Distribution profiles

Theoretical studies of diffusion aim to predict the distribution profile of an exposed substrate given the known process parameters of concentration, temperature, crystal orientation, dopant properties, etc. On an atomic level, diffusion of a dopant in a siUcon crystal is caused by the movement of the introduced element that is allowed by the available vacancies or defects in the crystal. Both host atoms and impurity atoms can enter vacancies. Movement of a host atom from one lattice site to a vacancy is called self-diffusion. The same movement by a dopant is called impurity diffusion. If an atom does not form a covalent bond with siUcon, the atom can occupy in interstitial site and then subsequently displace a lattice-site atom. This latter movement is beheved to be the dominant mechanism for diffusion of the common dopant atoms, P, B, As, and Sb (26). 

Energy Distribution Profile of Solute Molecules in the Stationary Phase... 

Velocity distribution profiles in Zone 3 of the jet were found to be simi-lar. They can be computed by applying momentum-transfer theory (Prandtl-Tollmein) and vorticity-transfer theory (Taylor-Goldstein). Modification of these theories with different assumptions has resulted in several equa-... 

The simplest way computationally of obtaining a sedimentation coefficient distribution is from time derivative analysis of the evolving concentration distribution profile across the cell [40,41]. The time derivative at each radial position r is d c r,t)/co /dt)r where cq is the initial loading concentration. Assuming that a sufficiently small time integral of scans are chosen so that Ac r t)/At= dc r t)ldt the apparent weight fraction distribution function g (s) n.b. sometimes written as (s ) can be calculated... 

Direct inversions of the concentration distribution profiles to obtain molecular weight distribution information are generally impossible because of comphcations involving non-ideality. Successful attempts have been given but only for simple discrete forms of polydispersity (two to three macromolecular species [93]). 

The lED of SiH on the substrate at different frequencies is shown in Figure 28b. With increasing frequency, the energy distribution profile becomes more... 

The distribution profiles are not necessarily symmetrical because the anion and the cation may have different partition coefficients. For both types of profiles, however, zwitterionic compounds have an approximately constant value of lipophilicity in the region around their isoelectric pH, so that they behave as lipophilicity buffers between their two values [143,327]. 

Fujino, M., Ogata, S., and Shinohara, H., The electric potential distribution profile in a naturally charged fluidized bed, Funt. Kog. Kaishi, 20 280-289 (1983) English translation inInt. Chem. Engrg., 25 149-159 (1985)... 

In related experiments by Johnson (1985), atomic deuterium was used instead of Hx to neutralize boron in Si. Similar results on spreading resistance were obtained. Furthermore, the distribution profile of D was measured by secondary-ion mass spectrometry (SIMS), as shown in Fig. 4. The distribution profile of D reveals 1) that the penetration depth of D is in good agreement with the resistivity profile and 2) that the D concentration matches the B concentration over most of the compensated region. In another sample, the B was implanted at 200 keV with a dose of 1 x 1014 cm-2, the damage was removed by rapid thermal anneal at 1100°C for 10 sec., and then D was introduced at 150°C for 30 min. As shown in Fig. 5, it is remarkable that the D profile conforms to the B profile. 

Such cells are often classified on the basis of their original source as either embryonic or adult stem cells. As the name suggests, embryonic stem cells are derived from the early embryo, whereas adult stem cells are present in various tissues of the adult species. Much of the earlier work on embryonic stem cells was conducted using mouse embryos. Human embryonic stem cells were first isolated and cultured in the laboratory in 1998. Research on adult stem cells spans some four decades, with the discovery during the 1960s of haematopoietic stem cells in the bone marrow (Chapter 10). However, the exact distribution profile, role and ability to manipulate adult stem cells (particularly those outside of the bone marrow) are subjects of intense current research, and for which more questions remain than are answered. 

Three main patterns of contamination were resolved by MCR-ALS analysis of [SE SO] data matrix (105 samples x 15 variables). Composition profiles (loadings) of the resolved components are shown in Fig. 11 (plots on the left). Variables are identified with a number in the x axis. In the y axis, the relative contribution of every scaled variable to the identified contamination pattern is given. Temporal and spatial sample distribution profiles of the contamination patterns (scores) are represented in Fig. 11 (plots on the right). In the x axis, samples are identified for the two compartments, SE and SO, successively ordered from first to third campaign and, within each campaign, form North-West to South-East. The y axis displays the contribution of every resolved contamination pattern to samples. 

Each phospholipid class in a given tissue has a characteristic fatty acid composition. Though the same fatty acid may be present in a number of lipids, the quantitative fatty acid composition is different for each class of lipids and remains fairly constant during the growth and development of the brain. A typical distribution profile of the major fatty acids in rat brain phospholipids is given in Table 3.1. Not only do the phosphoglycerides differ in the structure of the polar head groups, or phospholipid... 

TABLE 3-1 Distribution profile of the major individual molecular species in the diacylglycerol moieties of rat brain phosphoglycerides ... 

Once the radionuclides reach the sediments they are subject to several processes, prime among them being sedimentation, mixing, radioactive decay and production, and chemical diagenesis. This makes the distribution profiles of radionuclides observed in the sediment column a residuum of these multiple processes, rather than a reflection of their delivery pattern to the ocean floor. Therefore, the application of these nuclides as chrono-metric tracers of sedimentary processes requires a knowledge of the processes affecting their distribution and their relationship with time. Mathematical models describing some of these processes and their effects on the radionuclide profiles have been reviewed recently [8,9,10] and hence are not discussed in detail here. However, for the sake of completeness they are presented briefly below. 

The mass flux in the spray scales with liquid metal flow rate. Gas pressure tends to narrow the spray whereas melt superheat tends to flatten the spray)3] By changing the process parameters and/or manipulating the configuration and/or motion of the spray, the mass distribution profile can be tailored to the desired shape. For example, a linear atomizer produces a relatively uniform mass distribution in the spray. The mass flux distribution in the spray generated with a linear atomizer has been proposed to follow the elliptical form of the Gaussian distribution)178]... 

Buoso, M. C., Fazinic, S., Haque, A. M. I., el al. (1992). Heavy element distribution profiles in archaeological samples of human tooth enamel and dentin using the proton-induced X-ray-emission technique. Nuclear Instruments and Methods in Physics Research B 68 269-272. 

The polymerization temperature, through its effects on the kinetics of polymerization, is a particularly effective means of control, allowing the preparation of macroporous polymers with different pore size distributions from a single composition of the polymerization mixture. The effect of the temperature can be readily explained in terms of the nucleation rates, and the shift in pore size distribution induced by changes in the polymerization temperature can be accounted for by the difference in the number of nuclei that result from these changes [61,62]. For example, while the sharp maximum of the pore size distribution profile for monoliths prepared at a temperature of 70 °C is close to 1000 nm, a very broad pore size distribution curve spanning from 10 to 1000 nm with no distinct maximum is typical for monolith prepared from the same mixture at 130°C [63]. 

Conditions polymerization mixture 20 wt% ethylene dimethacrylate, 20% vinyl azlac-tone+acrylamide, 60% porogenic solvent, and azobisisobutyronitrile (1% with respect to monomers), temperature 65 °C polymerization time 24 h. b Percentage of vinyl azlactone (VAL) and acrylamide (AA) in polymerization mixture. c Median of the pore size distribution profile. d Total pore volume. 

Data belonging to distribution profiles may be compared either vertically along the release/response ordinate or horizontally along the time abscissa. The semi-invariants (moments) provide a complete set of metrics, representing both aspects in logical sequence AUC accounts (vertically) for the difference of the extent, the mean compares (horizontally) the rates, and higher-order moments and higher-order statistics (variance, etc.) characterize the shape aspect from coarse to finer. 

Figure 4 Differences between two distribution profiles, given as PDF (left) or CDF (right), and differing by extent (1), rate (2), shape (3).

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