The graph-theoretic field model— II. application of multi-terminal representations to field problems

This paper is a sequel to a paper entitled “The Graph-Theoretic Field Model—I: Modelling and Formulations” (1). Herein, the Theory of Multi-Terminal Representations is applied to the Graph-Theoretic Field Model to provide mathematical models of finite elements. The element models are obtained solely from the algebraic building blocks of the Graph-Theoretic Field Model, without recourse to any functional mathematics. The theory of Multi-Terminal Representations is developed for both linear and non-linear problems. Examples of the application of the theory to one- and two-dimensional field problems are presented from heat conduction and electrostatics.     

Essential gyrators and reciprocity in junction structures

This paper proposes an extended definition of reciprocity for a multiport junction structure based on the concept of essential gyrator coupling. Two theorems are given for junction structures containing gyrators and an algorithm is presented for identifying essential gyrators. The results are useful both theoretically and for designing efficient computation procedures for junction structures.     

The graph-theoretic field model—I. Modelling and formulations

The Graph-Theoretical Field Model provides a unifying approach for developing numerical models of field and continuum problems. The methodology examines the field problem from the first stages of conceptualization without recourse to the governing differential equations of the field problem; this is accomplished by deriving discrete statements of the physical laws which govern the field behaviour. There are generally three laws, and these are modelled by the “cutset equations”, the “circuit equations”, and the “terminal equations”. In order to establish these three sets of equations it is expedient first to spatially discretize the field in a manner similar to the finite difference method and then to associate a linear graph (denoted as the field graph) with the spatial discretization. The concept of “through” and “across” variables, which underlies the cutset and circuit equations respectively, enables one to define the graph in an unambiguous manner such that each “edge” of the graph identifies a pair of complementary variables. From a knowledge of the constitutive properties and the boundary conditions of the field it is possible to associate terminal equations with sets of edges. Since the resulting sets of equations represent the field equations, these equations provide the basis for a complete (but approximate) solution to the field or continuum problem. In fact, this system approach uses a two part model: one for the components and another for the interconnection pattern of the components which renders the formulation procedures totally independent of the solution procedure.This paper presents the theoretical basis of the model and several graph-theoretic formulations for steady-state problems. Examples from heat conduction and small- deformation elasticity are included.     

Infant approach behavior as related to attachment.

The chief purpose of this study was to identify characteristics that distinguish approach as an attachment behavior from approach serving other behavioral systems. Locomotor approaches of 16 male and 10 female white middle-class infants to an attachment figure (the mother) and to a nonattachment figure (the visitor-observer) were examined under naturalistic conditions at home. Observations were made during 4-hour home visits at 3-week intervals; those from 26 to 54 weeks were used. When approach was examined in a free-choice situation and without regard to behavioral context, infants approached the mother proportionally (though slightly) more often than the visitor (p less than .05). In 2 behavioral contexts, however, spontaneous infant approaches were sharply differential to the mother; approaches accompanied by crying and approaches terminating in a pickup appeal were directed almost exclusively to the mother (p less than .0001 for both). Touching upon completion of the approach was not differential, except in the context of a pickup appeal. Object-oriented approaches were more often directed to the visitor than to the mother (p less than .002) and may be either exploratory or affiliative. It is suggested that neither approach nor touching can be assumed to serve the attachment system without consideration of context- both environmental and behavioral.