Twist distribution

Relaxed and supercoiled DNA. (a) Circular DNA is relaxed, (b) One strand is broken, unwound by four turns, and the ends are then rejoined.The strain of unwinding is localized in the nonhelical gap. (c) Supercoiling by four twists distributes the strain of unwinding uniformly over the entire molecule of circular DNA. 

The helicoidal periodicity of smectic C phases, due to the twisted distribution of the molecular tilt is not given by the half-pitch... 

The application of an electric field results in a change of the tilt and twist distribution within the cell. Figure 3 shows calculated curves of the tilt and twist distribution as a function of the reduced distance z/d through the layer, with 0reduced voltage Vth [17]. The change of tilt is strongest in the middle of the cell and changes from the value of the pretilt in the unactivated state to a maximum value of 90° in the fully activated state. The tilt distribution is symmetrical around the cell cen-... 

The reason total twist is of interest is that the twist distribution w s) at t = 0 resembles a constant plus sinusoid from floor to ceiling. This is the slowest-evolving eigenfunction of the partial differential equation used by Pertsov et al. [46] to model the evolution of twist, and as such it decays exponentially, everywhere by the same fixed fraction per unit time. Thus the total twist also decays by the same fraction per unit time, and it suffices to measure that fraction. (Except in the limits of long time and small twist, which seem not to apply to this experiment, this logic is spoiled if the initial conditions are not a single clean sinusoid or if the approximate dynamical equation is not right, as maintained by Keener [35] and Keener and Tyson [39]... but these are refinements for a later experiment.)... 

Many papers focus on ring spinning. For example, in Tang et al (2010a), a mathematical model and a numerical simulation to analyze dynamic behavior and twist distribution in a modified ring spinning system are described (Fig. 14.4). 

Figure 8-6. Comparison of the radial distribution function of the ctiair, boat, and twist conformations of cyclohexane (hydrogen atoms are not considered).

The stmcture of activated carbon is best described as a twisted network of defective carbon layer planes, cross-linked by aHphatic bridging groups (6). X-ray diffraction patterns of activated carbon reveal that it is nongraphitic, remaining amorphous because the randomly cross-linked network inhibits reordering of the stmcture even when heated to 3000°C (7). This property of activated carbon contributes to its most unique feature, namely, the highly developed and accessible internal pore stmcture. The surface area, dimensions, and distribution of the pores depend on the precursor and on the conditions of carbonization and activation. Pore sizes are classified (8) by the International Union of Pure and AppHed Chemistry (lUPAC) as micropores (pore width <2 nm), mesopores (pore width 2—50 nm), and macropores (pore width >50 nm) (see Adsorption). 

Figure 7.27. Twisted-blade type of static mixer operating in the laminar flow regime (a) Distributive mixing mechanism showing, in principle, the reduction in striation thickness produced (f>) Radial mixing contribution...

Katsumura, Kitaura and their coworkers [74] found and discussed the high reactivity of vinylic vs allylic hydrogen in the photosensitized reactions of twisted 1,3-dienes in terms of the interaction in the perepoxide structure. Yoshioka and coworkers [75] investigated the effects of solvent polarity on the product distribution in the reaction of singlet oxygen with enolic tautomers of 1,3-diketones and discussed the role of the perepoxide intermediate or the perepoxide-Uke transition state to explain their results. A recent review of the ene reactions of was based on the significant intervention of the perepoxide structure [76], which can be taken as a quasi-intermediate. 

As the triplet energy of the sensitizer becomes less than that necessary to excite either form of the butadiene (Et < 50 kcal/mole), it is proposed that energy is transferred via nonvertical excitation to lower energy twist forms of the diene triplets.(11> The product distribution again reflects the ground state population of s-cis and s-trans forms ... 

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