Crossover parameter

Mossbauer spectra. Since the formation of different hydrogen bonding networks is predetermined by the presence of these isomers, the spin crossover parameter can alter. 

Modification of Fe spin-crossover parameters through mechanical coupling with R La moieties containing different lanthanide ions. Indeed, minute distortions of the octahedral, or pseudo-octahedral, coordination environment of the d transition metal ion leads to sizeable changes in these parameters and/or in the thermal hysteresis loop (Kahn and Kodjovi, 1999). This study is coupled with the investigation of the electrochemical behavior of the MLn helicates (Fe V Fe" Co"/Co" Ru /Ru" and Os"/Os ). 

Figure 5.18. Distribution function of segment density f r) for the normalized end-to-end distance, r = hl h yf (o), and distribution function of segment density versu.s distance r, 47rr /(r) (6). Numbers at the curves relate to the crossover parameter C (C = 0 corresponds to a Gaussian chain, C oo corresponds to a self-avoiding walk) (Oono and Freed, 1982) [Reprinted with permission from Y.Oono, K.F.Fiwed. J. Phys. A Math. Gen. 15 (1982) I93I-I95U. Institute of Physics Publishing Ltd.]...

In the second order in e, the crossover parameter is defined as follows (Kholodenko and Freed, 1983 Douglas and Freed, 1984)... 

Douglas and Freed (1984) introduce and discuss several crossover parameters. In particular. 

The hydrodynamic quantities and their ratios have been calculated as functions of the crossover parameters and S ... 

Upon increasing distance from the critical point, this crossover model provides a continuous transformation from Ising-like behavior asymptotically close to the critical point to mean-field behavior far away from the critical point. Due to the critical fluctuations, the position of the actual critical temperature is shifted with respect to the mean-field critical temperature Tc. The critical temperature shift Tg = (Tc — Tc)/Tc can be estimated from different properties such as the inverse susceptibility or the order parameter. These different estimates of Tg are all proportional to a unique combination of the crossover parameters (rg uA /ct). The transformation is generally controlled by two physical parameters the coupling constant u and the ratio A/k or, equivalently, by the ratio of the correlation length over the microscopic characteristic length d-... 

For very large values of the cutoff A, the two crossover parameters u and A/k in the crossover equations collapse into a single one, uA/k, which is related to the Ginzburg criterion (36). It has been shown by Anisimov et aL [13] that the crossover theory, based on RG matching, yields a crossover behavior of the free energy similar to those based on the -expansion [21, 22] and on the field theory [23] for large A, i.e., when cutoff effects are neglected. 

Figure 4.26 Voltage-current curves of DMFC with equal stoichiometries of methanol and oxygen, (a) A = 2 indicated are the values of the crossover parameter / . (b) / = 0.333 indicated are the values of A.

Figure 4.27 Characteristic scale of the exponent /it and local current density at the inlet as a function of mean current density J for the indicated values of A. Crossover parameter = 0.333.

Figure 4.32 (a) Model polarization curves of DMFC for the indicated values of oxygen stoichiometry A° and A = 100. Shown is the dimensionless total voltage loss E as a function of the mean current density in a cell J. Crossover parameter / = 1, and the other parameters are the same as in Figure 4.29. (b) Experimental polarization curves of DMFC for the indicated values of oxygen stoichiometry A° and A A°. Diamonds—the points where the jumper forms. 

FIGURE 4.24 Polarization curves of the DMFC cathode ( — for th indicated crossover parameter. Parameters for calculations are listed in Table 4.1. The shapes of local parameters in Figures 4.25 and 4.26 correspond to the points (open circles) on the curve for = 0.3. 

Ratio of the net water flux to proton flux Crossover parameter. Equation 4.207 Crossover parameter. Equation 4.208 Dimensionless parameter. Equation 4.127 Dimensionless solution to Equation 4.163 Surface tension (J cm )... 

In light of the abnormal behavior of ultrasound velocity and attenuation near the SmA-SmC transition [70, 71], Benguigui and Martinoty [72] advanced a theory to explain the experimental data. They concluded that the Ginzburg crossover parameter Gq) determined by the static properties, (e.g. heat capacity) could be much smaller than that obtained from the measurement of the elastic constant. However, a quantitative comparison between the theoretical prediction and the experimental data is still lacking. 

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