Orientation and polarization

We introduce in this section the concepts of orientation and polarization of an operation cluster. For conciseness, we consider one operation cluster C that contains C vertices, i.e. C = c i = 1. C.  

We make the following assumptions. First, the cardinality of the operation cluster must be greater than one ( C 1), since othowise the ordering is trivial. Second, each vertex Cj C must either be a data-dependent delay operation (i.e. anchor) or have non-zero fixed execution delay, i.e. (c ) 0. Note that registers have already been introduced prior to conflict resolution to latch the outputs of the shared resource. For example, the execution delay for shared calls to a combinational adder is 1 cycle because of the latching delay. 

The above assumptions translate into the following two requirements on any cycle connecting the elements of the cluster. 

Definition 7.2.2 The orientation of an operation cluster C is a relation Vc CxC, where x, y) Ve if the length of the longest path from x toy is greater than or equal to zero, i.e. length x, y) 0. 

Intuitively, an orientation of a constraint graph represents a partial order among the vertices that must be satisfied if the resulting serialized graph is to be valid. For example, x, y) g Vc implies that the serialization y x will violate the timing constraints, i.e. form a positive cycle. The induced partial order in Vc defines a predecessor-successor relationship among the elements of C. A vertex c G C is a predecessor to another vertex Cj C if there exists a pair (ci, Cj) G Vc successors are defined in a similar manner. 

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The physical picture in concentrated electrolytes is more apdy described by the theory of ionic association (18,19). It was pointed out that as the solutions become more concentrated, the opportunity to form ion pairs held by electrostatic attraction increases (18). This tendency increases for ions with smaller ionic radius and in the lower dielectric constant solvents used for lithium batteries. A significant amount of ion-pairing and triple-ion formation exists in the high concentration electrolytes used in batteries. The ions are solvated, causing solvent molecules to be highly oriented and polarized. In concentrated solutions the ions are close together and the attraction between them increases ion-pairing of the electrolyte. Solvation can tie up a considerable amount of solvent and increase the viscosity of concentrated solutions. 

The crystal structure of the cobalt-substituted enzyme was obtained with bicarbonate bound to the metal (Iverson et al. 2000). The structure shows Asn 202 and Gln75 hydrogen bonded to the metal-bound bicarbonate, suggestzing potential roles for these residues in either transition-state stabilization or orientation and polarization of CO2 for attack from the zinc-hydroxyl (Fig. 11.5). The crystal structure also shows three discrete conformations for Glu 84, suggesting a role for this residue in the transfer of protons out of the active site indeed, kinetic analyses of Glu 84 variants combined with chemical rescue experiments establish this residue as critical for proton transfer (Tripp and Ferry 2000). The location of Glu 62 adjacent to Glu 84 suggests a potential role in proton transfer as well. Although kinetic analyses of site-specific variants establish an essential role for Glu 62 in the CO2 hydration steps (Eqs. 11.3 and 11.4), the results were inconclusive regarding an additional role in proton transfer (Eqs. 11.5 and 11.6). 

Orientation and polarization effects in chemical reaction dynamics, J. Chem. Soc. Faraday Trans., 89, 1401-1590. 

This relation is applicable for excitation with photons of identical frequency (Fig. 3.1a). Thus, the excitation frequency of the virtual state is about one-half that of the TP excited state S . The term e is the complex polarization vector. This term is needed to describe the orientation and polarization affecting TP excitation [23, 238]. 

Photo-orientation of the chromophore was observed by TP induced isomerization. Such events can be accomplished by exposure to polarized light as shown for OP induced orientation and polarized light [554]. However, the molecular order induced by TP excitation is about half that of OP induced photo-orientation. Furthermore, the sign of the anisotropy induced by TP excitation is opposite that of OP excitation (Fig. 3.58). 

If a molecule is placed in a homogeneous electric field, its energy changes as a result of orientation and polarization. The new energy E can be expressed as a power series of the field strength S ... 

When the Coulomb interaction takes place in a medium other than a vacuum, the molecules of the medium will be oriented and polarized in the electric field created by these two charges, and the magnitude of V(r) is reduced so that Equation (21) becomes,... 

Hamaguchi, M. and Yoshino, K., Rubbing-induced molecular-orientation and polarized electroluminescence in conjugated polymer, Jpn. J. Appl. Phys. Part 2 — Lett. 34, L712-L715, 1995. 

In general, these elements are not sufficient to characterize a scattered radiation. For instance, the anisotropy of the scattering molecules may introduce orientation and polarization fluctuations. The electric field E , associated with a given propagation direction, has in this case random features. Let p be the probability associated with the value Ef of the /-component of the field (the index / = X, Y refers to the two polarization axes). 

For the sake of comparison with the ESCA spectrum of Nj, and to provide a more critical test of the EOM method, we calculate the peak intensities as well as the peak positions. The details of the intensity calculations are left to the Appendix. The dipole approximation is invoked, as the calculation is based on Fermi s golden rule. A plane wave approximation is employed for the outgoing electron. The cross section for the ejected electron is averaged over all possible molecular orientations and polarizations of the incident photon as described by Ellison. ... 

Usually, it is not just a calculation for an individual stracture, but an averaged result over the statistical ensemble and orientation that is required. Formally, such an averaging can be carried out by simple summation of the results calculated for various orientations and polarizations of the incident light, but this is inefficient. It is more convenient to perform orientation averaging for clusters using T-matrix formalism [65], even for arbitrary nonspherical particles [66]. If we formally invert Eq. (3.15), we get the T-matrix of an individual cluster-particle [62]... 

A calculation of the interaction between them at the account of surface electrostatic field (orientation and polarization of admolecule, deformation of admolecule and local surrounding of reactive site of the surface... 

Crosslinking can be used to overcome the aforementioned obstacles, as in the case of the calamitic networks in which the orientation and polarity are preserved. First experiments were performed by swelling a calamitic LCE with a low-molar-mass BCLC [182, 183]. Up to 35 mol% of this material could be incorporated into the network. The resulting gel had a flexoelectric cmistant e-i of 20 nC/m. This is one-third of the value of the low-molar-mass BCLC, which corresponds to the volume fraction of the BCLC. Only recently has a pure bent-core elastomer (BCFLCE) been made [139, 169]. Following the synthetic route of Finkelmann, an oriented, transparent nematic elastomer sample could be obtained. As a polysiloxane backbone was used, the Tg was close to room temperature. The flexoelectric constant of 40 nC/m is somewhat smaller than for the pure bend-core monomer, but larger than the value obtained for the swollen elastomer. 

Kawai s (7) pioneering work almost thirty years ago in the area of piezoelectric polymers has led to the development of strong piezoelectric activity in polyvinylidene fluoride (PVDF) and its copolymers with trifluoroethylene and tetrafluoroethylene. These semicrystalline fluoropolymers represent the state of the art in piezoelectric polymers. Research on the morphology (2-5), piezoelectric and pyroelectric properties (6-70), and applications of polyvinylidene fluoride 11-14) are widespread in the literature. More recently Scheinbeim et al. have demonstrated piezoelectric activity in a series of semicrystalline, odd numbered nylons (75-77). When examined relative to their glass transition tenq>erature, these nylons exhibit good piezoelectric properties (dai = 17 pCTN for Nylon 7) but have not been used commercially primarily due to the serious problem of moisture uptake. In order to render them piezoelectric, semicrystalline polymers must have a noncentrosynunetric crystalline phase. In the case of PVDF and nylon, these polar crystals cannot be grown from the melt. The polymer must be mechanically oriented to induce noncentrosynunetric crystals which are subsequently polarized by an electric field. In such systems the amorphous phase supports the crystalline orientation and polarization is stable up to the Curie temperature. 

Figure 6.7 shows some possible orientations for collisions between ethene and hydrogen chloride molecules. Only one of the possibilities shown (collision 1) results in a successful or effective collision. Discuss why this is and the reasons for the other collisions being unsuccessful. (You should consider the orientation and polarization of the interacting molecules.)... 

The position of electron density (atomie eoordinates) is the largest contributor to peak intensity, although temperature, preferred orientation, and polarization may also influenee the peak intensities. 

A major factor that influences the surface potential is not only protein molecule size, but also the orientation and polarization of dipoles. Although neutravidin possesses more positive charges than BSA, the surface potential of BSA is larger than that of neutravidin, which implies that the dipoles of the two... 

Whitaker, B. J. (ed.) (1989). Orientation and Polarization Effects in Reactive Collisions. Faraday Trans. 113. 

A. Salameh, A. Wustmann, S. Karl, K. Blanke, D. Apel, D. Rojas-Gomez, H. Franke, F.W. Mohr, J. Janousek, S. Dhein, Cyclic mechanical stretch induces cardiomyocyte orientation and polarization of the gap junction protein connexin43, Circ Res 106 (2010) 1592-1602. 

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