Analog Representation of Poisson's Equation in Two Dimensions

A new analog device, called a Poisson cell, has been developed which aids in obtaining solutions to either Laplace's equation or Poisson's equation. The cell may be used to simulate such potentials as electric potential, magnetic potential, gravitational potential, and the velocity potential of irrotational flow; it has applications in the fields of hydrodynamics, heat conduction, and aerodynamics. The cell is a solid volume-conducting medium made from a homogeneous mixture of hydrostone and graphite. Electrode configurations may be painted on the surface with conducting paint or imbedded directly in the structure. In the case of Poisson's equation, where ∇2ø(x, y) = f(x, y), the function f(x, y) is simulated by injecting currents into the underside of the cell. The application of the Poisson cell to numerous problems and in particular to problems in electron flow is discussed m detail, along with the incorporation of the cell into either an analog computer system or a combined analog-digital computer system.