Volume-conserving mechanism

The hula twist mechanism (HT, Fig. 2.3B), first validated with carotenoids, is not consistent with the time-scale of photoisomerization of chromoproteins since CTI of the retinal chromophore, which is inserted deep inside the protein, necessitates a major reorganization of the peptide molecular framework. Therefore, a new volume-conserving mechanism, called bicyclic pedal (BP, Fig. 2.3C), was proposed. In fact, all these mechanisms are still a topic of discussion since chromoprotein photo-intermediates highlighted by recent studies do not confirm this hypothesis. In particular, several photo-products of the retinal Schiff base in the... 

A volume-conserving mechanism such as hula-twist (H-T) that requires a concomitant twisting of the double bond and the adjacent single bond to accomphsh the double-bond ds-trans isomerization, different from the usual one-bond rotation mechanism. 

Figure 4.10 cis-Xo-trans isomerization of c/s-C2 in diethyl ether-isopentane (1 1) at 77 K by a volume-conserving mechanism [38]. (Reproduced with permission.)... 

Warshel first postulated the bicycle-pedal (BP) mechanism as a volume-conserving mechanism for photoisomerization.In it, two alternating double bonds rotate concertedly with only the two CH units turning in and out of the plane of the molecule. 

The photoisomerization of all-s-trans-all-trans 1,3,5,7-octatetraene at 4.3 K illustrates the need for a new mechanism to explain the observed behavior [150]. Upon irradiation, all-s-trans-all-trans 1,3,5,7-octatetraene at 4.3 K undergoes conformational change from all-s-trans to 2-s-cis. Based on NEER principle (NonEquilibrium of Excited state Rotamers), that holds good in solution, the above transformation is not expected. NEER postulate and one bond flip mechanism allow only trans to cis conversion rotations of single bonds are prevented as the bond order between the original C C bonds increases in the excited state. However, the above simple photochemical reaction is explainable based on a hula-twist process. The free volume available for the all-s-trans-all-trans 1,3,5,7-octatetraene in the //-octane matrix at 4.3 K is very small and under such conditions, the only volume conserving process that this molecule can undergo is hula-twist at carbon-2. 

Several years ago, we found that the isomerization of n-butylammonium ( Z,Z)-muconate produces the corresponding EE-isomer in a high yield in the crystalline state under photoirradiation [41]. This solid-state photoisomerization was re e e< t0 he a one-way reaction and no EZ-isomer was formed during the reaction, unsaturated compounds such as olefins, polyenes, and azo compounds generally undergo reversible one-bonded photoisomerization to form a mixture of omers. Previously, we pointed out the possibility that the isomerization of the but thni(i er Va ves the s°hd state f°ll°ws the bicycle-pedal reaction mechanism, et al [4 eta s °ffhe molecular dynamics ofthe reaction had not been clarified. Saltiel react an< fl have independently discussed volume-conserving... 

Fletcher s example is of great importance. It is the clearest, simplest treatment of a situation where only one material moves, but moves by two separate mechanisms—a volume-conserving viscous change of shape plus a diffusive mass transfer from higher-compression sites to lower-compression sites. The two mechanisms resemble those operating in situation (1), the elastic permeable host plus mobile fluid Fletcher clearly brings to light the fact that the two movement mechanisms remain distinct even when the same material travels by them both. 

Three different photoisomerization mechanisms of singlet excited polyenes have been proposed (1) one-bond twist, a typical process observed in fluid solutions but also in glassy media,525 553 565 (2) the bicycle-pedal mechanism involving simultaneous rotation about two original double bonds, assumed to occur in a constraining environment,566-568 and (3) a volume-conserving two-bond hula twist 531 569 510 (Scheme 6.7). In some cases, the existence of the last mechanism has been ruled... 

Z-E isomerization via simple geometric inversion (one-bond flip, OBF, Fig. 2.3A) involves the torsional relaxation of the perpendicular excited state via an adiabatic mechanism which implies a non-volume-conserving process. This is not compatible with the ultrafast CTI in polyenes, in particular retinyl chromophores, and two other possible ways of photo-CTI have been proposed over the past 15 years [11]. 

According to molecular mechanics calculations the protein matrix of wild-type GFP forms a cavity around the chromophore that is complementary to an excited state conformation in which the phenol and imidazolidinone rings are perpendicular to each other - a conformation that was obtained by a concerted t and cp 45° HT [48]. Therefore even though an HT motion in wild-type GFP may not be more volume conserving than the cp-OBF, it still occurs as it is intrinsically favoured [49] and is complementary with the protein matrix surrounding the chromophore. Similar behavior has been proposed for PYP [13]. 

Fig. 4 Electro-opto-mechanical effect of a monodomain nematic gel observed (a) without polarizer and (b) with crossed polarizers. A 26-pm thick gel with = 4 mol% is placed in a 40-pm thick EO cell filled with a nematic solvent (5CB). The 5CB content in the gel is 82 vol%. An AC field (E) with an amplitude of 750 V and a fi equency of 1 kHz is imposed in the z-direcUon. The field induces a two-dimensional deformation, i.e., a shortening of ca. 20% in the r-direction, no dimensional change in the y-direction, and a lengthening of ca. 20% in the z-direction (due to volume conservation). The appearance of the gel (and surrounding 5CB) under cross-polarized conditions changes from bright to dark as a result of the almost full rotatirai of the director toward the field direction. A and P stand for the optical axes of analyzCT and polarizer, respectively. An mpeg movie is available in the supporting information of [31]...

In conclusion, we reiterate that the growth of precipitation tubes is readily affected by buoyant gas bubbles. In such situations, the tube radius is selected by the radius of the bubble and its growth velocity follows from simple volume conservation of the injected solution. Clearly, additional work is needed to unravel the detailed mechanism of bubble pinning to the nonequilibrium but steady reaction zone at the top region of the growing tube. 

If the assignments in Scheme 7 are correct, formation of the Tachy products involves rotations at adjacent double and single bonds, providing the first experimental verification of an outcome consistent with Liu s hula-twist mechanism for ds— trans photoisomerization. They have stimulated the recent resurrection of this mechanism with spedal attention to the key role of the volume-conserving requirements of the rigid medium. ... 

The criterion of maintaining equal power per unit volume has been commonly used for dupHcating dispersion qualities on the two scales of mixing. However, this criterion would be conservative if only dispersion homogeneity is desired. The scale-up criterion based on laminar shear mechanism (9) consists of constant > typical for suspension polymerization. The turbulence model gives constant tip speed %ND for scale-up. 

Macroscopic and Microscopic Balances Three postulates, regarded as laws of physics, are fundamental in fluid mechanics. These are conservation of mass, conservation of momentum, and con-servation of energy. In addition, two other postulates, conservation of moment of momentum (angular momentum) and the entropy inequality (second law of thermodynamics) have occasional use. The conservation principles may be applied either to material systems or to control volumes in space. Most often, control volumes are used. The control volumes may be either of finite or differential size, resulting in either algebraic or differential consei vation equations, respectively. These are often called macroscopic and microscopic balance equations. 

Coalescence Coalescence is the most difficult mechanism to model. It is easiest to write the population balance (Eq. 20-71) in terms of number distribution by volume n v) because granule volume is conserved in a coalescence event. The key parameter is the coalescence kernel or rate constant P(ti,i ). The kernel dictates the overall rate of coalescence, as well as the effect of granule size on coalescence... 

Similarly, contaminant concentrations in rivers or streams can be roughly assessed based on rate of contaminant introduction and dilution volumes. Estuary or impoundment concentration regimes are highly dependent on the transport mechanisms enumerated. Contaminants may be localized and remain concentrated or may disperse rapidly and become diluted to insignificant levels. The conservative approach is to conduct a more in-depth assessment and use model results or survey data as a basis for determining contaminant concentration levels. 

Conservation relations are used to derive mechanical stress-volume states from observed wave profiles. Once these states have been characterized through experiment or theory they may, in turn, predict wave profiles for the material in question. For the case of a well-defined shock front propagating at constant speed L/ to a constant pressure P and particle velocity level u, into a medium at rest at atmospheric pressure, with initial density, p, the conservation of momentum, mass, and energy leads to the following relations ... 

In contrast to dissipative dynamical systems, conservative systems preserve phase-space volumes and hence cannot display any attracting regions in phase space there can be no fixed points, no limit cycles and no strange attractors. There can nonetheless be chaotic motion in the sense that points along particular trajectories may show sensitivity to initial conditions. A familiar example of a conservative system from classical mechanics is that of a Hamiltonian system. 

The quote is from the third volume of Henri Poincare s New Methods of Celestial Mechanics, and is a description of his discovery of homoclinic orbits (see below) in the restricted three-body problem. It is also one of the earliest recorded formal observations that very complicated behavior may be found even in seemingly simple classical Hamiltonian systems. Although Hamiltonian (or conservative) chaos often involves fractal-like phase-space structures, the fractal character is of an altogether different kind from that arising in dissipative systems. An important common thread in the analysis of motion in either kind of dynamical system, however, is that of the stability of orbits. 

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