Deformation energies

The above formula for H(x) contains three different terms which correspond to the bending energy of the plate, to the deformation energy of the midsurface, and to the work of the exterior force /, respectively. Also, we introduce the set of admissible displacements... 

The cross section of the collision region that the particle impacts with the Si surface with an incident angle of 45° at a speed of 2,100 m/s is shown in Fig. 16 [28]. As the particle impacts into the Si surface layer, the contact region of the Si surface layer transforms from crystal into amorphous phase immediately. The area of the depressed region and the thickness of the amorphous layer increase with the penetration depth of the particle (Figs. 16(a)-16(c)). After it reaches the deepest position, the particle then moves both upwards and rightwards, and some silicon atoms ahead of the particle are extruded out and result in a pileup of atoms. Then the released elastic deformation energy of the Si surface pushes... 

A crash test rig was developed to simulate the high loads on components in and on street vehicles in the case of a colhsion. It provides profiles of deformation, energy dissipation and retardation as a function of time. The effect of test velocity and temp, on the behaviour of PP foam (Neopolen P) samples of various density was examined. 2 refs. 

The discrepancies have to be attributed to differences in AGd, i.e. deformation energy to adjust the size of the preformed cavities to the cationic radii. It seems reasonable to assume a smaller cavity for monensin, because of its shorter skeleton and somewhat higher flexibility (fewer rings) as compared to nigericin. Thus, the differences in selectivity behavior of nigericin and monensin can qualitatively be accounted for. 

The deformation energy will be larger if the monomer geometry is substantially different in the complex than in the free monomer. We have encountered this in studies of HCO" (van Mourik and Dunning Jr.). Although the C-H bond is weak (the equilibrium bond dissociation energy, D, is approximately 8.2 kcal/mol (Berkowitz, private communication), the addition of H to CO has a pronounced effect on the CO distance. The CO distance in HCO" is calculated [CCSD(T)/aug-cc-pVQZ]tobe 1.2403 A, while it is 1.1318 A in a free CO molecule. 

The deformation energy increases rapidly if the CO molecule is distorted from its optimal distance (which is 1.1473 A for aug-cc-pVDZ) to the distance it has in HCO" (1.2552 A). on the other hand becomes more attractive with increasing CO... 

The convergence behavior of the corrected and uncorrected intramolecular r (HF) is very similar to ArHF (see previous section). The monomer deformation energies are small for this system as well. At the CCSD(T)/aug-cc-pVQZ level, AU (rA)+AUf (fb) is just 0.03 kcal/mol. However, as we have seen in the previous section, for systems in which the monomers are strongly distorted from their uncomplexed geometries the deformation energy can be significantly larger [see also (Xantheas, 1996)]. 

If the DNA is only slightly bent, as observed for the nucleosome-boimd DNA, then the required deformation energy is distributed over many base pairs. Tlie energy requirement per base pair is small and can easily be provided by the interaction energy with the protein. Furthermore, such bending displays little sequence specificty. 

Almost every biological solution of low viscosity [but also viscous biopolymers like xanthane and dilute solutions of long-chain polymers, e.g., carbox-ymethyl-cellulose (CMC), polyacrylamide (PAA), polyacrylnitrile (PAN), etc.] displays not only viscous but also viscoelastic flow behavior. These liquids are capable of storing a part of the deformation energy elastically and reversibly. They evade mechanical stress by contracting like rubber bands. This behavior causes a secondary flow that often runs contrary to the flow produced by mass forces (e.g., the liquid climbs the shaft of a stirrer, the so-called Weissenberg effect ). 

Calculated bond angles in general vary with conformation more so than do bond length due to the "softer" nature of their deformation energy functions,... 

The Maxwell construction would determine the condition of two phase coexistence or the points on the curves where the first-order phase change occurs [6,7]. It is the condition that the two phases have the same value of g or j d II = 0 from Eq. (2.6) at zero osmotic pressure, v2 and vx being the values of v in the two phases. However, this criterion is questionable in the case Kcritical point). This is because the shear deformation energy has not been taken into account in the above theory. See Sect. 8 for further comments on this aspect. 

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