Numerical modelling calculations

Numerous model calculations correlating aqueous VPIE s using simple harmonic or pseudo-harmonic cell models have been reported (see Fig. 5.8 and Table 5.8 for an ultra-simple version). Such calculations show the importance of the librational hydrogen bonded modes and the stretch-libration interaction in determining VPIE for D or T substitution. 

Solutions for this type of kinetics can only be achieved numerically. Model calculations with constant kinetic parameters have been made [H. Wiedersich, et al. (1979)], however, the modeling of realistic transport (diffusion) coefficients which enter into the flux equations is most difficult since the jump rate vA vB. Also, the individual point defects have limited lifetimes which determine the magnitude of correlation factors (see Section 5.2.2). Explicit modeling for dilute or non-dilute alloys can be found in [A.R. Allnatt, A.B. Lidiard (1993)]. 

A numerical model to simulate the lattice expansion behavior of the doped lanthanum chromites under a cell operating condition has been proposed, and the deformation of the lanthanum chromite interconnectors has been calculated [33], In the model, the sample deformation is calculated from the profile of the oxygen vacancy concentration in the interconnector. Under a practical cell operation, the oxygen vacancy concentration in the interconnector distributes unevenly from the air side to the fuel side. The distribution of the oxygen vacancy concentration in the interconnector depends on both the temperature distribution in the interconnector and the profile of the oxygen partial pressure at the interconnector surface. Here, a numerical model calculation for the expansion behavior of the LaCrC>3 interconnector under a practical cell operation is carried out, and the uneven distribution of... 

Numerical model calculations using the CFD code FLUENT 6.1 were performed to evaluate the time dependent behavior of fires ignited within a homogeneous porous canopy. These were compared with flow behavior from a similar fire in the absence of the canopy. Consideration was given to the effects of grid resolution, turbulence model (/c-RANS versus LES), wind speed (Uh = 0, 1, 2, 5 m/s), fire intensity (Q = 20, 50, 100 kW/m3), and inlet velocity profile (a = 0 or 0.14). The development of velocities, turbulence intensity, static pressure, and temperature fields were examined for such examples. Typical results are discussed below. 

Jones, R.L., and J.A. Pyle, Observations of CH4 and N2O by the NIMBUS 7 SAMS A comparison with in-situ data and two dimensional numerical model calculations. J Geophys Res 89, 5263, 1984. 

For intermediate chain lengths and for double-Helix Coil transitions refined models have to be used with the explicit inclusion of chain-end effects and the possibilities of staggering and sliding zipper, etc. mechanisms. Numerical model calculations have recently been used to approach the right model for the conformational transition of oligonucleotides [21], showing more than one relaxation time. 

The location of the main peaks is almost coincident and the radar signal shows some minor peaks too. The amplitude is a little different this can be imputed to the fact that the radar only measures the LOS component of the displacement and the two sensors are not exactly positioned in the same point. The agreement between radar observations and seismometer measurements was also confirmed by numerical model calculation and modal shape estimation (Negulescu et al. 2013). 

A calculation of tunneling splitting in formic acid dimer has been undertaken by Makri and Miller [1989] for a model two-dimensional polynomial potential with antisymmetric coupling. The semiclassical approximation exploiting a version of the sudden approximation has given A = 0.9cm" while the numerically exact result is 1.8cm" Since this comparison was the main goal pursued by this model calculation, the asymmetry caused by the crystalline environment has not been taken into account. 

Fig. 9. Comparison of the analytical SCF model [56] with the full numerical SCF calculation [53] for the segment density profile in flat, grafted layers at various surface densities (o is the fraction of the maximum possible surface coverage of grafted ends). The analytical profile is parabolic to its tip, while the numerical calculation shows that the density at the periphery of the layer drops off exponentially...

Obtaining an accurate and detailed depth-age relationship for an ice core is, of course, a necessary task for learning paleoclimate histories. Approximate time scales can be calculated using numerical models of ice and heat flow for the core site (Reeh, 1989), constrained by estimates of the modem accumulation rate and by measurements of ice thickness from radio-echo-sounding surveys. 

In accordance with the results reported previously (ref. 8), the different stability properties of the isomers and the model calculations using numeric s and p, parameters we can use the approximation of ki, k3 > > IC4, as well. Thus, Equations (9) and (10) can be rewritten in simplier forms... 

A common feature in the models reviewed above was to calculate pressure and temperature distributions in a sequential procedure so that the interactions between temperature and other variables were ignored. It is therefore desirable to develop a numerical model that couples the solutions of pressure and temperature. The absence of such a model is mainly due to the excessive work required by the coupling computations and the difficulties in handling the numerical convergence problem. Wang et al. [27] combined the isothermal model proposed by Hu and Zhu [16,17] with the method proposed by Lai et al. for thermal analysis and presented a transient thermal mixed lubrication model. Pressure and temperature distributions are solved iteratively in a iterative loop so that the interactions between pressure and temperature can be examined. 

The Geothermal Response Test as developed by us and others has proven important to obtain accurate information on ground thermal properties for Borehole Heat Exchanger design. In addition to the classical line source approach used for the analysis of the response data, parameter estimation techniques employing a numerical model to calculate the temperature response of the borehole have been developed. The main use of these models has been to obtain estimates in the case of non-constant heat flux. Also, the parameter estimation approach allows the inclusion of additional parameters such as heat capacity or shank spacing, to be estimated as well. 

In Equation (23), all input data are known from the earlier time step. This way of calculating the values for the next time step is called explicit method. More information on numerical modeling, and for example how to integrate convection, can be found in Farlow (1983) and Ozisik (1968). 

Before any simulation or basic calculation of a heat storage can be performed, the thermophysical properties of the PCM have to be determined. These properties are the most important input parameters for any analytical or numerical model. 

During our early experiments on chemical gels, when first observing the intermediate state with the self-similar spectrum, Eq. 1-5, we simply called it viscoelastic transition . Then, numerous solvent extraction and swelling experiments on crosslinking samples showed that the viscoelastic transition marks the transition from a completely soluble state to an insoluble state. The sol-gel transition and the viscoelastic transition were found to be indistinguishable within the detection limit of our experiments. The most simple explanation for this observation was that both phenomena coincide, and that Eqs. 1-1 and 1-5 are indeed expressions of the LST. Modeling calculations of Winter and Cham-bon [6] also showed that Eq. 1-1 predicts an infinite viscosity (see Sect. 4) and a zero equilibrium modulus. This is consistent with what one would expect for a material at the gel point. 

Such an experimental characterization is a necessary step to carry out a detailed comparison of emission properties as measured experimentally with the corresponding quantities as calculated by numerical models capable of describing transport and energy deposition of fast electrons in matter and consequent emission of characteristic X-ray emission. A possible modeling approach of fast electron transport experiments is given here, where the above results on Ka imaging were interpreted using the hybrid code PETRA [53] to... 

Mahrer YA (1980) A numerical model for calculating the soil temperature regime under transparent polyethylene mulches. Agric Meteorol 22 227-234 Mahrer Y, Katan J (1981) Spatial soil temperatures regime under transparent polyethilene mulch. 

Theoretical Calculations and Numerical Modeling of Droplet Processes... 

In this chapter, basic theoretical calculations and numerical modeling of droplet generation and deformation processes of both normal liquids and melts will be discussed in detail. The review of modeling efforts will outline the current status and recent developments... 

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