The classical maximum um principle for finite linear resistive networks asserts that every node voltage in a sourceless subnetwork is no greater (resp. no less) than the maximum (resp. minimum) node voltage at the boundary nodes of the subnetwork. A related result is that the absolute value of every branch current in the sourceless subnetwork is no greater than the sum of the absolute values of all the currents in all branch cuts within the subnetwork at the boundary nodes. These principles are extended to transfinite networks. Their proofs are far more complicated than those for the classical case. This is a consequence of the difficulty that Kirchhoff's laws are not always satisfied in transfinite networks. (Tellegen's equation is used instead.).

The computation of the capacitance coefficients for alternative interconnect configurations requiring repeated calculations as the configurations are changed can be substantially accelerated by using an "exterior template", that is, a set of "template capacitors" connected to the surface of the smallest rectangular region encompassing the planned interconnects. These template capacitors represent the effect of the medium for the fringing field outside the rectangle, and they eliminate the need to sample the fringing field every time a new calculation is made. The template capacitors can be determined by using the theory of infinite grids to eliminate almost entirely the medium-truncation error. All this works for both two-dimensional and three-dimensional (3-D) configurations, and it is especially advantageous in the 3-D case.

A significant problem in the computation of capacitance coefficients for microwave transmission and VLSI interconnection transmission systems is caused by the singularities in the electric field at the corners and edges of conductors. For two-dimensional models, a solution is given by the so called "Duncan Correction", which is based on polar expansion of the field. No such exact expansion exists in the three-dimensional case. Recent research has led to some appropriate asymptotic expressions for those singularities, and these are used to derive algorithms for correcting conventional capacitance computation. This correction accounts for the singularities at the corners of the conductors. Finally we present a few examples to illustrate the three-dimensional capacitance correction procedure and computational accuracy.

This paper gathers together and explains physically a variety of queer and paradoxical phenomena exhibited by infinite and transfinite networks.>

Three-dimensional simulations of metallization wires of VLSI/ULSI interconnections that are plagued with unreasonably large memory requirements and execution times are discussed. A strategy is presented for overcoming these problems. A principal feature is the use of a domain contraction technique, which accounts for the fringing electric field throughout the infinite domain above and below the levels where the wires appear and provides a major reduction in the number of nodal points for a finite-difference computation. Moreover, an iterative method (successive over-relaxation) is used to alleviate memory requirements, a nonuniformly distributed nodal array is used to reduce the number of nodal points still further, and parallel processing is used to reduce execution time. It is argued that rounded edges and corners for the simulation of the wires are the only appropriate configurations at current levels of miniaturization. This avoids the problem of electric-field singularities at sharp edges and corners and results in significantly reduced capacitance coefficients.>

The marketing networks of third-world countries are large systems having many markets and many agents. The dynamic behavior of one form is modeled in this paper by examining the actions of the traders. Recursive analysis yields time series in all prices and commodity flows. The network has a unique equilibrium state. Under certain conditions on supply and demand elasticities, that equilibrium state is locally asymptotically stable.

Abstract The determination of the currents and voltages in a countably infinite electrical network containing infinite energy requires not only the imposition of Kirchoff's laws and Ohm's laws but also the arbitrary assignment of the current‐voltage pairs in certain sets of branches, called joints. For finitely chainlike, countably infinite networks the maximal joint sets satisfy the base axioms of a matroid.

Recently, bounds were shown to exist on the transient response of networks whose system functions were appropriately restricted. Since the impulse response and real part, of the system function are Fourier cosine transforms of each other and the autocorrelation function and power spectrum for stationary processes are similarly related, many of these results may be applied directly to the autocorrelation. This analogy depends on the fact that. the power spectrum is a nonnegative function. The results will be stated without proof, since these proofs appear elsewhere. It is merely a matter of substituting the appropriate variables for those appearing previously in the papers on transient response.