Non linear properties of Metamaterials

[Sana5643]

im having diificulty in solving Equations in this research paper
how ohms law has been witten in Eq (1)
how can we write microscopic form of ohms law for non linear meta materials?

[Dr Lots-o'watts]

Reactance X is proportional to frequency, cross-section and inductance : X = omegaSL. Impedance is Imp = R + iX.
Ohm's law is j = E/Imp.

Agree?

[Sana5643]

j = E / ( R + iωSL)
& by substituting
R = d /ơS
we get
j = EơS / ( d + iωơS2L)
but this is not the required relation ??vj = E / ( R + iωSL)
& by substituting
R = d /ơS
we get
j = EơS / ( d + iωơSSL)
but this is not the required relation ??

[Dr Lots-o'watts]

j=E/impeditivity

j=E/(rho + i X)

j=(sigma/sigma)E/(rho + iX)

j=E/(1 + i(sigma)X)

j=E/(1 + i(sigma)(wSL))

[Dr Lots-o'watts]

... I mean:

j=E/impeditivity

j=E/(rho + iX)

j=(sigma/sigma)E/(rho + iX)

j=sigmaE/(1 + i(sigma)(wSL)

[Sana5643]

i was using relation Z= R +i X with resistance 'R'
it means we can use Z= ρ + i X with resistivity 'ρ' as well

[Dr Lots-o'watts]

Impedance = resistance + i reactance.

multiplying by (cross-section/length) gives:

Impeditivity = resistivity + i reactivity.

(the units are different, so the symbols should also be, but except rho, I'm not sure what they are)

[Sana5643]

Thanks for helping me to understand form of Ohms law given in this paper