Geometry constraints

In our last example we return to the issue of the possible damaging effects of the standard geometry constraints. Two long trajectories have been computed for a partially hydrated dodecamer DNA duplex of the previous example, first by using ICMD and second with Cartesian coordinate molecular dynamics without constraints [54]. Both trajectories started from the same initial conformation with RMSD of 2.6 A from the canonical B-DNA form. Figure 5 shows the time evolution of RMSD from the canonical A and B conformations. Each point in the figure corresponds to a 15 ps interval and shows an average RMSD value. We see that both trajectories approach the canonical B-DNA, while the RMSD... 

It appears that the mean chain length (L) in a state of equilibrium polymerization depends essentially on the geometry constraints for sufficiently small T>. In contrast to recent theoretical predictions [47], which treat the... 

The di- r-methane rearrangement is not confined to acyclic and mono-cyclic systems. Bicyclic 1,4-dienes such as barrelene (123) also rearrange, but they do so upon triplet sensitization (Zimmerman and Grunewald, 1966). In all probability, the built-in geometry constraint of a bicyclic molecule does not allow for the loose geometries otherwise characteristic of the triplet state, while in the singlet state other reactions such as [2 + 2] cycloaddition predominate. 

Fig. 4). Geometry constraints limit the 3-lobe design to a more shallow channel depth (lower OD/ID ratio) than 2-lobe units with identical centerline distances. This means that the 3-lobe machine can have a greater shaft diameter for power transmission, impose higher average shear rates on material, but have substantially less free volume. In practice, because of the low free volume relative to the available power, the 3-lobe extruder is often volume, i.e., rate, limited for many mixing tasks. 

Havel, Snow DISGEO/Co- None Distance geometry constraints... 

The last two terms are the orthogonality and geometry constraints. The Newton-Raphson equations derived from the Lagrangian (Eq. [96]) are given... 

Lagrange multipliers corresponding to energy, orthogonality, and geometry constraints, respectively. In the case of spin-forbidden reactions, the terms derived from in Eq. [96] should be neglected, and one should use the... 

Remark 10.9. Optimize the box-beam configuration with the objective of attaining maximum tip twist in consideration of the different actuation schemes while satisfying the stiffness and geometry constraints of Section 10.2.2. 

The objective function of this optimization problem is the evaluation of the twist solution, being given by Eq. (10.19) in conjunction with Eqs. (10.17) and (10.18), at the free end of the beam. For the constitutive coefficients appearing in the respective ratios, the relative layer thickness h of Eq. (10.27) is required besides the material properties and the particular actuation scheme configuration from Table 10.2. After introduction of the geometry constraints, specified in Eqs. (10.22) and (10.24), the tip twist may be found for any combination of the variables oi, 02, and u ... 

The physical condition of a Feature comprises a description in terms of such parameters as the geometry, constraints, etc. The behaviour of the Feature describes the performance, the responses to external actions, or the characteristics of its own actions. The function is the objectivity of the Feature to perform in the integrated structure under the influences of its environment or external actions. 

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