Volume 24, Issue 2, 01 February 1953

A Coupling Analog for Nonlinear Systems with More Than One Degree of Freedom
View Description Hide DescriptionA simple electromechanical analog for expressing the coupling between nonlinear oscillatory systems is constructed and checked. The strength of the coupling can be easily controlled by varying the output of a dc amplifier while the type of coupling is determined by the shape of an aperture in an integrating cylinder. The device has general applicability to analogs in which the motion of a component part can be translated into the motion of a mask before an integrating cylinder with a selected aperature.

Investigation of Back Diffusion of Photoelectrons in Various Standard Gases as It Affects Secondary Electron Emission Coefficients
View Description Hide DescriptionThe effect of back diffusion of photoelectrons of two energy distributions in standard molecular and inert gases has been measured, and the results applied to the analysis of the Thomson equation as a semi‐empirical formula for correcting the measurements of the secondary emission coefficients in gaseous discharges. The method brings the results of Lauer and Molnar into satisfactory agreement. The effect of electron attachment is briefly discussed.

The Detection of Weak Signals by Correlation Methods
View Description Hide DescriptionA procedure involving autocorrelation is described which, for long averaging time and incoming signals with continuous spectrum, has a detection threshold equal to that of a corresponding conventional system consisting of band pass filter, rectifier, and low pass filter. The autocorrelation procedure is quite complex; a full autocorrelation function is computed and then subjected to a ``filtering'' operation. A simpler procedure, such as computing autocorrelation coefficients for only one or a few delay times, will in general be less effective. A third process, involving multiplication by a local sinusoidal signal, is also discussed and shown to be closely parallel to the conventional system.

Time‐Resolved Spectroscopy of Ultraspeed Pellet Luminosity
View Description Hide DescriptionImproved optical instrumentation has resulted in high time‐resolution spectrograms of the luminosity associated with ultraspeed aluminum pellets. These data indicate that in many cases the light is emitted in two phases: (1) the ballistic, or air shock, characterized by atomic metal lines and a strong continuum; (2) AlO bands that appear about 150 μsec after the metal is ablated from the pellet.

Direct Determination of the Flow Curves of Non‐Newtonian Fluids. II. Shearing Rate in the Concentric Cylinder Viscometer
View Description Hide DescriptionAnother method has been developed for obtaining the rate of shear vs shearing stress curves of non‐Newtonian fluids from concentric cylinder viscometer data. The mathematical expression developed is a rapidly converging power series in lns, where s is the cup to bob radius ratio. An estimate of error shows that under favorable conditions only two terms of the series are significant, and that terms past the third will hardly ever be needed.

The Nature of the Coefficient of Friction
View Description Hide DescriptionThe modern theory of the friction between dry metal surfaces ascribes it to local minute welds or adhesions between the surfaces and suggests that for a given pair of surfaces the friction force is uniquely defined by the normal load alone. Herein it is demonstrated that this cannot in general be true and that some further condition of operation must also be defined. Experiments are reported indicating that one such possible condition is the sliding speed so that the friction force is actually a function of the normal load and the sliding speed. It is pointed out that the speed can influence the friction force in two ways—one, by the resulting shear strain rate in the vicinity of the welded junction, and the other by the length of time taken for a junction of full strength to form.

An Alternative Method of Solving Hallén's Integral Equation and Its Application to Antennas Near Resonance
View Description Hide DescriptionHallén's complex integral equation for the current in a cylindrical antenna is separated into two real integral equations for the components of current in phase and in phase‐quadrature with the driving voltage. Each of these equations is solved by iteration using zeroth‐order currents and vector‐potential differences to define expansion parameters. It is shown that for electrical half‐lengths near odd multiples of a quarter‐wavelength at least a third‐order solution is required in order to determine accurately the component of current in phase with the driving voltage and the conductance. Conductances for a range of radii are evaluated by the new third‐order formula and compared with the King‐Middleton second‐order values and with the experimental data of Hartig. The new formula agrees excellently with experimental results at h=λ_{0}/4, whereas the earlier second‐order formula has by far its greatest percent error—near 8 to 10 percent—in a small range near resonance. It is concluded that for antennas near resonance, just as for very short and very long antennas, adequate account must be taken in the iteration of both components of current.

The Motion of a Sphere Moving Parallel to a Plane Boundary
View Description Hide DescriptionThe motion of a rigid sphere moving through an incompressible, homogeneous, nonviscous fluid in the presence of a rigid, infinite plane boundary is examined. The direction of motion of the sphere is assumed to be parallel to the plane boundary. It is assumed that the motion is irrotational and that the sphere velocity is small. An exact treatment is presented. Several curves of the pressure variation on the plane boundary are plotted for different values of the ratio of sphere radius to the perpendicular distance from the center of the sphere to the plane boundary.

The Effect of the Rate of Cooling on the Allotropic Transformation Temperatures of Uranium
View Description Hide DescriptionAllotropic transformation in uranium has been studied over a range of cooling rates from 5 to about 8000°C/sec. The transformation temperatures of both gamma‐to‐beta and beta‐to‐alpha were found to decrease continuously with increasing rates of cooling. The extent of the beta‐range increased with increasing cooling rates. For rates of cooling up to 1000°C/sec, recalescence was observed in both transformations. For higher cooling rates, there was usually no recalescence.
In most of the recorded cooling curves, a small but definite thermal arrest was observed, between the two main arrests which correspond to the two known phase transformations. This additional thermal arrest was also present in a heating curve, where it occurred at about 740°C, compared with 666 and 771°C for the two known phase transformations. Possible explanations of the additional arrest are discussed.

Plastic Electrets
View Description Hide DescriptionA brief discussion of proposed explanations for the electret effect is presented. Plexiglas, Lucite, and Nylon electrets were prepared under fields ranging from 19 to 36 kv/cm and observed for as long as 2000 hours. The surface charge densities were measured by electrostatic induction using a commercial electronic electrometer and a shunt capacitance to reduce the readings to a maximum of 20 volts. The initial state was a heterocharge or a homocharge depending on the strength of the forming field. The steady state was a homocharge in every case. Charge densities as high as 5.5×10^{−9} coulomb/cm^{2} (16.5 esu) were observed. A Plexiglas disk was charged at room temperature under a strong field and its subsequent decaying homocharge recorded. The experimental results support the ideas of Mikola and Gross, i.e., the existence of two decaying polarizations of opposite sense due to ionic migration, one occurring within the dielectric, the other, across the electrode‐dielectric interface.

A Thermoelectric Study of the Electrical Forming of Germanium Rectifiers
View Description Hide DescriptionThe electrical forming phenomena on the etchedsurfaces of n‐type Ge crystals by ac voltages were studied thermoelectrically. Remarkable improvements in the i‐v characteristics were obtained by applying appropriate forming voltages. The thermoelectriccurrent observed on the etchedsurface showed n‐type direction but it was converted to p‐type by the forming. It has also been found out that the thermo‐emf depends sensitively on the pressure of the whisker contact after the forming (and on the polished surface), while the dependence is small before the forming on the etchedsurface.
Experimental results seem to show that some substance of relatively high resistivity and of p‐type thermo‐emf is produced by the forming between the whiskermetal and the Gesurface.

Hall Effect Modulators and ``Gyrators'' Employing Magnetic Field Independent Orientations in Germanium
View Description Hide DescriptionThree uses for the Hall effect in germanium crystals are described. These are (1) use of Hall effect probes in measuringmagnetic flux, (2) use of Hall effect in crystals to produce a pure product modulator, and (3) use of Hall effect in germanium crystals to produce a nonreciprocal transmission. If the resistances are shunted around such gyrators, the transmission can be made zero in one direction and finite in the other. In all these applications, use is made of a crystal orientation for which the cross magneto‐resistance effects are zero and the Hall effect constant does not vary with field by more than 2 percent out to a flux density of 20 000 gausses. This orientation was located by making a phenomenological study of the magneto‐resistance and Hall effect corrections for a cubic crystal and evaluating constants experimentally. Correction terms to fourth and fifth powers of the magnetic field have been obtained.

Screw Dislocations in Thin Rods
View Description Hide DescriptionIn connection with Galt and Herring's observation on thin whiskers of tin, the properties of a screw dislocation in a cylinder are worked out. When all boundary conditions are taken into account, the image force tends to keep the dislocation along the axis. Only when it is displaced about half‐way to the surface does the image force tend to pull it out of the rod. Generators of the cylindrical rod become helices when the dislocation is introduced. The dislocation can be ejected from the rod by twisting or bending it suitably.

Solution of Nonlinear Differential Equations by the Reversion Method
View Description Hide DescriptionBy the use of the reversion method certain types of ordinary nonlinear differential equations can be reduced to a set of ordinary linear differential equations which may conveniently be solved by the Laplace transform. The expression for the general member of the linear set is developed and written out in detail for certain illustrative terms. The method is applied to two simple problems for which the answers are exactly known so that some idea may be obtained as to the excellence of the approximations supplied by this method.

Quasi‐Degenerated Modes in High‐ε Dielectric Cavities
View Description Hide DescriptionThis paper deals with resonance effects in circularly cylindrical solid bodies of high‐ε dielectrics such as titanates, these bodies being either not metallized or partly or fully metallized by fired‐on silver. The high dielectric constant has two pronounced effects:
(a) Miniaturization, a linear reduction in size in the order of magnitude of 1/100, and
(b) Realization of boundary conditions approaching infinite wave impedance.
All four combinations of radial and axial wave impedance being zero (metallized) or infinite (interface dielectric/air) are investigated mathematically and experimentally. Special consideration is given to degenerated modes; that is, modes for which the axial dimensions of the cavity do not contribute to the resonance wavelength. Because of the inherent magnetic leakage through the dielectric, this is only conditionally true. These modes are therefore termed quasi‐degenerated.
In contrast to conventional cavity theory dealing only with metallic boundaries, quasi‐degenerated TE modes are realizable; namely, if the faces of the cylindrical cavities are not metallized. These cavities can be tuned by introducing magnetic rods into them or by application of conductive disks outside of them in the proper position.
A novel type of antenna can be evolved from the TE _{010} ^{∞∞} mode, comprising a dielectric spiral encircling a magnetic rod.
In many cases the relatively high temperature coefficient, dissipation factor, and noise level prevent for the time being the potential application of these high‐ε dielectrics.

The Flexural Response of a Submerged Solid to a Pulsating Gas Bubble
View Description Hide DescriptionA bubble in a liquid pulsates and generates a changing pressure field. This reacts with a submerged flexible solid and induces elastic motions. Equations are derived which show how the vibration modes and frequencies of the solid are modified by the presence of the water, and how each mode is excited by the bubble pulsation. The generalized force for each mode is proportional to the volume acceleration of the bubble. The initial analysis presupposes incompressive flow, but it is shown that the results remain applicable if the duration of any compressive phase is small compared to the pulsation period of the bubble and the vibration period of the solid.

Forced Oscillations with Nonlinear Restoring Force
View Description Hide DescriptionForced oscillations with nonlinear restoring force are studied in transient states as well as in steady states. The original differential equation characterized by a nonlinear term is transformed under certain restrictions to the following differential equation of the first order:
Following Poincaré and Bendixson, the singularities and the integral curves of the above equation are discussed, the former being correlated with the periodic states of oscillations, the latter with the transient states of oscillations. The stability of the periodic solutions is determined in accordance with that of the singular points, viz., according to the roots of the characteristic equation. The integral curves yield the relationship between the given initial conditions and the periodic solutions. Thus, once the initial conditions are prescribed, we can foresee the final periodic states which are started with those conditions.
With this method of investigation, we have first studied the harmonic oscillations presented in Part I and then the subharmonic oscillation of order ⅓ given in Part II. In both cases the theoretical results are compared with the experimental measurements carried out for an electric circuit containing a saturable iron core, and the satisfactory agreement is found between them.

Synthesis of Transfer Functions with Poles Restricted to the Negative Real Axis
View Description Hide DescriptionA procedure for the synthesis of general RC transfer functions by means of unbalanced networks is described. The transfer function need not be minimum phase but may have zeros anywhere in the complex plane except on the positive real axis. Use is made of the technique of zero shifting as in the Guillemin procedure; but the additional use of a network theorem divides the desired network into two parts, with a consequent reduction of the problem to two simpler problems. Zero shifting can now be performed in two directions from within the total network. The theorem plus a method of using fewer paralleled ladders yield a final network with fewer ladders and fewer elements than that given by the Guillemin procedure. In the illustrative example given, twenty‐six elements are used, whereas the Guillemin procedure would use sixty‐six.

Viscoelastic Properties as Functions of the Distribution of Activation Energies
View Description Hide Description1. Assuming that the elementary molecular deformation process conforms to the Maxwellmodel, and that the molecular elastic force G_{i} and viscous force η_{ i } are functions (of unspecified forms) of the free energy of activation F*, the following expressions for the dynamic modulusG_{d} and dynamic viscosity (internal friction) η_{ d } are obtained: ,and ,where A=area of sample, τ_{ i }=G_{i} /η_{ i }, ω=vibration frequency, and φ(F*)dF*=the number of elementary processes having activation energies lying between F* and F*+dF*.
2. By employing an expression relating the relaxation time τ_{ i } with F* for the elementary process, and adopting the so‐called ``box'' distribution of relaxation times, the following explicit form for the distribution of activation energies is deduced: ,where k=Boltzmann's constant and T=absolute temperature. When the box distribution, as represented by this explicit form for φ, is introduced into the foregoing expressions for G_{d} and η_{ d }, the integrated results are found to predict temperature and frequency dependencies which are in gratifying agreement with experiment.
 LETTERS TO THE EDITOR


Shot Noise in Germanium Filaments
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