Elastic-energy correction

It is possible to make elastic scattering corrections to the algorithm (24) in the case of an Einstein phonon spectrum and purely local exciton-phonon coupling. If we calculate the energy of the polaron state at the value E ss nuio only the matrix elements 5 " should be considered in Eqs.(16). In this case... 

Recently, Sahimi and Arbabi (1996) have observed that the cumulative elastic energy released during fracturing of heterogeneous solids follows a power law variation with the strain e of the solid, having a log-periodic correction ... 

The determination of adhesive fracture toughness involves the measurement of a toughness term with elastic deformation corrections and subtracting from this energy term a contribution due to plastic deformation. Therefore, the relative size of the plastic deformation term will govern the accuracy of the adhesive fracture toughness. 

Melt Viscosity. The study of the viscosity of poljmier melts (47-62) is important for the manufacturer who must supply suitable materials and for the fabrication engineer who must select polymers and fabrication methods. Thus, melt viscosity as a fimction of temperature, pressure, rate of flow, and poljmier molecular weight and structure is of considerable practical importance. Polymer melts exhibit elastic as well as viscous properties. This is evident in the swell of the polymer melt upon emergence from an extrusion die, a behavior that results from the recovery of stored elastic energy plus normal stress effects. Theoretical developments include a constitutive equation that correctly captures nonlinear behavior in both elongation and shear (63,64). 

This nudged elastic band result was compared with other N diffusion paths and mechanisms, and was determined to have unmatched agreement with experimental results. It was also shown that careful consideration of total energy corrections and the use of a fully temperature-dependent diffusion pre-factor had modest but important effects upon the calculation of diffusivities for paired and interstitial N. N.Stoddard, P.Pichler, G.Duscher, W.Windl Physical Review Letters, 2005, 95[2], 025901... 

Thus, the elastic energy stored at the capillary entrance is related to ttie correction term by the following expression [65]. 

For such a network the elastic free energy is given by the front factor Eq. (26) at all temperatures while the front factor coincides with the cycle rank at the 0-temperature. Equation (12) is incorrect if the front factor is calculated for a set of chains, but if it is calculated for a set of normal modes with infinite relaxation time, then this factor is unity at T = 0 and its temperature dependence describes the temperature dependence of the elastic force correctly. 

Resilin and elastin, unlike other structural proteins, fulfill both definitions of an elastic material. Colloquially speaking, resilin and elastin are stretchy or flexible. They also fulfill the strict definition of an elastic material, i.e., the ability to deform in proportion to the magnitude of an applied stress without a loss of energy, and the recovery of the material to its original state when that stress is removed. Resilin and elastin are alone in the category of structural proteins (e.g., collagen, silk, etc.) in that they have the correct blend of physical properties that allow the proteins to fulfill both definitions of elasticity. Both proteins have high extensibility and combine that property with remarkable resilience [208]. 

The basic postulate of elementary molecular theories of rubber elasticity states that the elastic free energy of a network is equal to the sum of the elastic free energies of the individual chains. In this section, the elasticity of the single chain is discussed first, followed by the elementary theory of elasticity of a network. Corrections to the theory coming from intermolecular correlations, which are not accounted for in the elementary theory, are discussed separately. 

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