Periodicity framework

FIG. 14 Construction of periodic framework and geometric objects from DNA. (a) Construction of two-dimensional DNA lattices from tetravalent four-arm DNA junctions (14) [8]. (b) Synthesis of a macrocyclic molecule from bivalent three-arm DNA junctions (13a) containing two cohesive ends [83]. For simplification, linear double-helical stretches are represented by parallel lines. 

To conclude this subsection, we expose an interesting paradox arising from the time dependence of the particle configuration. As discussed in Section III, Frankel and Acrivos (1967) developed a time-independent lubrication model for treating concentrated suspensions. Their result, given by Eq. (3.7), predicts singular behavior of the shear viscosity in the maximum concentration limit where the spheres touch. Within the spatially periodic framework, the instantaneous macroscopic stress tensor may be calculated for the lubrication limit, e - 0. The symmetric portion of its deviatoric component takes the form (Zuzovsky et al, 1983)... 

The goal will be to determine optimal equipment parameters and an optimal steady-state operating point such that feasible operation is maintained for all realizations of uncertain parameters within a specified uncertainty region, with a set of outputs controlled at their nominal values. The use of controller parametrization provides a performance limit for linear control. Feasibility with respect to imcertain parameter variation is handled by posing the problem directly within a multi-period framework. The plant will be assumed to be open-loop stable at the nominal operating point, permitting use of the control structure of Fig. 5. Note that while the search is restricted to linear controllers, path constraints are enforced for the nonlinear plant... 

Figure 2 (a) [2]Pseudorotaxane linker [lcCB 6 ] used to form PRF-1 and PRF-2 (b) coordination environment of Ag center in PRF-1 (c) X-ray structure of the linear one-periodic framework of PRF-1 (d) coordination environment of Ag center in PRF-2 (e) X-ray structure of the hexagonal two-periodic framework of PRF-2... 

While the PRFs developed by Kim and coworkers were some of the first examples of one-, two- and three-periodic frameworks with rotaxane linkers, very httle material analysis (e.g., VT-PXRD) was reported to indicate the stabihty of these materials. However, recently... 

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