Ordering parameters calculation

Another principal difficulty is that the precise effect of local dynamics on the NOE intensity cannot be determined from the data. The dynamic correction factor [85] describes the ratio of the effects of distance and angular fluctuations. Theoretical studies based on NOE intensities extracted from molecular dynamics trajectories [86,87] are helpful to understand the detailed relationship between NMR parameters and local dynamics and may lead to structure-dependent corrections. In an implicit way, an estimate of the dynamic correction factor has been used in an ensemble relaxation matrix refinement by including order parameters for proton-proton vectors derived from molecular dynamics calculations [72]. One remaining challenge is to incorporate data describing the local dynamics of the molecule directly into the refinement, in such a way that an order parameter calculated from the calculated ensemble is similar to the measured order parameter. 

Figure 2.32 Order parameters calculated for (a) anthracene and (b) anthraquinone dissolved in nematics with different dielectric anisotropy [9]. For the case Ae > 0, the results obtained in the absence of induction effects are also shown (dotted line). The temperature dependence of the dielectric anisotropy is taken into account, with the values eNI = 10.2, AeN/ = 8 and eNI = 5.2, AeN/ = —0.5 for the two cases at the nematic-isotropic transition. Atomic charges in absolute value greater than 0.1 are shown (in e units). The y axis is perpendicular to the molecular plane.

O Sullivan DBD, Jones CE, Abdelraheim SR, Brazier MW, Toms H, Brown DR, Viles JH (2009) Dynamics of a truncated prion protein, PrP(113-231), from N-15 NMR relaxation order parameters calculated and slow conformational fluctuations localized to a distinct region. Protein Sci 18 410... 

Fig. 2.3.2. Variation of the free energy with the order parameter calculated from the Maier-Saupe theory for different values of A/k TV. The minima in the curves occur at values of s which fulfil the consistency relation (2.3.13). ...

We have performed our simulation within the LL lattice spin model, on lattices of 30 x 30 x /i spins, where h — h + 2 represents h layers of nematic LC spins and two additional layers of fixed spins [16]. At the four lateral faces of the simulation sample we have employed periodic boundary conditions to mimic the bulk-like conditions. The standai d Metropolis procedure [56] has been used to update the lattice. The state of a system was monitored by the tensorial nematic order parameter calculated with respect to the fixed frame spanned by the orthonormal triad (e, e, Cz) Q = (3uj Ui - l)/2). 

Order parameters calculated for different motional models as a function of the angle 3 or... 

Figure 1. Order parameters calculated for the radial droplet at T = 0.8 (nematic phase). Local nematic (5, le/t) and external field right) order parameter...

Figure 9. Order parameters calculated for the bipolar droplet at T = 0.8 (nematic phase) local nematic (5, left) and external field ((P2)b, right) order parameter as a function of the distance from the droplet center. Curves are plotted for (top to bottom) = 1, 0.5, 0.2, and 0, respectively. External field enhances the degree of nematic ordering (left) and increases the size of the aligned core (right). The molecular alignment for = 0 is depicted schematically as inset.

Figure 7. Plot of P2) as a function of time defined for a system of 200 chains of semi-rigid units of 10 beads with additional orienting potential the ftill line represents the order parameter calculated with respect to a fixed axis, while the dashed line represents the order parameter defined with respect to an averaged sixis.

Fig. 4. Order parameters calculated for krypton adsorbed in the carbon nanotube, as a function of tenqrerature. In the left panel < 6 is shown for the first layer (in one layer regime). In the ti panel, the contact and second layer parameters are reported, calculated in the two layer regime.

FIGURE 3.12. Relative order parameters calculated from the aromatic chemical shifts at Tc. The theoretical data are taken from the mean field calculation of Marcelja (after Ref. [3.45]). 

Figure 6. Reduced values xt and Xi as a function of reduced temperature plotted according to Eq. (45) using order parameters calculated using mean field theory. Open squares ( ) assume no molecular bi-axiality, so D = Q full circles ( ) are for an assumed molecular biaxiality of 0.3 and a A value of 0.3.

A comprehensive analysis of the dynamics of the SH3 domain of chicken a-spectrin has been presented, based upon Ti and on- and off-resonance 7 ip relaxation times obtained on deuterated samples with a partial back-exchange of labile protons under a variety of the experimental conditions, taking explicitly into account the dipolar order parameters calculated from dipole-dipole couplings. It is demon-... 

Figure 6.6 Shows the order parameter calculated for lui.xGa As as a function of composition at several temperatures. Redrawn with permission from Masaya Ichimura and Akio Sasaki, Journal of Applied Physics, 60,3850 (1986). Copyright 1986, American Institute of Physics.

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