Multiple relaxation method

Hudock et al. [126] used the ab initio molecular dynamics multiple spawning method to go beyond the static picture based on PES and include the time dependent dynamical behavior and predict time-resolved photoelectron spectroscopy results. According to these results the first ultrafast component of the photoelectron spectra of uracil corresponds to relaxation on the S2 minimum rather than nonadiabatic transitions to the Si state. The authors suggest that the radiationless relaxation from... 

Termination rate coefficients can be measured using the y-radiolysis relaxation method. This involves initiation using y-radiation, followed by removal of the reaction vessel from the y-source. Conversion during the relaxation period is monitored by dilatometry, and the decay in polymerization rate over time is related to the rate of radical loss. When large particles are used, radical loss is dominated by intraparticle termination, rather than exit into the aqueous phase, and the rate coefficient for termination can be determined from the decay curve. By using multiple insertions and removals, the termination rate coefficient is determined over a wide range of polymer mass fraction (wp). 

Q. Zheng, D. J. Kyle. Accuracy and reliability of the scaling-relaxation method for loop closure An evaluation based on extensive and multiple copy conformational samplings. Proteins. 1996, 24, 209-217. 

This aspect was addressed in a model developed by Kovacs et al. [1979], which assumed that aging involves a distribution of relaxation times with multiple relaxation processes and that each relaxation time depends on the temperature and the glass structure. The model does not attempt to curve-fit the heat capacity data but, instead, uses a peak shift method [Hutchinson, 1992], which removes the need to assume a particular distribution of relaxation times. 

Abstract Among the noncontinuum-based computational techniques, the lattice Boltzman method (LBM) has received considerable attention recently. In this chapter, we will briefly present the main elements of the LBM, which has evolved as a minimal kinetic method for fluid dynamics, focusing in particular, on multiphase flow modeling. We will then discuss some of its recent developments based on the multiple-relaxation-time formulation and consistent discretizatirai strategies for enhanced numerical stability, high viscosity contrasts, and density ratios for simulation of interfacial instabilities and multiphase flow problems. As examples, numerical investigations of drop collisions, jet break-up, and drop impact on walls will be presented. We will also outline some future directions for further development of the LBM for applications related to interfacial instabilities and sprays. 

Several methods have been described for using 3D NOESY-NOESY cross-peak intensities for structural refinement such as the two-spin approximation (4,5), Taylor series expansion of the NOE-rate equation (6), and direct gradient refinement method (7). The two-spin approximation requires that the NOESY derived distances be obtained from vanishingly short experimental mixing times where the build-up of NOE intensity is linear with respect to interproton distance and the effect of spin diffusion (NOE intensity mediated by multiple relaxation pathways) are minimal. 

The multiple relaxations in PEBA copolymers have been studied by dynamic mechanical measurements, dielectric measurements, and thermally stimulated current methods [4-7,12,13]. These relaxation methods, in accordance with... 

Faruque H S and Lacabanne C ( 1986) Study of multiple relaxations in PEBAX, polyether block amide (PA12 2135 block PTMG 2032) copolymer using the thermally stimulated current method. Polymer 27 527-531. ... 

The GUPL equation includes the possibility of multiple relaxations characterized by a different fractional contribution fi. The application of BDS methods up to 1 GHz allows us to measure directly the ionic and segmental relaxation phenomena. These measurements yield the complex permittivity e (co) and the complex conductivity a (co). The latter two functions are complementary, as shown in equations 6.5 (Furukawa et al, 1997 Di Noto, 2002) ... 

Aniansson and Wall (A-W) appear to be the first to develop a relatively more accurate and convincing kinetic model for micellization in conjunction with the multiple-equilibrium reaction scheme as shown by Equation 1.20. - The superiority of the A-W model over the others is that it predicts the presence of two discrete relaxation times (Xj and Xj) during the course of micelle formation in the aqueous solutions of a single surfactant above CMC — a fact revealed by many experimental observations in related studies. Although this model successfully predicts the presence of two discrete relaxation times, it is not fully tested in terms of (1) reproducibility of kinetic parameters derived from this model by using various chemical relaxation methods, and (2) kinetic parameters obtained from both relaxation times x, and Xj have reasonably acceptable values. 

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