Volume filling factor

Once the boundary conditions are applied, the pressure field can be solved using the appropriate matrix solving routines. Note that for mold filling problems, there is a natural boundary condition that satisfies no flow across mold boundaries or shear edges, dp/dn = 0. Once the pressure field has been solved, it is used to perform a mass balance using eqn. (9.144) or (9.145). Once the flowrates across nodal control volume boundaries are known, a simulation program updates the nodal control volume fill factors using... 

The element side surfaces are formed by lines that connect the centroid of the triangular side and the midpoint of the edge. Kim s definition of the control volume fill factors are the same as described in the previous section. Once the velocity field within a partially filled mold has been solved for, the melt front is advanced by updating the nodal fill factors. To test their simulation, Turng and Kim compared it to mold filling experiments done with the optical lenses shown in Fig. 9.34. The outside diameter of each lens was 96.19 mm and the height of the lens at the center was 19.87 mm. The thickest part of the lens was 10.50 mm at the outer rim of the lens. The thickness of the lens at the center was 6 mm. The lens was molded of a PMMA and the weight of each lens was 69.8 g. 

Massive stars return mass into the HIM, because almost all massive stars in rich stellar clusters end their life within the super-bubble driven into the ISM by the SN explosions (e.g. Higdon Lingenfelter 2005). The expansion of the bubble is also largely responsible for the dispersion of the remaining part of the MC within which the cluster has formed. Due to their long lifetimes the mass return by low-and intermediate-mass stars occurs well after the dissolution of their parent stellar clusters. By that time they have become randomly distributed field stars. Because of the large volume-filling factors of HIM and WIM the mass return of these stars is to HIM and WIM, but not to CNM. 

Figure 11.107. Conductivity a vs. frequency co. Isolated particles have a proportional to m, whereas networks of particles have a frequency-independent conductivity like a bulk metal, (W particles in PS /= 0.11, d — 400 nm TiC particles in AI2O3 /=0,17, rf= 800 nm, where /is the volume filling factor). [Reproduced from ref, 132 with kind permission of Elsevier.]...

The samples used in our experiments were prepared using the Ag-Na ion exchange method for float soda-lime glass with following annealing in H2 reduction atmosphere [7]. This technique results in formation of spherical silver nanoparticles of 30-40 nm mean diameter. The volume fill factor of Ag nanoparticles was about 0.01 [6]. 

The most popular effective medium theories are the Maxwell Garnett theory [18], which was derived from the classical scattering theory, and the Bruggeman theory [19]. With these theories, an effective dielectric function is calculated from the dielectric functions of both basic materials by using the volume filling factor. At some extensions of these theories, a unique particle shape for all particles is assumed. There is also an other concept based on borders for the effective dielectric functions. The borders are valid for a special nanostructure. Between these borders, the effective dielectric function varies depending on the nanostructure of the material. The Bergman theory includes a spectral density function g(x) that is used as fit function and correlates with the nanostructure of the material [20]. 

For the calculation of the transmission or extinction spectra, the thickness of each layer d i, d, and d must be considered in the right way. In the following, the results from the particle size and shape analysis from the TEM micrograph of Figure 6.1 were transfered to the parameters that are necessary for the effective medium theories. These are the volume filling factor /, the depolarization factor L, and the composite film thickness dc. 

By comparison of the ratio of prism volume to the ellipsoid volume, a maximal volume filling factor/ ax follows from the area filling factor using/ ax =yFfl. This upper bound of the volume filling factor is valid if all particles have an identical size of D. In this case, the minimum composite film thickness corresponds with the mean vertical diameter of the particles dc = Ffe if all particles lie exactly in one plane. Because there is a statistical particle size distribution, the composite film thickness must be defined from the maximal vertical diameter of the largest particle dc = Db can be obtained from the image analysis data. It is better to calculate Db with Db = Dmax(l - Vl - inax ) The filling factor/is decreased further by the ratio between the mean particle... 

The theory of the susceptibility corrections in solid state NMR experiments with oriented membrane samples has been described. To determine the necessary corrections, a general analysis is presented for the demagnetizing field of a layered sample of rectangular block geometry, with the normal of the layers parallel to the main field or tilted about an axis of the block. The correction to the line position of the block sample was found to be approximately equal to that of the spheroid which can be inscribed into the block, and for which the correction is well known. It was shown that sample and support materials contribute to that average according to their volume filling factors. 

Other frequently used resonators are dielectric cavities and loop-gap resonators (also called split-ring resonators) [12]. A dielectric cavity contains a diamagnetic material that serves as a dielectric to raise the effective filling factor by concentratmg the B field over the volume of the sample. Hollow cylinders machmed from Ilised quartz or sapphire that host the sample along the cylindrical axis are conunonly used. 

The compounds were mixed in three steps The first two steps were done in an internal mixer with a mixing chamber volume of 390 mL. The mixing procedures employed in the first two steps are indicated in Table 29.2. The starting temperamre was 50°C and the cooling water was kept at a constant temperature of 50°C. The rotor speed was 100 rpm and the fill factor 66%. After every mixing step the compound was sheeted out on a 100-mL two-roll mill. The third mixing step was done on the same two-roll mill. The accelerators and sulfur were added during this step. 

FIGURE 29.13 Influence of air injection on the silanization efficiency (mixer volume 45 L, fill factor 0.4, silanization temperature 145°C, time 150 s). 

The third-order optical Kerr susceptibility of nanocomposites, Xeff. formed by a non-absorbing matrix, with dielectric constant containing metal nanoclusters with low volume fraction p (i.e., filling factor) is given [95] by ... 

Figure 7 presents in concise form the relation between closing pressures, P8, and three practically important parameters, the filling factor,/, the specific volume,... 

Fa, and the specific weight, a- Table I presents the specific volume, Fa, and the specific weight, a, for filling factors between 0.9 and 1.0. 

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