Volume 25, Issue 11, 01 November 1954

On the Concept of an Instantaneous Power Spectrum, and Its Relationship to the Autocorrelation Function
View Description Hide DescriptionA definition sufficient to define a function of frequency ρ(t,f) which could be regarded as the instantaneous power spectrum was given by Page. This function is not unique, since it may have added to it a complementary function of frequency ρ_{ c }(t,f) satisfying without changing the original signal in any way.
It is shown that when a signal is observed by different observers, starting their observations at different times, they will not derive the same ``instantaneous power spectral function,'' and the differences between their results will be complementary functions as defined above.
It is well known that the Fourier transform of the autocorrelation function is equal to the square of the magnitude of the spectral function. Analogously, a ``running autocorrelation function'' is defined and it is shown that the Fourier transform of its partial differential coefficient with respect to time is an instantaneous power spectral function.

Scattering from Dielectric Coated Spheres in the Region of the First Resonance
View Description Hide DescriptionFormulas for the backscattering and total scattering cross sections for dielectriccoating spheres of arbitrary size were developed following the methods of Hansen and of Aden and Kerker. Calculations based on the resultant formulas were made in the region of the first resonance (outside dimension of the concentric spheres is approximately 0.4 wavelength). It was found that certain choices of coating thickness and dielectric constant can lead to increases in the scattering cross sections of more than 100 percent relative to a solid metal sphere of the same outside diameter. A number of calculated and measured curves are presented, and they show the variation of the backscattering and total scattering cross sections as functions of coating thickness, coatingpermittivity, and outside diameter of the coating. Where both calculations and measurements were made for the same conditions, the values agree to ±2 percent.

Spectral Response of a Quadratic Device to Non‐Gaussian Noise
View Description Hide DescriptionIn order to compute the spectral response of a quadratic device to noise, a fourth‐order moment P of the input noise is sufficient, P being a function of three independent time delays. The function P _{1} by which this fourth moment for a non‐Gaussian noise differs from the corresponding moment for a Gaussian noise having the same spectrum is examined. The Fourier transform of this function is Q _{1}, a function of three frequencies. Q _{1} is capable of an interpretation in terms of nonlinear correlations between noise components at different frequencies. A specialization of Q _{1} leads to E, a function of two frequencies which is a measure of the correlation between the squares of the envelopes associated with those frequencies.
Several networks involving quadratic nonlinear elements are examined to illustrate the theory. It is shown that while the function P makes it possible to compute the complete spectral response of the network, the function E (together with the spectrum of the input) is sufficient in order to find the spectral density at zero frequency. Finally, for three examples of non‐Gaussian processes, the corresponding P _{1}, Q _{1} and E functions are computed.

Electron Emission from Metals under High‐Energy Hydrogen Ion Bombardment
View Description Hide DescriptionMeasurements of the electron emission from Mg, Al, Fe, Ni,Au, and Pb surfaces bombarded by atomic (H_{1} ^{+}) and molecular (H_{2} ^{+}) hydrogen ions with energies from 0.7 to 2.0 Mev showed a diminishing emission with ion energy and little dependence on either atomic number or on the field intensity at the metal surface.Measurements of this type are of interest in connection with the mechanism of high voltage discharges in vacuum. The expected variation of secondary emission with angle of incidence and with conditioning was found. The emission ratios are compared with measurements by others at lower ion energies.

Influence of Deuteron Bombardment and Strain Hardening on Notch Sensitivity of Mild Steel
View Description Hide DescriptionSchnadt‐type impact specimens of SAE 1019 steel were irradiated with 18.6‐Mev deuterons for the purpose of studying the influence of radiation on the brittle property as measured by the change in transition temperature. The effect was compared with that of two, five, and ten percent strain hardening. Microhardness studies were made to determine the extent and location of the radiation effect. An integrated flux of 29.6 microampere‐hr per cm^{2} shifted the transition temperature from −1°C to 18°C. The embrittling action was not a linear function of dose. Hardness was increased from 180 to 380 Knoop numbers. It was found to depend on the depth of penetration as well as the integrated flux. While radiation caused an effect similar to strain hardening, the nature of this effect was different. Annealing studies showed recovery of the irradiated material occurred between 260°C and 480°C. An interstitial vacancydiffusion process was indicated. Activation energies increased as recovery progressed. Recovery of the five percent strain hardened material occurred between 315°C and 371°C and would appear to be relaxation of internal stresses by the movement of dislocations.

Effect of Velocity Distribution on Traveling‐Wave Tube Gain
View Description Hide DescriptionThe density‐function method is applied to the one‐dimensional model of the traveling‐wave tube to determine the effect of velocity distribution on traveling‐wave tube performance. For narrow velocity spreads, a term is introduced into the root equation for the incremental propagation constants which is like the space charge term 4QC and directly added thereto. This term is proportional to the ratio of the variance of the distribution to the square of the gain parameter C. For a typical tube, thermal velocities are found to reduce the gain by less than one part in 10^{4}. In a tube employing confined magnetic focusing, and employing a high perveance beam, the velocity spread resulting from space charge lowers the gain by about 1 percent.

Conditions for Porosity Formation during Diffusion
View Description Hide DescriptionFormal relationships defining the regions of the diffusion zone where porosity tends to form during the Kirkendall effect are developed. The surfaces at which the intrinsic diffusional flux of each component reaches a maximum are also considered. The results are applicable to diffusion systems subject to the usual boundary conditions where the solutionN _{1}=N(x/√t) holds. The results are discussed in relation to presently available experimental findings.

Calibration of a Nickel‐Molybdenum Thermocouple
View Description Hide DescriptionA report is made of a calibration of a nickel (A) versusmolybdenumthermocouple up to 2242°F (50 mv).

Theory of Stress‐Strain Relations in Anisotropic Viscoelasticity and Relaxation Phenomena
View Description Hide DescriptionA thermodynamic derivation is given for the representation of a system having viscoelastic or relaxationproperties by means of a potential and dissipation function familiar in Lagrangian mechanics. This leads to modes of relaxation which are used as normal coordinates to derive general expressions for operational tensors relating stress and strain. A large variety of phenomena involving interaction of diffusion,chemical reaction, heat transfer, mechanical deformation, etc., is included in this theory.

Electrical Noise Pulses from Polarized Dielectrics
View Description Hide DescriptionElectrical noise pulses have been observed at elevated temperatures in polarized dielectrics(electrets) made of carnauba wax and of a vinyl acetate polymer. Pulse rate versus time was observed for electrets heated at a uniform rate and the results differ from those previously reported by others. Experiments devised to determine the origin of the pulses indicate that they are associated with the decay of volume polarization rather than with real surface charge. The total charge associated with the pulses from carnauba wax electrets is at least 5 percent of the maximum electret charge.

Kinetics of Piles with Reflectors
View Description Hide DescriptionAn integral equation for the time‐dependent reaction is derived on the basis of the two‐group model of neutron multiplication. When the effective multiplication constant is given, the solution reduces to a determination of the mean time T between consecutive generations, which is largely controlled by the circulation of neutrons in the reflector. If the steady distribution is known, T can be calculated from a simple formula.
To illustrate the orders of magnitude which are involved, T was calculated for a small pile surrounded by an infinite reflector. A value of T=450 microseconds was obtained assuming a mean lifetime in the core of 50 microseconds and a mean lifetime in the reflector of 14 000 microseconds.

Mechanics of Two Immiscible Fluids in Porous Media
View Description Hide DescriptionFlow of two and three immiscible fluids in porous media is considered in which the various fluids are separated into different saturation zones by gravity. An equation of flow for any one fluid is derived with the condition that the other fluids must be stationary. This equation is then applied to solve the question of the maximum rate of flow of one fluid into a well from a radially symmetrical porous medium without producing the other fluid or fluids present in the formation. Different well geometries and fluid systems are considered. These problems are sometimes called ``coning'' problems.

Forming Point‐Contact Silicon Transistors
View Description Hide DescriptionA new technique is reported in which silicon can be formed to provide transistor action. A suitable impurity is arced at the surface of the silicon causing the impurity to be diffused into a small region. Tests have been carried out using n‐type and p‐type silicon with various impurities. Initial results indicated voltage gains as high as 75 and power gains between 15 and 60. Other characteristics, such as variations in current multiplication with emitter current, were examined and the mechanism of alpha was compared with the theories developed by Sittner.

Ferrite Phase Shifters in Rectangular Wave Guide
View Description Hide DescriptionThe problem of the propagation of electromagnetic energy down an infinitely long rectangular wave guide partially filled by a ferrite slab is solved. The solution is expressed in the form of a transcendental equation involving the propagation constant. Calculations are carried out for a lossless ferrite, and the phase constant is evaluated as a function of the appropriate parameters, namely, the ferrite slab thickness, the lateral position of the slab in the guide, and the applied transverse static magnetic field intensity. The results are plotted in graphic form for values of the static magnetic field in the region of ferritesaturation both above and below ferromagnetic resonance. The electromagnetic field configurations within the wave guide are plotted in detail for values of the parameters of practical interest. Two versions of the nonreciprocal phase shifter are discussed. The first consists of a single slab placed asymmetrically in the wave guide, while the second consists of two symmetrically placed slabs with antiparallel static magnetic fields imposed. The nonreciprocal nature is summarized in terms of the differential phase shift β_{+}‐β_{−} which is pertinent in applications of this phase shifter.

Radioactive and Photoelectric p‐n Junction Power Sources
View Description Hide DescriptionAn electrical power source can be made by exposing a p‐n junction to radioactivity or light, so that the junction field separates electron‐hole pairs produced by the radiation. Expressions for maximum power, optimum load resistance, and efficiency are derived from an equivalent circuit and rectificationtheory. Power and efficiency increase with source current I_{g} of separated charges and zero‐bias junction resistance.I_{g} increases with energy and intensity of radiation, but is limited by self‐absorption in the radioactive isotopes. Estimates of attainable power and efficiency for silicon cells are 3·10^{−3} watt cm^{−2} and 15 percent for solar radiation, averaged, allowing for night, weather, and varying angle of incidence; and 3·10^{−4} watt cm^{−2} and 8 percent, for beta radiation from Sr^{90}–Y^{90} of activity 32 Curie/g. However, lattice defects produced by Sr^{90}–Y^{90} beta radiation impair cell performance by increasing electron‐hole recombination. A theoretical estimate of threshold energy for radiation damage in silicon is about 0.3 Mev, about half the experimental value reported for germanium. Avoiding radiation damage by annealing, by absorbers, and by use of less energetic isotopes is discussed. The Y^{90} beta spectrum is given; it is used in estimating damage rates in germanium, which are high, and efficiencies obtainable with absorbers, which are low. Theory and experiment are compared for Sr^{90}–Y^{90} cells of silicon and of germanium.
 LETTERS TO THE EDITOR


Failure and Survival in Fatigue
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Effect of Moving Striations on Microwave Conductivity of a Coaxial Discharge
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Germanium‐Stabilized Gray Tin
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Protective Films on Magnesium Observed by Electron Diffraction and Microscopy
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Entropy of Information and the Odd Ball Problem
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