Model semi-analytical

The accretion history of a parent galaxy is constructed using a semi-analytical code. The full phase-space evolution during each accretion event is then followed separately with numerical simulations [2]. Star-formation and chemical evolution models are implemented within each satellite. The star formation prescription matches the number and luminosity of present-day galaxies in the Local Group, whereas the chemical evolution model takes into account the metal enrichment of successive stellar populations as well as feedback processes. Below we present results of a sample of four such simulated galaxy halos, denoted as Halos HI, H2, H3 and H4. 

SARIPALLI, P. McGrail, P. 2002. Semi-analytical approaches to modeling deep well injection of C02 for geological sequestration. Energy Conversion and Management, 43, 185-198. 

Abstract. We use a semi-analytical model of supernova light curves that extends Arnett s scheme [1,2] to include the effect of recombination of hydrogen, helium and heavy elements in the expanding ejecta. Introducing in the model the physical parameters of Sanduleak -69 202, the salient characteristics of the light curve of SN 1987 A are reasonably reproduced over 100 days. 

Eqs. 3-4 are amenable to semi-analytical solution techniques because of the linear form. The use of more complex kinetic models (e.g., intraaggregate diffusion) has not been attempted, in part because the above models have proved adequate to describe the available data sets, and in part because of a limited understanding of the geometry of the soil/bentonite matrix (gel formation and the resulting diffusion geometry). 

Figure 10.4 A simulation of oligarchic growth in the inner region of a proto-planetary disk around a solar-mass star. In the inner disk, embryos grow to 0.1 Earth-masses in <106 years. Growth then slows dramatically. Embryos continue to grow larger beyond the snowline at 2.5 AU. The simulation uses the semi-analytic model of Chambers (2008) with Esom ccl/a.

A semi-analytical solution to these equations was derived by Dixon and Cresswell (16), who then matched the fluid phase temperature profile to the one-phase model profile to obtain explicit relations between the parameters of the two models. 

The mathematical problem presented by the model requires the simultaneous solution of equations (2) to (7). The starting point is a semi-analytical solution of equation (8) [I], previously only applied to single component systems, that satisfies the boundary conditions in equation (3) (4). 

The approach described in Sections 8.2.3 and 8.2.4.5.3 was used to construct quasi-2D (Q2D) analytical and semi-analytical models of PEFC [246, 247] and DMFC [248, 249], The Q2D model of a PEFC [246] takes into account water management effects, losses due to oxygen transport through the GDL, and the effect of oxygen stoichiometry. The model is fast and thus suitable for fitting however, the systematic comparison of model predictions with experiment has yet not been performed. Q2D approaches have been employed to construct a model of PEFC performance degradation [250], to explain the instabilities of PEFC operation [251, 252] and to rationalize the effect of CO2 bubbles in the anode channel on DMFC performance [253, 254],... 

As shown in Table 2.4, when local buoyancy effects are weak (i.e. Ug/Ub 1), the air flow over an urban area is generally a perturbation of the oncoming flow. Then from semi-analytic models using perturbation methods faster computational schemes have been devised, e.g. for lee-wave prediction scheme 3DVOM over mountains (Vosper and Mobbs, 1996 [639]), and are being developed in a general way to allow for... 

Simulations confirm that these are regions where fluid trajectories are well- mixed. This provides a basis for constructing FAM s for dispersion in these regions using semi-analytical diffusivity models. 

Many attempts have been made to obtain (semi-)analytical descriptions for non-Newtonian coating flows. These are necessarily approximate and the approximations made to obtain tractable mathematics are sometimes non-physical [58]. These models do not predict the coating behaviour very well from the rheological parameters. The thickness is usually considerably overestimated. It seems more advantageous to simulate non-Newtonian coating flows by computational fluid dynamic methods (see also Ref. [58]). 

In the framework of semi-analytical models of galaxy formation (Mo, Mao White, 1998), the evolution of galaxy disks can be described by means of scaling laws calibrated on the Galaxy with Vc and A as parameters (Jimenez et al. 1998 Prantzos Boissier, 2000), where Vc is a measure of the mass of the dark halo and A is a measure of the specific angular momentum of the halo. 

The deformation behavior of a compositionally graded metal-ceramic structure has been investigated by numerical and (semi)analytical simulations. Random microstructure models are able to predict the response of an FGM-structure in a more accurate way than the other approaches. The interwoven structure in the middle of the FGM can be accounted for using this modeling strategy. For the extended periodic unit cell models the predicted stress strain response depends strongly on the micro-arrangement of the inclusions. Detailed information on the microfields of the stresses and strains can only be obtained by the extended unit cell models. The incremental Mori-Tanaka method... 

In such an unsatisfactory state of affairs, the best one can do is to try to understand better the physics of neutrino-driven winds through the development of (semi-)analytical models some aspects of which may be inspired by (failed) explosion simulations, and to try to delineate on such grounds favourable conditions for the development of the r-process. These analytical models confirm that the wind nucleosynthesis depends on Ye, entropy s, and Tdyn, as in the o-process discussed in Sect. 7.2. The wind mass-loss rate M is influential as well. Ultimately, the quantities acting upon the synthesis in the neutrino-driven DCCSN model depend crucially on the details of the interaction of neutrinos with the innermost supernova layers, as well as on the mechanisms that might aid to get a successful DCCSN, and whose relative importance remains to be quantified in detail. 

Rowe, R.K., and J.R. Booker. 1989. A semi-analytic model for contaminant migration in a regular two-or three-dimensional fractured network Conservative contaminants. Int. J. Numer. Anal. Meth. Geomechan. 13 531-550. 

In Chapter 2 we discussed a number of studies with three-phase catalytic membrane reactors. In these reactors the catalyst is impregnated within the membrane, which serves as a contactor between the gas phase (B) and liquid phase reactants (A), and the catalyst that resides within the membrane pores. When gas/liquid reactions occur in conventional (packed, -trickle or fluidized-bed) multiphase catalytic reactors the solid catalyst is wetted by a liquid film as a result, the gas, before reaching the catalyst particle surface or pore, has to diffuse through the liquid layer, which acts as an additional mass transfer resistance between the gas and the solid. In the case of a catalytic membrane reactor, as shown schematically in Fig. 5.16, the active membrane pores are filled simultaneously with the liquid and gas reactants, ensuring an effective contact between the three phases (gas/ liquid, and catalyst). One of the earliest studies of this type of reactor was reported by Akyurtlu et al [5.58], who developed a semi-analytical model coupling analytical results with a numerical solution for this type of reactor. Harold and coworkers (Harold and Ng... 

Transfonnation processes are very important for the treatment of many organic contaminants with permeable reactive barriers. The components and their products undergo sorption reactions. This sorption reactions may be either in equilibrium or nonequilibrium. Desintegration of tetrachloroethene or trichloroethylene are two of many examples, that can be treated with this permeable reactive barriers. Khandelwal and Rabideau (1999) developed analytical and semi-analytical solutions for this problem. They consider the sorption reaction with a nonequdibrium model. We verified the numerical RF-RTM model with their analytical solution. 

Table 2.1 aims to give a flavour of typical models created during the past 20 years. The selection of the discussed models is restricted by full 3D FE models of unit cells, where yam paths are continuous and smooth. The list does not include (semi-) analytical, orientation averaging, inclusion, discrete mosaic models as far as they are founded on completely different modelling principles. 

A. A. Kulikovsky. Semi-analytical ID + ID model of a polymer electrolyte fuel cell. Electrochem. Comm., 6 969-976, 2004. 

White et al. proposed an one-dimensional, isothermal model for a DMFC [168]. This model accounts for the kinetics of the multi-step methanol oxidation reaction at the anode. Diffusion and crossover of methanol are modeled and the mixed potential of the oxygen cathode due to methanol crossover is included. Kinetic and diffusional parameters are estimated by comparing the model to experimental data. The authors claim that their semi-analytical model can be solved rapidly so that it could be suitable for inclusion in real-time system level DMFC simulations. 

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