Order Parameter


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Order Parameter

In a nonlinear dynamic system, a variable-acting link a macrovariable, or combination of variables-that summarizes the individual variables that can affect a system. In a controlled experiment, involving thermal convection, for example, temperature can be a control parameter; in a large complex system, temperature can be an order parameter, because it summarizes the effect of the sun, air pressure, and other atmospheric variables. See: Control parameter.
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Here S is referred to as the "scalar order parameter," and n is the distinguished eigenvector.
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.
The true delay is set to D* = 3, the attenuation factor is [beta] = 0.9, the approximation order parameter is M = 10, the delay search range is [[D.sub.min],[D.sub.max]] = [-10,10], and the search step size is [DELTA]D = [10.sup.-3].
In this model, the superconducting order parameter has two components (real and imaginary) as a wave function corresponding to one condensed.
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 [2].
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 [25], 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.