Free theory

The free theory for the quench models is provided by the potential (4), where A = 0 and m2(t) changes signs either instantaneously or for a finite period. In the Minkowski spacetime, we can apply the LvN method simply by letting R = 1. Before the phase transition (rrii = (mg + m2)1/2), all the modes are stable and oscillate around the true vacuum ... 

Fig. 8. Predictions of parameter-free theory for G"(co) and data for a star polybutadiene from [33]. Small shifts in the two prefactors bring the experiments and theory into quantitative agreement over five decades in timescale. Dilution exponent a=4/3 and Mg=1850...

Fig.9. Predictions of parameter-free theory for G (co) with 0(1) corrections to Gq and Tg as for Fig. 8 and data for a range of 3- and 4-arm star polyisoprenes from [5]. Arm molecular weights in 10 g mol are 11.4,17, 36.7,44,47.5, 95 and 105. The entanglement molecular weight has been taken as 5000 g mol" ...

Staddon, J. E. R., and Higa, J. J. (1998). Time and memory towards a pace-maker-free theory of interval timing. Manuscript submitted for publication. Stasko, J., and Lawrence, A. (1998). Empirically assessing algorithm animations as learning aids. In J. Stasko, J. Domingue, M. H. Brown, and B. A. Price (eds.), Software visualization (pp. 419-438). Cambridge MIT Press. 

Diglycidyl ether of Bisphenol A (DGEBA) is a stiff monomer and in the reaction with aromatic or even aliphatic diamines it exhibits a very low tendency to cyclization, so that the ring-free theory can be applied with success. This conclusion was derived from the fact that the critical conversion at the gel point was independent of dilution for DGEBA-diamine systems and that the critical conversions correspond to the ring-free modelThe same conclusion applies to DGEBA-dicarboxylic acids systems... 

In section 2 the theory of ensembles is reviewed. Section 3 summarizes the parameter-free theory of G par[ll]. The self-consistently determined ensemble a parameters of the ensemble Xa potential are presented. In section 4 spin-polarized calculations using several ground-state exchange-correlation potentials are discussed. In section 5 the w dependence of the ensemble a parameters is studied. It is emphasized that the excitation energy can not generally be calculated as a difference of the one-electron energies. The additional term should also be determined. Section 6 presents accurate... 

Milner, S. T., and McLeish, T. C. B., Parameter-free theory for stress relaxation in star polymers. Macromolecules, 30, 2159-2166 (1997). 

Gotoh (19) determined theoretically the solubilities of nonreacting gases in liquids from the free theory. 

This model can also be extended to further levels of librational motion, each with its own order parameter and correlation time, and has been underpinned more formally in the three-r case of two librational levels plus rotation [7]. It is clearly of a general nature. One may indeed choose to abandon relationship (4.23) and to re-interpret in (4.24) as a more general order parameter. One thereby achieves a model-free theory, which has advantages over alternative, more specific models for polymer motion (see chapter 6), when the motional details are not clear. 

Secondly, the exposition will be restricted to non-relativistic quantum mechanics, i.e. to the Schrodinger equation. This approach is justified, if we restrict ourselves to atoms of the first three rows of the periodic table, for which relativistic effects are generally unimportant. However, if we are interested in discussing properties, which include interactions with the spin of the electrons such as NMR and ESR couphng constants, the Schrodinger equation is not sufficient alone, because it is in principle a spin-free theory contrary to the Dirac equation. The necessary operators for the interaction with the electron spin are therefore derived from the Dirac equation and then added to the Schrodinger Hamiltonian in an ad hoc fashion. 

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