Search

International audience; From the viewpoint of torsional oscillations an internal combustion engine with a long crankshaft is generally considered to be equivalent to a uniform shaft carrying equidistant identical disks. It is here shown that advantage can be taken of the regularity of such a system to simplify the calculation of torsional oscillations. This is done by applying a mathematical method known as the calculus of finite differences. The procedure leads to a frequency equation (2.7) of remarkable symmetry in which appear as parameter the number n of cylinders in line and two simple functions K 1 and K 2 of the frequency which characterize the dynamical properties of the machines coupled at both ends of the crankshaft. These characteristic functions are of the nature of mechanical impedances, but due to their physical interpretation as a spring modulus (or spring constant) generalized to dynamic phenomena, the appellation dynamic modulus is being preferably used in the present paper. The concept of dynamic modulus is briefly introduced in the first section, while the second deals with the establishment of the frequency equation and an artifice for its rapid graphical solution avoiding the necessity of plotting an oscillatory function. Numerical applications to Diesel engines are treated in the last section. An example is also given of an extreme case where the fundamental frequency has a very low value and a special method is used for the calculation of this frequency.

This paper, consisting of three parts, describes investigations made with the objective of developing a simplified, practical microscope of the type which yields magnified images of transparent specimens with a resolving power superior to that of the best light microscopes. The first part deals with the general problem of design, including the electron gun and the imaging lenses. A later part will describe a completed instrument embodying many of the results of the investigations.

In this paper the field of a point charge inside a hollow, infinitely long circular cylinder is studied. The case of an axial point charge is treated in detail. Three different methods are developed. The first method shows how to calculate the induced charges at the surface of the cylinder without explicit knowledge of the potential itself. The surface charge‐density function is obtained as the solution of a Fourier‐type integral equation. Then the potential caused by these charges is calculated. The second method works in the opposite direction. Here the potential is obtained as solution of a boundary value problem, followed by the calculation of the corresponding charges at the surface of the cylinder.The integral, obtained for the surface charge density, is transformed by contour integration. Although the resulting series is very useful for numerical purposes, a stronger method is necessary, in order to calculate the charge density just opposite the point source. Figure 1 shows the calculated values of...

In a previous paper, the author reached a consideration that the endurance limit of a material should be determined by the amount of the mean stress in a certain small area around a point, instead of the stress at the point, and the extent of the area was determined for several kind of metals, by using the results of tension-compression fatigue tests. In this paper, the extent of area where the mean value of stress to be taken is determined for a mild steel in another way, viz., by a torsion fatigue test. The extent of the area for mild steel almost agrees with the one obtained in the previous tests, and the conclusion that the extent of area chiefly depends on the kind of metal and is independent of the course of the experiment was reached.

In the multianode cylindrical magnetron there exist favored phase velocities of the electromagnetic wave around the interaction space between anode and cathode. These velocities are characteristic of the resonant system attached to the anode segments. In the oscillating magnetron the electronic space charge within the interaction space is presumed to maintain sychronism with one of these velocities. Certain of the conditions of synchronism which can be discussed analytically are treated in this paper. The results, although based on restrictive assumptions, can be used in the interpretation of magnetron operation and in predicting regions of efficient behavior.

The basic equation for the mixing of radioactive isotopes is dR/dt = I grad a, where dR/dt is the flux of radioactivity; a, the relative specific activity; and I, the interfusion constant. The equation is applied to systems of compartments and some electrical analogies are presented. As special cases of the unconstrained systems treated in an earlier paper two constrained systems are discussed in which only a single radioactive isotope is required for the study of transport phenomena. One of these (mammillary system) consists of a central compartment communicating with a number of peripheral compartments. In the other (catenary system) the compartments are arranged chainwise. Equations are derived for the n‐compartment mammillary system relating the time dependent specific activities of the compartments to the exchange rates between the peripheral and central compartments and to their content of substance being exchanged. In analyzing the effect of lumping of a series of compartments into a single equival...

An investigation is made concerning the dependence of the array characteristic of a directional ring aerial on its number of elements. It is shown that an odd number of elements is more favorable than an even number in approximating the array characteristic of a similar ring aerial with infinitely many elements. It was previously shown by Page that a similar statement applies to an azimuthly omnidirectional, fading-reducing, concentric ring aerial; this result is contained as a special case in this investigation. The present paper deals especially with the case in which the principal direction of the antenna array is horizontal; the theory for this case is illustrated by a numerical example. Journal of Applied Physics is copyrighted by The American Institute of Physics.

When the anode potential of a nonoscillating magnetron is lower than the cut‐off potential, the discrete electron‐to‐electron interaction has an effect on the space‐charge distribution which would be negligible if only resulting in fluctuations about a known steady state. However the states proposed by Brillouin, Slater, and others are not steady states in this sense. The electron interaction must, therefore, be expected to produce a steady drift away from such initial states. This paper discusses qualitatively the final steady state to be expected and its dependence on the ratio of anode voltage to cut‐off voltage. Because of the involved nature of the electron distribution function no attempt is made to calculate the space‐charge distribution explicitly.

International audience; The paper deals with the propagation of unattenuated elastic waves in a cylindrical bore through an elastic material of infinite extent filled with a fluid. The phase and group velocity dispersion curves are plotted for axial symmetric waves in the coupled fluid‐solid system.

The article of record may be found at http://dx.doi.org/10.1063/1.1721325 The expression for the driving point impedance of a generalized electric circuit as vizualized by the author is partially integrated, and the physical significance of certain terms is discussed in connection with their application to antenna problems. Upon postulating an unattenuated traveling wave as a first approximation to the current along either a terminated rhombic or Vee antenna, a formula is derived for the free space radiation impedance of each. The expression radiation impedance is used for that portion of the driving point impedance which may be determined from the complex power into the external fields. The resistive component of the impedance for the rhombic antenna checks with the radiation resistance as listed by Leonard Lewin in a discussion of a paper by Donald Foster, with Lewin apparently obtaining his formula by the solid angle Poynting vector method.

The nature of the permanent damage retained in metals from irradiation has been investigated in somewhat greater detail than has been done in the past. The usual assumption has been that the damage in all metals consists chiefly of interstitial‐vacancy pairs. The model presented in this paper reduces to this picture for the light elements but introduces a new concept in the case of damage in the heavy metals, called a displacement spike. Calculations are made from which one can estimate the relationship between the density of interstitial‐vacancy pairs and the temperature of the associated thermal spike. An assumption regarding the extent to which interstitial‐vacancy pairs persist throughout the duration of the thermal spike has been made, based upon these calculations. The number of interstitial‐vacancy pairs predicted in the heavy elements is considerably smaller than that predicted by the former model. A mechanism is proposed by which small dislocation loops can be produced in the heavier metals by ir...

This paper reviews the theory of low angle x‐ray diffraction as applied in the long wavelength region for the determination of particle sizes and shapes and other structural features in the submicroscopic size range and emphasizes the advantages to be gained by employing the longer x‐ray wavelengths (8 to 25 A). It also is intended to serve as an introduction to a description of an entirely new instrumental technique developed for this long wavelength range utilizing a diffraction apparatus consisting of a special gas‐filled x‐ray tube and a total reflection camera in which the primary radiation is simultaneously monochromatized and made to converge to a point focus. The sample for study is placed in the converging part of the primary beam and the diffraction patterns are formed around the point focus on a photographic film.

Methods of treating the Boltzmann equation for the case of a sinusoidally distributed source of fast neutrons in a material containing hydrogen are discussed and compared. The effects of the simplifying assumptions commonly employed in reactor calculations are analyzed. A technique which is particularly suitable for accurate numerical integration of the Boltzmann equation in the above case is described. Numerical results are being obtained by this method, and will be presented and compared with results obtained from other approximate methods in a subsequent paper.

A variational method is presented which is used to calculate the energy appearing in the various diffracted orders set up when a plane wave is incident upon a periodic reflecting surface. Either the first or the second boundary condition can be so treated. A sample problem is worked showing that if the average absolute slope of the reflecting surface is small (segments of surface with large slope may be included) and if the displacement of the surface is not large compared with the wavelength of the incident radiation, the formulation gives results correct to within a few percent. The calculation shows the existence of Wood anomalies; these are discussed in the paper.

This paper discusses the effect of pressure‐diffusion flux upon the concentration distribution of gas mixtures in flow fields. The equation of concentration is formulated for a binary gas mixture in which the mass ratio is large and the concentration of the lighter gas is very small. An asymptotic solution to the steady‐state equation of concentration is given for an irrotational and incompressible flow.As an illustration, the diffusive separation (i.e., deviation from the original homogeneous state) of a mixture of helium and nitrogen along streamlines at the entrance to a long straight channel is calculated. It is assumed that the pressure inside the channel is 90% of that in the free stream, and that the diffusion coefficient of the mixture corresponds with the atmospheric conditions at 80‐km altitude.

This paper summarizes the results of calculations made in an attempt to explain the origin of the observed modulation effects in two-level maser experiments [1,2]. In a spontaneously oscillating spin system any transverse magnetization, which couples rf power out of the spin system, which is due to the presence of a transverse rf field, which is in turn induced by the transverse magnetization. Any consideration of the dynamics of the spin system or the build-up of the radiation field must consequently treat the two systems simultaneously. Our analysis uses a model first formulated by Bloembergen and Pound [3], except that our problem is inherently nonlinear [4] and we cannot make the simplifying assumption Mz = const, which linearizes the the equations of motion, and are forced to have rescourse to an IBM 704.

An approximate analytical approach for determining the temperature distribution in a hollow cylindrical cup of radius C, having a base thickness H, with a stem of radius A, and length L, is given. The outer radial surface of the cup is held at a temperature T0 and the temperature at the bottom of the stem is Ts. All other surfaces are adiabatic. This geometrical arrangement is used to observe marker motion under the influence of a large thermal gradient in a thermal diffusion experiment described in the following paper. In this setup, only the sink temperature Ts and the temperature at the bottom of the cup Tm can be measured. Equations are presented which enable one to calculate the temperature and its gradient along the axis of this arrangement with relative ease for the physically important case A/C

This paper analyses the maser oscillator equations which describe the interaction between the resonant cavity and the inverted population of the electron spin system of the paramagnetic substance. It is shown that these equations will not allow periodic solutions thus refuting the theory, based on computer solutions, that this interaction is responsible for the pulsed mode of operation of the oscillator.Characteristics of solutions of these equations are determined analytically, and the ambiguity of computer solutions is discussed with the aid of examples. Numerical solutions are presented which show that periodic solutions may be induced by supplementing the spin system equation with an additional term.

A method of etching high purity zinc to reveal various etch figures on {101¯0} planes is presented in this paper. Etch figures are formed by polishing in a dichromic acid solution after the introduction of mercury to the crystal surface. No measurable aging time is required to form etch figures at newly formed dislocation sites when mercury is on the surface prior to deformation. The mercury concentrates at the sites where etch figures form and may be removed by vacuum distillation and chemical polishing before it appreciably affects the purity of the bulk of the crystal.

In the long‐wavelength limit, the current distribution in a thin‐film superconducting strip transmission line can be described by an inhomogeneous Fredholm equation of the second kind. By considering a fluxoid conservation derivation of this equation, physical insight into the structure of the kernel follows naturally. An approximate analytic solution to the integral equation is derived for a specified range of geometrical parameters commonly encountered in practice. The solution is obtained by making use of the Liouville—Neumann method of successive iterations and approximating the resulting series by a series involving powers of a defined coupling factor. It is shown that the critical current of the thin‐film superconducting strip transmission line, based on the calculations in the paper and a critical‐current‐density hypothesis, is underestimated by less than 10%.

The analysis of the multiple Bragg reflection of a neutron beam of finite size in a semi‐infinite mosaic crystal given in a recent paper by Werner and Arrott is generalized to include bounded crystals. The coupled differential equations describing secondary extinction given by Hamilton are solved in general, and a method of piecewise solution, or solution by regions, is given.A discussion is given of experiments on the spatial distribution of the diffracted current from slab‐shaped crystals. Various methods for measuring the probability for Bragg scattering per unit path are compared and found not to agree. It is felt that the discrepancies are basic to the mosaic structure of crystals in general.