Model profile

Fig. 14. Hypothetical velocity profile models for a countercurrent-flow gas centrifuge, (a) The optimum velocity profile ia a countercurrent gas centrifuge.

The application of these assumptions allows the researchers to use the PROFILE model for calculation of critical loads in Europe (Posch et al., 1993,1997,1999) and Asia (World Bank, 1994 Shindoetal., 1995 Lin, 1998 Haoetal., 1998 Bashkin and Park, 1998). In spite of visible limitations connected with the numerated assumptions, a run of the PROFILE model can give comparable results for different ecosystems in regional and continental scales. 

Nitrification. The nitrogen reactions in the PROFILE model are very simple, since only nitrification and uptake are included explicitly. 

Each profile model needs its die, mandrel, calibrators and cooling fixtures whose cost is charged on each run. Consequently, the costs of the profiles depend on ... 

Perhaps the most studied laboratory flame is the premixed flat flame. As illustrated in the left-hand panel of Fig. 1.1, a steady flame is established above a porous burner face. Such flames are used widely in combustion laboratories, where a variety of optical and probe-based diagnostics are used to measure species and temperature profiles. Models play an essential role in assisting the interpretation of the data. In addition to the premixed flat... 

Fig. 6.4. Typical CARS spectral profile modeled for an isolated Lorentzian Raman line assuming (6.5) (Tr = 4.6 cm-1, AT = 4cm 1) and parallel-polarized input and CARS fields. According to (6.10), the total CARS spectrum (solid line) is composed...

Analysis of other border profile models (linear r(l) dependence with constant or variable radius of curvature at border mouth, the relation (5.23), etc.) shows that the simplest analytical equation for the profiles of both pressure and radius of curvature is obtained if the function r(l) is given as a parabolic expression r2 = 2p l (where p is the parabolic parameter). This equation is in good agreement with the experimental data. The parabolic parameter can be determined from the experimental r [) dependence measuring the pressure at various levels in the foam. 

Microposit 2400 resist, manufactured by Shipley Co., has been shown to be sensitive at this short wavelength ( ) and is being employed with the deep UV stepper. We report here the results of resist profile modeling for submicron photolithography at 248 nm. Various model parameters needed as input data were measured to characterize exposure and development of the resist. 

Sverdrup (1990) and Sverdrup and Warfvinge (1995) developed Ae PROFILE model to calculate mineral weathering rates by means of a geochemical mass-balance procedure. This model differs from the others in that it uses dissolution constants, which were, for the most part, determined in the laboratory. Empirical fitting parameters, such as surface area of mineral exposed, are used to adjust the model to the real system being described. The model appears to work satisfactorily in many catchments if the fitting parameters are chosen judiciously. This requires a considerable amount of knowledge... 

Hodson M. E., Langan S. J., and Wilson M. J. (1997) A critical evaluation of the use of the PROFILE model in calculating mineral weathering rates. Water Air Soil Pollut. 98, 79-104. 

Sverdrup et al. (1992) have developed the PROFILE model, which is based on the principle of continuity of alkalinity or ANC in soil. The critical load is defined as the allowable acid loading that will not acidify forest soils and cause the release of aluminum and hydrogen ions to soil solution ... 

It is noteworthy that the suggested improvements based on the canopy profile model and displacement height do not required to substantially modify the NWP model itself, because the first computational model level is usually above the canopy, so that the canopy parameterisation can be used only for diagnostic calculation of the wind for higher resolution UAQ modelling outside the NWP model or for diagnosis of 10 m wind in NWP. 

Several models have been suggested to simulate the behavior inside a reactor [53, 71, 72]. Accordingly, homogeneous flow models, which are the subject of this chapter, may be classified into (1) velocity profile model, for a reactor whose velocity profile is rather simple and describable by some mathematical expression, (2) dispersion model, which draws analogy between mixing and diffusion processes, and (3) compartmental model, which consists of a series of perfectly-mixed reactors, plug-flow reactors, dead water elements as well as recycle streams, by pass and cross flow etc., in order to describe a non-ideal flow reactor. 

Figure 7.12 The order of calculations in the PROFILE model of P. Warfinge and H. Sverdrup. From Calculating critical loads of acid deposition with PROFILE—a steady-state soil chemistry model. Water, air and soil pollution 63 119-143. 1992 by Kluwer Academic Publ. Used by permission.

In the PROFILE model of Sverdrup and Warfinge (1992), what is the significance of each term in the rate equation for mineral weathering ... 

Figure 7,14 The weathering rate of 15 European and American soil sites computed with the PROFILE model with and without correction for the effect of DOC, compared to the weathering rate estimated using historic and mass-balance methods. Reprinted from Applied Geochemistry, 8, H. Sverdrup and P. Warfvinge, Calculating field weathering rates with a mechanistic geochemical model PROFILE, 273-83, with permission from Elsevier Science Ltd., The Boulevard, Langford Lane, Kidlington 0X5 1GB, U.K.

Jonsson,C., P. Warfvinge, and H. Sverdrup. 1995. Uncertainty in predicting weathering rate and environmental stress factors with the PROFILE model. Water, Air and Soil Prdlution 81 1-23. 

The stirrer is thereby approximated for the calculation of turbulent flow by a tangential jet [288, 441], and for laminar flow by a cylinder [46-48, 50, 98J. The stirred tank is split up into a number of zones, to which one can assign characteristic flow patterns and analytically describable velocity profiles. Models with up to 8 zones have been developed, but only two models (for stream ejected by the stirrer and for circulation flow) have been able to explain the experimental results satisfactorily [440]. 

BOU 04] BOULLE A., MASSON O., GUINEBRETIERE R DAUGER A., Two dimensional XRD profile modelling in imperfect epitaxial layers , in MITTEMEIJER E.J., Scardi P., Diffraction analysis of the microstructure of materials. Springer Series in Materials Science, vol. 68, p 505-526,2004. 

Finite-difference techniques were used to compute numerical solutions as column-breakthrough curves because of the nonlinear Freundlich isotherm in each transport model. Along the column, 100 nodes were used, and 10 nodes were used in the side-pore direction for the profile model. A predictor-corrector calculation was used at each time step to account for nonlinearity. An iterative solver was used for the profile model whereas, a direct solution was used for the mixed side-pore and the rate-controlled sorption models. 

Fig. 5.10. Reaction profile, model of two intersecting parabolas. The activation energy is if the reaction energy AE is zero (solid parabola on the right). If the reaction energy AE is negative (dotted parabola on the right) AE is smaller than AEq and the transition state, i.e. the intersection of parabolas, is closer to the reactants. A modification of the simple model in which the two potentials interact (resonance energy H) is shown as dash-dotted line...

Fig. S.15. Reaction profile model of two shifted parabolas, representing related reactants undergoing the same reaction. If the same transition state geometry is assumed for both, the activation energies differ by AA = k xAx ...

Fig. 5.16. Reaction profile model of cubic curve (third-order polynomial) to describe asymmetric reactions. The lower profile illustrates the influence of a linear perturbation (dashed line) on the upper profile...

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