Showing papers on "Network theory published in 1981"

Network models of concentrated polymer solutions derived from the yamamoto network theory

Abstract: Several choices of the functions describing the creation and destruction processes of entanglement junctions in the Yamamoto network theory of concentrated polymer solutions have been examined. These choices are simple functions of the extension of the network segments bridging the entanglement points and it is demonstrated that the moments of the distribution function describing the network conformation can be solved for analytically. This has been done for a wide range of two-dimensional flows, both for the steady state and transient start-up and relaxation problems. The macroscopic stress tensor and flow birefringence are calculated and a variety of nonlinear effects are predicted and discussed.

Projective Matrix Transformations in Microwave Network Theory

Abstract: Recent theoretical investigations reveal the dominant role played by a new type of matrix transformation in the theory of microwave networks composed of multiport elements; this is an extension to multidimensional vector spaces of the well-known scalar fractional bilinear transformations. Projective matrix transformations have been found to map the scattering matrix, the impedance matrix, and the admittance matrix of an n-port network embedded in a 2n-port supernetwork. The transfer-scattering matrix and the chain- or ABCD-matrix of a 2n-port network embedded in a 4n-port supernetwork, are also mapped in a similar manner by matrix transformations of the same type. A fundamental application of this new transformation is the generalization of the concept of image-parameters known for 2-port networks to that of image-matrices for 2n-port networks. This generalization leads to a rigorous normal-mode analysis of wave-propagation on image-matched chains of cascaded 2n-port networks.

Foundations of nonlinear network theory : part II: losslessness

Abstract: This paper is the second in a two part series [1] which aims to provide a rigorous foundation in the nonlinear domain for the two energy-based concepts which are fundamental to network theory: passivity and losslessness. We hope to clarify the way they enter into both the state-space and the inputoutput viewpoints. Our definition of losslessness is inspired by that of a "conservative system" in classical mechanics, and we use several examples to compareit with other concepts of losslessness found in the literature. We show in detail how our definition avoids the anomalies and contradictions which many current definitions produce. This concept of losslessness has the desirable property of being preserved under interconnections, and we extend it to one which is representation independent as well. Applied to five common classes of n-ports, it allows us to define explicit criteria for losslessness in terms of the state and output equations. In particular we give a rigorous justification for the various equivalent criteria in the linear case. And we give a canonical network realization for a large class of lossless systems.

A possibility of filling the gap between local and global passivity of non‐linear networks and some of its consequences

Abstract: In the qualitative theory of non-linear networks the non-linear n-ports are generally considered either locally passive or globally passive even eventually globally passive (the most restrictive or the least restrictive properties respectively). Moreover the reciprocity condition in many cases (e.g. complete stability) restricts the area of applications. In the area of economics and other fields, basically motivated by Sandberg's results, the role of the off-diagonally monotone and antitone mappings is crucial. In this paper, based on the above facts and results, it is shown that partly similar classes of mappings could have a role in non-linear network theory. More precisely, the off-diagonally locally active (passive) n-ports, defined in the paper, could represent an important new class of n-ports. As an application of the features of this new class of n-ports two Theorems are given showing conditions under which in case of a network consisting of off-diagonally locally active n-ports the DC solution can be uniquely calculated using the standard iterative methods and an autonomous network is asymptotically stable in a given domain. Hence, this paper partially overcomes the so called ‘curse of non-reciprocity’.

Network Theory and Systems

Abstract: This chapter focuses on network theory and systems. A network is a set of nodes whose interconnections represent transmission or energy flow. These nodes may be resistors, capacitors, or even nerve cells in the visual system—the interconnections being the axonal and dendritic tree structures. Because of the great developments in electrophysiology, most network models for neural function involve concepts of electronic components used in general electrical networks. This chapter presents network models for retinal, cortical, and eye-movement systems to explain the way in which specific network properties are representative of visual function. With the development of microelectrode recording techniques, it has become possible to record the electrical activity of cells within the visual system. An essential property of systems analyses is that they can quantitatively evaluate one model against others. This involves assumptions about signal samples and response populations that are the linearity and nonlinearity of the system, and the application of specific statistical decision models.