Rescaling stretching

Fig. 7.17 Time evolution of the nuclear forward scattering for metallic Ni foil. All measurements except for the upper curve were performed with external magnetic field B = 4 T. The solid lines show the fit. The arrows emphasize stretching of the dynamical beat structure by the applied magnetic field. The data at times below 14.6 ns had to be rescaled (from [34])...

Muzzio, Swanson, and Ottino (1991a) demonstrated that the distribution of stretching values in a globally chaotic flow approaches a log-normal distribution at large n A log-log graph of the computed distribution approaches a parabolic shape (Fig. 8a) as required for a log-normal distribution. Furthermore, as n increases, an increasing portion of the curves in the figure (Fig. 8b) overlap when the distribution is rescaled as... 

Fig. 25. Drop size distributions f(V,p)] based on drop volume (V) obtained by repeated stretching and breakup in a journal bearing flow for different viscosity ratios (p) (left). The curves for the different distributions overlap when the distribution is rescaled (right) (Muzzio, Tjahjadi, and Ottino, 1991).

Fig. 4 a Mean-field result (solid line) for the rescaled brush free energy per polymer as a function of the inverse interaction parameter 1/F- The infinite stretching resnlt is indicated by a horizontal dotted line, the broken straight line denotes the infinite stretching result with the leading correction dne to the finite end-point distribntion entropy. b Rescaled lateral pressnre within mean-field theory (solid line) compared with the asymptotic infinite-stretching result (dotted line)... 

Fig. 5 Left Mean-field results for the rescaled averaged polymer paths which end at a certain distance Ze from the wall for (S = I, 10, 100 (from top to bottom), corresponding to stretching values of y = 1.1, 1.9, 5.6 (as defined in Eq. 18). The thick solid line shows the unconstrained mean path obtained by averaging over all end-point positions. Note that the end-point stretching is small but finite for all finite stretching parameters p. Right End-point distributions...

Figure 6 shows the behavior of the reduced monomer density p z)Rp/Np at increasing anchoring density. The stretching of the chains with increasing surface coverage, which is due to the repulsion between monomers, is evident. This plot has to be compared with Fig. 3b, where the same type of rescaling has been used. However, note that at this point, direct and quantitative comparison is not possible, since it is a priori not clear which value of the interaction parameter /3 in the self-consistent calculation corresponds to which set of simulation parameters ct, N, pa. 

If diffusion of the inhibitor is absent and diffusion constants Di and Dzu of the activator do not depend on the variables u and v, the anisotropy can be effectively eliminated. By introducing the rescaled coordinate x — x/A where A = (D uf DzuY we make diffusion isotropic with the diffusion constant Di . Therefore, any spatial pattern in such simple anisotropic media can be obtained by stretching the respective pattern in the isotropic medium along one of the coordinate axes (or, generally, along one of the two principal directions of the diffusion tensor). 

Fig. 2.16 Master plot obtained by rescaling the time and intensity axes of the HD-OKE signals. The inset shows the temperature dependence of the water relaxation times, obtained by the fit of HD-OKE signal decays with the time-derivative of the stretched exponential function...

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