Relationship between the stored energy density and intensity

Abstract

A model of a complex, composed of coupled one‐dimensional dynamic systems, is proposed. An analytical procedure is presented that yields the steady‐state stored energy density vector ε(x) = {εj(xj)} and the net power flow vector ι(x) = {ιj(xj)}, where εj(xj), ιj(xj), and xj are the stored energy density, the net power flow, and an observation position in the (j)th dynamic system, respectively. Under appropriate averagings and assumptions, the equation that describes the stored energy vector can be reduced to the central equation in the statistical energy analysis. On the other hand, the net power flow vector is the intensity. Using the analysis, one may argue that there could exist special situations in which some corresponding elements in ε(x) and ι(x) provide substantially identical information. However, in general, the two quantities are supplemental in the investigation of the energetics of a complex. Notwithstanding that, situations may arise in which the information provided by one or the other quantity may be deemed the more significant in seeking answers to specific questions.