Low-frequency currents induced in adjacent spherical cells

The term “interior” in the case with a membrane of finite thickness defines the region occupied by the cell with the exclusion of the membrane. In the limit of vanishingly small membrane thickness the interior does not include the boundary; the rest of space, including the boundary, is the “exterior” of the cell.

As mentioned in the Introduction, elongated cells may be excluded from our analysis.

The issue of convergence of this expansion is not addressed in this paper. It is expected that the expansion converges for sufficiently small $rc∕ξ$⁠.

The perturbation order $n$ (subscript in expansion terms) should not be confused with the index $j$ in $Rj$⁠, $∂Rj$ and other symbols of this section; $j$ specifies individual cells.

$A=O(x1,x2,…,xN)$ as $x=(x1,x2,…,xN)→0$ means that $limx→0(A∕xk)=O(1)$ if $xj∕xk=O(1)$ for all $j,k=1,2,…,N$⁠.

The reason for considering two symmetrically located dipoles instead of one is the ensuing convenience of eliminating any residual constant for the potential $Φ$ in the limit $h→∞$⁠. Specifically, $Φ$ remains zero at the origin for any distance $h$ $(h>0)$⁠.