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.     

Developmental priority of identity conservation: acceleration of identity and equivalence in normal and moderately retarded children

In an attempt to clarify the chronological relationship between identity and equivalence conservation, normal preschool-aged children (experiment 1) were exposed to brief videotape demonstrations of a model conserving identity and equivalence, identity only, equivalence only, or neither. Subsequent performances indicate that identity was easier to accelerate than equivalence, and training in both identity and equivalence appeared to be most effective in accelerating conservation. Trainable mentally retarded (TMR) children were then exposed to either the identity-equivalence-conserving or control model (experiment 2). This population, which some have argued remains at a preoperational level of functioning, was more likely to conserve identity than equivalence. In addition, conservation in the training group increased following training, though these gains were not maintained over a 3-week retention interval.     

Sex-related differences in response to practice on a visual-spatial test and generalization to a related test

93 first graders (mean age 6.5 years) were given a pretest and posttest on half of the items from the Children's Embedded Figures Test. Half of the children were randomly assigned to a training condition and received a brief training procedure on visual-spatial disembedding prior to the administration of the posttest. Children in the control condition received no training. The performance of girls improved significantly more from pretest to posttest than the performance of boys. Boys and girls showed similar beneficial effects of training in addition to the benefit of direct practice. The tendency that was observed for boys to perform higher than girls on the pretest, p less than .10, was not evident on the posttest. Scores on the pretest predicted scores on a different measure of visual-spatial ability only for children in the control group. The results are interpreted in terms of current theories of sex differences in visual-spatial perception.     

The effects of extraneous speech on visual vigilance performance of children

First-grade males performed a 30-min visual vigilance task under 5 conditions of auditory background stimulation. The 5 conditions consisted of (1) continuous conversation, in which subjects listened to a tape of conversation spliced so that there were no intervals of silence lasting longer than 3 sec; (2) continuous reverse, in which subjects heard the continuous conversation tape played in reverse; (3) intermittent conversation, in which subjects heard alternating segments of conversation and silence; (4) intermittent reverse, in which subjects heard alternating segments of reverse conversation and silence; and (5) silence control. Compared with silence or continuous stimulation, intermittent stimulation produced better detection regardless of whether or not it was meaningful. High achievers made more correct detections than low achievers, but only in the second and third time periods. Few subjects made errors of commission.     

Behavior of narcotics-addicted newborns.

The behavior of narcotics-addicted and nonaddicted newborns on the first 2 days of life was assessed with the Brazelton Neonatal Behavioral Assessment Scale. In addition to classic signs of narcotics abstinence, addicted infants were less able to be maintained in an alert state and less able to orient to auditory and visual stimuli. These deficits were especially pronounced at 48 hours of age. Addicted infants were as capable of self-quieting and responding to soothing intervention as normal neonates, although they were substantially more irritable. These characteristics and addicted infants' greater resistance to cuddling are discussed in terms of their potential impact on early infant-care-giver interaction.