Showing papers by "Technical University of Denmark published in 1969"

Scattering by a Cylindrical Post of Complex Permittivity in a Waveguide

Abstract: An exact solution of the discontinuity problem of a circular cylindrical post of arbitrary complex permittivity centered in a rectangular waveguide with the axis parallel to the electric field vector of the dominant mode has been set up and numerical results based directly on this solution have been found rising an electronic computer. The method used divides the waveguide up into three different regions by introducing two imaginary plane walls perpendicular to the waveguide walls. In the center region, which contains the cylindrical rod, the electromagnetic field is expanded in cylindrical waves and in the outer regions the field is expanded in waveguide modes. By setting up the boundary conditions at all discontinuity surfaces and performing numerical matching of the fields at the two imaginary walls, a system of linear equatious determining the coefficients of reflection, transmission, and absorption of the field due to the cylindrical rod is found. The structure which is of most interest in the case of a plasma column is a coaxial structure consisting of an inner dielectric cylinder with complex permittivity (the plasma) surrounded by a dielectric sleeve with real, positive permittivity (the glass tube). The theory is therefore developed to apply generally for such structures. From the numerical results, curves have been obtained showing the relationship between the coefficients of reflection and transmission and the (complex) permittivity of the rod material. Such curves maybe used for deducing the microwave properties of a cylindrical rod from measurements of the reflection and transmission coefficient of the rod.

On the use of the imperfect tracer pulse method for determination of hold-up and axial mixing†

Abstract: The imperfect pulse method is a powerful technique for experimental analysis of chemical engineering flow systems. The authors have employed this method in studies of holdup and mixing in gas-liquid fluidized beds. In the present paper are discussed two problems connected with reduction of the experimental data obtained in such studies. Tailing is a phenomenon that may seriously affect the accuracy of mixing coefficients determined by the imperfect pulse method. Accurate methods of data reduction, based upon analysis of moments, have been developed, and their applicability is demonstrated by analysis of experimental data. Interphase transfer of tracer material is of particular importance in investigations of gas phase mixing in a gas-liquid system where absorption of tracer gas into the liquid phase normally takes place. A semiempirical method is described for correction of the experimental data in such cases. La methode de pulsation irreguliere est tres utile pour l'analyse experimentale des systemes d'ecoulement en genie chimique. Les auteurs ont utilise le dit procede en rapport avec la retenue et le melange dans des lits fluidises ou entrant en jeu un gaz et un liquide. On discute dans le present travail deux problemes, lesquels ont trait a la simplification des resultats experimentaux qu'on a obtenus dans des etudes de ce genre. La retenue (tailing) est un phenomene qui peut affecter serieusement la precision des coefficients de melanges determines par la methode de pulsation irreguliere. On a mis au point des methodes precises de simplification de donnees, lesquelles sont basees sur l'analyse des moments, et l'on demontre leurs possibilites d'application par l'analyse des resultats experimentaux. Le transfert d'un traceur d'une phase a l'autre est particulierement importante dans l'etude du melange en phase gazeuse dans un systeme a base de gaz et de liquide, ou il se produit normalement absorption du gaz traceur dans le liquide. On decrit une methode semi-empirique pour corriger les resultats experimentaux dans de tela cas.

Computation of Laplacian potentials by an equivalent-source method

Abstract: An algorithm for the computation of the solution to Laplace's equation in a 2-dimensional region is given in terms of equivalent sources on the boundary. The region may be of an arbitrary shape, and the boundary conditions may be an arbitrary combination of Dirichlet, Neumann and impedance types. The solution is obtained by a moment method, using either a step approximation to the source, or a piecewise-linear approximation. Point matching is used for testing the boundary conditions. Computer programs are available for the general problem, and some electromagnetic-field applications are discussed.

An APW Calculation for Silver

Abstract: Various “muffin tin” potentials have been examined, and a potential leading to a band structure and a Fermi surface in agreement with experiments has been found. This potential is based on relativistic Dirac-Slater atomic wave functions. In the atomic calculations as well as in the crystal calculations inclusion of full Slater exchange led to the best results. Cyclotron masses, thermal effective mass, optical mass, drift velocities, and group velocities have been calculated. Verschiedene Berechnungsmethoden fur „muffin tin”-Potentiale wurden untersucht, und ein Potential fur eine Bandstruktur und eine Fermiflache, die beide mit experimentellen Resultaten ubereinstimmen, wurde gefunden. Dieses Potential basiert auf relativistischen atomaren Dirac-Slater-Wellenfunktionen. Sowohl in atomaren als auch in Kristallberechnungen hat die Einbeziehung des vollen Slater-Austauschs zu den besten Ergebnissen gefuhrt. Zyklotronmassen, thermische effektive Masse, optische Masse, Driftgeschwindigkeiten und Gruppengeschwindigkeiten wurden berechnet.

Brillouin Scattering Studies of Acoustoelectric Domain Formation in Semiconducting CdS

Abstract: The growth of the flux intensity in acoustoelectric domains in semiconducting CdS has been followed over five orders of magnitude for frequencies between 0.2 and 5 GHz using the Brillouin scattering technique. The form of the flux domains is exponential on both sides with a halfwidth of about 300 μm. By studying their formation in the very early stage before the current decay, it was found that the frequencies and amplification factors of the flux appearing first are close to those predicted by the linear theory. After the current has started to decay, higher and lower frequencies are observed, the lower with much higher amplification and intensities. It seems that the electric field inside the domain does not have an essential influence on the flux growth. The experimental results are compared with some acoustoelectric amplification models. In akustoelektrischen Domanen in CdS wurde die akustische Flus-Intensitat uber funf Grosenordnungen im Frequenzbereich von 0,2 bis 5 GHz gemessen. Dabei wurde die Methode der Brillouinstreuung benutzt. Die Form der Domane ist exponentiell auf beiden Seiten, ihre Halbwertsbreite betragt etwa 300 μm. Anfangs, wenn die Domane sich bildet, stimmen die Frequenzen und der Verstarkungsfaktor mit der linearen Theorie uberein. 200 bis 300 ns spater, je nach Dauer der Inkubationszeit, treten hohere und niederere Frequenzen auf, wobei besonders die niederen eine viel grosere Verstarkung und Intensitat aufweisen. Das elektrische Feld in der Domane scheint keinen grosen Einflus auf die Schallverstarkung zu haben. Die experimentellen Ergebnisse werden mit einigen der akustoelektrischen Modelle verglichen.

On the downhill method

Abstract: The downhill method is a numerical method for solving complex equations ƒ(z) = 0 on which the only restriction is that the function w = ƒ(z) must be analytical. An introduction to this method is given and a critical review of relating literature is presented. Although in theory the method always converges, it is shown that a fundamental dilemma exists which may cause a breakdown in practical applications. To avoid this difficulty and to improve the rate of convergence toward a root, some modifications of the original method are proposed and a program (FORTRAN) based on the modified method is given in Algorithm 365. Some numerical examples are included.

Leaky waves on a dielectric rod

Abstract: Complex solutions to the characteristic equation for wave propagation along a lossless dielectric cylinder are shown to exist, suggesting that the well known general features of leaky waves may be exhibited by this particular structure The influence of losses is discussed

Mathematical programming in economics by physical analogies Part I: The analogy between engineering and economics

Abstract: This article is the first of a series of three in which we establish and solve a physical analogy of the economic model underlying mathematical programming.Basically, the first article is a reexamination of the fundamental assumptions underlying quasi-static models in economics and engineering, with a view to the estab lishment of a conceptual framework common to both disciplines.At the microscopic level it is demonstrated that the assumptions of perfect competition can be cast in a form analogous to the one used in statistical physics.At the macroscopic level it is shown that measurements in economics and physics can be classified in identical manners with the result that derived relationships, like Ohm's law and demand curves or electric power and total revenue, can be made analogous concepts. On this basis it is then asserted that underlying economics we find two basic laws which, apart from a single change in sign, are completely analogous to the well-known first and second laws of thermodynamics.

Electronic Properties of Tin and Bismuth from Angular Correlation of Annihilation Photons

Abstract: A linear slit setup has been used to obtain results of angular-correlation measurements in (a) tin single crystals in three orientations: [001], [100], and [110], (b) bismuth single crystals in four orientations: [111], [100], [1\ifmmode\bar\else\textasciimacron\fi{}10], and [2\ifmmode\bar\else\textasciimacron\fi{}1\ifmmode\bar\else\textasciimacron\fi{}1], (c) solid and liquid tin and bismuth, and (d) deformed bismuth. For both metals, the single-crystal angular-correlation curves lie near to the free-electron parabola. The tin curves show more anisotropy than the bismuth curves. An important result is the clear anisotropy found in the high-momentum part of the curves---the tails---for both metals. Little agreement is found between simple theoretical models and these results. A calculation of the curves based on the one-electron theory of valence electrons in metals would be highly desirable. The peaks of the liquid-metal curves are narrower than the peaks of the polycrystalline curves. The tails of the liquid-metal curves are smaller and of another form than the tails of polycrystalline curves; no Gaussian with only one adjustable constant factor can give a fit to both tails. No useful method for interpreting liquid-metal angular-correlation curves seems to exist. Two deformed bismuth samples gave angular-correlation curves nearly equal to the polycrystalline curves.

Non‐Ohmic Behaviour in CdS Acousto‐Electric Oscillators

Abstract: In thin plane parallel photoconducting CdS platelets the current is observed to deviate from the ohmic value also outside the electric field range for net round trip gain in the longitudinal wave configuration. A N-type negative differential conductivity is observed for pulsed as well as for CW operation. Domain formation may take place and give rise to low-frequency current oscillations superposed on the well known high-frequency modes of the acousto-electric oscillator. The negative differential conductivity is most likely ascribed to field-dependent free carrier trapping though acousto-electric effects may also be important. Es wurde beobachtet, das der Strom in dunnen planparallelen Plattchen aus photoleitendem CdS, die als akustoelektrische Oszillatoren in longitudinaler Anordnung betrieben wurden, auch dann vom ohmschen Wert abweicht, wenn die elektrische Feldstarke auserhalb des Bereiches fur den “round trip gain” liegt. Es wurde eine N-formige negative differentielle Leitfahigkeit gefunden, sowohl im Betrieb mit gepulster als auch mit nicht-gepulster Gleichspannung. In einigen Fallen traten Domanen auf, die zu niederfrequenten Stromoszillationen fuhrten, welche den bekannten Hochfrequenzschwingungen des akustoelektrischen Oszillators uberlagert sind. Die N-formige negative differentielle Leitfahigkeit ruhrt hochstwahrscheinlich von feldabhangigen Einfangquerschnitten her, obgleich akustoelektrische Effekte auch von Bedeutung sein mogen.

Mathematical programming in economics by physical analogies Part II: The economic network concept

Abstract: REVIEW OF PART I AND PREVIEW OF PART IIThis article is the second of a series of three in which we establish and solve a physical analogy of the economic model underlying mathematical programming.B...

Drying shrinkage of concrete due to capillary action

Abstract: The effect of capillary tension on drying shrinkage of cement paste and concrete is explained. The theory is based on principles of thermo-dynamics and theory of elasticity.

Algorithm 365: complex root finding [C5]

Abstract: p r o c e d u r e drawarea (x, y, firstpoint, lasgpoint, section, numrows, numseats, regcolor, paintflag, paintcolor, sgn, dir, edge); v a l u e firslpoint, lastpoint, numrows, numseats, regcolor, paintflag, paintcolor, sgn, dir, edge; i n t e g e r firstpoint, lastpoint, numrows, numseeats, regcolor, paintcolor, sgn; r e a l edge; B o o l e a n paintflag, dir ; r e a l a r r a y x, y; i n t e g e r a r r a y section; c o m m e n t This procedure is a par t of a large program which produces the card s t u n t s for the S tanford Un ive r s i ty footbal l game halft imes. The ini t ial development was done by L. Breed, L. Tesler, and J. Sauter . T he au thor (a S tanford s t uden t a t t he t ime) made many fu r the r developments on this program which included producing an a lgor i thm for coloring in polygonal regions. Pr ior to the deve lopment of th is a lgor i thm, there were m a n y cases which did not work. The larger program takes as input an Engl ish descr ipt ion of the s t u n t s and produces as out pu t an image of each flip (similar to a f rame in a movie film), as a rectangle t h a t has 45 rows wi th 77 seats in each row. The main program, which will be considered the dr iver program for the purpose of the procedure drawarea, does all of the handl ing of the definition of regions and also the pr in t ing of the images. I t should be ment ioned t h a t the procedure drawarea in the ac tual program is jus t pa r t of a larger procedure and t h a t all of the parameters are global in order to increase efficiency. The purpose of drawarea is to take the cur ren t regions and draw them in the two-dimensional a r ray section, which is to be declared as section [1 : numrows, 1 : numseats] (the ar ray is 45 by 77 for S tanford). Each completed pic ture in section is t hen p r in ted and also wr i t t en out on tape. Another program la te r takes th is t ape and processes i t to produce an ins t ruc t ion card for each s t uden t holding a set of colored cards in the rooters section. The larger program allows objects of any shape to be defined b y a series of x, y-coordinates. I t will accept a series of points which are given an ident i fying name by the user and which can then be used as (1) a group of points , (2) a series of connected line segments , (3) a polygonal region enclosed by the points (with the first and las t point connected by a s t r a igh t line). I t also allows ellipses to be defined. Once an object is defined, i t can be expanded and cont rac ted in size, r o t a t ed about any fixed point , or moved anywhere, including all or pa r t i a l ly ou t of sight. As soon as all objects are in place, the user can ask t h a t an image of the p ic ture be made. Except for polygonal regions, producing the image of these objects is t r iv ia l . The procedure drawarea is the rout ine which places the polygonal regions in the ar ray section. The a r ray section is presumed to have a background color associated wi th it. All objects , which also have an associated color, are t hen drawn in to the a r ray in a specified order so t h a t the objects which are to be super imposed over o ther objects are d rawn last. The procedure drawarea takes the coordinates of the point (which may not be in tegra l ) f rom arrays x and y wi th subscr ip t values ranging fromfirstpoint to lastpoint and decides which sea t s in a r ray section will form the left and r igh t boundaries of th is new region. After the b o u n d a r y is determined, the in ter ior mus t be colored in. The a lgor i thm colors the region by tak ing each row and then examining each seat f rom left to r ight . For opt imizat ion, only the area of a minimal circumscribing rectangle is examined. At the beginning of each row the var iab le count is set to leflcount [row, 0] r igh tcount [row, 0], which will be zero unless the object is par t ia l ly out of s ight on the left . T h e n as long as count remains zero, the sea t is on the exterior and is not colored. As each seat is encountered, leftcount [row, seat] is added to count. When count is positive, the sea t is in the inter ior or on a boundary and is colored. After each seat is processed, rightcount [row, seat] is sub t r ac t ed from count. When count re tu rns to zero, the sea t is an exterior sea t and is not colored. In any row i t is possible to have the color tu rned on and off several t imes. Arrays leftcount and rightcount contain twice the number of lef t and r ight boundar ies which pass th rough each individual seat . These two arrays solve the problem created by hav ing several boundar ies passing th rough one seat . A fu r the r complicat ion to the rout ine is added by allowing a region to be gradual ly changing color. Thus each region always has a color (regcolor) associated wi th it, and if the region is being swept wi th a new color, t hen paintflag is t r u e and paintcolor, sgn, dir, and edge are used to de termine the sect ion of the region which is to be of the new color (paintcolor). The roles of the parameters for pa in t ing are: sgn and dir indica te the direct ion in which the imaginary pa in tb rush is moving, dir = t r u e means the direct ion is hor izonta l and dir = f a l s e means vertical, sgn = 1 means the direct ion is lef t or down and sgn = 1 means the direct ion is r igh t or up. edge is the row or sea t (column) where the new color (painteolor) ends and the old color (regcolor) begins. The dr iver program is expected to change edge with each new image so t h a t the region looks as if i t is being swept by a new color. A re la ted a lgor i thm which determines whether a poin t is inside a polygon is presented in Algor i thm 112 [1, 2]. REFERENCES: 1. HACKER, RICHARD. Cert if icat ion of Algor i thm 112, Pos i t ion of point re la t ive to polygon. Comm. A C M 5 (Dec. 1962), 696. 2. S~IMRAT, M. Algor i thm 112, Pos i t ion of point re la t ive to polygon. Comm. A C M 5 (Aug. 1962), 434; b e g i n i n t e g e r row, seat, toprow, rightseat, rit, lef, top, bet, iox, icy, inx, iny, sdx, sdy, j , ix, iy, count; real ox, oy, nx, ny, dx, dy, dxdy, const; i n t e g e r a r r a y leftcount, rightcount [0: numrows÷l , 0: numseats÷ l ]; i n t e g e r p r o c e d u r e max(x, y); v a l u e x, y; i n t e g e r x, y; max := i f x _~ y t h e n x e lse y; i n t e g e r p r o c e d u r e min(x, y); v a l u e x, y; i n t e g e r x, y; rain := i f x ~ y t h e n x e lse y; foprow := numrows Jr 1; rightseeat := numseats Jr 1; for row :-~ 0 s t e p 1 u n t i l toprow do for seat := 0 s t e p 1 u n t i l rightseat do leftcount [row, seat] := rigMcount [row, seat] := 0; ox := x[lastpoint]; rit := left := iox := ox; oy := y[lastpoint]; top := bet := icy := oy; c o m m e n t Draw the bounda ry by i te ra t ing th rough the points ; for j := firstpoint s t e p 1 u n t i l lastpoint do

Losses in dielectrically loaded coaxial cables

Abstract: Loss reduction in coaxial cables brought about by dielectric linings has been experimentally observed, but various theoretical considerations fail to explain this feature. To clarify this situation, the paper gives consideration to the general conditions for obtaining lower losses by means of a thin concentric dielectric shell placed anywhere between the two conductors. The analytical criteria obtained agree well with numerical results derived directly from the exact Maxwellian field problem, but are much easier to apply and give a more unified insight into the significance of the various parameters concerned. The analytical method is particularly useful in the range of special interest, namely for thin linings. For electrically thick linings, the exact results may be understood from coupled-mode considerations. While not explaining the experimental observations, the present analytical theory admits to reduced attenuation in other, more favourable circumstances discussed in the paper. This is in accordance with exact numerical computations, but restricts the use of quasistatic transmission-line theories to frequencies lower than previously assumed.

Specific heat anomaly of ferrites at the curie temperature

Abstract: Using the Neel model for a two-sublattice material, the magnetic contribution Cm to the specific heat in the vicinity of the Curie temperature is calculated in the molecular field approximation. At the Curie temperature the calculation reveals a discontinuity ΔCm in the specific heat, which is evaluated and compared with experiment. The theoretical and experimental values are in good agreement for Zn0.38Mn0.62Fe2O4 and Zn0.5Ni0.5Fe2O4 as measured by Verhaeghe et al, and for MnFe2O4, measured in the present work. The agreement is less satisfactory in the case of Zn0.5Mg0.5Fe2O4 as measured by Shulga (1957).

Mathematical programming in economics by physical analogies: Part III: System equilibrium and mathematical programming

Abstract: This article is the third of a series of three in which we establish and solve a physical analogy of the economic model underlying mathematical programming.In the third article the concept of equilibrium is de rived from the basic notion of a static mechanical system at rest, and it is shown how, by refining this concept, it can be extended to dynamic physical systems. In this process it is also explained why an extremum value of a state-function determines an equilibrium state of a system.From an economic viewpoint the physical concept of equilibrium is identified with that of a perfectly competi tive market, and it is demonstrated how this concept dif fers from the equilibrium concept of a monopolist. For comparison, industries with one and two outputs are considered.From a mathematical programming viewpoint both linear and quadratic problems are discussed in terms of methods of classical mechanics. In particular it is shown that the simplex method can be derived from Fourier's inequality for equilibriu...