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This nested decomposition algorithm is intended for solving linear programs with the staircase structure that is characteristic of dynamic multi-sector models for economic development. Staircase problems represent a special case of the discrete-time optimal control problem. Our method is based upon the same principles as that of Glassey [5], but appears easier to describe and to relate to control theory.

The paper presents feedforward control schemes for an electrowinning process, via experimentally established dynamic models.

The theoretical considerations developed in a previous paper (Kazantzis, 1973) are applied with the aid of the CDC-3300 computer and examples of new families of doubly symmetric solutions of the restricted three-dimensional problem obtained thereof are presented. Rough estimates of initial conditions of these families have been obtained by applying an extension of the scanning technique developed by Henon (1966).

In chemical engineering practice, deviation from a perfectly mixed equilibrium stage in phase separation processes is described by a stage efficiency. In dynamic models this parameter is in most cases meaningless, except when the deviation from equilibrium is caused by interfacial transport resistance. The present paper shows that when this resistance approaches zero, there is an eigenvalue related to the interfacial transport that goes to − ∞. The response mode attached to this eigenvalue expresses the deviation from equilibrium. Approximationg this mode by zero, may be defined as a “pseudo-equilibrium”. In a dynamic sense, the stage efficiency has a proper meaning only in this case, but it should be emphasized that this state space reduction is an approximation valid only for moderate deviations from true equilibrium. Hence, the stage efficiency has a much more narrow range of sound application than is usually considered in the chemical engineering literature.

This paper deals with turbulent motions in a homogeneous incompressible electrically conducting medium in the presence of a magnetic field which is on average homogeneous and stationary. Using a model in which the turbulence is produced by a stochastic body force, and supposing a weak interaction between motion and magnetic field, a method is developed for calculating the pair correlation tensor of the velocity field from that occuring in a zero magnetic field. As an example, the pair-correlation tensor for a homogeneous stationary turbulence, which is isotropic and mirror-symmetric for zero magnetic field, is determined. With obvious assumptions on the correlation for zero field, two results are obtained. Firstly, the turbulent velocity is reduced by the magnetic field, the component parallel to the field, however, less than those perpendicular to it. Secondly, the correlation length parallel to the field turns out to be greater than the one perpendicular to it, indicating a tendency towards two-dimensional motion. Finally, the possibility of special situations is briefly discussed in which the turbulent velocity is enhanced by the magnetic field, and the anisotropies of the velocity components and the correlation lengths are opposite to those above. Gegenstand dieser Untersuchung ist die turbulente Bewegung eines homogenen, inkompressiblen, elektrisch leitenden Mediums unter dem Einflus eines im Mittel homogenen und stationaren Magnetfeldes. Dabei wird die Turbulenz als Folge einer stochastischen Kraft betrachtet und die Wechselwirkung zwischen Bewegung und Magnetfeld als schwach vorausgesetzt. Es wird eine Methode entwickelt, die den Korrelationstensor zweiter Stufe fur das Geschwindigkeitsfeld aus der entsprechenden Grose fur verschwindendes Magnetfeld zu berechnen gestattet. Als Beispiel wird der Korrelationstensor fur eine homogene und stationare, ohne Magnetfeld isotrope und spiegelsymmetrische Turbulenz angegeben. Unter naheliegenden Annahmen uber die Korrelation ohne Magnetfeld gelangt man zu zwei Folgerungen. Erstens wird die turbulente Geschwindigkeit durch das Magnetfeld verringert, die Komponente parallel zum Magnetfeld jedoch weniger als die senkrecht zu diesem. Zweitens fallt die Korrelationslange parallel zum Magnetfeld stets groser aus als die senkrecht dazu; dies entspricht der Tendenz zu einer zweidimensionalen Bewegung. Schlieslich wird noch kurz die Moglichkeit von Sonderfallen erortert, in denen das Magnetfeld die Turbulenzintensitat erhoht und eine Anisotropie der Geschwindigkeitskomponenten und der Korrelationslangen auftritt, die der obengenannten entgegengesetzt ist.

Although dynamic models are now an important part of applied demand analysis, some of their fundamental concepts still suffer from a substantial lack of clarity. A particular case in point is the distinction between stock adjustment and habit formation in the Houthakker-Taylor model (1970). Empirical considerations prompted Houthakker and Taylor to specify a single state variable for each good and then to conclude that a good is habit forming or stock adjusting depending on the state variable's sign. However, besides having an obvious drawback of being ex post, this procedure is subject to the further criticism that, by treating expenditures for nondurables and services in the same way as expenditures for durables, it implicitly views habit formation and stock adjustment as arising from symmetrical processes. This is unfortunate, for stock adjustment and habit formation reflect intrinsically different phenomena, and to elaborate upon this, without the constraints imposed by thoughts of immediate empirical application, is one of the primary purposes of this paper.

There are now over 30 institutions around the world, where major projects both on world models and world issue modelling are underway. This article summarises some of the general findings about these activities and provides a descriptive account of (a) world dynamic models concerned with the major world subsystems and their interactions; (b) dynamic “issue” models concerned solely with a major sub-system representing a particular world issue or with local problems which have worldwide ramifications; (c) other research programmes relevant to global modelling. The view is taken that although such models may have an important speculative research function, ultimately they are to be of use in aiding policies aimed at the resolution of the urgent world problems they approach.

Using information concerning attractive junctions a quantitative theory is developed to predict the modulus defect and decrement associated with attractive junction break-down phenomena. A large hysteretic energy loss occurs when the jog movement in the moving primary dislocation after break-down is conservative. To formulate the theory a distribution in the symmetrical dislocation loop lengths bordering attractive junctions is considered. The spectrum in the junction breaking strengths is also employed. It is pointed out that this theory could be applicable to the large damping observed by direct measurements of the unidirectional closed stress cycle damping loops observed in copper crystals prestrained in one sense. The theory appears to be consistent with and explain quantitatively many of the salient features of this pertinent experimental data. Es wird eine Theorie entwickelt, welche Moduleffekt und Dampfung auf der Basis der Eigenschaften von Rekombinationen zwischen frei beweglichen Versetzungen und anziehenden Waldversetzungen beschreibt. Bewegt sich der beim Schneiden einer Waldversetzung entstandene Versetzungssprung konservativ, dann ist der Energieverlust zum uberwiegenden Teil hysteretischer (athermischer) Natur. Bei der Formulierung der Theorie wird angenommen, das die Rekombination in der Mitte der beweglichen Versetzung liegt. Es werden Spektren in der Lange der beweglichen Versetzungen und in der Starke der Rekombinationen berucksichtigt. Die Theorie erhalt die starke Dampfung, die man beobachtet, wenn man an einsinnig verformten Kupfereinkristallen geschlossen Dampfungsschleifen ohne Polaritatswechsel der Last durchfahrt. Die Theorie scheint mit vielen der wesentlichen Grundzuge dieser experimentallen Daten konsistent zu sein und diese quantitativ zu erklaren.

Structures resembling rift valleys and oceanic ridges are produced in dynamic models in which a buoyant body rises from the mantle and spreads laterally below the crust. Tension fractures accordingly tend to develop in the crust. In similar fashion, but on a somewhat smaller scale and at higher crustal levels, the rise of basement culminations through the geosynclinal column produces batholiths, folds, nappes and other structures characterizing orogenic belts. The models are generated in a large-capacity centrifuge.

Proper selection and ordering of the variables of uniform, linear, one-dimensional distributed, dynamic models are shown to simplify their analysis, particularly when several simultaneous energy flows are coupled. Symmetric and asymmetric product variables are identified in pairs, leading toward criteria for system symmetry and reciprocity and formulas for the desired transmission matrices. Standard operational matrix techniques allow the identification of generalized wave-scattering variables, leading to decoupled equations. Application of the technique is demonstrated for simple systems, counterflow heal exchangers, the Bernoulli-Euler beam, and flexible fluid-carrying tubes.

Concepts of sonic‐boom pressure loading of building structures and the associated responses are reviewed, and results of pertinent theoretical and experimental research programs are summarized. The significance of sonic‐boom load time histories, including waveshape effects, are illustrated with the aid of simple structural elements such as beams and plates. Also included are discussions of the significance of such other phenomena as three‐dimensional loading effects, air cavity coupling, multimodal responses, and structural nonlinearities. Measured deflection, acceleration, and strain data from laboratory models and full‐scale building tests are summarized, and these data are compared, where possible, with predicted values. Damage complaint and claim experience due both to controlled and uncontrolled supersonic flights over communities are summarized with particular reference to residential, commercial, and historic buildings. Sonic‐boom induced building responses are compared with those from other impulsive loadings due to natural and cultural events and from laboratory simulation tests.

Considerable simplification results when following steps are used singly or in combination: (1) special arrangement of variables in determinant form; (2) selection of repeating variables to represent dynamic, kinematic and geometric variables; dimensional analysis provides partial solution without revealing inner phenomena; dimensionless coefficients used to obtain similarity between model and prototype; example given of analyzing drag on ship.

Much information about the operation of the visual system has been garnered from data of experiments employing successive, cyclic stimuli. Spatial (Fry & Bartley, 1936; Granit, 1930; Foley, 1956), temporal (Granit & Hammond, 1931; Murphree, 1954; Battersby & Jaffe, 1953), spatio-temporal (Granit 8: Davis, 1931; Hylkema, 1942), interaction and induction (Motokawa, 1950) effects have been demonstrated. Evidence for chemical (Hecht, 1935; Jahn, 1946) and neural (Crozier & Wolf, 1943; Bartley, 1937) factors, as well as central (Walter & Walter, 1949; Walker, Woolf, Hdstead, & Case, 1943) involvement in these phenomena has been given. Dynamic models of visual system operation (Stroud, 1956; De Lange, 1952) have been constructed, based in part on data from such experiments. These researches might be characterized as psycho-physiological. In the context of the Gestalt school, pioneering contributions to the understanding of temporal factors in vision were made by Wertheirner ( 1912 ) by his specification of conuolling variables for simultaneity and apparent movement. Korte (1915) followed soon after and set forth his laws, concerning, among other variables, the time between visual stimuli necessary for optimal apparent movement. These laws have since been amended and modified by subsequent experimentation, notably that of Neuhaus (1930). With rare exception, however, flash-type stimuli used in these experiments came in regular succession, repeated at fixed, constant intervals, or else consisted of only two or three sequential elements. This being so, ic seemed vital to investigate the effects of trregalar, arhythmic (as well as regular), temporal cyclic patterns of visual flash presentation, anticipating that results of the interplay of such temporal factors might yield some useful new insights about the foregoing aspects of visual function. In accordance with the aim stated, a configuration of four pinhole-size dots of light, one at each corner of a diamond, was selected as the spatial pattern over which the stimuli of the experiment were presented. The four dots, flashed in sequence, constituted one cycle in a continuous train of cycles pre

Two body mechanical system operating within dynamics laws simulating backward and forward bending motions of falling cat

SUMMARY A derivation is presented of the variance-covariance matrix of endogenous variables in a linear dynamic system, given the variances and covariances of exogenous variables and disturbances. A general formulation of the stabilization problem for linear systems is proposed, using as a measure for stability a function variances and covariances of the endogenous variables.

Static and Dynamic Approaches. The static approach to social organization is a structural view of society that emphasizes order, continuity, symmetry, and timeless consensus. Its ideal representation is the inert, tradition-bound, technologically simple, culturally homogeneous, informally-controlled, isolated, and kinshipcentered society. (11, 12, 33) In this society the members, as individuals, presumably are also organized, because they uncritically accept a consistent and uniform value-system and have slight inclination to deviate because of the scarcity of alternate and particularly contradictory schemes of behavior. But this version of social

Photographic study of acceleration and pressure effects on Al agglomerates and combustion processes on solid propellant surface, describing pit growth by combustion model

Anomalous behavior has been observed when molecular band-models incorporating the Curtis-Godson or similar approximations are applied to problems characterized by a large variation in temperature along the optical path. The nature of this misbehavior has been examined and a procedure has been developed for its suppression by the introduction of a less restrictive assumption in the derivation of the band model from the basic equation of transfer.

Network synthesis technique applied to structural dynamics design, using topological formulas to express systems response transfer functions

Sensitive, high-powered radar have been used to study the dynamics of the convective process in optically clear air. Various stages in the development of the convective field have been identified on the basis of distinctive radar patterns of the cells. The characteristics of the convective field as a whole and the individual cells making up the field during each stage are discussed. During the initial formation stage, the radar returns are diffuse and mottled. Following the destruction of the surface inversion, the first doughnut or ring-shaped radar returns appear which mark the beginning of the field growth stage. At the onset of this stage, the cells are small, around 100-200 m in diameter. As time progresses, the height of the convective field increase at a rate of 4.5-6 m min− 1, while the convective cells themselves grow to several thousand meters in diameter. Based on a comparison of the radar patterns with previous aircraft measurements of the physical properties of convective cells, it i...

Tradicionalmente en la ingeniería civil el efecto de las personas sobre las estructuras se ha considerado sólo como una carga adicional sin tener en cuenta que esta ocupación puede cambiar los parámetros dinámicos de la estructura. Estos hechos han despertado el interés en emular las características de la carga humana a través de la formulación de modelos dinámicos que interactúan con el sistema estructural y modifican sus propiedades dinámicas. Este artículo presenta la caracterización de los efectos producidos por cargas humanas en la frecuencia natural fundamental y la razón de amortiguamiento viscoso correspondiente de una estructura que fue construida para ser representativa en el modo y la frecuencia natural de la tribuna sur del Estadio Olímpico Pascual Guerrero de Cali (Colombia). Se realizaron ensayos de vibración forzada en la tribuna, tanto con ocupantes humanos en diferentes configuraciones y densidades de ocupación como con cargas muertas equivalentes. Los resultados muestran que para el caso de las cargas humanas, la frecuencia natural fundamental y la correspondiente razón de amortiguamiento de la estructura pueden variar hasta en 35% y 27% respectivamente, en relación con los valores de la estructura con cargas muertas equivalentes.

Over 31,000 precision reduced optical observations of GEOS-I and II in 70 two-day orbital arcs have been used at Goddard Space Flight Center (GSFC) in a dynamical solution to determine center-of-mass coordinates for 15 tracking stations on the European Datum. Comparisons with the results obtained at Centre National d’Etudes Spatiales (CNES) give agreement of about 1.5 ppm for chord lengths. After considering a scale correction to the European Datum (ED) of 1950 to account for the absence of geoid heights at the time of its reduction, agreement to a few ppm between the CNES/GSFC and the ED chords is obtained. However, a small systematic difference between survey and satellite results remains for stations in south-eastern France and Switzerland.

The influence of projectile strength on cratering was investigated for projectiles of aluminum alloys impacting semi-infinite aluminum targets over the velocity range of 1 km/sec to 5.0 km/sec. The experimental results showed that crater diameters were not significantly influenced by varying projectile strength. The crater depths were found to vary appreciably with strength at lower velocities but to become virtually the same at 3.5 km/sec for the series of projectile alloys investigated. A simple dynamic model for cratering was developed and compared with the experimental results of this study and other experimental results at higher velocities. These comparisons showed that the model provided predictions of crater diameter which were within 8 percent for the experimental results of this study and within 13 percent for the hypervelocity data. Crater depth predictions showed good agreement with the experimental results of this study for projectiles having greater yield strength than the target material. The predictions of depth as a function of velocity showed qualitative agreement with the hypervelocity data.

Multijet electrothermal systems for attitude control and stationkeeping of synchronous communications satellite

A model of a general mechanical system, comprising a pneumatic system coupled to a linkage mechanism, is developed. The dynamic system behavior is studied using the digital computer as a design tool to determine the effect on the performance of changing design parameters. Within practical limitations, models of this kind have been used to achieve optimum design. Novel methods are used to treat the two major components of the system. The pneumatic system is modeled using an equivalent flow area which is a function of the time-dependent pressure ratio. Differential equations used to solve for the transient flow in the reservoir/piping/piston system are derived here. The mechanism driven by the pneumatic system consists of multiple series chains of four-bar linkages. The first- and second-order kinematic ratios required in the dynamics are computed from new explicit expressions derived here. Frictional losses, impact, and flexibility of the mechanism are included in the dynamic model. The nonlinearity of the differential equations arises from: (a) the kinematics, (b) drag forces depending on velocity squared, (c) magnetic forces depending on time squared, and (d) the strong nonlinearity of the time-dependent pneumatic system. The system of equations is solved numerically to obtain the record of pressure, temperature, and leakage in the pneumatic system and the travel of the mechanisms versus time. Good agreement is obtained between the theoretical solution and actual tests.

In a process of cumulative city deterioration, dynamic models which explicitly incorporate policy variables may be essential to determine policy measures capable of effecting desired long-run changes. This paper presents some simple dynamic models and explores their implications for policies to achieve various public goals. In particular, the analysis points up the distinction between policies, often quite attractive on the surface, which may in fact promise at best only short-run improvements and those which can alter the values of the parameters which determine the equilibrium characteristics of the city. To illustrate the potential use of such models, the paper also reports some empirical estimates of the parameters of two such models and discusses their policy implications.

Collisional rate coefficients measurement for helium-like carbon ions in plasma from emitted line intensities of theta pinch discharge

A general introduction to the area of off-line and on-line identification of systems is given, and applications of these techniques to machine tool problems, especially adaptive or optimal control, are discussed. The problem of identifying the dynamic model of the metal cutting process is given special emphasis. A general formulation of the nonsequential or off-line estimation problem is presented using state variable notation, so that nonlinearities and time varying parameters may be present. Two techniques tailored to the use of the high-speed digital computer are developed to solve this general problem. The first utilizes a direct multivariable search to match the output, of an assumed dynamic model to actual experimental observations in a least squares sense. The second method uses a modified quasilinearization procedure. Controlled digital experiments are used to refine and test the proposed techniques. The two algorithms are then applied to actual experimental cutting process data. Estimates of the cutting stiffness and damping factor in the dynamic model of the cutting process are obtained, thus demonstrating the effectiveness of the developed nonsequential identification schemes, and showing that the assumed linear dynamic model adequately represents the cutting process. A later paper will consider sequential estimation applications.

A generalized vorticity equation for a two-dimensional spherical earth is obtained by eliminating pressure from the equations of horizontal motion including friction. The generalized vorticity equation is satisfied by formal infinite series representing the density and wind fields. The first few terms of a particular series solution are obtained explicitly. The series appear to converge near the north pole, and determine a model of a polar air mass. Within the air mass, the coldest winds are northeasterly and the warmest are southwesterly, while the coldest air of all is at the north pole. Heating occurs in the northwesterly winds and cooling in the southeasterlies, while aside from the effect of friction the air mass as a whole is cooled. The energy balance of the air mass is investigated. It is suggested that an analogous distribution of heating and cooling may be instrumental in maintaining the general circulation of the atmosphere.

Nonelastic unloading microstrains in Cu crystals after stage II macroscopic prestraining, discussing stresses action on dislocations

Airborne and groundbased OH measurements showing short-term temporal variations in OH rotational temperature are presented. These variations are interpreted in terms of a dynamic model of the OH emitting layer in which the intensity variations result from the changes in temperature the OH layer undergoes as it moves during the night.

Unsteady nonlinear aerodynamic loads measurements in wind tunnel, using linearized mathematical analog

A dynamic mathematical model of a glass melting and conditioning system has been developed based on the conservation of energy and mass. Emphasis has been placed on the dynamic interactions between the gas, batch, glass, and refractory temperatures and glass flow rates in the tank, refiner and forehearth. Models of the composition, glass levels and flow rates, and forehearth centerline drawdown have also been developed, as have design studies of model approximations, parameters and sensitivity coefficients. A digital computer program simulates the dynamic models and design studies. Operating data from a tank, refiner and forehearth have been taken for comparison with the energy and mass flow model.

An attempt has been made to invert a large set of attenuation data for Love waves and toroidal oscillations in the earth, using a recent method by Backus and Gilbert. The difficulty in finding an acceptable model of internal friction which explains the data, under the assumption that the internal friction is independent of frequency, casts doubt on the validity of this assumption. A frequency-dependent model of internal friction is presented which is in good agreement with the seismic data and with recent experimental measurements of attenuation in rocks.

The wall shift of the atomic hydrogen maser has been determined by a series of 18 measurements on a variety of storage bulbs coated with FEP Teflon. The result is −24.3 mHz for a 15.25 cm (6 in.) bulb at 30°C. This is about 25% smaller than the previous values. It is most likely that a change in the properties of the Teflon caused the difference, which is far larger than possible measurement errors. The systematic correction due to the entrance stem has been estimated using several independent models. The fractional variation of the wall shift with temperature has been measured in the range 27 to 56°C and found to be (−11.4±0.4)×10−3/deg at 35°C. It is suggested that care be taken in applying the value of the wall shift found by one laboratory to bulbs prepared by different techniques or with different samples of Teflon.

This paper describes a systematic analysis which has been carried out on a commercial ammonia synthesis plant. Steady state and dynamic models of its performance are derived and investigated, and a new concept-the ''stability margin''-which is an extension of the ideas of Van Heerden [8] is found to lead to a fuller appreciation of the properties of the models. The accuracy of the model predictions are investigated by performing tests on the plant and it is shown how knowledge of the accuracy is important when deciding how the model should be used to improve the plant performance. Apart from the concept of a ''stability margin'' the solution of an identification problem, an experimental optimisation scheme and a control scheme for the maintenance of optimality and stability are the most important outcomes of the work.

An investigation was made to determine the feasibility of isolating the effects of site conditions on strong earthquake accelerograms. The set of accelerograms recorded simultaneously in 1952 at the roof, in the basement and on the ground outside the 14-story Hollywood Storage Building was chosen for analysis. Fourier spectra were computed for the two horizontal components at each of the three recording places and were used after smoothing to compute the ratios of spectra for adjacent points. Dynamic models of the subsurface conditions, the foundation and the building were established. Certain of the spectral ratios were also determined theoretically. The primary result is the development of a method of isolating effects of site conditions in Fourier spectra of accelerograms. Good theoretical checks were obtained on soil-structure interaction and structural response in the east-west direction. The absence of bedrock accelerograms prevented the obtaining of a theoretical check on free-field amplification, although plausible bedrock Fourier spectra were obtained. The subsurface model should be useful for further analyses.

Human body attitude control in space, using ten body complex geometry system, noting astronaut training jig

Three discrete physical models, obtained by lumping the flexibility and the mass of the continuous system, or both, are used to compute the dynamic response of beams. The beams may have general elasto-inelastic bending moment curvature relations such as the linearly elastic, elasto (perfectly) plastic, and strainhardening relations. The method of solution, based on simple physical concepts, follows from considerations of geometry of deformation, material properties, kinetics, and a numerical integration procedure in the time dimension. The relative merits of the models are discussed from the standpoint of accuracy, arranging equations, programming, and computer time. Rather extensive results were obtained for the response of a simply supported beam. The data shows that all models yield the same apparent "limit" deflection. Presented also are several other numerical examples to compare with certain numerical results available in the literature; comparisons generally indicate good agreement.

Dynamic plane shear of incompressible viscoelastic material with temperature dependent viscosity determined, using electric transmission line analog

This paper introduces a philosophy of industrial dynamics based on obtaining results in as quick and economical a fashion as possible. This economy is achieved by stating explicitly the objectives expected and tailoring the model toward the achievement of those objectives. Three specific and widely differing uses of a dynamic model are proposed. These are called analysis, feasibility, and control, and are demonstrated in terms of the dynamic model of earnings for a cement company.

Dynamic derivation of surface layer representation of lunar gravitational field from Doppler observations on polar and equatorial lunar orbiters

The conventional formulation of the transformation laws for certain thermodynamic quantities has been questioned by several authors. Their objection is based on a particular force that arises in the conventional picture whenever a heat transfer is observed in a frame other than the rest frame. The claim is made that this force is fictitious and hence should be disregarded when computing the mechanical work. In this paper we show that if a suitable mechanical model of heat is adopted this force becomes quite understandable in mechanical terms and thus perhaps not so fictitious after all.

Evaluation of results of laboratory scale model studies and theoretical analyses for prediction of characteristics of flow in fluid mechanics design; theory of dynamic similarity; equations are derived for determination of laws of homologous operation of turbomachines; reformulation of laws of dynamic similarity required by vector nature of fluid flow variables; discrepancies in geometrically distorted models and possible model adjustments for compensation.

Room with windows and open doors under sonic boom, determining cavity resonance model for impulsive loading conditions