Figure11 also shows the simulation results of extinction efficiency of the mixed system when the fraction of ellipsoid was decreased while the fraction of sphere was increased.
To measure the fraction of sphere-forming cells where μ equals the number of positive wells and r equals the total number of wells, the Poisson discrete distribution probability was used where negative wells (F o= e− μ) and positive wells (F1=μ e− μ) are plotted as a semi log plot (Lefkovits and Waldmann, 1999).
The response time of the sensing chemistry within the spheres is primarily dependent on the diffusivity of hydrogel, the size of the spheres, and the porosity (volume fraction) of the spheres for whatever system they are placed in.
The fraction of broken spheres as a function of the applied strain were computed from experimental values of the Weibull parameters for the strength of the spheres, and the local stress computed in the simulations.
It was found that the presence of clustering greatly increased (by a factor between 3 and 6) the fraction of broken spheres, leading to a major reduction of the composite flow stress and ductility.
The mean settling speed is shown to be where U0 is the settling velocity of a single fluid sphere falling under gravity through an unbounded quiescent fluid, σ is the ratio of the viscosities μ′/μ where the upper prime indicates the disperse phase, c is the volume fraction of the spheres, and K is a numerical factor whose values are displayed in Table 1.
For spherical cells, the maximum packing fraction, ρmax, might be set to approximately 0.74 the close-packing fraction of uniform spheres.
These results are in agreement with prior studies of Hg sorption on Fe(III) oxides that interpreted most sorbed Hg as inner-sphere complexes with a smaller fraction of outer-sphere complexes.
Since only a small fraction of prostate sphere cells and prostate colony cells are capable of replating to respectively form secondary spheres and colonies, they may represent a committed basal progenitor population, or transit-amplifying cells [49].
When the matching thickness is 4 mm, the calculated reflection loss of the sample with 70% volume fraction of Fe3O4 carbon sphere composite exhibits a broad microwave absorption ranging from 2.5 to 18 GHz.
