Contour deformation

Purified solubilized bovine collagen is used as biomaterial for the treatment of soft tissue defects and has been used for the treatment of stress urinary incontinence since the late 1980s (1). Injected material precipitates at body temperature, forming a matrix allowing fibroblastic infiltration and formation of new tissue. It has been used for cosmetic purposes by injection in the dermis to correct scars and other contour deformities of the skin. 

S.L. Spear, H.B. Wilson, M.D. Lockwood, Fat injection to correct contour deformities in the reconstructed breast. Hast. Reconstr. Surg. 116 (2005)1300-1305. 

Of obvious importance to aircraft is the smoothness of exterior surfaces. Smooth aerodynamic surfaces reduce aerodynamic drag, resulting in higher airspeeds and increased efficiency. Mechanical fasteners, even countersunk flush fasteners, introduce disruptions in the airflow over the exterior surface. Even the slight deformation of thin sheets around fasteners produces drag. Adhesively bonded structure has no fasteners to disrupt airflow and is more capable of producing the smooth continuous contours that are so common on aircraft. 

Of course, the network strands cannot be stretched completely. Stretching ratios of 1.4 for PC [31, 90] and of 1.3 for epoxy polymers [37] have been reported. The chain contour length of the strands is an appropriate measure for a simple estimation of the number of strands that are stretched across the deformation zone. The chain contour length of the strands is assumed to be proportional to... 

Figure 2. L-alanine. Dynamic deformation density in the COO plane, (a) Model dynamic deformation density A Modei. (b) MaxEnt dynamic deformation density (Agj, (x)) map obtained with a non-uniform prior of spherical-valence shells. Map size 6.0A x 6.0A Contour levels from -1.0 to 1.0 eA 3, step 0.075 e A-f...

Figure 6. l-Alanine. Fit to noisy data. Calculation A. MaxEnt deformation density and error map in the COO- plane Map size, orientation and contouring levels as in Figure 2. (a) MaxEnt dynamic deformation density A uP. (b) Error map qME - Model. 

Figure 6(b) shows the difference between the MaxEnt valence density and the reference density, in the COO- plane. The error peaks in the bonding and lone-pair regions, where the deformation features are systematically lower than the reference map (negative contours). The deviation from the reference is largest in the region around the Cl atom valence shell, and reaches -0.406 e A 3. 

Figure 3. Static deformation density in Si-O-Si bridge planes Si,-0,-Si2 and Si,-O,o-Sij. Contours as in Figure 1.

Figure 6. Experimental deformation map for nitromalonamide. The contour interval is 0.1 e/A3. The dotted line is the zero contour. Solid lines are positive contours, broken lines are negative contours sinS/k < 0.7. The plane shown is the one spanned by the Ql)-O(l) and the C(l)-C(3) vectors. 

Figure 6.9 (a) Standard deformation density of tetrafluoroterephthalonitrile in the molecular plane. Contour interval is 0.1 e A-3, terminated at 1.5 e A 3. (b) Molecular diagram with a box around the fragment shown in the deformation map (a). (Reproduced with permission from F. L. Hirshfeld, Acta Crystallogr., B40, 613, 1984.)... 

Strain in dents may be estimated using data from deformation in-line inspection (ILI) tools or from direct measurement of the deformation contour. Direct measurement techniques may consist of any method capable of describing the depth and shape terms needed to estimate strain. The strain estimating techniques may differ depending on the type of data available. Interpolation or other mathematical techniques may be used to develop surface contour information from ILI or direct measurement data. Although a method for estimating strain is described herein, it is not intended to preclude the use of other strain estimating techniques. See also Fig. D-l. 

The orbitals of the second row can be hypothetically obtained from those of the first row by deforming the orbital around the benzene ring in a clockwise direction. If the orbital is moved even further in that direction, one can pass from the second row to the third row, and eventually from the third row to the fourth row. In fact, this transition from the first row to the last row is a continuous process, and there exist infinitely many sets of localized orbitals of intermediate character, only two of which have been indicated in the second and the third rows.s7) Again the first column contains the superimposed fifth strongest contours for each set of molecular orbitals (in the case of the orbitals of the third row the fifth strongest contour happens to divide up into two disconnected parts). 

The upper part of Fig. 26 (see p. 114/115) contains several examples of localized 7r orbitals of pure type 7t 2, the prototype being naphthalene. It is seen that, even in fairly asymmetric molecular situations, the localized orbitals are still of quite pure type 7r 2. Really strong asymmetry is seen in the two molecules at the bottom of the figure, which show orbitals of the type 7r 22. The type 7t 2 would result from type ir 2 if all the contours from the right side of the orbital were pushed over to the left side. On the last figure (see Fig. 27,p. 116/117), there are further examples of pure and deformed type 7r 2. It can be seen that in sufficiently asymmetric molecular situations this type of orbital, which extends over four minor atoms, can have quite irregular forms. 

The applied strain is affine and the whole of the tube is deformed along with the polymer. As the strain is infinitesimally small the contour length is unaltered. At very short times / after the strain is applied, t < re tr the stress is relaxed as a Rouse chain. At short times we can make an approximation and replace our sum by an integral ... 

Fig. 4. Two-angle fibers can be easily deformed via the bending and twisting of their linkers. This can be most easily seen for the special case of a planar zig-zag fiber under an external tension F, which extends the fiber via the bending of its linkers from its unperturbed state with contour length Lo (a) to a stretched state of length L>Lo (b).

Contour Length Relaxation. Doi and Edwards have proposed an additional, faster relaxation mechanism for which they use the term contour length relaxation (5). As shown in Figure 3, contour length relaxation is a process by which a deformed linear (or star shaped) chain should retract towards the center of mass of the chain. Since the overall contour length increases upon deformation, the proposal by Doi and Edwards is that the deformed chain would want to resume the same chain density along the overall contour of the chain as that... 

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