Equal probability surface

The tensor Uik may be represented by its equal probability surface, which, according to Eq. (2.21) is given by... 

C-H bonds are spinning around tire vertical axis in tire acetate species, so tliat an almost equal probability of H emission exists in all azimutlial directions. If tlie surface is cooled to very low temperatures, tlie rotation of tlie -... 

The structure of alumina on NiAl(l 1 0) was the subject of a surface X-ray diffraction study by Stierle et al. [46]. The model derived by Stierle et al. from the analysis of the X-ray diffraction data was based on a strongly distorted double layer of hexagonal oxygen ions, where the Al ions are hosted with equal probability on octahedral- and tetrahedral-coordinated sites the resulting film structure was closely related to bulk k-A1203. An attractive feature of Stierle s model was that it provided a natural explanation of the domain structure of the alumina overlayer, which is induced by a periodic row matching between film and substrate lattices. However, as pointed out recently by Kresse et al. [47], this structure model has two bonds with... 

In this relatively simple random walk model an ion (e.g., a cation) can move freely between two adjacent active centres on an electrode (e.g., cathode) with an equal probability A. The centres are separated by L characteristic length units. When the ion arrives at one of the centres, it will react (e.g., undergoes a cathodic reaction) and the random walk is terminated. The centres are, therefore absorbing states. For the sake of illustration, L = 4 is postulated, i.e., Si and s5 are the absorbing states, if 1 and 5 denote the positions of the active centres on the surface, and s2, s3, and s4 are intermediate states, or ion positions, LIA characteristic units apart. The transitional probabilities (n) = Pr[i-, —>, Sj in n steps] must add up to unity, but their individual values can be any number on the [0, 1] domain. 

It indicates that for RD as well as RDWD, the number of active sites increases with decrease in surface roughness. As the surface roughness decreases, the surface becomes smooth and the difference between the heights of the columns decreases or becomes zero. Therefore there is nearly equal probability of reaction at the top of all the columns. Hence, the... 

If we assume an equal probability for all adsorbed molecules to evaporate we can readily calculate the average life of a molecule on the surface between the acts of condensation and re-evaporation from the rate of condensation and the amount of surface covered. Such calculations have been made by Langmuir J.A.G.S. XL. 1393, 1918) who gives the following data for the mean length of life in... 

In a small ( 100 A) region, the 22 X., 3 reconstruction is uniaxial. The ridge runs in one direction. However, the gold surface has threefold symmetry (p3ml). On a large area, the reconstruction should run in three directions 120° apart with equal probability. Between regions with different reconstruction orientations, domain boundaries should be observed. While no scattering method may provide detailed information about these domain boundaries, STM may. 

Fig. 4.17 (a) and (b) Field ion images of the two structures found for the Si 023 surfaces. These two structures are formed with nearly equal probabilities. They also have exactly the same unit cell size. 

The total number of cross-links per gram is directly proportional to radiation dose. Either RSMW or JRg(Mw)2/3 should be independent of initial molecular weight, depending on whether all repeating units or only those near the surface of the coils have equal probabilities for intermolecular cross-link formation. Complete coil collapse is clearly ruled out by the results. Moreover, detailed calculations (46) show that a trend in the product RgMw due to systematic differences in intramolecular cross-linking, should be observed even for only partially collapsed random coils. If the coil radii in bulk polystyrene were reduced by even as much... 

If one considers an elementary model of a metal consisting of a latlice of fixed positive ions immersed in a sea of conduction electrons that are free to move through the lattice, every direction of electron motion will be equally probable. Since the electrons fill the available quantized energy states staring with the lowest, a three-dimensional picture in momentum coordinates will show a spherical distribution of electron momenta and, hence, will yield a spherical Fermi surface. In this model, no account has been taken of the interaction between Ihe fixed posilive ions and the electrons. The only restriction on the movement or "freedom" of the electrons is the physical confines of the metal itself. 

For a catalyzed surface reaction like the exchange of H2 with D2 we cannot talk about a single mechanism for the reaction. We must specify the experimental conditions (pressure, surface coverage, temperature, and surface structure) as the reaction mechanism is likely to change with changing conditions of the experiments. Also, since there are several reaction paths available at the various surface sites, even under specified experimental conditions it is likely that the experimental technique utilized to monitor the reaction rate and product distribution may not detect products that form along the various reaction branches with equal probability. Thus, a combination of techniques that are employed over a wide range of experimental variables is necessary to reveal the nature of the complex catalytic process. 

Spontaneous resolved two chiral domains are formed in equal probability. In other words, enantiomeric excess (ee) is zero. We now ask whether ee can be controlled or not. The answer is yes. Several methods used in bent-shaped mesogenic phases will be introduced. The direct method is of course an addition of chiral dopant. Actually this has been shown to be a viable method [6, 61]. Use of chiral surface is also effective [62], By using polyimide with chiral side chains at both substrate surfaces, imbalance of two chiral domains (10% ee) has been achieved. Another method using macroscopic helical structure was demonstrated by Jakli et al. [63]. They used a nonchiral polymer network, which was formed in the N phase. After the polymerization, N compounds were washed out, then bent-core mesogens were introduced. Because of the polymer helical fibers, bent-core mesogen shows a chiral domain. 

Scheme 1 Statistical approach of the formation of D2-D5 product. a) The product D2 is formed in a concentration 1 2 = 6 Prot with 6 = surface concentration (in %) of the rotating species and b) Pdes = fractional probability on desorption,c) Species I is bonded at C-C bond (A), d Adsorbed species has a fractional probability Prot of rotating right and an equal probability Prot of rotating left Prot=(l-Pdes)/2. After the first rotation, the species rotated to the left and right are equal. Species VI has been through the following route adsorption on bond A B A E and desorption would result in the D4 product. The route for species VII has been A B A B.

The process of haemolysis is probably a penetration or displacement of the films normally surrounding the red blood corpuscles by the capillary active substances which constitute the haemolytic agents. Gorter and others1 found that haemolysis was complete when just enough was present to cover an area equal in surface to the corpuscles. The correspondence between penetration in monomolecular films, and haemolysis, by various substances, has been discussed by Schulman and Rideal.2... 

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