Dimensionless parameter, crossover

It has been shown in [8] that the frequency dependence of the AC conductivity may exhibit a maximum at a frequency a> , whose position depends on the dimensionless parameter 4 = e y/(2K/o). Under standard conditions, A is of the order of unity and the crossover frequency C0c> co ,. It follows that in the entire frequency range of interest a <2Iq h), when specifying the states with energies gl, gy, one cannot disregard correlations between these energies. 

Note that single-particle oscillator strengths correspond to ca = 1. We thus conclude that interactions affect strongly the peak heights for u /Al 1, i.e., in the high frequency domain. In fact, even for an arbitrary relation between Ai and A2, the crossover between single-particle and many-body domains of the spectrum is governed by the dimensionless parameter... 

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 )... 

Here t =(T-T )/T ) is the reduced temperature with being the transition temperature. The coefficients a and c are usually positive constants. For a continuous SmA-SmC transition b>0 and for a first order one b<0. The special case, b = 0, is the mean-field tricritical point. Huang and Viner [55] proposed a dimensionless parameter tQ=b l(ac) to describe the crossover temperature between the mean-field tricritical region (111 1q) the ordinary mean-... 

K 01 0 4 lhody Tp S, t) X Xb Xc overlap volume iraction. laimensioniessi. d. overlap volume fraction for /9-solvents, [dimensionless], p. 172 semidilute-concentrated crossover volume fraction, [dimensionless], p. 180 crossover volume fraction in mean-field theory, [dimensionless], p. 181 probability for segment s to still be part of the tube at time t, [dimensionless], p. 405 Flory interaction parameter, [dimensionless], p. 142 Flory interaction parameter for a binodal, [dimensionless], p. 150 critical interaction parameter, [dimensionless], p. 152 Florv interaction oarameter for a soinodal. 

The crossover equation contains the parameters Ct Cp, iZ, and A, but with two constrains (aq = 6 and uq = 9) imposed by the classical van der Waals equation. Hence, there still remain two microscopic parameters that cannot be specified on the basis of the classical equation the parameter A, which represents a microscopic cutoff wave number made dimensionless by dividing with and the parameter q = which is inversely... 

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. 

The limits of high salt and low salt have been addressed in Seetions 4.1.1 and 4.1.2, respeetively. In experiments, the salt coneentrations are not neeessarily in sueh extreme limits. Similarly, the dimensionless exeluded volume parameter wVn and the electrostatic excluded volume parameter defined in Equation 4.40 can assume intermediate values, instead of being either zero or very large. The crossover formula for the free energy that recovers the limits of Equations 4.30 and 4.38 is (Muthukumar 1987)... 

---