Asymmetrical experimental domain

Response surface designs can be divided into symmetrical and asymmetrical designs (7). The first type examines the factors in a symmetrical experimental domain, while the second can be chosen when an asymmetrical experimental domain is to be examined. 

Two types of response surface designs, applicable in an asymmetrical experimental domain, are discussed, that is, D-optimal designs and designs constructed with the Kennard and Stone algorithm (93). 

As for the symmetrical designs and in agreement with the philosophy of experimental designs, the experimental domain is mapped as well as possible. This explains why, except for a central point, often all experiments of the D-optimal design are situated toward the boundaries of the experimental domain (Figure 2.10d). During method optimization, D-optimal designs with a symmetrical experimental domain were applied in References 19,60, and 95, and with an asymmetrical experimental domain in Reference 92. 

This observation is expected from theory, as the observed thickness distributions are exactly the functions by which one-dimensional short-range order is theoretically described in early literature models (Zernike and Prins [116] J. J. Hermans [128]). From the transformed experimental data we can determine, whether the principal thickness distributions are symmetrical or asymmetrical, whether they should be modeled by Gaussians, gamma distributions, truncated exponentials, or other analytical functions. Finally only a model that describes the arrangement of domains is missing - i.e., how the higher thickness distributions are computed from two principal thickness distributions (cf. Sect. 8.7). Experimental data are fitted by means of such models. Unsuitable models are sorted out by insufficient quality of the fit. Fit quality is assessed by means of the tools of nonlinear regression (Chap. 11). 

The self-assembly of block polymers, in the bulk, thin film and solution states, produces uniformly sized nanostructured patterns that are very useful for nanofabrication. Optimal utilization of these nanoscopic patterns requires complete spatial and orientational control of the microdomains. However, the microdomains in the bulk state normally have grain sizes in the submicron range and have random orientations. In block copolymer thin films, the natural domain orientations are generally not desirable for nanofabrication. In particular, for composition-asymmetric cylindrical thin films, experimental... 

Every second protein domain in PDB is represented by more than one PDB entry 20% of proteins have two structures, and the remaining 30% more than two structures. Some of them are mutants (e.g., 400 of T4 lysozyme structures from Brian Matthews s laboratory) but in most cases, these multiple structures represent snapshots of the pocket conformational diversity. Furthermore, many entries contain more than one chain in an asymmetric unit. These protein structures related by noncrystallographic symmetry can also be used as a source of multiple pocket conformations. The noncrystallographic symmetry-related subunits increase the number of domains already represented by multiple experimental conformations from 50% to the overall level of 75% (Fig. 2). About 5% of the domains are represented by more than 30 copies. 

It is expected that a similar physical picture also holds for interacting PE stars. At distances between core domains 2d > 2R, the star coronae would start to contract due to the overlap of ionic atmospheres. As a result, the stars would become asymmetric and remain separated by a water layer in a range of distances 2d < 2R. The long-range interactions due to the overlap of ionic atmospheres are essential for PE stars with a moderate number of arms (typical for experimental systems), and at low ionic strength in the solution [27],... 

We can further characterize the structure by the distribution function of u in Fig.7. At low temperature the motion of each particle is nearly harmonic, so that the distribution function is Gaussian. As the temperature increases, the distribution becomes asymmetric, and above it is symmetric again and almost independent of temperature. At 850 K we have found a phase alternation between the aj and a phases, which correspond to the experimental observation that the domain boundary between the two phases is constantly vibrating just below Tc [37]. We cannot tell exactly whether Tc is below or above 850 K in this simulation because the system size is too small. At 900 K the MD-synthesized quartz is clearly in the / ... 

An approach alternative to the SPT, namely the domain model derived from the significant structure theory, was applied by Jhon et al. (1967) to the surface tension of water. According to the model, the water molecules at the surface layer are in an asymmetric field, having no neighbours in a direction perpendicular and outward from the surface. Water domains, the molecules of which are favourably oriented with respect to the field, fhen grow till equilibrium is reached. The surface tension is due to the orientation of molecules in the top layer and partly to changes in density within a few molecular diameters from the surface. The details of the calculation are, unfortunately, not provided in that paper. The values of y calculated by this approach agree within 1 % with the experimental ones from 0 to 100 °C and provide also correct values for the surface entropy. 

The SPH method provides an efficient way for the numerical simulations of the phase-separation phenomena in polymer blends. For instance, Okuzono used this approach to simulate a specific type of phase separation - the so-called viscoelastic phase separation - experimentally found in polymer solutions and dynamically asymmetric mixtures. Examining the effect of stress relaxation time on morphology of domains, it was shown that the more viscous phase forms network-like domains when the stress relaxation time is large. 

For both the dielectric and the aqueous films, the role of asymmetry (either mechanical or electrical) has been investigated [64 65l In both systems, the asymmetry increases the unstable domain. For thin lipid films [64] agreement is obtained with experimental observations on asymmetric black lipid membranes [68]. 

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