Topological duality in threehyphen;dimensional eddyhyphen;current problems and its role in computerhyphen;aided problem formulation

摘要

When a region containing a threehyphen;dimensional magnetoquasistatic field is broken up into a nonconducting regionRand a conducting regionRc, which share a common boundary part;R, the Alexander duality theorem expresses a topological duality which induces a lumped parameter duality: The lsquo;lsquo;electromotive forcesrsquo;rsquo; inRcare related, via Faradayrsquo;s law, to the time rate of change of magnetic fluxes inRjust as the magnetomotive forces inRare related, via Amperersquo;s law, to the conduction currents inRc. From this vantage, cuts inRare surfaces used to calculate magnetic flux linkage while, in the zerohyphen;frequency limit, cuts inRcare surfaces used to calculate conduction currents. This paper shows how the formal description of the boundaries of the cuts and the topological interrelationship betweenRandRcyield insight into the generation of cuts inRwhich are related to a given set of currents or closed loop voltages inRc. We show how a computational treatment of lumped parameter aspects is possible.