulations as that of de Arcangelis et al but they covered the whole range of p from 1 to Pc = 0.5. They also checked the dependence of If on L and the distribution of the failure currents. These simulations were also made on a square lattice. 

Their calculation of the dependence of If on p gives the possibility to check the interpolation formula (2.29) that was proposed above, assuming 

In Fig. 2.6, we show the results of the simulation from the results of Duxbury et al and a fit with (2.29). One can see good agreement. However, to get a satisfactory fit, it is necessary to take 0 = 1, instead of 1.33, as expected from the above theoretical analysis. This means that it is better to take the exponent 0 in (2.29) as an effective one. 

Duxbury et al determined also the dependence of Vf on p and their result is very similar to that of de Arcangelis et al The difference is only in the interpretation. The finite value of Vf at Pc is demonstrated by comparing the variation of If and of the conductance near Pc- 

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Fig. 2.65 Comparison between numerical simulation and experimental results for the temperature field on the heater surface. The solid line represents simulation, and triangles (A) experimental results (line 1 in Fig. 2.64) dotted line represents simulation, and squares experimental results (line 2 in Fig. 2.64). Reprinted from Mishan et al. (2007) with permission...

B. Borderie, D. Lavabre, G. Levy, J. C. Micheau, and J. P. Laplante, The bistable TP1D/CHC13 photoreaction Numerical simulation and experimental results, Int. J. Chem. Kinet. 24, 309-317... 

ABSTRACT In order to investigate the effect of coal particle size on gas desorption and diffusion law at constant temperature, the constant temperature dynamic coal particle gas adsorption and desorption experiment with different particle sizes was conducted in the coal gas adsorption and desorption experiment system. The results suggest that gas desorption laws of different particle size of coal samples show a good consistency at different pressures, and the cumulative desorption of gas coal particle is linear with time. For the same particle, the higher the initial pressure, the more the maximum gas desorption the smaller the coal particle is, the more quickly the gas desorption rate is at the same initial pressure. Then, the gas spherical flow mathematical model is built based on Darcy law and is analysed with finite difference method. At last, the gas spherical flow mathematical model is constructed with Visual Basic. The contrast between numerical simulation and experimental results shows that the gas flow in the coal particle internal micropore accords with Darcy s law. 

Palto, S.P., Geivandov, A.R., Bamik, M.I., Blinov, L.M. The new role of alignment layers in bistable switching of ferroelectric liquid crystals. Numerical simulations and experimental results. Ferroelectrics 310, 95-109 (2004)... 

The measurements of homonuclear /-couplings in solids are an important experimental method for studying conformational and structural effects as well as hydrogen bonding. The principles of spin-echo modulation by homonuclear /-couplings in systems containing isolated pairs of spin have been studied by Duma et The theoretical conclusions have been supported by numerical simulations and experimental results obtained for three representative samples containing spin pairs. 

Fig. 10.50 Location of the pressure gauge (P) and the thermocouples (7) at the five axial barrel positions. The three cross sections A-A, B-B and C-C are used for contour plots of the numerical results. [Reprinted by permission from T. Ishikawa, S. Kihara, K. Funatsu, T. Amaiwa, and K. Yano, Numerical Simulation and Experimental Verification of Nonisothermal Flow in Counterrotating Nonintermeshing Continuous Mixers, Polym. Eng. Sci., 40, 365 (2000).]...

Magnetic multipoles of rank higher than one become active in spin systems with I > 5 and their contribution to relaxation depends on dynamics. The appearance of multipole terms complicates the relaxation description and supports the multiexponential behavior of relaxation. Nosel et al. presented the effects of high rank multipoles on lineshape and longitudinal relaxation of 7=3 systems. Results obtained from both numerical simulation and experimental data show that longitudinal and transverse relaxation are strongly influenced by these multipole terms, especially at lower temperatures where, due to molecular mobility, the extreme narrowing condition is not fulfilled. 

Other Parameters Defining Soil Properties. In lieu of measured data on the Maui soils, the hydraulic properties and bulk density for the Wahiawa soil on Oahu were used in numerical simulations (3.) Experimental results (29) for the soil depths of 20, 60 and 90 cm were used in simulations of a three layer system with a tilled layer of 45 cm depth, a subsoil layer 45 to 90 cm, and a substratum layer at depths exceeding 90 cm. Bulk density values corresponding to these three layers were 1.25, 1.25 and 1.4 g/cm3. 

Figure 4.23 Comparison of numerical simulation with experimental results for the full thermomechanical cycle (a) strain evolution with 30% pre-strain, (b) strain evolution with 20% pre-strain, and (c) thermomechanial cycle in terms of the stress-strain-time response. Source [86] Reproduced with permission from ASME...

In order to analyze the damage of wood plastic composite, the identification of wood/ plastic interfacial properties seems to be essential. Therefore, the wood/plastic cohesive parameters ware determined through optimization technique [205]. The Nelder-Mead algorithm was applied to optimize the force-displacement results of the numerical simulation and experimental data using the following equation. 

The simulated and experimental results for the three bands below 7 eV are shown in Fig. 3. The simulated absorption spectrum was computed with Eq. (23) with numerical-integration error (gray area) given by Eq. (25). Parameters... 

The mental images, no matter how well grounded scientifically, are individually and collectively biased, as they have been developed after considerable filtering. The filters result from the scientific training of individuals, available supporting information from other processes, existing theoretical methods, limitations of numerical simulation, and characteristics of experimental methods. 

Illustration Satellite formation in capillary breakup. The distribution of drops produced upon disintegration of a thread at rest is a unique function of the viscosity ratio. Tjahjadi et al. (1992) showed through inspection of experiments and numerical simulations that up to 19 satellite drops between the two larger mother drops could be formed. The number of satellite drops decreased as the viscosity ratio was increased. In low-viscosity systems p < 0(0.1)] the breakup mechanism is self-repeating Every pinch-off results in the formation of a rounded surface and a conical one the conical surface then becomes bulbous and a neck forms near the end, which again pinches off and the process repeats (Fig. 21). There is excellent agreement between numerical simulations and the experimental results (Fig. 21). 

HAp is a good model compound for the study of DQ coherence excitation profile.85 The closest P-P distance in HAp is 4.143 A. The numerical simulations and the experimental data were shown in Figure 5. The maximum DQ coherence excitation efficiency decreases as the spin cluster size increases. The reason is simply due to the fact that all the spins in the cluster will contribute (different combinations of two spins) to the DQ coherence. The passive spins in close proximity would provide a strong dipolar dephasing of the excited DQ coherence. As expected, the simulation results converge towards the experimental data as the cluster size increases. 

An extensive literature survey shows that very little attention has been given to modelling and simulation of batch reactive distillation, let alone optimisation of such process. The published literature deals with the mathematical modelling and numerical integration of the resulting dynamic equations systems, with few presenting computer simulation vs experimental results. Only few authors have discussed the design, control and optimal operational aspects of batch reactive distillation processes. 

After explaining the process concept, this paper presents the two steps of the process development. First a simulation software allows to set the different process parameters and gives an idea of the SF-SMB performances. Then, the pilot plant is described and experimental results confirm the numerical simulation expectations and prove the great interest of this process. 

In conclusion to this section we can say that the numerical simulations and the experiments are in full agreement with the theoretical expectations. They were made only in two dimensions and it is clearly desirable to have more experimental results, particularly in three dimensions. 

By contrast to the oxidation of higher alkanes, there is no qualitative way of distinguishing evidence for a diperoxy radical mechanism during the low-temperature oxidation of propane. It is possible that the considerably lower reactivity of propane than that of higher alkanes, as demonstrated by phenomenological aspects (Section 6.4.4), may be explained by the absence of these types of processes. The matter may not be resolved until more insight is obtained from numerical modelling and simulation of experimental results. 

The measurements displayed in Fig. 8.7 and Fig. 8.8 exhibit both an exponential increase in the total number of pitting sites followed by saturation, consistent with numerical simulations and former experimental results [14, 15]. This was also found for each of the three growing bright regions individually (see Fig. 8.8E). 

Numerical simulations and analyses were performed for both the continuous stirred-tank reactor (CSTR) and the plug-flow reactor (PER). A comparison between the microkinetic model predictions for an isothermal PFR and the experimental results [13], is presented in Fig. 2 for the following conditions commercial low temperature shift Cu catalyst loading of 0.14 g/cm total feed flow rate of 236 cm (STP) min residence time r = 1.8 s feed composition of H20(10%), CO(10%), C02(0%), H2(0%) and N2(balance). As can be seen, the model can satisfactorily reproduce the main features of the WGSR on Cu LTS catalyst without any further fine-tuning, e.g., coverage dependence of the activation energy, etc, which is remarkable and provides proof of the adequacy of the... 

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