Exact Analogue Research Articles

Exact Electric Analogy to the Vernotte Hypothesis

The Fourier equation of heat conduction predicts the paradoxical result that the effect of a thermal impulse in an infinite medium will be felt instantaneously in all parts of the medium. In other words, a thermal impulse is propagated at infinite velocity. The result is paradoxical because it is incompatible with a dynamic interpretation of the mechanism of heat transfer in solids. In order to avoid this apparent paradox, Vernotte has proposed a modification of the Fourier hypothesis. This modification results in the transformation of the equation of heat conduction from a parabolic to a hyperbolic differential equation predicting finite velocity of propagation of thermal impulses. Vernotte's proposal is shown here to have an exact electric analogy. The proposal is equivalent to postulating the existence of a heat transfer quantity which is analogous to the electric quantity inductance. The transformed equation of heat transfer is therefore analogous to the differential equation of telegraphy.

Electromagnetic Acceleration of a Plasma Slug

The slug model of a plasma accelerator is formulated and analyzed. The coupled nonlinear system equations involving seven parameters are transformed into a three-parameter set. The formulation includes as special cases Artsimovich's treatment, which neglects all system resistances, and Schock's treatment, which assumes negligible resistance of the accelerator electrodes. Small coupling, as well as small and large time asymptotic, solutions, which include the effect of variable rail resistance, are derived and compared with exact analog computations. In cases of practical concern, the small time solutions are valid well past the first maximum of the current discharge, bridging the gap left by Schock's approximate solution whose applicability is restricted to cases where the acceleration takes place over a number of cycles. Finally, it is shown how to optimize the efficiency of an accelerator through suitable adjustment of the system parameters.

On existence, uniqueness, and numerical evaluation of solutions of ordinary and hyperbolic differential equations

After a preliminary survey of related results, a general uniqueness theorem for the ordinary differential equation dy/dx=f(x, y) is given in section 4. The general uniqueness theorem for the hyperbolic partial differential equation uxy=f(x, y, u), proved in section 5, is an exact analogue of the general uniqueness theorem for the ordinary differential equation dy/dx=f(x, y).

Digital Array Phasing

The extension of digital techniques to the problem of processing the output of an array of point receiving elements in an acoustic field has given rise to a method of phasing called DIMUS (digital multibeam steering). This digital technique incorporates the use of shift registers as delay line elements which results in a number of operational advantages. A description of the DIMUS technique is given. The effects of amplitude and time quantization imposed by the digital circuits are considered in the light of the relative signal processing gain of the array referred to an exact analog phasing network. The processing gain is computed as a function of sampling frequency for a number of types of signals.

Digital Array Phasing

The extension of digital techniques to the problem of processing the output of an array of point receiving elements in an acoustic field has given rise to a method of phasing called DIMUS (Digital Multi-beam Steering). This digital technique incorporates the use of shift registers as delay line elements which results in a number of operational advantages. A description of the DIMUS technique is given. The effects of amplitude and time quantization imposed by the digital circuits are considered in the light of the relative signal processing gain of the array referred to an exact analog phasing network. The processing gain is computed as a function of sampling frequency for a number of types of signals. [This work represents one of the results of research carried out under Contract Nonr 2216 (10) with the Office of Naval Research.]

The Thermal Equivalent Circuit of a Transistor

An exact electrical analogue is given for the thermal system between the collector junction and the constant-temperature environment of a transistor. For this circuit analogue, the voltage response to an applied current is equivalent to the temperature response of the collector junction to an applied-power dissipation. The objective of this paper is (1) to prove that this thermal equivalent circuit is entirely consistent with the rigorous, academic approach to the problem, which is to solve a boundary-value problem for heat flow in the transistor system; (2) to present an experimental method for obtaining the circuit parameters in the thermal equivalent circuit; and (3) to demonstrate the utility of the thermal equivalent circuit for the circuit designer and the transistor designer.

3 beta-Methoxy-5-androsten-16 beta-ol: a cytostatic and fungistatic steroid.

IN our search for a superior ‘androgenic’ steroid for use in human cancer of the breast, we have submitted many such steroids to study in the zebra fish-egg test1. Using this bioassay method for determination of cytostatic activity, intensely cytostatic compounds in the C-19 or ‘androgenic’ steroids are difficult to find. To date, our most active compound is 3β-methoxy-5-androsten-16β-ol2, this steroid having LD50 of 1–2 parts per million. It is very interesting that this compound is the exact analogue of the steroidal œstrogen 3-methoxyœstra-1-3,5(10)-trien-16β-ol3, which had been previously selected by us for use against cancer of the prostate, based on fish-egg cytostasis4. Also of much interest in steroidal cytostasis is the fact that methyl ether formation at C3 of 5-androstene-3β,16β-diol2 so strongly enhances the activity of this diol, which itself is virtually inactive (LD50 > 10 p.p.m.). Methyl ether formation at C3 of l,3,5(10)-œstratrien-3,16β-diol3 had also caused an enhancement (100 per cent) of cytostatic activity in the fish-egg test.

Electronic-analogue-computer study of synchronous-machine transient stability

The paper describes a method of solution of synchronous-machine transient-stability problems by a more exact electronic analogue representation of the system equations than has hitherto been employed. In the machine analysis emphasis is placed on the variation of field flux linkage during transient disturbances, and reasons are given why this is necessary. The equations of performance are derived in the most convenient form for analogue computing.The equivalent analogue interconnections are given both for time-varying and for constant field flux linkage. The components required for these analogues are considered briefly.The section on computer control deals with the control of integrators with reference to the introduction of ‘initial conditions’, ‘hold’ and ‘compute’ states. A delay unit is described which enables the switching out of a faulted transmission line to be simulated.The results of various problems solved by the computer are presented in graphical form as boundaries between stable and unstable states. It is shown how instability subsequent to the first rotor oscillation may occur, and an explanation is proposed to account for this phenomenon.Synchronous-machine and transmission-line analysis are excluded from the main text for clarity and are presented in detail in the Appendices.

Characteristic ideals and the structure of Lie algebras

The purpose of this note is to study the radical and such concepts as semi-simplicity and simplicity for Lie algebras in terms of characteristic ideals. The program follows the outlines of part of a fundamental paper of Fitting on finite groups, and the final result displaying an isomorphism of an algebra V with no solvable characteristic ideals into the Lie algebra of derivations of a uniquely determined completely reducible characteristic ideal in V is an exact analogue of a result of his on semi-simple groups. In case the base field is of characteristic zero, the theory collapses to the classical theory. An example is given to show that this is not the case at prime characteristic.

Dynamical Principle for Classical Mechanics

The dynamical principle underlying nonrelativistic classical particle mechanics is stated in a way which brings it into exact analogy with the quantum principle. The classical equations of motion for a dynamical variable are then displayed in forms analogous to the Schrödinger, Heisenberg, and interaction forms in quantum theory.

"Improvement in color kinescopes through optical analogy"

The relationship between phosphor dots on the screen and the holes in the shadow mask has been determined by light beams emanating from small light sources located at the red, green and blue color centers. This is acceptable for tubes with small deflection angles, but becomes less acceptable for tubes with large deflection angles. This is due to the fact that in an operating tube the electrons do not appear to originate from points in a fixed deflection plane, but rather from points in a deflection plane which moves closer to the shadow mask as the deflection angle is increased. This causes a color impurity for the larger deflection angles. The color impurity has been eliminated by determining the relationship between phosphor dots on the screen and the holes in the shadow mask with an exact light analogy for the electron trajectories.

A Note on Trace-Differentiation and the Ω-operator

In theory of polarizing operators in invariants the operatorwhere X = [xij] is an n × n matrix of n2 independent elements xij, holds an important place. Acting upon particular scalar functions of X, namely the spur or trace of powers of X, or of polynomials or rational functions of X with scalar coefficients, it exhibits (Turnbull,. 1927, 1929, 1931) an exact analogy with results in the ordinary differentiation of the corresponding functions of one scalar variable. Turnbull denotes this operation of trace-differentiation under Ω by Ω8; and we shall follow him. Our purpose is to show how, with a suitably modified Ω, the results may be extended to the case of symmetric matrices X = X′ having ½n(n + 1) independent elements.

Thermodynamics of Crystallization in High Polymers. IV. A Theory of Crystalline States and Fusion in Polymers, Copolymers, and Their Mixtures with Diluents

The configurational entropy of a mixture of solvent and polymer molecules composed of segments connected by flexible bonds has been derived for the case in which the lattice they occupy contains limited regions of perfect order (i.e., the crystallites), which are reserved for occupancy by polymer segments exclusively. Although the derivation is carried out primarily for polymer chains of uniform length, modifications required for the treatment of heterogeneous polymers are included. An expression for the free energy of fusion ΔFf of the semicrystalline mixture of polymer and solvent is derived assuming a vanLaar heat of mixing term. The equilibrium (average) crystallite length ζe, derived by differentiation of ΔFf, depends principally on the ``nucleation parameter'' D which, though it evades explicit evaluation from theory, represents the relative ease with which the first layer of a crystallite tends to form; ζe may depend to a lesser extent on the degree of crystallinity. The equilibrium degree of crystallinity, similarly deduced, depends primarily on the temperature. Fusion is predicted to occur over a range of temperatures, but the temperature Tm (the ``melting point'') at which crystallinity totally disappears is sharply defined. The melting range is predicted to be narrower the greater the chain length. If the degree of polymerization is greater than 100, the range (depending on the heat of fusion) for equilibrium melting should be quite narrow, as much as 75 percent of the fusion occurring within a few degrees of Tm. The dependence of the melting point on chain length is expressed approximately by a proportionality between the temperature depression given by ΔTm=Tm0—Tm, where Tm0 is the melting point for infinite chain length and the reciprocal of the degree of polymerization. Incorporation of a diluent should markedly broaden the melting range. If the degree of polymerization is very great, ΔTm should be proportional to the number of moles of diluent per unit volume. Extension of the treatment to random copolymers yields 1/Tm−1/Tm0=(R/hu)[−lnXA−μ′(1−vA)2],where hu is the heat of fusion, μ′ is the heat of mixing parameter, and XA and vA are the ``mole'' fraction and volume fraction, respectively, of the crystallizing structural unit in the copolymer. This expression is the exact analog of the freezing point relationship for ``regular'' binary mixtures of monomeric substances. Crystallinity in an ordered copolymer (the partial analog of an ``irregular'' solution) in which the structural units of a given type are arranged in long sequences should disappear at a temperature only slightly below Tm for the pure polymer. The phase rule cannot be applied to the crystal-amorphous transformation in polymers since the free energy per unit amount of the amorphous ``phase'' is not a unique function of the composition. Copolymers should melt over a wider temperature range and their crystallinity-temperature relationship is predicted to be sigmoid in character.

Spectrographic observations of short-period Cepheids.

view Abstract Citations (1) References Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Spectrographic observations of short-period Cepheids. Struve, O. Abstract During the summer of 1947 a series of 390 spectrograms of RR Lyrae, whose principal period is 13.6 hours, was obtained at the Mc- Donald Observatory in order to study the effect upon the velocity curve of the long period of 41 days, which is known from the light curve. The spectrograms were measured by Dr. A. Blaauw and the writer. On June 5 and again on July 17 the velocity curve was retarded by 20 minutes-a conspicuous phenomenon for a velocity curve in which a change of 2okm/sec takes place in 24 minutes. Approximately half- way between, on June 26, the velocity curve was advanced by 20 minutes. This shift along the time-axis of the short-period curve agrees exactly with the shift of the light-curve as observed by Walraven at Leiden in 1947. After the short-period velocity curve was corrected for this oscillation it disclosed only relatively insignificant, though probably real, changes in shape, within the ~I-day cycle, when the metallic lines were used. The hydrogen lines, H~, H~ and H~ however, differ in a remarkable manner from the metallic lines. For them the descending branch of the curve is steeper and the range larger than for the metallic lines. The minimum velocity for H is about - I I5km!sec while for the metals it is about - Iookm/sec. The higher members of the Balmer series agree with the metallic lines. In the case of H~ alone, the minimum velocity is nearly - I2okm!sec, so that we are concerned with a phenomenon which depends upon the quantum number of the upper state. The maxima are less strikingly different. The H velocity curves show an interesting connection with the 41-day period: when the velocity curve is most retarded, that is, near June 5 and July 17, the curve rises to a peaked maximum at about -25km!sec. When the velocity curve is most advanced the maximum is about -45km!sec. The peaked curves correspond to the greatest intensity of the sharp H emission lines which are observed at about median decreasing velocity. It is possible that the sharp H absorption line which dominates the spectrum at minimum light continues to increase in velocity until it fades out, while at the same time a broad line with Stark wings is already present at a shorter wave length. The transition from peaked maximum to very nearly minimum velocity occurs in about 40 minutes. The roundeff minimum of the A-type lines is probably real, in the sense that the deeper layers at first have a moderate velocity of recession, reaching minimum at phase o.4oP. But there is no such rounding off at the peaked maxima, so that it would seem that the fading line from the upper level continues to show inward acceleration until it has disappeared. When the emission lines are absent, the transition is a more gradual one since there are then no peaked maxima. During the present summer Dr. A. van Hoof and the writer have been observing the cluster- type variable XZ Cygni-suggested to us by Dr. E. C. Yowell, who has made an exhaustive study of its light curve. There are also two periods, a shorter one of I I hours, and a longer one of the order of 57 days. These observations are now being discussed. Thus far, we have found no definite evidence of bright H lines, but near the phase of median increasing brightness there are indications of two H components. The red component is sharp and becomes rapidly weaker, while the violet component is broad and at first very shallow, becoming rapidly strong enough to obliterate the weakening sharp component. In this respect we have an exact analogue of RR Lyrae. We conclude that during the rise in brightness the motions are not uniform throughout the pulsating atmosphere and that in both stars there are indications of the simultaneous existence of an inner, expanding, and an outer, contracting layer. Verkes Observatory, Williams Bay, Wis., and McDonald Observatory, Fort Davis, Tex. Publication: The Astronomical Journal Pub Date: October 1948 DOI: 10.1086/106192 Bibcode: 1948AJ.....54...50S full text sources ADS |

A Mechanical Analogy for Transverse Electric Waves in a Guide of Rectangular Section

It is shown that transverse wave motion in a stretched rubber strip clamped at the edges is in exact analogy with certain `transverse electric' types of electromagnetic wave in a hollow wave guide of rectangular cross-section. The vertical displacement of the strip at any point corresponds to the electric vector and the slope of the strip is related to the magnetic vector. The analogy has been found useful to demonstrate the existence of a critical frequency for propagation and it is suggested that useful application may be found in predicting the effect on `Hon' waves in such guides of certain irises, bends and tapers, and in finding some of the resonant frequencies of prism-shaped cavity resonators.

A study of the nature of the field theories of the electron and positron and of the meson

The field theories of the electron and positron and also of the meson are developed by means of a close analogy with the photon. The analogy consists in the representation of the tracks of these particles by means of null-geodesics. The choice of notation is guided by the attempt to arrive at a theory in which the lengths (h/m 0 c) and (e 2 /m 0 c 2 ) occur naturally without reference to the structure of the particles, and in which the concept of quantization of electric charge is included. It is found that these objects can be attained by assuming that an additional degree of freedom is necessary for the description of the particles. If this is regarded as an additional dimension, it is found that an exact analogy can be made with the field theories familiar in the theory of relativity. An important feature is the union, in a single tensor, of energy, momentum and current density. A certain arbitrariness, not unlike that associated with the Poynting vector, is revealed, and it is shown that if this is removed by making a definite choice of the magnitude of the magnetic moment of the electron and positron, the spin angular momefttum is ^hereby fixed at the value 1/2h. In the development of the meson field the analogy shows* that the nuclear sources of the field act as if contributing a current density analogous to a magnetic current density in the electromagnetic case. The use of the additional degreb of freedom in the sinusoidal form indicates that the ratio of the constants g 1 and g 2 introduced into field theories as measures of the strengths of the sources is determined by the mass of the particle emitted in the neutron-proton transition.

Contracting Cones Giving Uniform Throat Speeds

A difficult problem in fluid mechanics which comes up frequently, especially in the design of venturi meters and wind tunnels, is to find the geometric form of contracting cones having uniform flow speeds a t the throat. The solution given in this report** makes use of the exact analogy between the magnetic field tha t is created by two coaxial and parallel coils carrying electrical current and the velocity field tha t is created by two corresponding ring vortices. The high uniformity of the magnetic field over a core area when the coils are suitably arranged is well known. A corresponding uniformity of the velocity field over the same core area is here obtained by simply translating the electromagnetic solution into an aerodynamic one and by choosing one of the stream surfaces as a flow boundary. The geometric form of the stream surfaces is found without difficulty. A family of these contracting cones is developed, the inner eight of which give throat speed distributions tha t are uniform theoretically within a fifth of 1 per cent. The distributions become less uniform for the outer cones, but variations from uniformity are still less than 1 per cent even for the outermost one. Essentially, the same throat uniformities will occur in the case of real airflows, provided the upstream flow is uniform and the downstream, or diffuser, flow does not separate.

On the basis theorem for differential systems

As originally proved by Hilbert, this theorem applied to polynomials whose coefficients were either elements of a field, or rational integers. In keeping with the modern tendency toward abstraction, however, one now finds the theorem proved for polynomials whose coefficients are elements of a commutative ring with unit element in which every set has a finite basis. When one turns to differential polynomials and differential ideals one finds that the exact analogue of the Hilbert theorem is lacking('). It is not true that every system of differential polynomials z contains a finite subset F1, * *, F8 such that

THE RISE OF THE GENTRY, 1558‐1640.1

T HE first French translators of Locke's Thoughts on Education introduced it with the remark'that foreign readers, in order to appreciate it, must remember the audience to whom it was addressed. It was composed, he explained, for the edification of an element in society to which the Continent offered no exact analogy, but which had become in the last century the dominant force in English life. To M. Coste, in x695, the triumphant ascent of the English gentry-neither a noblesse, nor a bureaucracy, but mere bons bourgeois-seemed proof of an insular dynamic of which France, with the aid of his translation, would do well to learn the secret. His compatriots, a century-and-a-half later, hailed the effortless survival of the same class in an age which had seen sezgneurs in flight from their castles, and even junkers cajoled into some semblance of concessions, as an example of social stability as eccentric as it was remarkable, and marvelled at the depth to which the tree had struck its roots. De Tocqueville in the 'forties, de Lavergne in the 'ffties, Taine in the 'sixties and 'seventies, wrote in a mood of reaction ; but they had some excuse for opening their eyes.3 In spite of the influx in the interval of Scots, Nabobs, some merchants, a few bankers, and an occasional industrialist, not less

Electrical computer eliminates calculations

Based upon an exact electrical analogy of a mechanical system, a specially constructed electrical computer eliminated many laborious calculations in designing the overhead catenary system for an extensive railroad electrification