Butterfly shape

This plastic deformation is localised around the crack tip and is present in all stressed engineering materials at normal temperatures. The shape and size of this plastic zone can be calculated using Westergaards analysis. The plastic zone has a characteristic butterfly shape (Fig. 8.83). There are two sizes of plastic zone. One is associated with plane stress conditions, e.g. thin sections of materials, and the other with plane strain conditions in thick sections-this zone is smaller than found under plane stress. 

A structural variation shows the borido cluster d HFe4(CO),2(Et3PAu)2B, where the B atom is within bonding contact of all six metal atoms and the two Au atoms symmetrically bridge the wingtips of the butterfly-shaped complex ... 

The thyroid gland is a butterfly-shaped structure lying over the ventral surface of the trachea just below the larynx. This gland produces two classes of hormones synthesized by two distinct cell types ... 

The equivalent of the tryptic fragment of human transferrin receptor has been expressed in Chinese hamster ovary cells and its structure determined at a resolution of 0.32 nm (Lawrence et ah, 1999). The asymmetric unit of the crystals contains four transferrin receptor dimers. Interpretable electron density is found for the entire tryptic fragment except for Arg-121 at the amino terminus, and density is also seen for the first N-acetylglucosamine residue at each of the N-glycosylation sites. The transferrin receptor monomer is made up of three distinct domains, organized such that the dimer is butterfly shaped (Figure 5.10, Plate 7). The likely orientation of the dimer with respect to the plasma membrane has been assigned on the basis of the... 

In the course of investigation of potential antitumor compounds, the triazolobenzodithiazine derivative 37 seemed of special interest (Scheme 4). As no unambiguous proof could be provided by spectroscopic data (cf. Section 11.19.6.) X-Ray analysis of the crystalline product has been carried out <2003BMC1259>. The results revealed that in crystals the molecules formed centrosymmetric dimers by the help of weak NH- N hydrogen bonds. Because of the conformation of the central six-membered ring, the tricyclic molecule had a butterfly shape. 

Tetraalkyl-9,10-dihydrodistannaanthracenes 4 have been prepared via the lithiation73 or the magnesiation of 1,2-dibromobenzene,166 followed by reaction with R2SnCl2. The tetramethyl derivative is butterfly shaped with a dihedral angle of 142°, but the tetra-/-butyl derivative is planar.73 The stannepin 5 and stannolane 6 were obtained as byproducts of the former reaction. 

The short program Lorenz.m calculates the concentrations for A, B and C for the initial conditions. c0=[l l 20]. Figure 3-37 displays the trajectories in a fashion that is not common in chemical kinetics. It is a plot of the time evolution of the values of A vs. B vs. C (see also Figure 3-35). Most readers will recognise the characteristic butterfly shape of the trajectory. The important aspect is that, in contrast to Figure 3-35, the trajectory is different each time. This time, it is not the effect of numerical errors but an essential aspect of the outcome. Even if the starting values for A, B and C are away from the butterfly , the trajectory moves quickly into it it is attracted by it and thus the name, Lorenz attractor. 

Fig. 5.5. Factors influencing the reactivity of the f-lactam bond a) amide resonance, and b) the nonplanar butterfly shape of penicillins...

Silicon tetrafluoride is tetrahedral but SF4 has a see-saw or butterfly shape. Carry out the VSEPR predictions of these shapes. Consider the MO treatment of SiF4 as a o-only case, by using Figure 6.3. Decide if the distortion of a tetrahedral SF4 to the C,v symmetry is consistent with the HOMO/LUMO stabilization rule, discussed in Chapters 5 and 6. 

Addition of galactomannan to agarose-water systems profoundly alters the optical rotation behavior. Thus, both in the absence and presence of locust-bean gum, there is, below 35°, a sharp shift in optical rotation. However, these shifts are opposite in sign, as shown in Fig. 6. The reheating curves also differ, in that, when locust-bean gum is present, a butterfly-shaped hysteresis curve is obtained.40... 

The analogous selenium and tellurium chemistry has not been explored. The [Tl2Te2]2-anion has been obtained by reacting KTITe with [2.2.2]cryptate in ethylenediamine to give [K([2.2.2]crypt)]2[Tl2Te2]2- en, in which the anion is butterfly-shaped with a 50° fold.328 The assignment of oxidation numbers is somewhat arbitrary in such systems (cf. Section 25.2.6.1.2), but it seems clear that thallium is in a low oxidation state. 

This reaction is reversible by treating 5 with methanol to regenerate 4. The molecule (Fig. 6) comprises an open butterfly shaped Fe4C core, with three terminal carbonyls bound to each iron atom. The thirteenth carbonyl bridges the two iron atoms, which make up the backbone of the butterfly. Details of the structure are described below in comparison with other members of this family. 

An alternative explanation of the observed turbidity in PS/DOP solutions has recently been suggested simultaneously by Helfand and Fredrickson [92] and Onuki [93] and argues that the application of flow actually induces enhanced concentration fluctuations, as derived in section 7.1.7. This approach leads to an explicit prediction of the structure factor, once the constitutive equation for the liquid is selected. Complex, butterfly-shaped scattering patterns are predicted, with the wings of the butterfly oriented parallel to the principal strain axes in the flow. Since the structure factor is the Fourier transform of the autocorrelation function of concentration fluctuations, this suggests that the fluctuations grow along directions perpendicular to these axes. 

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