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Parabolic relaxation function

Other choices are possible for the relaxation function r. For these choices, expressions similar to Eq. (19) may be derived. Although it is awkward to deal with the absolute value in Eq. (14), a parabolic form meeting the principal requirements is more readily expressed in Fourier space. A simple quadratic (Willson, 1973) and its generalization to other powers have been used by Blass and Halsey (1981) ... [Pg.107]

The subscripts have the same meaning as in (12.29), (12.30). Indeed, (12.29), (12.30) show that in the parabolic free energy function, the static free energy is the linear term with respect to Aq, while the relaxation free energy is the quadratic term. Thus,. A/l[A) and /L4[fxc are, respectively, the static and the relaxation free energies to insert a unit charge into the reactant state. [Pg.435]

As an example, we consider the multiphonon relaxation of a local mode caused by an anharmonic interaction with a narrow phonon band. We suppose that the mode is localized on an atom and take into account two diagonal elements of the Green function which stand for the contribution of two nearest atoms of the lattice to the interaction the non-diagonal elements are usually much smaller [16] and approximate the density of states of the phonon band by the parabolic distribution... [Pg.158]

With the liquid mobile phase off and the channel rotating at an appropriate speed, the sample mixture is injected into the channel. The channel is rotated in this mode for a relaxation or pre-equilibrium period that allows the particles to be forced towards the accumulation wall at approximately their sedimentation equilibrium position. Particles denser than the mobile phase are forced towards the outer wall. Diffusion opposite to that imposed by the centrifugal force causes the particles to establish a specific mean thickness near the accumulation wall as a function of particle mass. Liquid mobile phase is then restarted with a parabolic velocity front. Small particles are engaged by the faster moving central streamlines and are eluted first. Large particles near the wall are intercepted by the slower streamlines and are eluted later. Thus particles are eluted from the channel in order of increasing mass. [Pg.280]

Fig. 18 The evaluated interfacial relaxation, extracted from the data on s-polarized electroreflectance, as a function of electrode potential. The insert plots show schematically, the shape of the a(a) and do( Fig. 18 The evaluated interfacial relaxation, extracted from the data on s-polarized electroreflectance, as a function of electrode potential. The insert plots show schematically, the shape of the a(a) and do(<r)/dor curves for parabolic approximation (Eq. (62)).
Fig. 4.10. Relaxation time t of the twist fluctuation mode circles) as a function of sample thickness d. For thicknesses below 3 (im a parabolic behaviour is observed solid line) and in this range the anchoring coefficient can be determined. For larger thicknesses the influence of higher fluctuation modes becomes apparent and the relaxation time decreases and approaches its bulk value [32]. Fig. 4.10. Relaxation time t of the twist fluctuation mode circles) as a function of sample thickness d. For thicknesses below 3 (im a parabolic behaviour is observed solid line) and in this range the anchoring coefficient can be determined. For larger thicknesses the influence of higher fluctuation modes becomes apparent and the relaxation time decreases and approaches its bulk value [32].
The semi-infinite medium is employed to study the spatiotemporal patterns that the solution of the non-Fick damped wave diffusion and relaxation equation exhibits. This medium has been used in the study of Pick mass diffusion. The boundary conditions can be different kinds, such as constant wall concentration, constant wall flux (CWF), pulse injection, and convective, impervious, and exponential decay. The similarity or Boltzmann transformation worked out well in the case of the parabolic PDF, where an error function solution can be obtained in the transformed variable. The conditions at infinite width and zero time are the same. The conditions at zero distance from the surface and at infinite time are the same. [Pg.198]

Fig. 4.6 Orientational fluctuation relaxation time as a function of sample thickness for nematic liquid crystal 5CB on rubbed Nylon with strong anchoring at the boundaries. The squares are the measured data and the solid line best fit of the parabolic approximation. Reprinted with permission from [8]. Copyright by the American Physical Society... Fig. 4.6 Orientational fluctuation relaxation time as a function of sample thickness for nematic liquid crystal 5CB on rubbed Nylon with strong anchoring at the boundaries. The squares are the measured data and the solid line best fit of the parabolic approximation. Reprinted with permission from [8]. Copyright by the American Physical Society...

See other pages where Parabolic relaxation function is mentioned: [Pg.64]    [Pg.113]    [Pg.11]    [Pg.192]    [Pg.194]    [Pg.15]    [Pg.432]    [Pg.119]    [Pg.54]    [Pg.514]    [Pg.477]    [Pg.3378]    [Pg.62]    [Pg.111]    [Pg.1154]    [Pg.315]    [Pg.172]   
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