Hello Makhdoom, for me the term is also new.

You can write to the authors directly and then share with everyone.

Universality is defined on Wikipedia [ https://en.wikipedia.org/wiki/Universality_(dynamical_systems) ]:

... universality is the observation that there are properties for a large class of systems that are independent of the dynamical details of the system.

Here, it looks like the universality class is disordered media.

In paper 1 (on page 876), ac conductivity of the vast majority of disordered solids follows the power law [

https://en.wikipedia.org/wiki/Power_law#Universality ] of equation 4:

σ'(ω) ∝ ω^n

So it seems that "AC universality" is just the obervation that the ac conductivity for a large number of disordered solids follows the same behavior with frequency (i.e., equation 4).

In paper 1 (on page 885), the detailed definition they give is:

Universality refers to the fact that these [critical] exponents depend only on dimension and order-parameter symmetry, not on microscopic details.

It looks like they are implying that the critial exponent n in equation 4 can be varied, such that equation 4 can be universally used to fit the ac conductivity-frequency curve of many different disordered solids independent of other property differences of those solids (i.e., independent of microscopic details).

This is probably also why the equation

σ(ω) = σ_dc + A*ω^s

is called the "ac universality law" [ equation 9 in http://www.escm.eu.org/docs/eccm/C220.pdf ]

Ok, I know the universal law that you can find in the Jonscher's book (power law).

Dear Dr. Makhdoon:

In a similar way to the Dr. de la Torre, I also know the function w^s as Jonscher's law. In this case, concepts applied to ceramics with semiconducting features, ordered system.

Such Law is operational at high frequency domain, where dc conductivity cannot be highlighted; due in major part by the inertia of the carrier that is the electron.

Phenomena involved in high frequency domain are of type classified as short-range conductivity (the carrier is only  mobile on the short distances).

Typically in a double logarithmic plot, the electrical-conductivity Log (Sigma) is a linear function of angular frequency log (ogmega) or log (frequency).

From a plot Log (Sigma) versus log (f) is possible to derive the coefficient of inclination angular that is proportional to s.

The parameter s change in the range from 1 to zero. In my works, I had observed a decreasing of s parameter as a function of temperature, s decreases while temperature.

See, here, a complex event emerge. As can be observed in paper attached to question, there is clear and further mention of application of the  theory involving w^s for disordered system, in which can be modeled as having as further and major model of mechanism of conduction: the hopping mechanism.

In crystalline system, data are a bit more difficulty to model. Typically, in addition to the analysis and hypothesis at about s value, the model should be feasible to accommodate a kind of crystalline defect that provide further support to model and the set of parameters derived.

As a whole, the Jonscher’s law and its approach is not connected to small signal complex impedance or small signal impedance spectroscopy. I think that the impedance function has both real part and imaginary part interconnected via Laplace transform. Seems that such feature is lost with inclusion of the contribution of Jonscher’s. But, both approaches can be used in a coherent sequence if exist further model reaching up to defect chemistry.

kind regards

Marcos Nobre

Dear ALL,

Please find below the answer of the same question from the author : Dr. Dyre.

"In this context the term "universality" refers to the shape of the function sigma(omega) (conductivity as a function of frequency). Two different systems - or the same system at different temperatures - may have the same frequency-dependent conductivity, except for a scaling of frequency and conductivity. In other words, the idea is that one can write

 sigma(omega)= F(T) f(omega*tau(T))

 in which T is the temperature and tau a characteristic time. This is time-temperature superposition. But if the same function f() appears for many different systems, we speak about universality."

Thanks for sharing that.

Ok, that is different idea.

Thanks for sharing that.