By J.T. Oden
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Extra resources for Computational Mechanics
12. Plateau value fq=0 of CKN as function of temperature T measured by impulsive-stimulated-light-scattering spectroscopy for the small wave numbers q indicated. The√ full lines exhibit the functions: fq=0 − const. for T > Tc , fq=0 – const. ∝ Tc − T for T < Tc , where Tc ≈ 378 K. 235 µm−1 . Reproduced from Yang and Nelson (1996). The plateau value increases by about 15% upon decreasing√ T . This increase can be described by a square-root law: f (T ) − f (T = Tc ) ∝ Tc − T , T < Tc , as is shown by the lines.
75. 70 requires an increase of t by more than a factor 70. This variation of φ(t) is stretched so much that it cannot be exhibited adequately on a linear t axis. The relaxation curves for the two lowest temperatures, which are shown in Fig. 7, demonstrate that the φ(t) versus log(t) curves for t ∼ tcr become ﬂatter if T decreases. Let us deﬁne a plateau region t− ≤ t ≤ t+ by the request that the decay function deviates from f by less than some positive margin , |φ(t± )/φ(t = 0) − f | = . 22 Glassy dynamics of liquids The mentioned ﬁgures suggest that log(t+ /t− ) increases upon lowering T .
These general properties of susceptibilities are discussed in Chapter 2. The mentioned increase of 0 is due to that of the static susceptibility χs = χ(ω = 0) = χ (ω = 0). The latter varies according to a Curie–Weiss law, χs ∝ 1/[T − T0 ], T0 ≈ 100 K, as is shown in the right inset of the lower panel. The full lines in Fig. 14 show simultaneous ﬁts of (ν) and (ν) within the low-frequency-loss-peak region by the Cole–Davidson expression for χ(ω). The ﬁt describes (ν) very well. , the weight factor χs f accounts for not less than 95% of the spectral weight.
Computational Mechanics by J.T. Oden