Unknown Charge Research Articles

A critique of the Deutsch assumption

The field equations of a small-scale point-plane negative DC corona discharge in air have been solved in a particular case by the authors. The technique was to use a finite-element method for solving Poisson's equation, and an algorithm for finding the charge density from a current-continuity relation. A single mobility coefficient was adopted and the methods were used alternately until convergence was obtained. Boundary conditions for this technique are the potentials of the electrodes and the measured current distribution. Geometric convergence occurs before arithmetic convergence, with the accuracy of the latter being better than 1% for the electric field (typically 0.5% everywhere except at the tip of the active electrode). The uncertainty in the solution because of the unknown charge distributions in the small glow region has been accurately quantified by using two extreme models. Geometrical and numerical differences between these models have been shown to be very small.

A convected K distribution model for hot ions in the Jovian magnetodisc

Hot ion angular anisotropies measured by the Low Energy Charged Particle (LECP) instrument during the Voyager 2 encounter with the Jovian dayside outer magnetosphere (60–30 RJ) have been fitted to a 2 species convected K distribution function using a non‐linear least squares technique. The resulting parameters are well constrained by the data. The heavy ion species was assumed to be either sulfur or oxygen of unknown charge. The light species was assumed to be protons. The bulk flow speeds deduced from the model were found, contrary to some theories, to increase with increasing radial distance from Jupiter within the radial region addressed, remaining a substantial fraction (∼0.6) of the rigid corotation speed. Agreement with the averaged Voyager Plasma Science (PLS) results was obtained near 30 RJ. The core Maxwellian temperature of the heavy ion distribution functions (∼30–100 keV) increased with increasing radial distance, following the trend anticipated from the corotation pickup of heavy ions. The proton temperature (∼20 keV) remained nearly constant.

Transient response of photorefractive bismuth silicon oxide in the pulsed regime

The transient response of bismuth silicon oxide in the regime, pulsed exposure time ⪡≪ carrier recombination time, is modelled using the linearized band transport equations. The theory predicts a rapid build-up of photorefractive grating on a nanosecond time scale with response time inversely proportional to exposure. The build-up is followed by a decline in grating strength to a finite final value on a microsecond time scale. A permanent grating remains as time tends to infinity. The transient response is investigated experimentally by writing gratings in BSO with a frequency-doubled Q-switched Nd-YAG laser. The two main predictions of the theory - fast build-up followed by microsecond decline - are verified and the transverse photocurrent response confirms the carrier recombination time to be in the microsecond range. It is unexpected that the photorefractive grating continues to rise over a millisecond time scale indicating the presence of an unknown charge transfer mechanism. Another result is an induced absorption at the red (633 nm) wavelength.

Abnormal redox reactions in photosynthetic O 2-evolving centers in NaCl/EDTA-washed PS II. A dark-stable EPR multiline signal and an unknown positive charge accumulator

Redox events that occur in photosynthetic O 2-evolving centers in NaCl/EDTA-washed PS II membranes were investigated by means of low temperature EPR and thermoluminescence. The following results have been obtained: (i) In the washed membranes, O 2 centers could maintain the S 2 state more than 3 h in darkness at room temperature. This dark-stable S 2 was modified as seen by a multiline EPR signal with reduced hyperfine line spacing and also by a thermoluminescence band with upshifted peak temperature. (ii) This modified S 2 state had an abnormally long life of t 1 2 = 7 h at 20°C, and its appearance required the presence of EDTA in the medium. On addition of exogenous Ca 2+, the modified S 2 was converted in darkness to normal S 2, and then decayed rapidly to be undetectable. (iii) On illuminating this modified S 2, an EPR signal centering at aroung g = 2 was newly induced at no expense of the dark-stable EPR multiline signal. This EPR signal was accompanied by a new thermoluminescence band peaking at around 5°C, suggesting the presence of a new redox component whose oxidized form is capable of providing a positive charge for thermoluminescence in place of Mn. (iv) This new component was efficiently oxidized by illumination at −5°C but much less at −60°C, showing a half-inhibition temperature at around −40°C. (v) Addition of various divalent cations in place of Ca 2+ variously affected both thermoluminescence glow peaks arising from the dark-stable S 2 or from the new redox component, suggesting a cation-species-dependent modulation of the redox properties of both components. (vi) Both of these two thermoluminescence bands showed no dependency on flash number, suggesting interruption of further oxidation beyond their respective abnormal states. On addition of Ca 2+, all these abnormal properties were abolished and normal period-four flash pattern was restored. These abnormal properties of the redox events in NaCl/EDTA-washed PS II membranes were discussed in relation to the demand for exogenous Ca 2+ in recovery of normal properties.

The Low-Temperature Structure of Magnetite Studied by CBED

Magnetite (Fe3O4) has the cubic inverse spinel structure for T > TV = 119 K and undergoes a firstorder metal-insulator Verwey transition below TV. The transition from hopping conductivity to insulating behaviour below TV is believed to be due to a condensation of localised electrons onto the Fe++ and Fe+++ ions on the octahedral (B) sites. Tetrahedral (A) sites contain only Fe+++ ions. The aim of this research is to determine this unknown charge ordering below TV by CBED, taking advantage of the high sensitivity of low-angle electron diffraction to ionicity. Below TV the c axis of the cubic cell doubles, and there is a small monoclinic distortion.Previous CBED work established that the space-group is Cc (C centering, glide plane normal to b, displacement along c). Anderson proposed that the building block for the low-temperature structure consists of two Fe++ and two Fe+++ ions per tetrahedron (see, e.g. figure 1).

The Continuity Gauge - Does It Work?

This paper reviews the electromagnetic gauges and discusses the new continuity gauge in detail. It is shown that by introducing a complex Laplace's equation instead of a real Poisson's equation, the new gauge circumvents the difficulty of dealing with an unknown charge density as in the case of the Coulomb gauge. Justification is given for employing a differential rather than an integral equation formulation when working with the new gauge. Two problem scenarios are described in the formalism of the continuity gauge to explain how the new gauge can be used to solve low and high frequency electromagnetic field problems.

On a dynamic contact problem for a single electrode

The dynamic problem of surface-wave excitation by the main element of electrode transducers, a single electrode simulated by a strip stamp lying freely on the surface of a piezoelectric half-space, is considered. The vertical component of the displacement and the electrical potential is given in the contact region, while the surface outside this region has no electrical and mechanical loads. The boundary value problem of electroelasticity mentioned reduces to investigating a system of inhomogeneous Fredholm type integral equations of the first kind in the unknown normal stress and charge distribution density functions.

RESISTIVITY AND INDUCED POLARIZATION RESPONSES OF ARBITRARILY SHAPED 3‐D BODIES IN A TWO‐LAYERED EARTH*

ABSTRACTNumerical computations using the integral equation method are presented for resistivity and IP responses due to arbitrarily shaped 3‐dimensional bodies in a layered earth. The unknown surface charge density distribution is expressed as the solution of Fredholm's integral equation of the second kind. Use of moment method (with pulse basis function and point‐collocation) yields the matrix equations for the unknowns. The contributions to Green's function are solved (a) analytically for the primary and (b) by convolution for the secondary contributions resulting in a fast algorithm. The further step of computing potential, apparent resistivity, chargeability etc., for any electrode system, is straightforward. Our results show a good agreement with those from finite difference methods and physical tank experiments. The CPU time is only 138 s on a super‐minicomputer for an apparent resistivity pseudo‐section, even with 96 elementary cells as used for discretization. A large number of models for different geological situations were studied; some are presented here.

A current source emitting in the presence of an insulating and a conducting disk over stratified media

The mixed boundary value problem of two different disks, one conducting, and one insulating involving a point current source is sovolved. We generalize the approach of Tranter, and apply his method to a set of vector dual integral equations. The unknown charges on the conducting disk, and the unknown dipole layer on the insulating disk are expanded in terms of basis functions. The basis functions are Jacobi polynomials. The integral equations are then converted to a matrix equation where the unknown charges and dipole layers can be solved for. The method is variational, and converges very rapidly. With the solution, we can plot the current flow patterns around the disks. Such current flow patterns provide insight into the problem.

Charge distribution on a fiber

The charge distribution of a single line of equal charges was determined using a small laboratory computer. Two basic assumptions were made about the distribution and symmetry of the charges on a straight line. Using Coulomb's law, a matrix was set upas a function of the unknown charges and the relative distances between each charge. The results show that the charge at the ends is almost double the value of those in the center. The tension is uniform, i.e., the net force on each internal charge is zero, along the entire length of the fiber, and the potential field differs only slightly from that of a uniform charge distribution.

Relation of the charge and spin correlation functions to the structures of π electron wave functions in alternant hydrocarbons

AbstractWe analyze, in the Pariser–Parr–Pople (PPP) model of alternant hydrocarbons, how the charge and spin correlation functions (CF's) are related to the structure of a CI wave function and the MO's of the systems. The analysis is based on the fact that an uncorrelated electron present in an orbital does not contribute to the linked dynamically correlated parts of the CF's. By using the fact, simple rules are deduced predicting the covalent or ionic nature of the correlation structure in a low‐lying state with two correlated electrons. The rules predict that the singlet minus and triplet plus states are covalent, while singlet plus and triplet minus states are ionic, where the plus and minus mean the alternancy symmetry. The rules also give a prediction for the unknown charge and spin correlation structures between different sites.

A Rapid Semi-Analytic Method for Solving Laplace's Equation

A relatively new semi-analytic method for solving Laplace's equation has been studied in detail and compared with various long-established techniques, which are also briefly reviewed. The method involves dividing the boundary of a region into N segments, each of which has an unknown surface charge. The surface charge on each segment is assumed to be constant or to be represented by a low-degree polynomial. In the latter case, charge and even derivative continuity at the segment boundaries can be imposed. The potential produced by each segment is expressed analytically and satisfaction of the boundary conditions determines the unknown charges. The latter calculation requires the solution of N linear simultaneous equations. The resulting charge pattern enables one to evaluate the potential and/or electric field at any point with no further difference approximations. This procedure compares favorably both in computation speed and accuracy with other numerical and semi-analytic techniques, viz., net, Monte Carlo, and collocation methods.

Electroosmosis and electrolyte conductance in charged microcapillaries

AbstractInteractions between the electrostatic double layer and transport rates in long capillary pores were investigated experimentally. Track‐etched mica sheets with extremely narrow pore size distribution and large length‐toradius ratio were used as model membranes to examine the electrokinetic phenomena enhanced conduction and electroosmosis as a function of pore size and electrolyte (potassium chloride) concentration. Of experimental significance was that the capillary pores were of radius comparable to or even less than the solution Debye length parameter even at moderate (10−4 – 10−3 M) electrolyte concentrations. Heparin, a negatively charged polyelectrolyte, was adsorbed to the pore wall to augment electrostatic effects. The data were compared with numerical calculations based on a diffuse double‐layer model, and the unknown pore wall charge densities were computed for each experiment. The results show that the classical analysis is somehow deficient and also that adsorption of the potential determining ion (heparin) is dependent on electrostatic potential at the pore wall.

Static voltages on the guy insulators of m.f. and i.f. broadcast tower antennas

A new approximate method for calculating the static voltages on the guy insulators of m.f. and i.f. broadcast tower antennas is given. The method is based on an integral-equation technique, where the integral equation is solved by the so-called point matching method; the unknown charge densities are approximated by polynomials. The polynomial expansion provides very significant advantages, primarily because it leads to the integrals in closed form, and because itrequires a very low order of polynomial. A numerical example is given to illustrate the method.

On the Determination of the Phases of Electromagnetic Scattering Amplitudes from Experimental Data

The scattering of electromagnetic waves by systems of unknown charge distribution is considered with the aim of establishing that the phase of the scattered radiation (relative to the incident one) can be computed theoretically from experimentally obtainable data, such as the intensity and the polarization of the scattered wave. By means of the unitarity relation of classical electromagnetic scattering theory, it is demonstrated that, subject to certain restrictions on the magnitude of the scattering data: (i) For an unpolarized incident beam and a spherically symmetric target, knowledge of the differential cross section and the polarization of the scattered radiation is sufficient to determine uniquely the phases of the scattering amplitude tensor. (ii) For a parity-invariant scatterer, and fully circularly or linearly polarized incident beams, knowledge of the differential cross section and the ellipticity of the outgoing radiation is sufficient to completely determine the phases of the scattering amplitude tensor. The scattering data must be available for both the left and the right circularly polarized incoming wave (or for two linearly polarized beams pertaining to the two orthogonal polarizations). (iii) In the above cases it is shown that the phases can be calculated systematically by converging iterative procedures. Conditions for convergence are established, and bounds are provided on the errors associated with the approximants obtained after an arbitrary (but finite) number of iterations. On the basis of result (ii) with the same data assumed to be known, a formal solution to the phase determination problem is given for a general scatterer. However, for this case rigorous results on convergence conditions and error bounds have not been obtained. An outline of the corresponding treatment valid within the framework of the quantum-electrodynamical theory of light scattering is given. To illustrate the proposed methods for phase determination, we apply them to the scattering of light by very simple systems. These include the free electron and an oscillating charge. We conclude by discussing the possibility of applying the above results to obtain solutions of the phase problem in systems of practical interest.

Charge Distribution and Electric Field Gradients in Ionic Crystals

A method is presented by means of which one can investigate the validity of the point-charge model often used for the calculation of electric field gradients in ionic crystals. The asymmetry parameter of the electric field gradient at a nucleus and the Eulerian angles describing the orientation of the field gradient's principal axes with respect to the crystallographic axes are linear functions of the point charges assigned to each set of atoms in the lattice. If the unit cell is of low symmetry and if there are more than one set of nuclei for which quadrupole interaction data can be observed, the number of observables and equations may equal or exceed the number of unknown charges, thereby enabling the charge distribution to be determined and its internal consistency checked. Such is the case for spodumene, for which the charge distribution thus calculated is neither internally consistent nor very reasonable. An analysis is made of the sensitivity of the apparent charge distribution to experimental errors in the quadrupole interactions, and the errors are found to be much too small to account for the anomalies. However, further investigations, including a refinement of the crystallographic parameters of spodumene, are necessary before the anomalies could be attributed to deficiencies in the point-charge model. With allowance for the uncertainties in the charge distribution, the analysis lends some support to a value of ≈0.04 b for Q7, the nuclear quadrupole moment of Li7. Further charge distribution anomalies result from a similar, but less detailed treatment of another silicate, beryl, which gives a very approximate value of Q9≈0.1 b for Be9.

Electrostatic Inductor Alternator

The electrostatic inductor alternator is a special form of variable condenser that is able to yield a s'nusoidal alternating current when excited by a D. C. electromotive force or by a static charge. It may be designed so that the magn-tude of its output can be determined f-om the magnitude of its input and from the constants of its design. Equations for this design and calculation are given. N:umerous circuits for the use of the alternator are poss;ble. In one type of circuit the alternator is used as an electrometer, and operates by a null point balance between the effects of a known and unknown static charge or D. C. electromotive force. Electrostatic Inductor Alternator The idea of making an electrostatic inductor alternator first occurred to me July, 1927. During the spring of 1928, Mr. T. H. Stevens, who was then o:.r shop technician, constructed most of the apparatus for me, and gave valuable assistance in perfecting its details, as did also my colleague, Professor E. V. Floyd. The construction was completed during the summer of 1928 by Mr. V. V. Cool for whom I was major instructor in the direction of his research, the latter consisting of certain tests and calb,rations made upon this instrument. Briefly, the present model of the electrostatic inductor alternator consists of a toothed aluminum wheel revolving between two stationary Wimshurst plates. Nuimerous circuits for its use have been tested. Its operation depends upon the periodic variation of capacity between the rotating toothed wheel and the electrodes upon the Wimshurst plates,-the stators. If one set of stators be connected to an unknown E. m. f. with respect to ground, the other set be connected oppositely to an adjustable known E. m. f. with respect to ground, and the rotor be connected through phones (or through amplifier and phones) to ground, the unknown may be measured by the known when adji:stment of the latter has caused the musical note in the phones to vanish. This works as well for a static charge, such as an antenna potential, as for a battery potential. The present model measures down to 0.05 volt, at which point frictional electricity developed by the rotation of the toothed wheel in air begins to introduce too much uncertainty. I have plans for making a small electrostatic inductor alternator sealed in a vacuum, and operating the input of one of the new General Electric FP-54 pliotron tubes, hoping thereby to develop a quick-acting and rugged competitor for This content downloaded from 157.55.39.4 on Thu, 08 Sep 2016 04:30:42 UTC All use subject to http://about.jstor.org/terms