Ground Nodes Research Articles

Walk-Based Transfinite Graphs and Networks

The theory of transfinite graphs developed so far has been based on the ideas that connectedness is accomplished through paths and that the infinite extremities of the graph are specified through one-way infinite paths. As a result, a variety of difficulties arise in that theory, leading to the need to restrict such path-based graphs in various ways to obtain certain results. In this work, we present a more general theory of transfinite graphs, wherein connectedness and the designation of extremities are accomplished through walks rather than paths. This leads to a simpler and yet more general theory, wherein new kinds of transfinite extremities are also encompassed. For instance, an ordinal-valued distance function can now be defined on all pairs of walk-connected nodes, in contrast to the path-based theory, wherein no distance function is definable for those pairs of nodes that are not path connected even though they are walk connected. Some results concerning eccentricities, radii, and diameters are presented in this more general walk-based graph theory. Another new result herein is the development of an electrical network theory for networks whose graphs are walk based. A unique voltage-current regime is established under certain conditions. The current regime is built up from current flows in closed transfinite walks—in contrast to a prior theory based upon flows in transfinite loops. A notable advantage of the present approach is that node voltages with respect to a given ground node are always unique whenever they exist. The present approach is more general in that it provides nontrivial voltage-current regimes for certain networks for which the prior approach would only provide trivial solutions having only zero currents and voltages everywhere.

Trajectory control of mobile gateways for range extension in ad hoc networks

In order to facilitate scalability in a mobile ad hoc network (MANET) and to provide connectivity between partitions that might occur in wireless networks as a consequence of mobility, we can envision a `range extension' network that consists of airborne communication platforms, and satellites. These airborne or satellite nodes will maintain communication links with specific `gateway' nodes among the mobile ground nodes. To communicate with a node that is geographically distant or belongs to a different network partition, an ad hoc node can relay its data packets through an appropriate mobile gateway and via the range extension network. If we envision that the MANET is divided into different groups and a mobile gateway is deployed for each such group, an objective then, is to determine the trajectory of the mobile gateway to best serve the ad hoc group to which it belongs, in terms of network performance metrics such as throughput and latency. In this paper, this problem of computing the optimal position for a gateway is reduced to a linear optimization problem by means of some simplifying but realistic assumptions. We suggest methods that may be deployed to enable the gateway to follow this optimal trajectory as closely as possible (within the practical constraints imposed by its velocity and maneuverability). Simulation results for various scenarios show a 10–15% improvement in the throughput and in latency (per group containing a gateway) if a gateway has a dynamic trajectory whose locus follows the computed optimal position, as compared to a gateway that is statically placed at a regular position, or to a gateway that has a random trajectory.

Finite element analysis (FEA) as a model to predict effects of farriery on the equine hoof.

A finite element (FE) hoof capsule was built as a small, symmetrical forelimb hoof on IDEAS* as a model for calculation and visualisation of stress and displacement of the equine hoof capsule. The model's loading was performed according to the suspension of the coffin bone within the hoof wall (pulling force) and over the sole and frog (compressing force) with a total of 3000 N. Restraints of the model's ground nodes and surface wall nodes were defined for simulation of 4 shoeing situations: a regular horseshoe, a horseshoe with a toe clip, a horseshoe with regular side clips and a horseshoe with a toe clip and more caudally-placed side clips, all fixed to the hoof capsule with 3 nails on each side and each calculated in a tense and a loose nailed condition. Von Mises stresses were taken ranging from 1.22 N/mm2 in the weightbearing border of the side clip shoe fixed loosely to the capsule up to 16.67 N/mm2 in the hoof horn material surrounding the third nail. Further high stress zones were calculated in the proximal dorsal wall, the distal heel and the lateral hoof wall. Displacement values were taken showing movements of hoof wall, sole and frog according to the shoeing conditions. Maximal displacement was calculated in the hoof capsule shod with a regular horseshoe without a clip. Minimal displacement was found in the capsule with a toe clip and 2 side clips placed behind the 3rd nail. All models showed higher displacements when calculated with a loose nail fixation. Validation of the detailed features of the models is not yet possible. Finite element analysis (FEA) can be used practically to predict influences of various farrier techniques on the equine hoof in order to avoid possible harm to horses' feet in field studies.

5518832 Apparatus for simulating high battery temperature used in recharging lithium ion cells

A battery (200) includes a device (201) used for simulating a high temperature condition of a thermistor (216) located in battery (200). The battery (200) includes a charging node (203), temperature node (205) and ground node (207). A control circuit (209) is used with lithium ion cell (211) to measure voltage of lithium ion cell (211). Control circuit (209) produces a control signal when a desired voltage is reached during recharging. The control signal works with a high voltage switch (217), thermistor (216), diode (213) and resistor (215) to control the voltage on temperature node (205). Any change in voltage on temperature node (205) may then be detected by an attached charging system to allow it to change its mode of operation.

The existence and uniqueness of node voltages in a non‐linear resistive transfinite electrical network

Transfinite resistive electrical networks have unique voltage-current regimes under very broad conditions on their resistances and source values; this has been established previously. However, as is shown by example in this paper, such networks need not have unique node voltages with respect to a chosen ground node either because the voltages along every path from ground to another chosen node may not be summable or because the voltages along two such paths to the same node may be summable but with different sums. A second result of this work is the establishment of a sufficient set of conditions for the existence and uniqueness of node voltages in a non-linear transfinite network. The theory of modular sequence spaces is used for this purpose.

Connectedness in transfinite graphs and the existence and uniqueness of node voltages

Unlike connectedness in ordinary graphs, transfinite connectedness need not be transitive. As a result, sections of a transfinite graph that are maximal with respect to transfinite connectedness may overlap while being different, as is shown by an example. A sufficient condition is established under which transitivity holds, in which case the said sections partition the transfinite graph. A related phenomenon is that it may not be possible to assign a unique voltage to a node of a transfinite electrical network because the sum of the branch voltages along a path between that node and a chosen ground node may depend upon the choice of the path. This too is shown by example. Sufficient conditions are established that insure that all nodes have unique node voltages, being independent of the choices of the paths to ground. The proofs are based on a characterization of the totally ordered set of nodes along any transfinite path, the characterization being a certain hierarchical structure of nested sequences.

On the convergence of block relaxation methods for circuit simulation

The authors developed sufficient conditions for the convergence of several block relaxation methods. They first consider time-point relaxation methods, namely the block Gauss-Seidel-Newton (G-S-N) and the block Newton-Gauss-Seidel (N-G-S) algorithms. The previously known sufficient condition for convergence of the G-S-N and the N-G-S algorithms requires: (1) a capacitor connected between every node in the circuit and the reference ground node: and (2) the choice of a sufficiently small time step for the implicit integration formula used to discretize (in time) the circuit equations. The authors derive a sufficient condition that is less restrictive than (1) above. For a given partitioning of a circuit, they define a set (possibly empty) of feedback nodes that capture the topology of the partitioned circuit to a certain extent. They then show that the G-S-N and the N-G-S algorithms converge. >

An HP-67/97 network analyser for EE students

This paper describes an a.c. network analysis program designed for R/g m/C networks which contain up to 4 nodes, including the reference (ground) node. It gives the transfer function A(f) = V out V in for specified frequency f. either as single-frequency points or as multiple-frequency sweep. It also gives the band-edge (3 dB) frequencies and poles zeros of the transfer function. The network is specified by entering component values and node numbers associated with each component. The program is segmented in two parts, each of 224 HP-67/97 program steps: part 1 deals with internal computation of the polynomial coefficients of the network, while part 2 computes and displays the output parameters. The program is of interest to Electrical Engineering students, particularly those who are studying the basics of linear circuit analysis and design.

A Switched-Capacitor Digital Capacitance Bridge

A switched-capacitor bridge has been developed for capacitance measurements. It consists of four arms connected between the low-impedance output and virtual ground nodes of an op-amp, and hence is insensitive to parasitic capacitances. The capacitance to be measured is first given a proportional charge. This charge is then compared successively with charges quantized by means of a programmable binary-weighted capacitor array, until a balance is reached. This digital balance operation makes it possible to accomodate an automatic calibration scheme, which affords, in conjunction with the parasitic-insensitive configuration, an accurate measurement. Error analysis has shown that a 10-bit quantization accuracy and a relative error as small as 0.1 percent are attainable when the bridge is fabricated in LSI circuit form using present MOS technologies. A prototype bridge built using discrete components has confirmed the principles of operation. Examples of measurement are also given.

Note on the Analysis and Synthesis of Active RC Filters

Transfer functions with complex poles, as well as zeros, are sometimes implemented by means of arrangements in which feedback is applied to the ground node of a passive network. Formulation of the voltage transfer function of the passive network <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T(s) = P(s)/Q(s)</tex> , in terms of admittance products, permits topological organization of the components of the network into subsets of numerator two-trees and denominator two-trees. All numerator two-trees are immune to feedback. Some denominator two-trees are susceptible to feedback, others are not. Identification of susceptible two-trees simplifies the mathematics; it also facilitates determination of alternative designs.

Radio Interference Studies on Extra-High-Voltage Lines

Investigations were carried out to determine the long-time average radio interference levels on ehv power lines. From an analysis of a large number of records, frequency distribution curves and typical r.i. levels for different weather conditions were established. The nature of line corona generation was studied oscillographically. Positive corona was found to be responsible for interference from conductors. Also, for a horizontal single-circuit construction, the centre phase conductor appeared to be the main contributor to the line noise. The tower proximity effect was found to be significant for both wood and steel structures. To aid in obtaining a correlation between a short and long line, lateral profiles for the test line were obtained and compared with those for operating lines. The effect of standing waves was also studied using artificial noise sources placed at a node and autinode points for a resonant frequency, and observing the behavior of the line and ground nodes.