Compaction model

Chemical vapor deposition (CVD) of carbon from propane is the main reaction in the fabrication of the C/C composites [1,2] and the C-SiC functionally graded material [3,4,5]. The carbon deposition rate from propane is high compared with those from other aliphatic hydrocarbons [4]. Propane is rapidly decomposed in the gas phase and various hydrocarbons are formed independently of the film growth in the CVD reactor. The propane concentration distribution is determined by the gas-phase kinetics. The gas-phase reaction model, in addition to the film growth reaction model, is required for the numerical simulation of the CVD reactor for designing and controlling purposes. Therefore, a compact gas-phase reaction model is preferred. The authors proposed the procedure to reduce an elementary reaction model consisting of hundreds of reactions to a compact model objectively [6]. In this study, the procedure is applied to propane pyrolysis for carbon CVD and a compact gas-phase reaction model is built by the proposed procedure and the kinetic parameters are determined from the experimental results. 

This approach is, at the same time, the great advantage and a major limitation of membrane potential models. As they are rather compact, models of this type were the first to be used in investigations of the spread of excitation in multi-dimensional tissue representations consisting of relatively large numbers of interconnected excitable elements their role in assessing biophysical behaviour like cardiac impulse propagation is undiminished. 

Iniguez, B. Picos, R. Veksler, D. Koudymov, A. Shur, M. S. Ytterdal, T. Jackson, W. 2007. Universal compact model for long- and short-channel thin-film transistors. Proc. of the International TFT Conference (Jan 7). 

Efficient Dynamic Compact Models By T. Bechtold, E.B. Rudnyi, and J.G. Korvink... 

System Identification Techniques. In system identification, the (nonlinear) resi pnses of the outputs of a system to the input signals are approximated by a linear model. The parameters in this linear model are determined by minimizing a criterion function that is based on some difference between the input-output data and the responses predictedv by the model. Several model structures can be chosen and depending on this structure, different criteria can be used (l ,IX) System identification is mainly used as a technique to determine models from measured input-output data of processes, but can also be used to determine compact models for complex physical models The input-output data is then obtained from simulations of the physical model. 

Two matrix flow submodels have been proposed the sequential compaction model [15] and the squeezed sponge model [11], Both flow models are based on Darcy s Law, which describes flow through porous media. Each composite layer is idealized as a fiber sheet surrounded by thermoset resin (Fig. 13.9). By treating the fiber sheet as a porous medium, the matrix velocity iir relative to the fiber sheet is given as (Eq. 13.5) ... 

In the sequential compaction model, once a ply is completely compacted, the adjacent ply may begin compaction. This model assumes that matrix flow normal to the fibers and along the fibers may be decoupled. Another critical assumption is that the matrix supports the entire... 

We now describe an approach for estimating the reaction temperature. Viewed at a microscopic level, this is a very complex stochastic thermal problem involving the frictional interaction of a relatively smooth surface with a rough one in the presence of a cooling lubricant that contains abrasive particles. Rather than treat this problem fully, we try to capture the most important features while neglecting other potentially interesting ones. The end result will be a simple estimate of the reaction temperature that can be used in a compact model. 

When used as a compact model for data description, there are five parameters in the model E, A, Cp, P, and e. Since most polishing tools do not... 

Given E, the above compact model is applied to data by varying the four remaining parameters A, Cp, jS, and e to minimize the RMS error between the... 

Keith, L.A. and J.D. Rimstidt, 1985. A numerical compaction model of overpressuring in shales. Mathematical Geology, Vol. 17, no. 2, pp. 115-135 Klein, R.J. and M.V. Barr, 1986. Regional state of stress in western Europe. In Stephensson, 0. (ed.), 1986. Rock stress and rock stress measurements. Centek (Lulea, Sweden), pp. 33-44... 

Keith, L. and Rimstidt, J. 1985. A numerical compaction model of overpressuring in shales. Math. Geol., 17 115-136. 

FIG. 21-141 Density developed in one-half of a tablet during compression, based on plasticity and compaction models. Lewis et al. Casting and Powder Compaction Group, Department of Mechanical Engineering, University of Wales Swansea, http //www.swan.ac.uk/nfa/, with permission.)... 

Brenner S, Elgar G, Sandford R, Macrae A, Venkatesh B, Aparicio S (1993) Characterization of the pufferfish (Fugu) genome as a compact model vertebrate genome. Nature 366 265-268... 

Ransing RS, Gethin DT, Khoei AR, et al. Powder compaction modelling via the discrete and finite element method. Mater Des 2000 21 263-269. 

In crystalline furanose 8.16, the chlorine atom adopts a pseudo-axial orientation and the nitrogen atom, a pseudo-equatorial one. The orientation of the N-O bond is given by the Newman projection along the C-l-N bond, 8.18. A compact model indicates that one face of the N=O bond is very hindered. It is probable that the same conformation exists in solution and that this is what imposes the endo approach as shown in 8.19 in which the cyclohexadiene tries to avoid the sugar support of the nitroso chloro derivative. 

T. Chiang, K. Banerjee, K. Saraswat. Compact modeling and spice-based simulation for electrothermal analysis of multilevel ULSI interconnects. Proceedings of International Conference on Computer-Aided Design, 2001, pp.165 - 172. 

Chemical compaction is controlled by the thermodynamics and kinetics of mineral reactions and can be modelled when calibrated against sediments of known subsidence history in terms of stress, temperature and time. The mineralogy and the texture must also be known because they are required as input for the chemical compaction models. 

The large-scale distributed muscle model can be reduced to a compact model analogous to the ventricle model previously presented (Equation 8.8). Muscle fibers (cells), or strips, can be described as force... 

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