QuoteOriginally posted by: ppauperOK: the steady state heat conduction equation is Laplace's equation a steady system of point vortices satisfies this equation except at the vortices themselvesso....what's the interpretation of point vortices in 2D steady heat conduction ? a steady infinite heat source at isolated points ? or something else ?and we can go from Black-Scholes to heat conduction and vice versa, so what's the interpretation in finance ?any takers ?ppauper,I don't know what the equivalent of a vortex or a point heat/flow source is in finance. However, what I can add to your comments is that a vortex is generally associated with fluid flow. I'm not aware of anything in heat conduction that's analogous to a vortex. In classical fluid mechanics, there are two distinct uses for Laplace's equation. One is in reference to the stream function and the other to the potential function. The stream function is derived from the continuity equation for incompressible flows. The potential function, on the other hand, relates to inviscid, irrotational flows. In irrotational flows, both satisfy Laplace's equation.It is the potential function that you're probably referring to in relation to heat flow in heat conduction problems. In this case, the point flow source in fluid mechanics would be exactly equivalent to a point heat source in heat conduction. It is the "isotherm," or the line of constant temperature in heat conduction.
Last edited by rcohen
on May 3rd, 2007, 10:00 pm, edited 1 time in total.