A. RESEARCH OBJECTIVESFinding the force of electromagnetic origin in a continuous medium is an old problem that has not been solved except in rather special cases. (An exception is the work of Meixner and his associates. -4) It involves the unification of two physical theoriescontinuum mechanics and electromagnetism.Since nonrelativistic mechanics is not, in general, compatible with electromagnetism, relativistic mechanics must be used.The relativistic theory of continuum mechanics (without electromagnetic fields) is fairly well understood, at least insofar as its basic equations are concerned. Electromagnetism in stationary bodies is also fairly well understood.To unite the two theories, the effect of each upon the other must be calculated. The study of the effect of mechanical motion and deformation upon electromagnetism is known as "electromagnetism of moving media," and there are several theories that 5 are formally different but lead to the same physical predictions.The inverse problem, finding the effects of the electromagnetic fields upon the mechanical equations, has never been solved adequately, and it is this problem that we wish to discuss now.The fundamental equations of relativistic continuum mechanics are: (1) Newton's Law, which, in its simplest form, is expressed aswhere n is the number of particles per unit volume, m the relativistic mass per particle, V the velocity, and fmech the force density, now of entirely mechanical origin; and (2) a specification of the way in which fmech is related to n, the strain, the strain rate or other kinematic variables. That is, the fundamental equations are Newton's Law, and the mechanical (and thermodynamic) constitutive relations of the material.The fundamental equations of electromagnetism of stationary bodies are Maxwell's equations, and relations among the field quantities, that is, electromagnetic constitutive relations of the material.It is instructive to consider how mechanical motion affects electromagnetism because the inverse problem, broadly speaking, is similar. Fundamentally, mechanical motion can affect electromagnetism in two ways. First, additional terms may enter, as source terms, into Maxwell's equations. Second, the constitutive relations may be altered in form.There is essentially only one theory of electromagnetism in free space, but, if materials are present, there are several, including (among others) the Minkowski QPR No. 70

In MOS integrated circuits, signals may propagate between stages with fanout. The HOS interconnect may be modeled by an RC tree, Exact calculation of signal delay through such networks is difficult.However, upper and lower bounds for delay that are computationally simple are presented here.The results can be used (I) to bound the delay, given the signal threshold; or (2) to bound the signal voltage, given a delay time; or (3) to certify that a circuit is "fast enough", given both the maximum delay and the voltage threshold.

A. RESEARCH OBJECTIVESFinding the force of electromagnetic origin in a continuous medium is an old problem that has not been solved except in rather special cases. (An exception is the work of Meixner and his associates. -4) It involves the unification of two physical theoriescontinuum mechanics and electromagnetism.Since nonrelativistic mechanics is not, in general, compatible with electromagnetism, relativistic mechanics must be used.The relativistic theory of continuum mechanics (without electromagnetic fields) is fairly well understood, at least insofar as its basic equations are concerned. Electromagnetism in stationary bodies is also fairly well understood.To unite the two theories, the effect of each upon the other must be calculated. The study of the effect of mechanical motion and deformation upon electromagnetism is known as "electromagnetism of moving media," and there are several theories that 5 are formally different but lead to the same physical predictions.The inverse problem, finding the effects of the electromagnetic fields upon the mechanical equations, has never been solved adequately, and it is this problem that we wish to discuss now.The fundamental equations of relativistic continuum mechanics are: (1) Newton's Law, which, in its simplest form, is expressed aswhere n is the number of particles per unit volume, m the relativistic mass per particle, V the velocity, and fmech the force density, now of entirely mechanical origin; and (2) a specification of the way in which fmech is related to n, the strain, the strain rate or other kinematic variables. That is, the fundamental equations are Newton's Law, and the mechanical (and thermodynamic) constitutive relations of the material.The fundamental equations of electromagnetism of stationary bodies are Maxwell's equations, and relations among the field quantities, that is, electromagnetic constitutive relations of the material.It is instructive to consider how mechanical motion affects electromagnetism because the inverse problem, broadly speaking, is similar. Fundamentally, mechanical motion can affect electromagnetism in two ways. First, additional terms may enter, as source terms, into Maxwell's equations. Second, the constitutive relations may be altered in form.There is essentially only one theory of electromagnetism in free space, but, if materials are present, there are several, including (among others) the Minkowski QPR No. 70

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