Hierarchical channel router

The channel routing problem is a special case of the wire routing problem when interconnections have to be performed within a rectangular strip having no obstructions between terminals located on opposite sides of the rectangle.We present here a new channel routing algorithm, based on reduction of the problem to the case of a ($\text{2 × n}$) grid and on consistent utilization of a ‘divide-and-conquer’ approach. For the current implementation of the algorithm, the running time is proportional to $\text{N}{}^1\text{n}\text{log}\text{(m)}$ where $\text{N}$ is the number of nets, $\text{n}$ the length of the channel (number of columns) and $\text{m}$ the width of the channel (number of tracks).Traditional technological restrictions are assumed, ie, net terminals are located on vertical grid lines, two wiring layers are available for interconnections. One layer is used exclusively for vertical segments and another for horizontal. Vias are introduced for each layer change.This algorithm consistently outperforms several known routers in quality of wiring. We tested the algorithm on several benchmark problems. One of them, Deutsch's ‘difficult example’, was routed with only 19 horizontal wiring tracks (the absolute minimum for this case), whereas all other known routers required 20 or more tracks.     

Two algorithms for three-layer channel routing

A channel router is an important design aid in the design automation of VLSI circuit layout. Many algorithms have been developed based on various wiring models with routing done on two layers. With the recent advances in VLSI process technology, it is possible to have three independent layers for interconnection. In this paper two algorithms are presented for three-layer channel routing. The first assumes a very simple wiring model. This enables the routing problem to be solved optimally in a time of $\text{O}\text{(}\text{n}\text{log}\text{n}\text{)}$. The second algorithm is for a different wiring model and has an upper bound of $\text{O(}\text{n}{}^2\text{)}$ for its execution time. It uses fewer horizontal tracks than the first algorithm. For the second model the channel width is not bounded by the channel density.     

Stability of the nonparallel developing flow in a channel

A theoretical investigation into the linear, spatial instability of the developing flow in a twodimensional channel, incorporating the effects of non-parallelism of the main flow, has been made at several axial locations. It is found that the critical Reynolds number, frequency and wavenumber decrease with increasing axial distance in the entry region and approach asymptotically the corresponding values for the fully developed flow. From all the growth rates considered herein the critical Reynolds number obtained from the growth rate of the stream function at the centre line of the channel is the minimum. In comparison to this value, the parallel flow theory overpredicts the critical Reynolds number by 22.8 percent at $\text{X}\text{?}\text{= 0.001}$, reducing to 8.3 percent at $\text{X}\text{?}\text{= 0.008}$. The neutral curves based on growth rates of different flow quantities tend to merge into the neutral curve for the parallel flow theory as $\text{X}\text{?}$ increases, thereby implying that the nonparallel effects vanish for large $\text{X}\text{?}$ as they should.     

Calculation of flow between two rotating coaxial disks by differentiation with respect to an actual parameter

A method which allows to find the dependence of the solution $\text{x(ξ, s)}$ on the parameter $\text{s}$ for a nonlinear boundary value problem will be presented. The calculation of the dependence of $\text{x(ξ, s)}$ on $\text{s}$ is performed in a non-iterative way. The technique is employed to solve a difficult two-point boundary value problem: steady state flow of an incompressible viscous fluid between two rotating coaxial disks.     

Optimal utilization of fixed-capacity channels in feedback control

The performance limitations on the linear control of a linear plant, due to the presence of a feedback channel with finite information capacity, are considered in this paper. This situation may arise in such diverse applications as (a) the remote control of a plant, using a digital data link for feedback, (b) where quantization errors and bit errors of a digital controller may be modelled as occurring in a noisy digital channel in cascade with an ideal controller, and (c) in human-operator modelling, where the sensory feedback channels are characterized by fixed information capacity due to neural noise. The principle result obtained is that, given the state-dimension n of the plant and the channel capacity ?, reliability function E(R), and block encoding time $\text{T> >}\text{1}\text{C}$, the optimum data-rate R satisfies the equation 2R=nE(R). This rate provides the optimum tradeoff between the effects of quantization errors and message errors. It is seen that R_opt→C as n becomes large, but that good channel performance is retained provided that $\text{> >}\text{n}\text{T}$.     

Simplified discrete method for the design of helical rectangular beams of very large width

Helical rectangular beams are defined as beams circular in plan and supported only at their two ends. They are in general three-dimensional structures indeterminate to the sixth degree. In the present study only symmetric helical beams of circular plan are considered. The redundancy is therefore reduced to the second degree. They are analysed as linear space structures loaded vertically with a uniformly distributed live and dead load and with a ratio of width to height: $\text{b}\text{d}\text{? 0.50}$. The proposed method has practical application for the design of concrete stairs and rumps.The principle of virtual work [1, 2], is used for the analysis by chosing the appropriate release system to arrive at final expressions which are solved using appropriate design charts prepared for shallow-wide and thin beams, $\text{b}\text{d}\text{? .50}$, $\text{b}\text{d}\text{< 0.50}$, with fixed supports. This discretization is necessary because of the shape of selection which defines its structural form. For both types of structures the solutions are valid for beams with both ends fixed. Only shallow-wide beams are considered in this paper. A numerical example is worked out and comparison of the values of stress resultants obtained by the proposed method and other methods. Some conclusions are deduced.     

Off-line feed-forward and H∞ feedback control on a vibration rig

This paper discusses the improvement of the tracking accuracy on an automotive test rig by extending the industrial available off-line controller with an $\text{H}{}_{\mathrm{\infty }}$ feedback controller. The improvement is shown by comparing the tracking error for both control schemes: the industrial controller on the one hand and the industrial controller with $\text{H}{}_{\mathrm{\infty }}$ feedback controller on the other hand. The $\text{H}{}_{\mathrm{\infty }}$ controller is designed based on a mixed sensitivity approach. After a theoretical analysis, the results are illustrated by simulations and experimental results on one axis of a hydraulic test rig which is used in the automotive industry for vibration comfort evaluations of new vehicle prototypes.     

Study of incompressible flow separation using primitive variables

The flow in a channel with an asymmetric constriction has been analyzed, using the primitive variables. The objective of this study is to develop a reduced form of the Navier-Stokes equations that is regular at the separation point. The resulting formulation is a semi-elliptic model comprised of the parabolized momentum equations together with an elliptic equation for the pressure distribution. Analytic coordinate transformations are used to provide surface-oriented coordinates with proper resolution for the viscous regions near the channel walls, as well as for the separated-flow regions. Results are obtained for several flow configurations using a semi-implicit numerical method of solution. These are presented in terms of streamling contours and shear-stress and pressure distributions at the channel walls. Comparison with the corresponding Navier-Stokes results shows that the semi-elliptic model performs very well as regards the separation singularity. Some of the qualitative flow features predicted by the available asymptotic analysis for constricted-channel flows are also well reproduced in some of the present results obtained for $\text{Re=1000}$.     

“ExTHERM”: the interactive support package of experimental thermodynamics

The presented program package “ExTHERM” consists of three parts: (i) cETD, a simple interactive open data bank module covering all types of metal alloys (over 150 binary phases and some ternaries), (ii) cMod, a module for algebraic conversion among different representations of excess data, and (iii) cM3_(KMS/ EMF/HTC), three interactive evaluation units suitable for overall best fits of experimental investigations expandable to mass spectrometric (KMS), EMF, and calorimetric investigations (HTC). The concept is based upon the multi-component TAPS ($\text{T}$hermodynamically $\text{A}$dapted $\text{P}$ower $\text{S}$eries) concept of excess quantities covering all types of solutions, includingn liquid alloys showing short range ordering. The data bank is based upon the Hultgren data of binary systems and on new experimental data. Individual supplements may be performed easily. The conversion module employs a modular concept procedure which makes the conversions independent of the actual system data. For all software modules contact the author.     

Miscibility gap and critical point behavior for a cubic margules solution model

It is pointed out that a four parameter, binary solution model, in which the temperature independent enthalpy and excess entropy of mixing are cubic functions of the atom fraction, has provided quantitative fits to the thermodynamic properties of many metallic solution phases. It is therefore desirable to understand this semi-empirical model, in particular its miscibility gap and critical point behavior. It is shown that the latter is governed by two parameters, ? and η, that depend upon the temperature and the values of the four, temperature and composition independent, solution parameters. ? is the excess Gibbs free energy of mixing at $\text{x =}\text{1}\text{2}$ divided by RT/4. The parameter η is the difference in the excess chemical potentials at $\text{x =}\text{1}\text{2}$ divided by RT/4. The solution parameters define half of an infinite straight line in the ?-η plane called the constant-parameter trajectory, whereas the classical critical points fall along a parabola-like curve through ? = 2, η = 0. The appearance or disappearance of a miscibility gap is associated with the intersection of the constantparameter trajectory and the critical locus. The critical composition can be anywhere. Besides the normal miscibility gap, an inverted gap that first appears at high temperatures can occur and both types can occur in the same system. Equations for the gap width and asymmetry that are asymptotically correct near the critical temperature are developed. These show how the magnitude of the gap-width depends upon the solution parameters for a given temperature and critical point. The results are illustrated by application to some III–V systems and in obtaining a quantitative fit to the Pb-Ga system.     

Generation of all possible trees of a graph in independent groups

A special graph, the PS graph, is introduced and an algorithm is developed to generate all trees of such graphs. It is proved that for any given graph, $\text{G}$ there exists certain number of PS graphs, obtained from $\text{G}$, such that the collection of all trees of all such PS graph span all trees of $\text{G}$ with no duplication. In addition to a number of properties of PS graphs indicated, the procedure seems very useful for topological analysis and design of networks, or any other types of systems that can be represented by a linear graph.     

Separating clouds from ocean in infrared images

To use digital infrared images for quantitative sea surface temperature studies, data which do not represent ocean temperatures must be identified and labeled so that they will not be used in subsequent analysis. A pair of algorithms, run in sequence, were designed to sort the 57 coregistered images which were collected from the satellite NOAA-6 for the Coastal Ocean Dynamics Experiment (CODE) in 1981.¹ A combination of threshold tests and uniformity tests are used on two infrared channels to eliminate data which are from clouds or land. The goal of the procedure is to sort many images efficiently, eliminating only obviously contaminated data. To maintain the best temporal resolution, the algorithms do not rely on a visible channel and thus sort both daytime and nighttime images. The large number of measurements ( $\text{> 250,000}\text{per image}$) makes an automatic procedure desirable; however, some variations in input parameters from one image to the next were found to be essential to retain all reasonably cloud-free data.     

Planning the route system for urban buses

It is assumed that the number of buses to be operated during the various periods of the day, which is the primary factor determining costs, has already been determined and is a problem constraint. The method determines the frequencies on each route but no attempt at scheduling is made. The city is divided into zones and the number of journeys to be made by the public between each pair of zones is a data input expressed in matrix form. The objective function, to be minimized, is the sum of the journey time (which includes allowance for transfer times) plus discomfort penalties proportional to the number of passengers who cannot find seats.The planning method has two phases. In the first, desirable routes, which may be added to an initial set of routes, are generated; and routes, which may be deleted from the augmented set of routes, are pointed out. The routes to be added are selected from a set of candidate routes each of which is based on a route skeleton consisting of four zones with the extremes restricted to a set of terminal zones. In the second phase, optimal frequencies for a set of routes, under the constraint of a given number of available buses, are determined by a gradient method. The optimal value of the objective function in the second phase serves as a more accurate evaluator of a generated set of routes.Fortran programs implementing the two phases have been run for the Haifa area which was represented by 41 zones. The route determining algorithm produces a set of routes in 3 min C.P.U. on an I.B.M. $\text{360}\text{50}$. The frequency program effectively minimized the objective function for 20 routes in 15 min run time on an I.B.M. $\text{360}\text{44}$.There is strong evidence that the programs provide useful results and they appear to be useful planning tools.     

A method for the calculation of eigenfunction expansions

In this paper, a method is presented for the calculation of the coefficients of the series expansion of a function f(t), in the base orthonormal set made up by the eigenfunctions of the self-adjoint operator $\text{L: L(x(t)) = (}\text{d}\text{dt}\text{)( p(t)(}\text{dx(t)}\text{dt}\text{))?q(t)x(t)}$. We show that the values of the numbers $\text{t}\text{}$x_k> can be obtained by solving the differential equation L + λ) y(t) = Kf(t), in the interval of definition, for each of the eigenvalues λ of L and by using as initial conditions those which determine one of its associated orthonormal functions. This makes the method specially interesting for its implementation on a hybrid computer: One advantage of the proposed method is that the analysis of f(t) does not require the simultaneous presence of the functions of the base set and the problem signal, thus eliminating both the problems of the synchronized generation of signals and the need for storing it in memory.     

Characterizations for functional dependency and Boyce-Codd normal form families

A functional dependency (fd) family was recently defined [20] as the set of all instances satisfying some set of functional dependencies. A Boyce-Codd normal form, abbreviated BCNF, family is defined here as an fd-family specified by some BCNF set of functional dependencies. The purpose of this paper is to present set-theoretic/algebraic characterizations relating to both types of families.Two characterizations of $\text{F}$($\text{I}$), the smallest fd-family containing the family $\text{I}$ of instances, are established. The first involves the notion of agreement, a concept related to that of a closed set of attributes. The second describes $\text{F}$($\text{I}$) as the smallest family of instances containing $\text{I}$ and closed under four specific operations on instances. Companion results are also given for BCNF- families.The remaining results concern characterizations involving the well-known operations of projection, join and union. Two characterizations for when the projection of an fd-family is again an fd-family are given. Several corollaries are obtained, including the effective decidability of whether a projection of an fd-family is an fd-family. The problem for BCNF-families disappears since it is shown that the projection of a BCNF-family is always a BCNF-family. Analogous to results for fd-families presented in [20], characterizations of when the join and union of BCNF-families are BCNF-families are given. Finally, the collections of all fd-families and all BCNF-families are characterized in terms of inverse projection operations and intersection.     

Laminar compressible flow between close rotating disks: An asymptotic and numerical study

Laminar steady compressible flow between close rotating thermally conducting axisymmetric disks with inflow was investigated by means of a numerical solution of the Navier-Stokes equation and an asymptotic analysis. The approximate solution, obtained for small ?, E and H (Rossby and Ekman numbers, and height/radius, respectively) is valid for “merged”, “close” and “separate” boundary layers on the disks, corresponding to β? 1, $\text{β ? 1}$ and β? 1, respectively (where $\text{β =}\text{H}\text{2}\text{√}\text{E}\text{ρ}$, and ρ is the non-dimensional density). These three cases may appear simultaneously in different regions of the same system due to the large variation of ρ in the radial direction. The small ? (i.e. negligible convection terms) does not necessarily imply small perturbations of the pressure, and a special treatment of the pressure term was used in order to account for this feature, which sometimes culminates in inversion of the radial pressure gradient. Thenumerical solution was obtained by a finite-difference, modified Cheng-Allen method, using a non-uniform mesh. The numerical and the approximate solution are in good agreement.     

Estimating the quality of computational algorithms — Part 1

Computational algorithms for approximate calculation of the mapping $\text{A:X → Y}$ on some element $\text{f}$ of the compactum $\text{X}$ are considered, where $\text{A}$ is a one-to-one continuous mapping. Topology on $\text{X}$ and $\text{Y}$ is set by imbedding them into some Banach spaces. The relation between $\text{?(N; X)}$ and $\text{?(N);Y}$ plays the main role in the problems concerning the construction of such computational algorithms. Here $\text{?(N);X)}$ is a function reciprocal to the ?-entropy of the compactum $\text{X}$. The computational algorithm $\text{U}$ is characterized first of all by the volume of the input data $\text{N}$ and that accuracy ? with which elements $\text{g}$ on the output are defined. If $\text{N}$ is given (but under condition that a table of any $\text{f}$ is admissible), then inf $\text{? = ?}{}_1\text{(N)}$ exists.For the given concrete algorithm the quantity $\text{?/?}{}_1\text{(N)}$ characterizes its qualities and is one of the most important characteristics of the algorithm. In this paper some of the simplest current algorithms are analyzed, and their quality is determined as well. A number of recommendations relative to the questions of the construction of computational algorithms is proposed.     

Finite difference representations of vorticity transport

Explicit finite difference representations of the steady two-dimensional laminar vorticity transport equation of fluid dynamics are summarized and discussed. The approximations known as ‘upwind differencing’, ‘locally exact’ after Alien and Southwell [1], Briggs [4] or Dennis and Hudson [12] are all shown to be the central difference approximation with the addition of numerical diffusion of the order of the error term in cell Reynolds number, R_c, which makes the associated matrix diagonally dominant. The local truncation error of this type of approximation can be minimized thus: (i) for ¦$\text{R}{}_{\mathrm{c}}\text{¦? 2}$, the central difference approximation, (ii) for ¦$\text{R}{}_{\mathrm{c}}\text{¦ > 2}$, upwind differencing applied to the inviscid equations, and therefore can be considered as a boundary layer approximation. This is the scheme introduced by Spalding [35]; successfully tested by Runchal [33].The local truncation error of the boundary condition, after Woods [39] for the vorticity is minimized in such a way that the formula is third-order accurate in grid size, in rectangular Cartesian coordinates.     

A PC-based decision support and expert system for labour market analysis

Due to the worsening national economy, labour market analysis will receive increasing attention in the near future. This article describes an operating Decision Support (DSS) and Expert System (ES) for labour market analysis and its designing process. The $\text{DSS}\text{ES}$ is designed following the process of Pictorial Approach to modelling, and it provides researchers with timely and credible analysis of labour market information. This $\text{DSS}\text{ES}$ uses graphic presentation to delineate employment trends and magnitude, and it takes into consideration the special needs of business research centers by its implementations via spreadsheet application to improve the learning curve. By applying rule indices directly in the spreadsheet, the ES integrates with the DSS fully, and the decision makers are able to retain access to the historical data for ad hoc computations.