Open chain dynamics

This equation implies perfect dynamical equivalence of all the chain atoms this is physically true only for the ring, whereas it is a model assumption in the periodic case. However, it should be noted that, apart from the first few collective modes, the periodic chain gives a good description of the open-chain dynamics and may be safely retained when investigating local chain motions, as suggested by Akcasu, Benmouna, and Han [81] and shown by us [82, 83]. The general solution of Eqn. (3.1.5) may be cast in the form... 

A number of other syntheses were discussed by Takeuchi and Furusaki and the most common involved reaction of hydroxylamine with selected a,/3-unsaturated ketones to give isoxazolidine-3- or -5-ols, which exist in equilibrium with an open-chain counterpart (77AHC(21)207). A similar equilibrium was observed in the reaction of a,/3-unsaturated ketones with N-hydroxyurea. The geometric orientation of the ring substituents was studied as a dynamic process (Scheme 158) (75TL2337). 

Niedzwiedzki, D., J. F. Koscielecki, H. Cong, J. O. Sullivan, G. N. Gibson, R. R. Birge, and H. A. Frank. 2007. Ultrafast dynamics and excited state spectra of open-chain carotenoids at room and low temperatures. J. Phys. Chem. B 111 5984-5998. 

As a model system PS-fc-PI exhibits a number of disadvantages The high Tg of polystyrene in conjunction with the thermal instability of PI results in a limited temperature range open for experiments. The chain dynamics of PS is often slow and sluggish, leading to uncertainties in the interpretation of kinetic data. 

Thermal decomposition of a doubly labelled azidotriazole gave rise to the open-chain triazine (117) in which the labels were not scrambled. Laser flash photolysis of the triazole leads to (117) within 20 ns with no observable intermediate. Ab initio calculations indicate that a dynamic equilibrium between the open-chain triazine (117) and a cyctic nitrene (118), as originally proposed, is highly disfavoured. 

This indeed verifies the dynamic kinetic resolution of roc-3 through enzymatic reduction, representing the first example for the dynamic kinetic resolution of an open-chain 2-alkyl-substituted 1,3-diketone through reduction under neutral conditions. 

Dynamic Kinetic Resolutions (DKR) are documented in the chemical literature [17, 18], and it was envisaged that such a system was, in theory, possible with the aryl-substituted morpholinols 2. The morpholinol ring system may exist, in part, as the open chain hydroxyl ketone (see Scheme 10.1), and it has been reported [19,... 

Computer simulation studies by Stillinger and Rahman (1974) suggest that the pentamer is the most likely structure to spontaneously arise in water at many temperatures, followed in frequency by hexamers, and squares. In a review of water, Frank (1970) noted that closed rings of bonds are always more stable than the most stable open chains of the same cluster number, due to the extra energy of the hydrogen bond. Through molecular dynamics studies of many five-molecule clusters, Plummer and Chen (1987) argued that the cyclic pentamer that comprises many hydrate cavities is the only stable five-member cluster above 230 K. 

The open-chain transform should be used when dealing with the overall size of the chain and, in dynamics, when separate consideration of the first, most collective modes of motion is required. In the following, the more expedient periodic-chain transform will generally be adopted unless specified otherwise. 

A small number of defects can also have a drastic effect on dynamics at low temperature, when the correlation length becomes very large. The problem of finite size scaling has been discussed by J.H. Luscombe et al. in the frame of the single-spin-flip Glauber model [30]. For an open chain of size L = na (with... 

Starting from a pyrimidine, sodium borohydride reduces the C=N bond in various 1,2,5,6-tetrahydropyrimidines to the hexahydro derivative <79RTC282>. Overreduction can be seen because C2 in the product, the hexahydropyrimidine, is an aminal carbon with the possibility for a dynamic equilibrium with imine and immonium forms which may be reduced to propane-1,3-diamines either by catalytic hydrogenation or by metal hydrides in the formation of an open-chain 1,3-diamine <67AJC1643, 68JA771>. 

Stepanenko, Y. and Vukobratovias M., Dynamics of articulated open-chain active mechanisms. Math. Biosci. 28 137-170,1976. 

Our interest is focused on the chemistry of molecular stannasiloxanes, and recently we have described a number of both cyclic and open-chain compounds with different silicon-to-tin ratios [3-6]. In this report we present the syntheses and structures of new stannasiloxane complexes and discuss their dynamic behaviour in solution. 

Previous research in the dynamic simulation of robotic mechanisms includes the examination of both open-chain mechanisms [2,3,12,42] and closed-chain configurations [4, 16, 22, 31, 33, 39]. Although many of these earli results are useful and impextant, further improvements in the computational efficiency of dynamic simulation algorithms are necessary for real-time implementation. 

In an attempt to circumvent the computational complexity of matrix inversion, some researchers are pursuing solutions for the joint accelerations which have a linear recursive form. The inversion of the in tia matrix is explicitly avoided. The resulting linear recursive algorithms have a reduced computational complexity which is 0(N). This is the second basic solution approach to the Direct Dynamics problem, and it has been rqjplied to serial open chains [3,7], single closed chains [22], and some more genoal multibody systems [4, 37]. It is believed that the structure of linear recursive algorithms may also facilitate their implementation on parallel computer systems. 

We will now extend the recursive articulated-body dynamic equations for an open chain to describe the dynamics of a chain which is constrained at the tip. For this task, we will refer again to Figure 4.3. Now, however, we will assume that f, the spatial force exerted by the tip, is nonzero. 

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