Order parameters, convergence

In the present cases, in contrast, when the order parameter increases, the ESR lineshapes are narrowed, because the relaxation processes are less effective. Thus, narrowing in turn involves a reduction in the number of ex-dt states necessary to obtain convergence and thoeby a faster attainntont of the result. 

In addition to corrections tising an appropriate spectral density function, in principle one also needs to consider an ensemble of structures. Bonvin et al. U993) used an ensemble iterative relaxation matrix approach in which the NOE is measured as an ensemble property. A relaxation matrix is built from an ensemble of structures, using averaging of contributions from different structures. The needed order parameters for fast motions were obtained fi um a 50-ps molecular dynamics calculation. The relaxation matrix is then used to refine individual structures. The new structures are used again to reconstruct the relaxation matrix, and a second new set of structures is defined. One repeats the process until the ensemble of structures is converged. The caveat espressed earlier that the accuracy of the result is limited by the accuracy of the spectral density function applies to all calculations of this typ . 

The push to highlight performance on GPUs has meant that not one of the currently published papers on GPU implementations of MD actually provide any validation of the approximations made in terms of statistical mechanical properties. For example, one could include showing that converged simulations run on a GPU and CPU give identical radial distribution functions, order parameters, and residue dipolar couples to name but a few possible tests. 

NMR structure calculation alone cannot describe the dynamic structure of protein. If structure calculations (Section 6) and NMR-derived information (Sections 8 and 9) are reliable enough, a poor convergence (if it remains in the NMR ensemble) likely arises from the internal mobility of atoms. The molecular motion is usually confirmed by order parameters of spins derived from relaxation time experiments.107-109... 

Figure 8.1 also shows two examples of floppier residues, with order parameters less than 0.8 and internal decay times that are comparable to overall tumbling times, such as residue 41 in GB3, whose internal correlation function decays with a Tg of 2.1 ns. Such slow decays have received less attention, since they can only be reliably observed with fairly long simulations as a rule of thumb, simulation times need to be 50-100 times longer than the examined decay times in order to obtain reasonably converged time correlation functions [16,17,13]. With 100 ns simulations now becoming available (and which are needed to examine overall rotational diffusion an)rway), better comparisons to experiment for these slower internal motions are becoming feasible. 

Above all, an order parameter other than s-wave symmetry has been argued for intensively in order to explain the experimental results from, e.g., NMR, penetration depth, speeifie heat, neutron scattering, and phase-sensitive SQUID measurements. Up to now, it seems that the argument has been converging to consider that the symmetry of the order parameter in these materials essentially has d-wave symmetry. 

In this study, adaptive control algorithms have been utilized for designing active controllers for smart structure test articles. Adaptive control schemes require only a limited a priori knowledge about the system in order to be controlled. The availability of limited control force and inherent deadband and saturation effects of shape memory actuators are incorporated in the selection of the reference model. The vibration suppression properties of smart structures were successfully demonstrated by implementing the conventional model reference adaptive controllers on the smart structure test articles. The controller parameters converged to steady state values within 8 s for both direct and indirect MRACs. 

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