Calculation of strong-field magnetoresistance in some periodic composites

Magnetotransport in a periodic composite medium: New phenomena in a classical physics context

“…This means that we can calculate J 2 z from a knowledge of J z , leading to the following result for the bulk effective longitudinal resistivity at the points (minima) where it is saturated: 11) where p ac is the (active) volume fraction of the current-carrying slabs. When B and J are along the (100)-like directions, we have p ac = 1 − 2a (a is the cylinder radius, 1 is the edge length of the square unit cell), and this leads to reasonable agreement of (2.11) with the values of ρ (e) /ρ (2) 0 at the saturated minima in those directions-see Figs 5B, E, and H. In the directions of the other minima, p ac has smaller values-those are consistent with the larger values of ρ (e) /ρ (2) 0 at those minima, some of which are unsaturated (i.e., (2.11) then provides an upper bound on the actual value at the minimum). We note that a strict step-function structure of J z , as described here, is of course inconsistent with J y ≡ J x ≡ 0 for any finite value of H .…”

Induced anisotropic magneto-resistance in a composite medium with a periodic microstructure: numerical results and exact relations

“…Therefore, if the ssystem is a conductor/perfect insulator mixture, then msystem will be (according to above expression for # m ð1Þ ) a normal conductor/perfect conductor mixture with the same columnar microstructure. Relations (1) and (2) in terms of components of the 3D resistivity tensor now become [2] (note that r ðeÞ jj and * r ðeÞ > denote the in-plane components of # r e along the directions parallel and perpendicular to the planar component of B; respectively, while H is the Hall-to-Ohmic resistivity ratio [3]) …”

On the effective conductivity of the magnetized bounded partially ionized plasma with random irregularities

“…A special case of two-phase systems with periodical inclusions has been considered by Bergman and Strelniker [20] and Tornow et al [21]. They predicted an effect of the strong anisotropy of the conductivity in the strong magnetic field.…”

“…Such a statement for σ eff ik is valid assuming the following: (1) the free path of the current carriers should be significantly less than the scale length of inclusions; and (2) the characteristic frequency of variation of the applied electric field is small compared to the longitudinal conductivity σ 0 (along the ambient magnetic field) and to the dispersion frequency of the conductivity (is an order of collision frequency of charge carriers with neutrals). The first condition enables us to use local Ohm's law (19) and the second one to use steady Maxwell's equations (20).…”