Two-dimensional patterns

The extension of generic CA systems to two dimensions is significant for two reasons first, the extension brings with it the appearance of many new phenomena involving behaviors of the boundaries of, and interfaces between, two-dimensional patterns that have no simple analogs in one-dimension. Secondly, two-dimensional dynamics permits easier (sometimes direct) comparison to real physical systems. As we shall see in later sections, models for dendritic crystal growth, chemical reaction-diffusion systems and a direct simulation of turbulent fluid flow patterns are in fact specific instances of 2D CA rules and lattices. 

Assume we are on a cubic lattice. Define a Conway object as any pattern of live sites that emerges during Conway s Life. Without loss of generality, we may suppose that the two-dimensional pattern lives on the 2 = 0 plane of the cubic lattice. 

The observation that Langmuir monolayers often exist as phase-separated domains has begun to be exploited as a means to produce LB monolayers with two-dimensional patterns. This approach aims to form, transfer, and stabilize these domains on appropriate substrates by combining the Langmuir-Blodgett method with the covalent bonding aspect of self-assembly. There are a small number of studies, and the possible further functionalization of the domains and use of different combinations of materials make this area promising for the construction of patterned films. 

Orbital pictures have an advantage over electron density plots in that they can indicate the three-dimensional nature of orbitals. One type of orbital picture is a two-dimensional color pattern in which the density of color represents electron density. Figure 7-19Z> shows such an orbital density picture of the 2s orbital. This two-dimensional pattern of color density shows a cross-sectional slice through the middle of the orbital. 

Sawadaishi, T. and Shimomura, M. (2005) Two-dimensional patterns of ultra-fine particles prepared by self-organization. Colloid. Surf. A, 257-258, 71-74. 

The potential of photolithography for the construction of protein microarrays has also been demonstrated (Mooney et al., 1996). For these experiments, antibodies were assembled in precise two-dimensional patterns on silicon wafers. This was accomplished by first forming a self-assembled monolayer of n-octadecyltrimethoxysilane (OTMS) on a silicon-dioxide... 

Park, J. D. Lee, K. D. 2007. Method for manufacturing stamp for nanoimprint lithography having two-dimensional pattern of uniform size and shape, and method for photonic crystal using the same. LG Electronics Inc., S. Korea. 

A two-dimensional pattern decomposition method has been developed and implemented for this purpose. Since the pattern decomposition method does not require an initial structure model, the method can be successfully applied to texture patterns from samples with irrrknown structure. 

A two-dimensional micropatterned tissue can be easily obtained by utihz-ing the inherent differences in cell adhesiveness between different micropatterned photografted regions. This was attained by photoiniferter graft polymerization with a projection mask placed on an iniferter-derivatized surface. Since protein adsorption and cell adhesion are markedly suppressed on nonionic graft polymers, such as polyDMAm, any anchorage-dependent cells such as endothelial cell adhere and proliferate only on nonirradiated surfaces, resulting in the formation of a two-dimensional patterned tissue or cellular sheet (Fig. 24). 

In three-dimensional LEED, the two-dimensional pattern is supplemented by the intensities of the diffraction spots (thereby focusing the attention on the periodic part... 

Color Plate 24 Polychromator for Inductively Coupled Plasma Atomic Emission Spectrometer with One Detector for All Elements (Section 21-4) Light emitted by a sample in the plasma enters the polychromator at the upper right and is dispersed vertically by a prism and then horizontally by a grating. The resulting two-dimensional pattern of wavelengths from 165 to 1 000 nm is detected by a charge injection device detector with 262 000 pixels. All elements are detected simultaneously. [Courtesy TJA Solutions, Franklin, MA.J... 

Fultz, C. D. and Witzmann, F. A. (1997) Locating western blotted and immunostained proteins within complex two-dimensional patterns. Anal. Biochem. 251,288-291. 

The immunoreaction of two-dimensional patterns is performed on agar gel after the transfer of the protein pattern from the paper into the gel. This is done in the following way. A sandwich is built up composed of three layers, the first being the paper on which the protein pattern was run, the second a layer of gelose, and the third a paper soaked with antiserum (P2b). Preliminary results allow the detection of most known fractions as being encircled by a precipitation line. After star electro-... 

P2b. Peeters, H., and Vuylsteke, P., Immunoelectrophoresis of two-dimensional patterns. Protides of the Biological Fluids, Proceedings of the Seventh Colloquium. Elsevier, Amsterdam, 1959. In press. 

We may expect the adsorbability to depend on the work function and also on geometrical factors, such as for example the fitting in of the dimensions of the adsorbed atom or molecule in the two-dimensional pattern of the surface. Geometrical factors have played an important role in the catalytic literature at various times (288,289). Both factors depend on the orientation of the crystal faces of the surface. They may either work in opposite directions or may collaborate in the same direction. 

Isoelectric focusing can be combined with SDS-PAGE to obtain very high resolution separations in a procedure known as two-dimensional gel electrophoresis. The protein sample is first subjected to isoelectric focusing in a narrow strip of gel containing polyampholytes. This gel strip is then placed on top of an SDS-polyacrylamide gel and electrophoresed to produce a two-dimensional pattern of spots in which the proteins have been separated in the horizontal direction on the basis of their pi, and in the vertical direction on the basis of their mass (Fig. 4). The overall result is that proteins are separated both on the basis of their size and their... 

Fig. 10.6. Percolation cluster model of tunnel current in composite film containing M/SC nanoparticles (a) two-sphere model of spherical M/SC nanoparticle of radius Rq surrounded by outer sphere (radius Rd) that is defined by a degree of electron delocalization extending the nanoparticle and characterizes electron tunneling (see text) (b) the distribution of conductivity G(r) over the two-sphere particle (c) two-dimensional pattern of cluster from overlapping two-sphere particles (overlapping areas of outer spheres are shown).

Figure 8-4 presents two band decorations one of them has a polar axis while the other has a nonpolar axis. An important feature of these patterns is that they have a polar singular plane, which is the plane of the drawing. This plane is left unchanged during the translation. Such two-dimensional patterns with periodicity in one direction are called one-sided bands [5],... 

The large amount of data which has to be collected in time resolved measurements, especially if full two-dimensional patterns are recorded, leads to the development of dedicated high speed data acquisition systems. This is the third component which is necessary together with the source and detectors, to bring synchrotron radiation X-ray experiments to their full deployment. 

MWPC-devices have been used successfully in X-ray diffraction work, in recent years. In synchrotron radiation experiments, however, it will not be so much the detector, but more the read-out electronics which will not be able to deal with the enormous event rates, which are to be expected in two-dimensional patterns. 

---