Numerical modelling experimental approach

Jankovic, D. and Van Mier, J.G.M. (2003) Drying of Porous Media Numerical and Experimental Approach. Proceedings of EURO-C 2003, Computational Modeling of Concrete Structures, St. Johann im Pongau, Austria, 453—461. 

This paper is structured as follows in section 2, we recall the statement of the forward problem. We remind the numerical model which relates the contrast function with the observed data. Then, we compare the measurements performed with the experimental probe with predictive data which come from the model. This comparison is used, firstly, to validate the forward problem. In section 4, the solution of the associated inverse problem is described through a Bayesian approach. We derive, in particular, an appropriate criteria which must be optimized in order to reconstruct simulated flaws. Some results of flaw reconstructions from simulated data are presented. These results confirm the capability of the inversion method. The section 5 ends with giving some tasks we have already thought of. 

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... 

In the Lagrangian frame, droplet trajectories in the spray may be calculated using Thomas 2-D equations of motion for a sphere 5791 or the simplified forms)154 1561 The gas velocity distribution in the spray can be determined by either numerical modeling or direct experimental measurements. Using the uncoupled solution approach, many CFD software packages or Navier-Stokes solvers can be used to calculate the gas velocity distribution for various process parameters and atomizer geometries/configurations. On the other hand, somesimple expressions for the gas velocity distribution can be derived from... 

A general advantage of numerical modeling is that we have access to quantities which are difficult or impossible to measure experimentally. One example in our calculation is the probability that a tracer atom had an encounter with a vacancy, but its net displacement was zero. Although this value is non-zero, its temperature dependence is weak, which means that it can be incorporated in the constant jump-rate prefactor. This justifies the simplifying approach in the analysis of the experimental measurements to associate In-vacancy encounters with detectable (non-zero) jumps of the indium atom. 

At temperatures close to RT, on most surfaces, it is well established that steps are the sole sources and sinks for adatoms [6]. Although never experimentally proven, the same can be expected for surface vacancies. In fact, this assumption was already explicit in the development of the numerical model that we presented in the previous section. In this section, we review data that directly supports this idea, again limiting ourselves to the case of In/Cu(00 1). These data justify the approach that was used in the previous section. 

Why should one bother with these thermodynamic quantities when the overall aim of this chapter is to determine the structure of liquids near ions The answer is the same as it would be to the generalized question What is the utility of thermodynamic quantities They are the quantities at the base of most physicochemical investigations. They are fully real, no speculations or estimates are made on the way (at least as far as the quantities for salts are concerned). Their numerical modeling is the challenge that the theoretical approaches must face. However, such theoretical approaches must assume some kind of structure in the solution and only a correct assumption is going to lead to a theoretical result that agrees with experimental results. Thus, such agreement indirectly indicates the structure of the molecules. 

The stability constant is probably the most important quantitative parameter for the characterization of a metal-ligand complex in that it provides a numerical index of the affinity of the metal cation for the ligand and allows the development of quantitative models able to predict the speciation of metal ions in the system studied. Several different theoretical and experimental approaches have been attempted for the determination of stability constants of metal—HS complexes and modeling metal-HS complexation reactions. Data analysis and interpretation is, however, still controversial, due to the intrinsically complex and ill-defined nature of HSs. The multiligand, polyelectrolitic nature of HS macromolecules results in the inability to describe quantitatively the types, concentrations, and strengths of the several nonidentical binding sites in HSs and in the impossibihty to ascertain and measure the stoichiometry of metal-HS complexation (MacCarthy and Perdue, 1991). 

Semiempirical molecular orbital (SEMO) methods have been used widely in computational studies [1,2]. Various reviews [3-6] describe the underlying theory, the different variations of SEMO methods, and their numerical results. Semiempirical approaches normally originate within the same conceptual framework as ab initio methods, but they overlook minor integrals to increase the speed of the calculations. The mistakes arising from them are compensated by empirical parameters that are introduced into the outstanding integrals and standardized against reliable experimental or theoretical reference data. This approach is successful if the semiempirical model keeps the essential physics and chemistry that describe the behavior of the process. 

Fu et al. [4] presented a numerical model for electrokinetic dispensing in microfluidic chips where simple cross, double-T, and triple-T configurations were considered. In this model, the Nemst-Planck equation was employed to describe the ionic concentration instead of the Boltzmann distribution, which is a more general approach. The model was numerically solved using the finite difference method where the artificial compressibility method was employed to deal with the pressure term in the N-S equation. It is found that the applied potentials play an important role in crnitroUing the loaded and dispensed sample shape. The unique feature of this study is the concept of the multi-T injection system which can function as a simple cross, double-T, or triple-T injectimi unit. Their numerical results agreed well with their experimental results. More injection techniques were also developed by the same group later. 

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