String Covering: A Survey

The numerical evaluation of five Cauchy integrals frequently encountered in thin‐airfoil‐wing theory are presented based on the work of Stark. Of these, the quadrature rules for four of the integrals appear in a very simple form which make it particularly easy for coding on digital computers and pocket calculators. Finally, it is indicated how these quadrature rules may be used to solve an integral equation of the type

Publication Rights Reserved This paper was prepared for the Society of Petroleum Engineers Gas Technology Symposium to be held in Omaha, Nebr. Sept. 15–16, 1966. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by whom the paper is presented. Publication elsewhere after publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon requested to the Editor of the appropriate journal, provided agreement to give proper credit is made. Discussion of this paper is invited. Three copies of any discussion should be sent to the Society of Petroleum Engineers Office. Such discussions may be presented at the above meeting and, with the paper, may be considered for publication in one of the two SPE magazines. Abstract This paper attacks the problem of computing transient flow in gas pipeline networks by means of finite differences and digital computation. Pressure (P) and flow (Q) are assumed to he dependent upon a single space variable (x) along the pipe and on the time (t). A greatly simplified but generally accepted mathematical model consistent, of a system of nonlinear partial differential equations is the point of departure: Following simple changes of variable (w = p2, v = Q2), the problem is reduced to the solution of: A stable predictor-corrector method of finite difference approximation due to Jim Douglas, Jr. and B.R. Jones, Jr. is employed to reduce the computation to the solution of a system of linear algebraic equations (matrix inversion). The incorporation of initial conditions, boundary conditions, and internal flow conservation equations, all of which in finite difference form become linear algebraic equations, results in a single matrix equation for the calculation of pressures and flows in the pipeline network. DERIVATION OF FINITE DIFFERENCE EQUATIONS The computation of transient flow in gas pipeline networks is complicated mathematically by the nonlinearity of the governing partial differential equations. This is in marked contrast, of course, to the situation in steady state flow, where the corresponding equations, at least in their simplest form, have exact mathematical solutions. The mathematical model we assume has resulted from a number of simplifications, including the neglect of altitude and temperature variation. Although it is beyond the scope of this note to discuss the validity and significance of these simplifications, it is generally believed that the equations we will discuss are an accurate first order description of the actual physical system.

Analysis of correlated multiple input/multiple output systems are of paramount importance in problems concerning the system identification of physical systems like missiles, spacecraft, aircraft, rotorcraft, acoustics. To study the dynamic behaviour of such physical systems, it is important to investigate the spectral nature of correlated inputs/outputs and evaluate their separate and combined effects on any desired response of the vehicle. In this paper iterative algorithms for the solution of multiple input/multiple output problems formulated from flight test data are developed and presented in a simple form. A joint multiple coherence function is developed to study the combined effects of both states and controls. The algorithms are efficient to compute, analyse and interpret the results. Specific MIMO applications studied in this paper are the extraction of high quality frequency response functions and estimation of some lateral handling qualities of the BO-105 helicopter. A model structure for roll rate response to lateral cyclic stick representing dutch roll, coupled roll/rotor regressing flapping and lead lag/air resonance dynamics are presented in the transfer function model form. The time response simulation is also conducted to verify the accuracy of the extracted model. The results are compared with those available in the literature.

Diffraction of electromagnetic waves by longitudinally periodic media (reflection gratings) is rigorously analyzed using an exact coupled-wave approach. The analysis is formulated in a simple matrix form easily implemented on a digital computer. The intensities of the two waves, the diffracted (reflected) and transmitted waves, are calculated for a wide range of parameters. These exact results are then compared to results obtained with approximate two-wave modal, and with multiwave and two-wave coupled-wave analyses. The applicability of these approximate theories is discussed. The case of other than first-order Bragg incidence is also included.

The transfer matrix method together with a digital computer form the foundation of the dynamic analysis of rotor-bearing systems. The properties of each segment of the rotating shaft are expressed in simple matrix form and the overall dynamic behaviour is then obtained by successive multiplication of the element matrices. The main drawback associated with this method is the numerical instability in calculating natural frequencies for complex systems. The finite element method, on the other hand, uses the element stiffness and mass matrices to form the global equation of motion for the complete system. This avoids the numerical problems of the transfer matrix method at the expense of the computer memory requirements. The new method described in this paper combines the transfer matrix and finite element techniques to form a powerful algorithm for vibration analysis of rotor-bearing systems. It is shown that the accuracy improves significantly when the transfer matrix for each shaft segment is obtained from finite element techniques. The accuracy and efficiency of the hybrid method are compared with the transfer matrix method for a simply supported uniform rotating shaft where an analytical solution for the critical speeds and mode shapes is available. The method is then applied to a flexibly supported uniform shaft and a non-uniform shaft with a large disc to show the capability of the method for finding the critical speeds of complex rotor-bearing systems.

Efficient and consistent string processing is critical in the exponentially growing genomic data era. Locally Consistent Parsing (LCP) addresses this need by partitioning an input genome string into short, exactly matching substrings (e.g., "cores"), ensuring consistency across partitions. Labeling the cores of an input string consistently not only provides a compact representation of the input but also enables the reapplication of LCP to refine the cores over multiple iterations, providing a progressively longer and more informative set of substrings for downstream analyses. We present the first iterative implementation of LCP with Lcptools and demonstrate its effectiveness in identifying cores with minimal collisions. Experimental results show that the number of cores at the i^th iteration is O(n/c^i) for c ~ 2.34, while the average length and the average distance between consecutive cores are O(c^i). Compared to the popular sketching techniques, LCP produces significantly fewer cores, enabling a more compact representation and faster analyses. To demonstrate the advantages of LCP in genomic string processing in terms of computation and memory efficiency, we also introduce LCPan, an efficient variation graph constructor. We show that LCPan generates variation graphs >10x faster than vg, while using >13x less memory.

This paper describes a number of programmes for digital computers that have been developed by the authors' firm to eliminate many of the tedious hand calculations which are encountered in the preliminary stages of steam-turbine and condenser design. By their use a considerable amount of the designers' time is saved and fatigue is reduced. These programmes also eliminate mistakes and inaccuracies which may occur in long calculations made by hand. The programmes described have been chosen as being representative of the range of programmes used in preliminary turbine design and optimization and are as follows: a programme to enable steam properties to be calculated, based on the formulae given in the Keenan and Keyes Steam Tables; a programme which can be used to determine the efficiency of small industrial turbines; a feed-heating programme which will carry out the calculations necessary to determine the preliminary energy balance for a feed-heating cycle; a detailed energy-balance programme incorporating turbine-efficiency calculations; a condenser-optimization programme for determination of the ideal parameters to be used in the design of a condenser. The programmes are arranged so that unskilled operators can run them on the computer without the help of an experienced programmer. Facilities are also made available for writing programmes in a simplified form called ‘autocode’ which can be used by an engineer after the briefest of trainings. Some programmes are described in considerable detail to assist others who may wish to write a similar programme or to compare them with programmes of their own. All these programmes have been in regular use for more than three years and have greatly enlarged the scope of investigations which may be carried out in the project stage of the design of a steam-turbine generator and associated power-station equipment.

Computer Aided Design and Computer Control Using Minicomputer

A recently suggested three-phase oscillator model system is developed further. The resulted model, although it is relatively simple and merely of a seventh order, represents fairly accurately the features and the dynamic behavior of a regulated synchronous generator (the simulated results on a digital computer are compared to measurements on a 2.2-kVA generator system). The model, in spite of its demonstrated simplicity, embraces a fully three-phase dynamics which includes variations directly at the line frequency. The three-phase oscillator signals represent in the model the components of a rotating magnetomotive force. Magnetomotive forces are regarded as the main variables, since the regulation in an experimental generator system, which is employed for comparison, is achieved by controlling the rotor current via a current source.

Starting from the relations between entries of block pulse operational matrices, block pulse regression equations corresponding to the original differential equation models with time-varying parameters are obtained. Based on simple forms of the regression equations, algorithms developed in discrete-time model identification can be applied directly to estimate the time-varying parameters of the continuous models without much modification. Compared with other identification methods for the same problem, this new method is simple, and can be applied to both batch and recursive estimations of continuous time-varying linear systems from their sampled input and output data by means of digital computers.