Homogenization analysis

A weak but useful carbon line [Cl] 8727.13 A disappears in halo dwarfs with metallicities below —1. To measure carbon abundance in halo stars one can use four Cl high excitation lines near 9100 A and the CH band at 4300 A. The Cl lines at 9100 A together with the OI triplet at 7771 A have been used by Tomkin et al. (1992) and Akerman et al. (2004) to study the behaviour of C/O versus metallicity. However, Cl and OI lines employed in these papers are sensitive to a non-LTE effects and one has to bare in mind that this sensitivity is different for C and O. The CH band at 3145 A used by Israelian et al. (1999) is almost saturated in disk stars and several blends makes the abundance analysis less accurate. To ensure a homogeneous analysis of the C/O and N/O ratio from NH,CH and OH lines in the near-UV, we used the same model atmospheres and tools as in our previous studies. The oxygen abundances were compiled from Israelian et al. (1998, 2001) and Boesgaard et al. (1999). 

After a decade of intensive development, ACE is widely recognized nowadays as a powerful tool in the study of different kinds of biomolecular interactions. More than 400 scientific reports related to ACE can be found in the literature, covering almost all fields of bioanalytical chemistry. Unique features of homogeneous analysis coupled with the separation power of CE makes ACE especially favorable for precise determination of affinity parameters, such as binding constants and binding stoichiometries. Automation, multicapillary arrows, and chip technology increase throughput of ACE analysis, a factor which still limits... 

Figure 4. Through-thickness normal stress distributions in the functionally graded TBC with the coarsest microstructure (top) cross section c-c 1 (HOTFGM-2D analysis) (middle) cross section c-c 2 (HOTFGM-2D analysis) (bottom) homogenized analysis.

Recently, EVOTEC has developed a system for the homogeneous analysis of bead-surface interactions. This system will enable compound screening to take place without the need to remove compounds from the surface of the bead. The system also enables direct recovery of single beads for further analysis. By enabling the rapid, on-bead analysis of thousands of beads, the EVOTEC system eliminates a critical bottleneck, namely the need for deconvolution of solid-phase diversity. 

WATER FLOW AND DIFFUSION PROBLEM IN BENTONITE MOLECULAR SIMULATION AND HOMOGENIZATION ANALYSIS... 

Abstract We here treat a diffusion problem coupled with water flow in bentonite. The remarkable behavior originates from molecular characteristics of its constituent clay mineral, namely montmorillonite, and we show the behavior based on a unified simulation procedure starting with the molecular dynamic (MD) method and extending the obtained local characteristics to a macroscale behavior by the multiscale homogenization analysis (HA Sanchez-Palencia. 1980). Not only the macroscale effective diffusion property but also the adsorption behavior is well defined based on this method. 

For characterizing the microstructure we use a confocal laser scanning microscope (CLSM). By CLSM we can specify a 3-D configuration under atmospheric condition. Smectite minerals are extremely fine and poorly crystallized, so it is difficult to determine the properties by experiment. We inquire into the physicochemical properties by a molecular dynamics (MD) simulation method. Then, we develop a multiscale homogenization analysis (HA) method to extend the microscopic characteristics to the macroscopic behavior. We show numerical examples of a coupled water-flow and diffusion problem. 

We here showed that for bentonite clay, we can determine the nano-scale material properties such as diffusion coefficient and viscosity by molecular dynamics (MD) simulation and extend the microscale characteristics to the macroscale behavior by the multiscale homogenization analysis (HA) method. A seepage flow and diffusion problem is treated. The micro/macro problem can be simulated well by this procedure if we know the microscale geometrical characteristics. 

Homogenization analysis of multi joint set problem by the Stress Compensation-Displacement Discontinuity Method (SC-DDM) (1st Report)-, Shigen-to-sozai, 117(11), pp.251-257. 

Peak purity (or peak homogeneity) analysis of the main peak, to assess for the presence of impurities under the main peak, is an essential part of the validation of a SIM. Determination of peak purity is more difficult than it seems as one can never be certain that a peak is truly pure. Confidence can be improved by the use of multiple approaches for either direct or indirect evaluation of peak purity. 

McCulloch, A.D. and Omens, I.H., Non-homogeneous analysis of three-dimensional transmural finite deformations in canine ventricular myocardium, /. Biomech., 24,539-548,1991. 

Many polymer scientists have used homogenous analysis for the determination of molecular size via limiting viscosity numbers and translational and rotary diffusion constants but few recognize that these techniques and investigations of birefringence of polymer solutions were pioneered by Charles Sadron. 

Moyne C, Murad MA (2006) A two-scale model for coupled electro-chemo-mechanical phenomena and Onsager s reciprocity relations in expansive clays I homogenization analysis. Transp Porous Media 62 333-380... 

A mathematical scheme that can treat a micro-inhomogeneous material uniformly at the microscale and the macroscale is referred to as Homogenization Analysis (HA) (see Sanchez-Palencia 1980 Bakhvalov Panasenko 1984). In the HA method, we introduce a perturbation scheme by using both a macroscale coordinate system and a microscale one, and derive a microscale equation, which represents the geometry and material properties in the micro-domain. Then, using the solution of the microscale equation, we determine the macroscale equation (Fig. 1.2). However, since the HA method is implemented within a framework of continuum mechanics, it also experiences difficulties when the material properties of micro-inhomogeneous materials need to be obtained. 

We outline the essential features of a multiscale homogenization analysis. A problem of a one-dimensional elastic bar is given as an example. 

The periodic microstructiu e is referred to as a unit cell. In homogenization analysis we assume that the size of the unit cell is sufficiently small, and by taking the limit 0 we derive a system of differential equations that relates the microscale behavior to the microscale characteristics. 

In conclusion, the homogenization analysis procedure can be stated as follows (1) The microscale equation (7.12) is first solved under the periodic boundary condition, which gives the characteristic function Ai(xi). (2) Using the characteristic function Ai(xi) we then calculate the averaged elastic modulus E. (3) The macroscale equation (7.14) can then be solved, giving the first perturbed term o(- °). Sinee Mi(x ,x1) is calculated by (7.11), the first order approximation of M (x) can be represented as... 

If a homogenization analysis (HA) is applied to porous media flow, which is described by the Stokes equation, we can immediately obtain Darcy s formula and the seepage equation in a macroscale field while in the microscale field the distributions of velocity and pressure are specified (Sanchez-Palencia 1980). We can also apply HA for a problem with a locally varying viscosity. 

Homogenization Analysis and Seepage Problem of Porous Media... 

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