Abstract: A gray scale image of a fingerprint composed of a field of pixels is converted to a binary image composed of a field of pixels by a technique which takes into account the directivity of the ridge and valley structure. Three intermediate binary im­ ages are developed, one by the use of a vertical filter, one by the use of a horizontal filter and a reference image by the use of a filter which is not directionally biased. Corresponding sub­ fields around each pixel in each of the three images are com­ pared. If the subfield for the vertically derived image is closer to that of the reference image then is the subfield for the horizon­ tally derived image, then the binary value for the pixel from the vertically derived image is used in the final image; and vice versa. In this fashion, a fourth a final binary image is derived from a combination of the vertically derived image and horizon­ tally derived image which includes the best imagery from each of those two intermediate images.

Abstract: The anisotropic rotational motion of the backbone and the side chains of poly(L-glutamic acid) in the α-helical structure was investigated using the 13C-T1 and T2 relaxation times of all carbon atoms with directly attached protons, obtained at a 13C-Larmor frequency of 67.89 MHz. The evaluation of the nmr data was carried out according to the previously derived anisotropic diffusion model, in which the macromolecule is considered a rigid rod. The rotation of the backbone is characterized by two diffusion constants, D1 and D3, describing the rotation perpendicular to and around the symmetry axis. The additional internal motion of the Cβ-methylene group is described as a jump process with a jump rate, k1, between two allowed rotametric states. Steric considerations indicate that the occupation of the third rotameric position is forbidden. The rotation of the Cγ-methylene group is decribed as a one-dimensional diffusion process around the Cβ–Cγ bond. Investigation of the temperature dependence of the relaxation parameters led to the temperature dependence of the dynamic parameters. Activation energies were determined from these data. The dynamic parameters obtained for poly(L-glutamic acid) at 291 K are compared with the corresponding results of a previous study of poly(L-lysine). The development of an anisotropic diffusion model for the motions of the rod-shaped poly(L-lysine) α-helix and its application to the interpretation of the 13C-relaxation data of this molecule have already been published previously. In this model, both the overall molecular tumbling and the various internal motions have been characterized by diffusion constants or jump rates typical for each process. These dynamic parameters can be calculated from the spin–lattice relaxation times, the spin–spin relaxation times and the NOE factors of the Cα, Cβ, and Cγ nuclei of the polypetide. In the present paper, we describe the application of the above-mentioned dynamic model to the interpretation of 13C-relaxation studies of a further homopolypeptide, poly(L-glutamic acid), in the α-helical structure. Furthermore, we studied the temperature dependence of the relaxation times of this polymer and determined the anisotropic diffusion parameters at each temperature. From their temperature dependence and from comparison of our present results with the data of our previous study of poly(L-lysine), we were able to derive new insights into the intramolecular diffusion processes and the excitation of various motions.

Abstract: Reequilibration processes are often encountered within solids and they have long been described mathematically. However, computation of reequilibration data over entire processes is often difficult. An algorithm has been developed specifically for this purpose. It allows a fast and efficient computation of reequilibration parameters. Anisotropic diffusion can, moreover, be taken into account.

Abstract: A diffusion model is presented which allows an experimental test for the existence of an anisotropic region at a crystal surface induced by the asymmetry of the vacuum-crystal interface. The model is a generalization of that developed by van Gorkum and Kornelsen1 which assumed a diffusion coefficient independent of position in the crystal. The model was modified by assuming that the anisotropy can be described by a variable diffusion coefficient very near the surface. It is shown that if such an anisotropic region exists, the fraction of trapped particles f should increase with the temperature at which the crystal is held during diffusion. If the region does not exist, the fraction of trapped particles should not depend on the crystal temperature. An attempt was made to measure the dependence of f on temperature for He trapping at very shallow He V traps in Mo (100). The results indicate that even at the depth of the shallowest traps in Mo (100) (≤ 5 A), no significant anisotropic diffusion of th...

Abstract: For quasi-one-dimensional (quasi-ld) and layered materials, for highly anisotropic two-dimensional systems and wires the influence of weak disorder due to randomly distributed impurities is studied in a diagrammatic self-consistent approximation (SCDT). It is shown that for quasi-ld systems there is a threshold value, wc, for the interchain exchange integral. For w wc it is in a metallic state. In contrast with a quasi-ld case, for a layered material extended states in an upper part of energy band appear almost immediately when a weak interlayer tunneling is switched on. The mobility edge is determined as a function of the strength of this tunneling. An expression for the AC conductivity σ(ω) is found in both cases. For highly anisotropic 2d systems localization radii r‖ and r⊥ are determined and σ(ω) is found. A possible relevance of this model to a system of dislocations on the grain boundaries of a germanium bicrystal is noted. A model of a wire consisting of N parallel, weakly coupled chains is considered. It is shown that with an increase in interchain coupling a rather sharp transition from a localized state with a small localization radius (rc ∼ l, where l is the mean free-path) to a localized state with a large localization radius (rc ≃ Nl) should take place. A very important conclusion is that for any anisotropic system, the effect of anisotropy can be completely absorbed into anisotropic diffusion coefficients D‖, (ω) and D⊥ (ω) and that the ratio D⊥ (ω)/D ‖ (ω) remains constant for 0 < ωT < 1. The accuracy of SCDT is discussed. A short review of the present state of the theory of the metal-insulator transition in disordered systems is given.

Abstract: Exact scaling treatments are given of anisotropic diffusion in pure and diluted chains, and in a fractal. A dynamic decimation method is used to obtain detailed dynamic scaling descriptions. The results for chains show crossover to drift or localised behaviour, induced by anisotropy or dilution. The fractal results include bias-induced crossover, with exponent unity, from anomalous diffusion behaviour (exponent log2 5) to drift behaviour and scaling corrections (exponent log2 5/3) arising from rotational anisotropy.