  When inclusions with extreme conductivity (insulator or perfect conductor)
are closely located, the gradient of the solution to the conductivity equation
can be arbitrarily large. And computation of the gradient is extremely
challenging due to its nature of blow-up in a narrow region in between
inclusions. In this paper we characterize explicitly the singular term of the
solution when two circular inclusions with extreme conductivities are adjacent.
Moreover, we show through numerical computations that the characterization of
the singular term can be used efficiently for computation of the gradient in
the presence adjacent inclusions.
