Complex topology

The use of a normal conducting probe offers the advantage to apply a mobile head, that is able to work on complex topologies. It is suitable for handhold and mechanized inspection as well. 

It may be safely assumed that each of these sets of receptor locations is structurally somewhat heterogeneous, and that it occupies a specific area of the sensory epithelium, with a characteristic, possibly very complex, topology. Because knowledge of this taste modality is still minimal, the topological structure of the taste modality is pure speculation. One such speculation was offered by Beets. To simplify his reasoning, Beets assumed the topology to refer to a two-dimensional area of the sensory... 

Gurtovenko, A. A. and Blumen, A. Generalized Gaussian Structures Models for Polymer Systems with Complex Topologies. Vol. 182, pp. 171-282. 

From the computational point of view the Fourier space approach requires less variables to minimize for, but the speed of calculations is significantly decreased by the evaluation of trigonometric function, which is computationally expensive. However, the minimization in the Fourier space does not lead to the structures shown in Figs. 10-12. They have been obtained only in the real-space minimization. Most probably the landscape of the local minima of F as a function of the Fourier amplitudes A,- is completely different from the landscape of F as a function of the field real space. In other words, the basin of attraction of the local minima representing surfaces of complex topology is much larger in the latter case. As far as the minima corresponding to the simple surfaces are concerned (P, D, G etc.), both methods lead to the same results [21-23,119]. 

In system 1, the 3-D dynamic bubbling phenomena in a gas liquid bubble column and a gas liquid solid fluidized bed are simulated using the level-set method coupled with an SGS model for liquid turbulence. The computational scheme in this study captures the complex topological changes related to the bubble deformation, coalescence, and breakup in bubbling flows. In system 2, the hydrodynamics and heat-transfer phenomena of liquid droplets impacting upon a hot flat surface and particle are analyzed based on 3-D level-set method and IBM with consideration of the film-boiling behavior. The heat transfers in... 

The discovery of new controlled polymerization techniques in the mid-1990s and the progress achieved in living polymerization toward well-defined block copolymers with complex topologies have certainly played a key role in the development of block copolymer micelles. 

The process of chain retraction can be applied to more complex topologies of entangled polymers under the same assumptions discussed for linear polymers... 

Table 2.1 below gives the more important properties in this group, that are affected by LCB the list is not complete. Though it is easy to see qualitatively that most of the properties mentioned in Table 2.1 will be affected by LCB, to quantify this conclusion poses difficult theoretical problems, which have not yet been completely solved. Part of the difficulty is due to the basically complex topology of branched structures. It is impracticable to consider structures requiring more than a very few parameters for their specification, so that only molecules of rather few and simple types have been discussed theoretically these present difficulties enough. 

Are there any other possible uses for the construction of complex topological species One possible application is in the mass production of DNA polyhedral catenanes by biological means, such as the polymerase chain reaction (PCR) (Saiki et al. 1986) or by production in vivo. Figure 21 illustrates that semi-conservative replication (the mechanism used by DNA polymerases) cannot reproduce a stable branch. The DNA with different sequences in the two arms of the branch (cartooned as dashed and solid lines) leads to two heterologous duplex DNA molecules, rather than a second branched molecule. 

The plectonemic nature of the DNA double-helix makes it a tractable molecule for experiments in molecular topology. This is a very rich vein for the exploration of the topological properties of matter. In this chapter, we have tried to illuminate some of the techniques by which the single-stranded topology of DNA can be directed in synthetic molecules. Catenanes and knots, periodic braids, and Borro-mean rings are available from simple protocols, and it is to be hoped that the physical properties associated with complex topologies (Moffatt 1990) will become available through the medium of DNA constructions. 

To single out the peculiarities in the phase behavior of ionic fluids, it is convenient to consider first the behavior of nonionic (e.g., van der Waals-like) mixtures. We note, however, that the subsequent considerations ignore liquid-solid phase equilibria, which in real electrolyte solutions can lead to far more complex topologies of the phase diagrams than discussed here [150],... 

D networks based on the lanthanides with their high coordination numbers (typically 7-11) are less predictable than those based on transition metals and the high oxophilicity of the lanthanide (III) ions means that they do not bind strongly to ligands such as pyridine derivatives. As a result lanthanide coordination networks are less common in the literature however, they represent tremendous potential in terms of ever more complex topologies. 

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