Here S is referred to as the "scalar order parameter
," and n is the distinguished eigenvector.
The range of the order parameter
S can be calculated as follows :
With increasing of the order parameter
[q.sub.1] from 0.91, the fractional-order system enters into chaos by a series of period-doubling bifurcations.
The SC order parameter
is defined as the operator which measures the formation of singlet pairs of equal and opposite spins on neighboring sites.
(1) for constant volume V consists in expanding the order parameter
[PSI] in a basis of eigenfunctions of the corresponding linearized GL problem [10, 11, 16-18] and numerically evaluating the expansion coefficients which minimize the full nonlinear functional Eq.
The aforementioned [u.sub.j]([g.sub.j]) is considered the order degree of the order parameter
[g.sub.j] of the subsystems.
S is the magnitude of the order parameter
tensor [S.sub.[alpha][beta]] = S(T)[[n.sub.[alpha]][n.sub.[beta]] - [[delta].sub.[alpha][beta]]/3], where [n.sub.[alpha]] and [n.sub.[beta]] are the spatial components of the director axis unit vector.
Landau and Ginzburg established that the free energy of a superconductor near the semiconducting transition can be expressed in terms of an order parameter
.Asymptotic analysis indicates that an implication of thecomplexfractionalGinzburg-Landauequationisarenormalization of the transition temperature owing to the competing non-locality .
This present study suggests an alternative numerical implementation of the stabilization diagram that intends not to calculate the difference between consecutive modal order parameters
but to compare every modal order parameter
with all the other modal orders (see Figure 1).
Particularly, in , the authors have presented two ideas to extend the conventional Model Reference Adaptive Control (MRAC) by using fractional order parameter
adjustment rule and fractional reference model.