Mixing random variation

In the laboratory-frame NOE experiments the coherent transfer can be eliminated by a random variation of mixing time within a range that represents a small fraction of the total mixing time. In these conditions, the sin(wirm) terms average to zero, and the incoherent exchange averages to a nonzero value. 

A viscous flow takes place when the effects of viscosity become significant. This type of flow can be categorized as either a laminar flow or a turbulent flow [72], A laminar flow is one with no considerable mixing of neighboring fluid particles, apart from molecular motion. In a turbulent flow, the quantities which typify the flow exhibit a random variation with the time and space coordinates. The quantity used to predict the type of flow regime is the Reynolds number (Re), which is a dimensionless parameter defined as [72]... 

Short-term studies indicate that Thermopave mixes generally attain their ultimate stability after a curing time between one to five days, depending upon the sulfur/asphalt ratio and sand type. The results of a long-term aging study of Marshall briquettes stored at room temperature are presented in Table V. The data indicate a random variation in stability values but no significant change in stability over a five-year period. 

Figure 8.36. The variation of NOE and ZQC intensities during the NOESY mixing time. The ZQC contributions may be suppressed by making small random variations to Xm, whereas this has negligible effect on the NOE intensities.

Mixed random-strategic designs (e.g., stratified-random design) to account for indicator variation in space and time... 

To achieve randomization, the order of experiment is scrambled so that any bias present will be mixed up and become a part of the random variation. One of the following options can be taken... 

Outcomes are determined by a combination of the patient s underlying condition and the care they actually receive. Any kind of outcome indicator, such as wound infection is only a very indirect refleaion of the safety and quality of care provided. Comparing units or institutions on such indicators is therefore problematic, as any differences may simply reflect differences in patient populations as well as other factors, such as data quality and random variation. Case mix adjustment, in which rates or mortality or morbidity are statistically adjusted to allow for differences in patient population, is widely used but there will always be some uncertainty about the validity of comparisons based on such data. This is not to suggest that case mix adjustment is not valid or that comparisons should not be made, only to point out that the differences that emerge need thoughtful interpretation (Bottle and Aylin, 2008). 

In a part of the mixing process of particulate solids in addition to the stochastic nature of solid mixing at the micro-level, important macro-level random effects are present too. This paper suggests a theoretical approach to model these large-scale random variations and to calculate the residence probability of the particles. A simulation method is also presented on the basis of the stochastic model. The stationary state is also investigated and a sufficient condition for the existence of the stationary state is given. 

Figure 3 The collapse of the peptide Ace-Nle30-Nme under deeply quenched poor solvent conditions monitored by both radius of gyration (Panel A) and energy relaxation (Panel B). MC simulations were performed in dihedral space 81% of moves attempted to change angles, 9% sampled the w angles, and 10% the side chains. For the randomized case (solid line), all angles were uniformly sampled from the interval —180° to 180° each time. For the stepwise case (dashed line), dihedral angles were perturbed uniformly by a maximum of 10° for 4>/ / moves, 2° for w moves, and 30° for side-chain moves. In the mixed case (dash-dotted line), the stepwise protocol was modified to include nonlocal moves with fractions of 20% for 4>/ J/ moves, 10% for to moves, and 30% for side-chain moves. For each of the three cases, data from 20 independent runs were combined to yield the traces shown. CPU times are approximate, since stochastic variations in runtime were observed for the independent runs. Each run comprised of 3 x 107 steps. Error estimates are not shown in the interest of clarity, but indicated the results to be robust.

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