scholarly journals Auxiliary branch method and modified nodal voltage equations

2008 ◽  
Vol 6 ◽  
pp. 157-163 ◽  
Author(s):  
A. Reibiger
Keyword(s):  
Constitutive Equations ◽  
System Of Equations ◽  
Terminal Behavior ◽  
Set Up ◽  
Nodal Voltage

Abstract. A theorem is presented describing a transformation by means of which it is possible to assign to an elementary multiport with fairly general constitutive equations (including all kinds of controlled sources, nullors, ideal transformers, etc.) a modified multiport with the same all-pole terminal behavior. The branch set of this modified multiport is augmented with so called auxiliary branches whereas its constitutive equations are always in conductance form. Therefore an interconnection of a family of multiports transformed in this manner can always be analyzed by means of a system of nodal voltage equations. It will be shown that this system of equations is equivalent to a system of modified nodal voltage equations set up for the network that is an interconnection of the elementary multiports originally given.

II. Determination of constitutive coefficients and illustrative examples

1989 ◽  
Vol 327 (1595) ◽  
pp. 449-475 ◽  
Keyword(s):  
Turbulent Flow ◽  
Constitutive Equations ◽  
Theoretical Calculations ◽  
Equations Of Motion ◽  
Plane Channel ◽  
General System ◽  
Turbulent Fluctuation ◽  
System Of Equations ◽  
Constitutive Response

This paper is a continuation of Part I under the same title and is concerned mainly with the determination of the constitutive response coefficients, as well as some simple illustrative examples. First, a system of simplified constitutive equations for incompressible viscous turbulent flow is obtained from the more general system of equations in Part I through a judicial choice of retaining only those terms which appear to represent major features of the turbulent flow. Even for this simplified system of equations, the identification of some of the constitutive coefficients presents a formidable task; and this is especially true in the case of those coefficients that are associated with the presence of the additional independent variables of the theory due to the manifestation of the alignment of eddies (on the microscopic scale), turbulent fluctuation and eddy density. Because of this difficulty, the present effort for identification of the various constitutive coefficients must be regarded partly as tentative, pending future availability of suitable relevant experimental data and/or pertinent numerical simulation results. Keeping this background in mind, most of the relevant coefficients in the constitutive equations are determined, or the nature of their functional forms are estimated, through consideration of‘cartoon-like’ models on the microscopic level and these results are then used in conjunction with the macroscopic equations of motion to examine a number of simple solutions. These include the possibility of a flow possessing a constant uniform velocity gradient and solutions pertaining to decay of flow anisotropy and plane turbulent channel flows. The predicted theoretical calculations are in general accord with experimental observations. In addition, for plane channel flow, plots of variation along the width of the channel for the turbulent temperature and the macroscopic velocity compare favourably with corresponding known experimental results.

Transforming Walras Into a Marshallian Economist: A Critical Review of Donald Walker's Walras's Market Models

1999 ◽  
Vol 21 (4) ◽  
pp. 413-435 ◽  
Author(s):  
Michel De Vroey
Keyword(s):  
Recent Book ◽  
System Of Equations ◽  
Fourth Edition ◽  
Market Models ◽  
Main Thrust ◽  
History Of Economics ◽  
Mature Phase ◽  
World Markets ◽  
History Of ◽  
Set Up

The history of economics can be compared to a calm sea that once in a while happens to be shaken by heavy storms. This arises when works come out aimed at turning upside down the received interpretation of a great bygone economist's views. Professor Donald A. Walker's recent book, Walras's Market Models (1996), is likely to be among them. Its main thrust is that the view present-day economists have of Léon Walras is incorrect. The basic reason, he claims, is that to date all interpretations of Walras have been based on the last (posthumous) edition of the Eléments d' économie pure (henceforth the Elements), itself a slightly amended version of its fourth edition. To him this is a pity because Walras's most interesting theoretical ideas are to be found in its second and third editions—the embodiment of what he calls Walras's mature phase of theoretical activity—yet were abandoned by him when he revised his work for the fourth edition. The aim of Walker's book, then, is to bring to the fore the picture of what he considers to be the real Walras: an economist interested in the functioning of real-world markets and abiding by a realistic methodology who is attentive to the institutional set-up underlying his system of equations, and who is keen to provide his readers with disequilibrium models. In other words, Walker is trying to make the same claim apropos Walras as Axel Leijonhufvud (1968) did thirty years ago about Keynes when defending the view of a breach between the economics of Keynes and Keynesian economics. To Walker, modern Walrasian economics, or neo-Walrasian theory as it is more often called, is a betrayal of Walras's economics.

SPINORS IN THE DYNAMICAL THEORY OF SPINNING PARTICLES

1952 ◽  
Vol 30 (3) ◽  
pp. 226-234 ◽  
Author(s):  
S. Shanmugadhasan
Keyword(s):  
Hamiltonian Dynamics ◽  
Equations Of Motion ◽  
Dynamical Theory ◽  
Total Spin ◽  
System Of Equations ◽  
Poisson Brackets ◽  
Spin Angular Momentum ◽  
Canonical Variables ◽  
Spinor Form ◽  
Set Up

The correspondence between self-dual six-vectors and symmetric spinors of the second rank is used to put into spinor form the rotational equations of motion of a particle analogous to a pure gyroscope or to a symmetrical top. These equations are then split up into an equivalent system of equations in terms of spinors of the first rank. The Lagrangian of each system is set up, and the canonically conjugate variables obtained from it in terms of covariant spinors. But the canonical variables, being not all independent, lead to weak equations in the sense of Dirac. Therefore, Dirac's generalized Hamiltonian dynamics is used in the canonical formulation in terms of Poisson Brackets. The detailed discussion of the symmetrical top case shows that, though the fundamental Poisson Brackets for the total spin angular momentum and the "spin" are the usual ones, those Poisson Brackets-involving the derivative of the "spin" are not unique.

Velocity‐stack and slant‐stack stochastic inversion

Geophysics ◽  
1985 ◽  
Vol 50 (12) ◽  
pp. 2727-2741 ◽  
Author(s):  
Jeffrey R. Thorson ◽  
Jon F. Claerbout
Keyword(s):  
Missing Data ◽  
Seismic Data ◽  
A Priori ◽  
Linear Operators ◽  
Velocity Space ◽  
System Of Equations ◽  
Reflection Seismic ◽  
Gradient Descent Algorithm ◽  
Set Up ◽  
Priori Information

Normal moveout (NMO) and stacking, an important step in analysis of reflection seismic data, involves summation of seismic data over paths represented by a family of hyperbolic curves. This summation process is a linear transformation and maps the data into what might be called a velocity space: a two‐dimensional set of points indexed by time and velocity. Examination of data in velocity space is used for analysis of subsurface velocities and filtering of undesired coherent events (e.g., multiples), but the filtering step is useful only if an approximate inverse to the NMO and stack operation is available. One way to effect velocity filtering is to use the operator [Formula: see text] (defined as NMO and stacking) and its adjoint L as a transform pair, but this leads to unacceptable filtered output. Designing a better estimated inverse to L than [Formula: see text] is a generalization of the inversion problem of computerized tomography: deconvolving out the point‐spread function after back projection. The inversion process is complicated by missing data, because surface seismic data are recorded only within a finite spatial aperture on the Earth’s surface. Our approach to solving the problem of an ill‐conditioned or nonunique inverse [Formula: see text], brought on by missing data, is to design a stochastic inverse to L. Starting from a maximum a posteriori (MAP) estimator, a system of equations can be set up in which a priori information is incorporated into a sparseness measure: the output of the stochastic inverse is forced to be locally focused, in order to obtain the best possible resolution in velocity space. The size of the resulting nonlinear system of equations is immense, but using a few iterations with a gradient descent algorithm is adequate to obtain a reasonable solution. This theory may also be applied to other large, sparse linear operators. The stochastic inverse of the slant‐stack operator (a particular form of the Radon transform), can be developed in a parallel manner, and will yield an accurate slant‐stack inverse pair.

Should a Flexible Rotor Be Balanced in N or (N + 2) Planes?

1972 ◽  
Vol 94 (2) ◽  
pp. 548-558 ◽  
Author(s):  
W. Kellenberger
Keyword(s):  
Critical Speed ◽  
System Of Equations ◽  
Flexible Rotor ◽  
Orthogonal Functions ◽  
Linear System Of Equations ◽  
Flexible Rotors ◽  
Speed Range ◽  
Set Up ◽  
Limiting Case ◽  
Analytical Expressions

The problem of balancing flexible rotors consists mainly of eliminating rotating bearing forces. Analytical expressions are derived for the deformation and the rotating bearing forces of a rotor, using orthogonal functions. With this kind of representation it is possible to set up simple conditions for the vanishing rotating bearing forces. They lead to a linear system of equations giving the compensating unbalances in each of a set number of balancing planes. Two methods used in practice are theoretically explained and compared. The “N” method employs N planes for balancing a speed range up to, and including, the Nth critical speed and can be characterized by the condition A = 0, see equation (13). The “(N + 2)” method requires two more planes for the same speed range and is characterized by A = 0 and B = 0. It is proved that limlimN→∞B=0, so that in the limiting case of an infinite number of balancing planes (speed range from zero to infinity) both methods are of equal value. The two methods differ for finite N in their accuracy and the amount of calculation. Considering simple examples with known unbalance distribution it will be shown that the main error of the N method is the result of treating B as equal to 0, which it is not, thus accounting for the greater accuracy of the N + 2 method. The additional effort needed for the latter method is justified in those cases where greater accuracy is demanded.

Free element method and its application in CFD

2019 ◽  
Vol 36 (8) ◽  
pp. 2747-2765 ◽  
Author(s):  
X.W. Gao ◽  
Huayu Liu ◽  
Miao Cui ◽  
Kai Yang ◽  
Haifeng Peng
Keyword(s):  
Fluid Mechanics ◽  
Numerical Method ◽  
Compressible Fluid ◽  
System Of Equations ◽  
Individual Element ◽  
Governing Equations ◽  
Content Type ◽  
Set Up ◽  
Free Element ◽  
Element Method

Purpose The purpose of this paper is to propose a new strong-form numerical method, called the free element method, for solving general boundary value problems governed by partial differential equations. The main idea of the method is to use a locally formed element for each point to set up the system of equations. The proposed method is used to solve the fluid mechanics problems. Design/methodology/approach The proposed free element method adopts the isoparametric elements as used in the finite element method (FEM) to represent the variation of coordinates and physical variables and collocates equations node-by-node based on the newly derived element differential formulations by the authors. The distinct feature of the method is that only one independently formed individual element is used at each point. The final system of equations is directly formed by collocating the governing equations at internal points and the boundary conditions at boundary points. The method can effectively capture phenomena of sharply jumped variables and discontinuities (e.g. the shock waves). Findings a) A new numerical method called the FEM is proposed; b) the proposed method is used to solve the compressible fluid mechanics problems for the first time, in which the shock wave can be naturally captured; and c) the method can directly set up the system of equations from the governing equations. Originality/value This paper presents a completely new numerical method for solving compressible fluid mechanics problems, which has not been submitted anywhere else for publication.

SURVEYING THE EFFECT OF GAS-VENT HOLE DIAMETER AND CLEARANCE BETWEEN PISTON AND CYLINDER ON AUTOMATIC FIRING SYSTEM OF 23mm ЗY23-2

2021 ◽  
pp. 77-86
Author(s):  
Anh Quang Mai
Keyword(s):  
Mathematical Modeling ◽  
Research Method ◽  
Model Building ◽  
System Change ◽  
Hole Diameter ◽  
System Of Equations ◽  
Real Model ◽  
Physics Model ◽  
Set Up ◽  
Firing System

On the basis of analyzing the real model 23mm ЗY23-2, the paper chooses an alternative physics model, building a mathematical modeling dynamics, set up a system of equations and solve to find the cycle of operation on automatic firing system, change some parameters of cylinder and study on its effect to do automatic firing system; besides surveying the effect of gas-vent hole diameter and clearance between piston and cylinder on automatic firing system of 23mm ЗY23-2. The research method is based on the calculation theory to ensure compliance with the manufacturer's gun design and use documents.

The Effects of Drying Techniques on Clay-Rich Soil Texture

1974 ◽  
Vol 32 ◽  
pp. 466-467
Author(s):  
T. G. Naymik
Keyword(s):  
Critical Point ◽  
Liquid Nitrogen ◽  
Liquid Nitrogen Temperature ◽  
Drying Methods ◽  
Air Drying ◽  
Freeze Dried ◽  
Critical Point Drying ◽  
Set Up ◽  
The Relationship ◽  
Quartz Grains

Three techniques were incorporated for drying clay-rich specimens: air-drying, freeze-drying and critical point drying. In air-drying, the specimens were set out for several days to dry or were placed in an oven (80°F) for several hours. The freeze-dried specimens were frozen by immersion in liquid nitrogen or in isopentane at near liquid nitrogen temperature and then were immediately placed in the freeze-dry vacuum chamber. The critical point specimens were molded in agar immediately after sampling. When the agar had set up the dehydration series, water-alcohol-amyl acetate-CO2 was carried out. The objectives were to compare the fabric plasmas (clays and precipitates), fabricskeletons (quartz grains) and the relationship between them for each drying technique. The three drying methods are not only applicable to the study of treated soils, but can be incorporated into all SEM clay soil studies.

Evaluation of Freezing Methods by Low Temperature X-Ray Diffraction

1977 ◽  
Vol 35 ◽  
pp. 330-333
Author(s):  
T. Gulik-Krzywicki ◽  
M.J. Costello
Keyword(s):  
Biological Materials ◽  
Molecular Organization ◽  
X Ray Diffraction ◽  
Glass Capillary ◽  
X Ray ◽  
Rate Dependent ◽  
Before And After ◽  
Freeze Etching ◽  
Diffraction Patterns ◽  
Set Up

Freeze-etching electron microscopy is currently one of the best methods for studying molecular organization of biological materials. Its application, however, is still limited by our imprecise knowledge about the perturbations of the original organization which may occur during quenching and fracturing of the samples and during the replication of fractured surfaces. Although it is well known that the preservation of the molecular organization of biological materials is critically dependent on the rate of freezing of the samples, little information is presently available concerning the nature and the extent of freezing-rate dependent perturbations of the original organizations. In order to obtain this information, we have developed a method based on the comparison of x-ray diffraction patterns of samples before and after freezing, prior to fracturing and replication.Our experimental set-up is shown in Fig. 1. The sample to be quenched is placed on its holder which is then mounted on a small metal holder (O) fixed on a glass capillary (p), whose position is controlled by a micromanipulator.

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