Elements Of Computation Research Articles

Boundary spectral method for acoustic scattering and radiation problems

The spectral method is considered in solving boundary integral equations. By subtracting known solutions from the Helmholtz integral equation, the singularities of the Helmholtz integral equation are removed. Therefore, any order of basis functions, used in spectral methods, that times nonsingular kernels in the modified Helmholtz integral equation can be integrated easily and efficiently. Instead of solving the variables at collocation points using conventional methods, the generalized Fourier coefficients are solved by the spectral method which reduces the number of unknowns and the storage of matrix elements in computation. Scattering and radiation problems from a sphere are used to illustrate the technique in the present paper.

Curvilinear and higher order 'edge' finite elements in electromagnetic field computation

Edge type finite elements are very useful in computation of electromagnetic fields. Unlike nodal-based finite elements, they guarantee continuity of tangential components of the field variables across element interfaces. This, in turn, eliminates the so-called spurious solutions in eigenvalue, analysis in cavities. However, most of the work in this important area is done with linear, tetrahedral elements. With the exception of a few, specially constructed elements, higher order elements do not exist because there is no systematic way of constructing such elements. A method for the systematic construction of first and second order edge and facet finite elements and their use is presented in this work. Higher order elements are also considered. Both tetrahedral and hexahedral elements am presented. These are intimately related to the corresponding nodal-based elements, allowing an easy implementation in existing nodal-based finite element computer programs. The elements constructed are then used for mode analyses in electromagnetic cavities and in eddy current calculations.

Temporal filtering in retinal bipolar cells. Elements of an optimal computation?

Recent experiments indicate that the dark-adapted vertebrate visual system can count photons with a reliability limited by dark noise in the rod photoreceptors themselves. This suggests that subsequent layers of the retina, responsible for signal processing, add little if any excess noise and extract all the available information. Given the signal and noise characteristics of the photoreceptors, what is the structure of such an optimal processor? We show that optimal estimates of time-varying light intensity can be accomplished by a two-stage filter, and we suggest that the first stage should be identified with the filtering which occurs at the first anatomical stage in retinal signal processing, signal transfer from the rod photoreceptor to the bipolar cell. This leads to parameter-free predictions of the bipolar cell response, which are in excellent agreement with experiments comparing rod and bipolar cell dynamics in the same retina. As far as we know this is the first case in which the computationally significant dynamics of a neuron could be predicted rather than modeled.

Hardware for two-dimensional digital filtering using Fermat number transforms

Two-dimensional convolution computed using minicomputers is very time-consuming when Fourier transform techniques are used because of the large number of complex multiplications required. The Fermat number transform (FNT) has been proposed as an efficient and exact method of implementing one-dimensional and two-dimensional convolutions. Nonetheless, certain inherent restrictions of this transform limit its usefulness in one-dimensional applications. The restrictions associated with the FNT do not, however, appreciably encumber two-dimensional filtering. An implementation of a small two-dimensional convolution using the FNT on a PDP-11/40 minicomputer is presented. In order to decrease the time required to compute the convolution, a specially designed hardware unit is interfaced to the minicomputer. This unit computes the basic element of computation in the FNT, the butterfly, in hardware. An algorithm is given which removes the need for a matrix transposition required by some transform techniques when the main memory of the computer cannot accommodate the entire input matrix. The algorithm is useful on small disk-based computers since a matrix transposition is a very time-consuming operation. This algorithm, in conjunction with the FNT, is compared with other convolution techniques and is shown to be computationally more efficient in certain instances.

The application of photo-conductors as voltage variable operational elements in iterative analogue computation†

The application of a doped silicon element in association with a crystal lamp as a variable resistive element is a logical extension of previous work. A simple control circuit is used to obtain a linear relationship between an input signal voltage and the ohmic value of the silicon element, the overall control system having a settling time of 200 µsec.

The application of photo-conductors as voltage variable operational elements in iterative analogue computation

This paper is concerned with the application of photo-conductors as variable operational resistor elements in iterative analogue computation. Suitable control circuits have been devised which achieve a linear relationship between a controlling voltage level and the resistance of the variable operational element. The use of crystal lumps in conjunction with silicon photo-detectors enables control circuit settling times of the order of 180 µsec to be achieved and results indicate that with the correct choice of detector, the speed of the controlled response is limited only by the performance of the operational amplifier in the control circuit.

Motivating Engineering Freshmen through an Authentic Design Experience

As an integral part of the required course "Introduction to Engineering," every freshman engineer at Arizona State University is involved in a realistic design project. The object is to give the student a clear idea of the role of the engineer, the challenges he faces, and the skills he must acquire. In this project, each student works as a member of an "engineering firm" which develops a new design that is based on one of a number of ideas originally generated by the students themselves. This paper describes how this design competition is organized. This design experience, running through the entire semester, is paralleled by weekly lectures by prominent engineers from industry, as well as by formal conventional instruction in the elements of engineering analysis and computation.

(1) The School Geometry: Matriculation Edition (2) Modern Geometry: The Straight Line and Circle (3) The Elements of Analytical Conics (4) An Algebra for Engineering Students (5) Elements of Vector Algebra (6) Graphical and Mechanical Computation

(1) THIS book is in reality sections i.–iv. of JL the authors' “Geometry: Theoretical and Practical,” adapted to the requirements of students preparing for the matriculation and similar examinations. It combines the theoretical with the practical. After an introductory course of practical geometry based on intuition, there follows a series of propositions and theorems amounting, roughly, to “Euclid,” Book I., Book III., Book II., and Book IV. The presentation and treatment call for no special comment; they are clear and concise, in the well-known -style of the University Tutorial Series. There are many exercises of all kinds and of all grades of difficulty; many of the riders are provided with hints as to which theorems they are based on, and the student is thus led on to discover for himself the best methods for dealing with such exercises. (1) The School Geometry: Matriculation Edition. By W. P. Workman A. G. Cracknell. Pp. xi + 348. (London: W. B. Clive, University Tutorial Press, Ltd., 1919.) 4s. 6d. (2) Modern Geometry: The Straight Line and Circle. By C. V. Durell. Pp. x + 145. (London: Macmillan and Co., Ltd., 1920.) 6s. (3) The Elements of Analytical Conics. By Dr. C. Davison. Pp. vii + 238. (Cambridge: At the University Press, 1919.) 10s. net. (4) An Algebra for Engineering Students. By G. S. Eastwood J. R. Fielden. (With answers.) Pp. vii + 199 + xv. (London: Edward Arnold, 1919.) 7s. 6d. net. (5) Elements of Vector Algebra. By Dr. L. Silberstein. Pp. vii + 42. (London: Longmans, Green, and Co., 1919.) 5s. net. (6) Graphical and Mechanical Computation. By Dr. J. Lipka. Pp. ix + 264. (New York: J. Wiley and Sons, Inc.; London: Chapman and Hall, Ltd., 1918.) 18s. 6d. net.

On the fundamental elements of computation in their relation to systematic stellar motion

On the fundamental elements of computation in their relation to systematic stellar motion