Simple Computational Technique Research Articles

Approach to the theory of mode locking by synchronous pumping

We present a simple computational technique that, in the case of mode locking by synchronous pumping, allows the steady-state pulse profiles to be generated essentially without approximation. The results cast doubt on the validity of previous theoretical treatments of this problem.

Stagnation Line and Upwash Formation of Two Impinging Jets

When two jets in reasonable proximity exhaust into ambient surroundings and impinge on a ground plane, radial wall jets are formed which interact and form a stagnation region. The flow then is deflected upward to form an sheet. These individual upwash flows are the heart of the complicated effects experienced by VTOL aircraft when they operate in ground proximity. It is the intent of this study to develop relatively simple flow models and prediction techniques, based primarily on momentum principles and empirical observations, for the estimation of two-jet ground impingement phenomena. Comparisons with experimental data indicate that these simple computational techniques can yield very reasonable estimates of certain overall aspects of the two-jet impingement problem.

Hybrid Simulation of Queuing-System Dynamics

This paper presents a simple hybrid computer technique to study the transient behaviour of queueing systems. This method is superior to stand-alone analog or digital solution because the hardware requirement is excessive for analog technique whereas computation time is appreciable in the latter case. By using a hybrid computer one can share the analog hardware thus requiring fewer integrators. The digital processor can store the values, play them back at required time instants and change the coefficients of differential equations. By speeding up the integration on the analog computer it is feasible to solve a large number of these equations very fast. Hybrid simulation is even superior to the analytic technique because in the latter case it is difficult to solve time-varying differential equations.

Computing Expected Mean Squares

SUMMARY The evaluation of the expected mean squares arising from the analysis of unbalanced mixed ANOVA models has long been an analytically intractable problem. Irl this paper we present a theoretically and computationally simple technique for computation of the coefficients in the expected mean squares.

New extremal properties for constructing conformal mappings

It is well known that for a given simply connected regionR containing zero the uniform norm $$\left\| f \right\| = \mathop {\sup }\limits_{z \in R} \left| {f(z)} \right|$$ attains its minimum in the class of all holomorphic functions normalized byf(0)=0 andf?(0)=1 only for the conformal mappingf?R?D(r)={z?|z|<r}. It is shown that this theorem is still valid if one replaces the ordinary modulus | | on ? by any other norm on ?. For instance it is possible to obtain direct mappings ofR onto parallelograms, rectangles and ellipses. For the special norms |1 and |? this leads to a simple and fast computational technique involving linear programming methods. Several numerical examples are given.

Bounds for the zeros of partially symmetric multivariable systems

The real parts of the invariant zeros of an mx system S (A,B,C) satisfying a partial symmetry condition can be bounded from above and below by the eigenvalues of the symmetric part of A. Where applicable the results provide a simple computational technique for assessing the minimum phase structure of the system.

A rapid on-line computer method for electrochemical investigations

It is demonstrated that a simple on-line computer technique can be used to measure the electrochemical characteristics of a fast electrochemical reaction at modest frequencies. The technique is very suitable for making rapid electrochemical measurements where time effects are involved, e.g. in metal deposition.

Energy conservation through urban transportation planning

A large number of techniques for conserving energy in urban passenger transport are described. A systems approach for evaluating these simultaneously in order to formulate areawide passenger transportation energy policy is presented. It consists of a simple computer technique for estimating the conservation value of various schemes. The program is also of value in assessing the energy impact of individual energy conserving programs. Because only local planners are familiar with the economic, environmental, and political constraints on policy and programs, the tool is intended for use in urban regions. It is, however, written in general terms and as such, if used in all urban areas in the U.S., could offer realistic national estimates of urban passenger transportation energy requirements in the short term (0–10 yr).

Methods for the Bethe-Salpeter Equation. I. Special Functions and Expansions in Spherical Harmonics

Elements of the structure of the Bethe-Salpeter equation are studied. Properties of useful special functions are obtained and free-particle solutions to the truncated expansion of the equation in four-dimensional spherical harmonics are derived in terms of known special functions. The validity of the truncation approximation is examined in terms of a convenient representation of the Green's function. In particular, it is shown that the method of truncating the differential Bethe-Salpeter equation cannot succeed for scattering. The development of alternative procedures is deferred to the paper following. As a by-product, a simple computational technique for the approximation of integrals by Gaussian quadrature is derived.

Comparison of Airborne and Ground Based Weather Radars

Radar PPI photodata on thunderstorm echoes, obtained in a cooperative FAA/NSSL experimental program utilizing a 3-cm airborne radar and a 10-cm ground radar, are examined within the framework of a simplified storm reflectivity model and applicable radar theory. The analysis and data comparison is generally restricted to thunderstorms of moderate intensity and size, and aircraft altitudes to 40,000 ft MSL. Within these boundaries, there is reasonable agreement between the model, the airborne radar data, and the ground radar data. The results show that the airborne radar, operated under controlled conditions in the 30,000–40,000 ft altitude range with a grazing angle antenna tilt, can detect moderate storms to ranges of 200–300 n mi, and can provide storm pattern identification at ranges from 125–175 n mi. At altitudes between 20,000 and 30,000 ft, storm patterns can be identified at range of ≤100–150 n mi, and individual storms resolved within ranges of 50–100 n mi. At altitudes from 10,000–20,000 ft, storm patterns can he identified within ranges of about 75–125 n mi, and excellent resolution of individual storms can be obtained between 20 and 70 n mi. The compatability of airborne radar performance deduced analytically by a simple computational technique with that provided under actual flight conditions suggests that a suitably designed computer program could provide accurate estimates of radar performance for many potentially hazardous meteorological situations.

A Robust Point Estimator in a Generalized Regression Model

The objective of the present paper is to define a robust point estimator of the parameter $\beta$ in the model \begin{equation*} \tag{1.1} y_j = \alpha + g_j(\beta) + z_j,\quad j = 1, 2, \cdots, n,\end{equation*} where $\alpha$ and $\beta$ are unknown parameters, $g_1, g_2, \cdots, g_n$ are real-valued functions of real variable satisfying suitable conditions and $z_1, z_2, \cdots, z_n$ are independent identically distributed random variables having a distribution function belonging to a specified class. An important special case of (1.1) is the regression model obtained by taking $g_j(\beta) = \beta x_j, j = 1,2, \cdots, n$, where the $x$'s are known constants. Robust point estimators of $\beta$ in this case have already been given by Adichie [1], who followed the method of Hodges and Lehmann and by Brown and Mood [7], who considered the so-called "median" estimators. The estimator presented in this paper, which is also a Hodges-Lehmann type estimator, therefore, provides a third alternative for the regression model. In Section 2 of this paper, a robust point estimator for $\beta$ in the model (1.1) under some suitable regularity conditions on $g_j$ and $z_j$ is defined. In Section 3, a simple computational technique for the calculation of this estimator is given. A small sample property of the estimator is given in Section 4, and in Section 5, asymptotic normality is established under some regularity conditions. In Section 6, some special cases of the model are considered.

A technique for digital computer processing of data from radioisotope sediment tracing studies

A simple computer technique for directly producing isoactivity contour maps from data obtained from radioisotope sediment tracing experiments is described. The method is used to process sets of readings of counting rate, position and time, taken at many points which are not necessarily on a regularly spaced grid. A Fortran program using this method has been written for an IBM 7040 computer and tested on results from a silt tracing experiment in Botany Bay, Australia. The technique could be adapted to radioisotope water tracing experiments and also meteorological, oceanographic and other geophysical investigations.

The use of a digital computer for the calculation of successive complex formation constants

A simple digital computer technique is described for the calculation of the successive complex formation constants in systems in which only 2 types of complexes are formed. This method should prove useful for the calculation of equilibrium constants in more complicated systems.

The Structure of Space and the Formalism of Relativistic Quantum Theory. II

A purely group theoretical treatment of interactions of relativistic particles is shown to be possible in the connection of a finite geometry of space-time. The S operators are constructed by means of the reductions of the irreducible unitary representations of the relativity group of space-time. The dependence of the S-matrix elements on the momenta is still nontrivial, since there is a nontrivial distribution of observable momenta in a finite geometry. The Feynman graphs are easily evaluated by a simple computational technique involving five rules. The coupling schemes corresponding to nuclear electromagnetic, and weak forces in finite geometry are considered.

Objective Computation of Some Meteorological Quantities

This paper describes research in formulating objective weather analysis and forecasting aids for calculation by an electronic computer. Methods based upon single-station techniques for analysis of rawinsoundings are presented for computing wind shear, lapse rate, thermal advection and a parcel stability index. These quantities are useful in identifying phenomena such as fronts, troughs, the tropopause and the level of maximum wind. Average values of height, temperature, humidity and wind components are computed in six arbitrarily defined layers for purposes of representing the gross atmospheric structure. A simple computer technique for calculating kinematical values of horizontal divergence, vorticity, deformation, vertical motion and geostrophic departures from layer-averaged wind and height data at three stations is developed and demonstrated for an area comprised of the midwestern United States. For this region, the computations require only 20 min on a computer of modest speed; therefore, the magnitude of the calculations is no longer an obstacle to their routine application. Limitations of the methods are described. Our experience indicates that these computer routines are adaptable to several operational and research problems even though the multiple-station computations are subject to considerable noise. Further developments of objective techniques and possible means of suppressing noise are described.