Mathematical Model and Characteristics of the Induction Motor with a Power Supply from a Current Source

. Methods and mathematical models for studying the modes and characteristics of the three-phase squirrel-cage induction motor with the power supplied to the stator winding from the current source have been developed. The specific features of the algorithms for calculating transients, steady-state modes and static characteristics are discussed. The results of the calculation of the processes and characteristics of induction motors with the power supply from the current source and the voltage source are compared. Steady-state and dynamic modes cannot be studied with a sufficient adequacy based on the known equivalent circuits; this requires using dynamic parameters, which are the elements of the Jacobi matrix of the system of equations of the electromechanical equilibrium. In the mathematical model, the state equations of the stator and rotor circuits are written in the fixed two-phase coordinate system. The transients are described by the system of differential equations of electrical equilibrium of the transformed circuits of the motor and the equation of the rotor motion and the steady-state modes by the system of algebraic equation. The developed algorithms are based on the mathematical model of the motor in which the magnetic path saturation and skin effect in the squirrel-cage bars are taken into consideration. The magnetic path saturation is accounted for by using the real characteristics of magnetizing by the main magnetic flux and leakage fluxes of the stator and rotor windings. Based on them, the differential inductances are calculated, which are the elements of the Jacobi matrix of the system of equations describing the dynamic modes and static characteristic. In order to take into account the skin effect in the squirrel-cage rotor, each bar along with the squirrel-cage rings is divided height-wise into several elements. As a result, the mathematical model considers the equivalent circuits of the rotor with different parameters which are connected by mutual inductance. The non-linear system of algebraic equations of electrical equilibrium describing the steady-state modes is solved by the parameter continuation method. To calculate the static characteristics, the differential method combined with the Newton’s Iterative refinement is used.

An evaluation of some assumptions underpinning the bidomain equations of electrophysiology

Tissue level cardiac electrophysiology is usually modelled by the bidomain equations, or the monodomain simplification of the bidomain equations. One assumption made when deriving the bidomain equations is that both the intracellular and extracellular spaces are in electrical equilibrium. This assumption neglects the disturbance of this equilibrium in thin regions close to the cell membrane known as Debye layers. We first demonstrate that the governing equations at the cell, or microscale, level may be adapted to take account of these Debye layers with little additional complexity, provided the permittivity within the Debye layers satisfies certain conditions that are believed to be satisfied for biological cells. We then homogenize the microscale equations using a technique developed for an almost periodic microstructure. Cardiac tissue is usually modelled as sheets of cardiac fibres stacked on top of one another. A common assumption is that an orthogonal coordinate system can be defined at each point of cardiac tissue, where the first axis is in the fibre direction, the second axis is orthogonal to the first axis but lies in the sheet of cardiac fibres and the third axis is orthogonal to the cardiac sheet. It is assumed further that both the intracellular and extracellular conductivity tensors are diagonal with respect to these axes and that the diagonal entries of these tensors are constant across the whole tissue. Using the homogenization technique we find that this assumption is usually valid for cardiac tissue, but highlight situations where the assumption may not be valid.

Interfacial Energy Level Alignment at Acid Oxidized Carbon Nanotube - Triphenyldiamine Contacts

We report an ultraviolet photoelectron spectroscopy study of the energetics at the interface between acid oxidised carbon nanotubes and the archetypical molecular N,N'-diphenyl-N,N'-bis(3-methylphenyl)-1,1'biphenyl-4,4'diamine(TPD). Electrical equilibrium is achieved across both interfaces within the experiment time frame due to the formation of an interfacial dipole layer which abruptly shifts the vacuum level at the interface. To the authors knowledge this is the first reported measurement of the electronic structure of a carbon nanotube / organic semiconductor interface; a system in which the magnitude of the dipole layer formed at the interface upon contact formation is proportional to the difference in work function between the substrate and organic semiconductor overlayer.

A General Method for a Piezothermoelastic Plate of Crystal Class 6mm Subjected to Axisymmetric Loading

Applications of piezoelectric materials for the development of “intelligent” structural and mechanical systems through sensing, actuation, and control have received considerable recent interest. In this document, we present a general solution method for piezothermoelasticity for hexagonal piezoelectric solids of class 6 mm. In the formulation presented, potential functions are introduced to represent the coupled thermal, elastic, and mechanical fields, which satisfy the thermal, mechanical, and electrical equilibrium and prescribed boundary conditions. The formulation is similar to those presented by Ashida, Tauchert, and Noda (1993, 1994), however, it is simpler and direct, and it eliminates the need to discuss special cases. To demonstrate applications of the technique, a piezothermoelasticity problem subjected to axisymmetric thermal, electrical and mechanical loads on a plate is considered. Numerical calculations for the stresses and the electrical potential are carried out for a cadmium selenide body exhibiting class 6mm symmetry. Results of these calculations are presented graphically.

IV. On peristaltic induction of electric currents

Recent observations on the propagation of electricity through wires in subaqueous and subterranean telegraphic cables have brought to light phenomena of induced electric currents, which, while they are essentially different from the phenomena of what has hitherto been called electro-dynamic induction, are exactly such as might have been anticipated from the well-established theory of electrical equilibrium, had experiment afforded the data of relation between electrostatical and electro-dynamic units wanted for determining what dimensions of wire would be required to render these phenomena sensible to ordinary observation. They present a very perfect analogy with the mutual influences of a number of elastic tubes bound together laterally throughout their lengths, and surrounded and filled with a liquid which is forced through one or more of them, while the others are left with their ends open ( uninsulated ), or stopped ( insulated ), or subjected to any other particular conditions. The hydrostatic pressure applied to force the liquid through any of the tubes will cause them to swell and to press against the others, which will thus, by peristaltic action, compel the liquid contained in them to move, in different parts of them, in one direction or the other.

On the nature and origin of the Aurora Borealis

The author deduces from.his own observations made during a residence of two winters in high northern latitudes, taken in con­junction with the concurring testimony of various navigators and tra­vellers, the general fact that the Aurora Borealis is developed chiefly at the edge of the Frozen Sea, or wherever there is a vast accumu­lation of ice; and he conceives that it is produced in situations where the vapours of a humid atmosphere are undergoing rapid congelation. Under these circumstances, when viewed from a distance, it is seen fringing the upper border of the dark clouds, termed the “sea blink,” which collect over these places; and it generally forms an arch a few degrees above the horizon, shooting out vertical columns of pale yellow light. He concludes that the Aurora Borealis is an electrical phenomenon, arising from the positive electricity of the atmosphere, developed by the rapid condensation of the vapour in the act of freezing, and the induced negative electricity of the surrounding portions of the atmosphere; and that it is the immediate consequence of the restoration of the electrical equilibrium by the intervention of the frozen particles, which being imperfect conductors, become lumi­nous while transmitting this electricity. In tropical and temperate climates this phenomenon does not occur, because the electric equi­librium is restored by means of aqueous vapours, a process which often gives rise to thunder and lightning, but never to the Aurora Borealis; the latter being peculiar to clear, cold and dry weather.