Quasi-elastic approximation

One theory which has been successfully applied to the magnetic properties of R-compound alloys containing non-S-state R-ions is the theory of random magnetic anisotropy (RMA) of Harris et al. (1973). This has been used to calculate the magnetoresistivity of amorphous alloys exhibiting RMA. Bhat-tacharjee and Coqblin (1979) first obtained the static spin-spin correlation function of the RMA model by using a self-consistent two-spin cluster approximation. The quasi-elastic approximation of de Gennes and Friedel is then... 

An approximate method to analyze viscoelastic problems has been outlined by Schap-ery.(30) jn this method, the solution to a viscoelastic problem is approximated by a correspond ing elasticity solution wherein the elastic constants have been replaced by time-dependent creep or relaxation functions. The method may be applied to linear as well as nonlinear problems. Weitsman D used Schapery s quasi-elastic approximation to investigate the effects of nonlinear viscoelasticity on load transfer in a symmetric double lap joint. By introducing a stress-dependent shift factor, he observed that the enhanced creep causes shear stress relief near the edges of the adhesive joint. 

The average over the beam, in our quasi-elastic approximation, gives (SX) = 0, and so... 

When the quasi-elastic method is used, the viscoelastic resultant moment can be approximated by substituting the time-dependent stiffnesses for elastic stiffnesses in Equation 8.30 and making use of the convolution integral. The resulting moments are... 

The superscripts Q stands here for quasi-elastic scattering, and the subscript pre means the pre-average approximation. 

We investigate here the dynamic behavior of fully charged NaPSS solutions with multivalent salt (LaCl3) measured by quasi-elastic light scattering. The bimodal decay of the correlation function of polyelectrolyte concentration (C) at constant salt concentration (Cs) is studied first. The ratio Cs/C varies from 0.2 to 10 2. Then the dynamics of the solution at constant C as a function of Cs from Cs/C approximately 10 2 to 0.2 are investigated. 

Using real values, it is easy to make sure that at a quasi-elastic impact (0.005bubble surface (a=4) the values of h. at 2ap = 100 pm they are approximately... 

Here J,(r) refers to the recoverable compliance, and the subscript e indicates that while the energy is stored reversibly, in a quasi-elastic system, the response is time dependent. One serious oversimplification of this expression is that it presumes that all volume elements experience the same deformation history, which is clearly not the case. Nevertheless, Equation (14.3) serves as a useful starting point for an approximate viscoelastic model. 

Coherent quasi-elastic neutron scattering due to the pair-correlation of atomic motions is more complex than incoherent scattering from single particle motion. Therefore, the theory of coherent scattering function is not yet fully developed. However, approximate expressions for the coherent scattering function exist (incoherent approximation). 

Note that Young s formulation impUes that the soUd is nondeformable and insoluble, so that only the horizontal projection of the tensions is considered. Assuming three tension forces act upon the triple hne from the directions of the three phases, the balance of the horizontal projection of these forces leads to Eq. (1). As far as the vertical component of the force, it is balanced by the elastic response of the soUd surface. This is a vahd assumption for the thermodynamic equiUbrium (the quasi-thermodynamic approximation). If the system is not at eqitihbrium, the tensile stress, caused by the vertical component, would locally increase the chemical potential of the system, so that the material can dissolve and change its shape. ... 

---