Bifurcated structure

The relaxed bifurcated structures, IB and IIB are 1.7 and 1.0 kcal/mole less stable than the optimal structures, IA and IIA. The crystal structures, are another 2.0 and 1.5 kcal./mole less stable than the bifurcated structures. 

The crystal structure can be rationalized by considering the influence of interactions with the neighboring chains. For I, II, and V, the bifurcated structure leaves the second amino hydrogen more available for interactions with a neighboring chain than the more energetically favored head-on dimer. The shortening of the hydrogen bond to the ortho substituent (in C vs. B-type structures) that is often apparent may also serve to bet-... 

Bifurcation structures are self-replicating patterns which serially branch channels until a multitude is reached. In this way, a main stream can be split into many substreams just relying on flow symmetry. These sub-streams can be contacted in an interdigital-type arrangement with the sub-streams of a second feed and then be guided into a main channel or into an inverse bifurcation structure. 

Temporal Development of Pattern. The solutions of this TDGL for the amplitude of the pattern are qualitatively as seen in Fig. 3h. Note that this dynamical pattern forming phenomenon is qualitatively different from the bifurcation structure of Fig. 3 when constraint parameters (here X) change on a time scale comparable to that of the growth of pattern. 

Fig. 2.9 Two-dimensional bifurcation diagram outlining the main bifurcation structure for the /3-cell model in the (Vs, ks) parameter plane. Notice the squid-shaped black region with chaotic dynamics. Vs characterizes the voltage dependence of the gating variable for the calcium conductance, and k is a measure of the ratio of the fast and the slow time scales.

E. Mosekilde, B. Lading, S. Yanchuk, and Y. Maistrenko Bifurcation structure of a model of bursting pancreatic cells. BioSys-tems 2001, 63 3-13. 

Fig. 12.9 Two-dimensional bifurcation diagram for the single-nephron model. The diagram illustrates the complicated bifurcation structure in the region of 1 1, 1 2, and 1 3 resonances between the arteriolar dynamics and the TGF-mediated oscillations. In the physiologically interesting regime around T = 16 s, another set of complicated period-doubling and saddle-node bifurcations occur. Here, we are operating close to the 1 4...

Tsuda, Ichiro, "On the abnormality of period doubling bifurcation in connection with the bifurcation structure in. the Belousov-Zhabotinsky reaction system", preprint (1981). 

The ubiquitous occurrence of water and its importance as a solvent medium have motivated a great deal of research into the fundamental nature of the interaction between water molecules by theoretical as well as experimental means. Some of the more recent work has been summarized in a review article. Prior to experimental elucidation of the geometry of the water dimer in the gas phase or to the ability of calculations to provide an unambiguous resolution to this question, a number of different candidate structures were considered. In addition to the standard linear arrangment wherein the bridging hydrogen lies near the O O axis in Fig. 2.8, cyclic and bifurcated structures were considered as illustrated in Fig. 2.9. 

Further examination by Marsden et al. of the namre of the bifurcated structure applied a basis set containing three sets of diffuse functions, along with a doubly polarized quadruple- valence set, amounting to 146 contracted Gaussians. These workers concluded that... 

The matrix isolation method was also applied to the study of the H bonding of water by Van Thiel et al. (2097). In solid nitrogen at 20°K the IR absorptions of dimeric water permit inferences concerning the structure of this species. Van Thiel et al. consider the possible structures shown in Fig. 3-16. The bifurcated structure was suggested by Errera, Gaspart, and Sack on the basis of IR spectra of H2O and HDO in dioxane solutions (614). Van Thiel et al. reject both the open and bifurcated structures for HjO dimer and conclude that a cyclic structure is formed (2097). 

Robbins, K. A. (1979) Periodic solutions and bifurcation structure at high r in the Lorenz system. SIAM J. Appl. Math. 36,457. 

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