摘要:

A set of principles and a systematic procedure are presented to establish the exact solutions of very large and complicated physical systems, without solving a large number of simultaneous equations and without finding the inverse of large matrices. The procedure consists of tearing the system apart into several smaller component systems. After establishing and solving the equations of the component systems, the component solutions themselves are interconnected to obtain outright, by a set of transformations, the exact solution of the original system. The only work remaining is the elimination or solution of the comparatively few superfluous constraints appearing at the points of interconnection.The component and resultant solutions may be either exact or approximate and may represent either linear or, with certain precautions, nonlinear physical systems. The component solutions may be expressed in numerical form or in terms of matrices having as their elements real or complex numbers, functions of time, or differential or other operators, etc. Boundary value, characteristic value, and time‐varying problems of partial differential equations, as well as problems in ordinary differential equations and algebraic equations may be solved in this manner.The method shown may be extended and generalized so that one can tear apart and afterward reconstruct the solution of extremely large or highly intricate physical systems, often without calculating any inverse matrices at all and always without carrying along unduly large matrices. This extension and generalization of the method is analogous to building skyscrapers by erecting first a steel framework and only afterward filling the gaps between the girders as needed. Those versed in the science of tensorial analysis of interrelated physical systems on the one hand and of large electrical networks on the other, should thereby be able to solve, with the aid of already available digital computers, highly complex physical systems possessing tens of thousands and, in special cases, even hundreds of thousands of variables. The accuracy of machine calculations, of coding and even the correctness of the analytical procedure itself may be simultaneously checked by physical tests at various stages of the computation. The saving in computing time is considerable even in smaller problems; by tearing a physical system intonparts, the usual machine calculations are reduced, in matrix inversion for instance, to a fraction of about 2/n2.The present paper develops in detail the solution of a simple boundary value problem of Poisson's equation. A numerical example of interconnecting the solutions of large electric‐power transmission systems appears in reference 3. Many simpler numerical examples are worked out in reference 1.

ISSN:0021-8979    

DOI:10.1063/1.1721447

出版商:AIP    

年代:1953

数据来源: AIP

摘要:

The interpretation of certain phenomena occuring at nominally flat surfaces in stationary or sliding contact is dependent on the assumed distribution of the real area of contact between the surfaces. Since there is little direct evidence on which to base an estimate of this distribution, the approach used is to set up a simple model and compare the deduced theory (e.g., the deduced dependence of the experimental observables on the load) with the experimental evidence. The main conclusions are as follows. (a) The electrical contact resistance depends on the model used to represent the surfaces; the most realistic model is one in which increasing the load increases both the number and size of the contact areas. (b) In general, mechanical wear should also depend on the model. However, in wear experiments showing the simplest behavior, the wear rate is proportional to the load, and these results can be explained by assuming removal of lumps at contact areas formed by plastic deformation; moreover, this particular deduction is independent of the assumed model. This suggests that a basic assumption of previous theories, that increasing the load increases the number of contacts without affecting their average size, is redundant.

ISSN:0021-8979    

DOI:10.1063/1.1721448

出版商:AIP    

年代:1953

数据来源: AIP

摘要:

Ultrasonic waves (shear or longitudinal) in the 10–30 mc range are transmitted down a fused silica rod, through a polystyrene or silicone one‐quarter wavelength seal, and into the solid specimen. Measurement of reflections within the specimen yields values for velocities of propagation and elastic constants.Data obtained over a temperature range of 78° to 300°K for silicon and germanium single crystals, and 1.6° to 300°K for fused silica are listed. For the latter, a high loss is noted, with an indicated maximum near 30°K.

ISSN:0021-8979    

DOI:10.1063/1.1721449

出版商:AIP    

年代:1953

数据来源: AIP

摘要:

A general expression is given for calculation of the coupling coefficients between an arbitrary number of modes simultaneously excited in a cavity resonator. The mechanism of energy conversion between modes is discussed for several practical coupling devices. The technique is applied to the unlimited numbers of degeneracies available in spherical geometry and is shown to offer many interesting possibilities. An experimental model of a spherical cavity is described and shown to demonstrate the theory.

ISSN:0021-8979    

DOI:10.1063/1.1721450

出版商:AIP    

年代:1953

数据来源: AIP

摘要:

In this paper, the author considers an approximation to the Rayleigh equation,y¨+&egr;(13y˙3−y˙)+y=A cos&ohgr;t, and its equivalent form under the transformationy˙=v,y=&egr;&xgr;. A cubic function13v3−v+&xgr;that appears in the altered equation is replaced by a piecewise linear function. For large &egr;, the existence of periodic solutions of the approximating equation is demonstrated. Strong orbital stability properties of neighboring solutions is also shown.

ISSN:0021-8979    

DOI:10.1063/1.1721425

出版商:AIP    

年代:1953

数据来源: AIP

摘要:

The diffusion of Ba through activated BaO&sngbnd;SrO cathode coatings was studied as a function of temperature. Most of the radioactive tracer material diffused according to a dependence of log10D vs1/Tsimilar to that obtained by Redington for diffusion of Ba in single crystals of BaO. The activation energy was 4.1±0.6 ev above 1280°K and 0.40±0.07 ev below that temperature.

ISSN:0021-8979    

DOI:10.1063/1.1721426

出版商:AIP    

年代:1953

数据来源: AIP

摘要:

The decrease of viscosity on shearing in a capillary at 37.8°C and a nominal rate of shear of 65 000 sec−1has been measured for 5, 10, and 15 weight‐percent solutions ino‐dichlorobenzene of 10 polyisobutylenes having viscosity‐average molecular weights from 40 000 to 2 300 000. Very little, if any, viscosity decrease was observed for polymers having molecular weights below 500 000, but marked decreases were observed for polymers with molecular weights above 500 000. The observed decreases were not recovered on standing and correspond to appreciable decreases in the molecular weights of the polymers. The molecular weight reduction can be explained on the basis of polymer chain rupture if the mechanical energy developed in a volume less than that enveloping a single polymer molecule can be concentrated into a single bond.

ISSN:0021-8979    

DOI:10.1063/1.1721427

出版商:AIP    

年代:1953

数据来源: AIP

摘要:

A phenomenological theory for the nonlinear voltage‐current characteristic curve displayed by a granular aggregate of silicon carbide is presented. The theory, which should apply to granular semiconductors other than silicon carbide, is based on a very simple model of the aggregate and on the assumption that the essential resistance is located at the grain‐grain contacts, the impedance of the bulk material being considered negligibly small. The currentiis related to the voltageVby the equationi=kAPn/mdn−2Vn/tn,whereAis the cross‐sectional area of the aggregate,tthe thickness,Pthe applied pressure, anddthe average particle diameter. The constantsk, n, andmare structure‐sensitive, that is, they depend on the physical‐chemical nature of the particles forming the aggregate. Factors influencing the values of these constants include impurity concentration in the semiconductor, elastic constants, and particle shape. The validity of this equation is supported by careful measurements made on granular aggregates of silicon carbide.

ISSN:0021-8979    

DOI:10.1063/1.1721428

出版商:AIP    

年代:1953

数据来源: AIP

摘要:

Radar clutter is distinguished from thermal noise by being caused by random reflection of transmitted electromagnetic energy. This paper considers what may be done by means of linear filtering to improve the detection of small radar signals in the presence of this clutter. Defining the signal‐to‐clutter ratio as the ratio of the peak signal to the rms value of the clutter, the optimum linear filter is derived for enhancing this ratio. The optimum filter has a frequency characteristic given by the conjugate of the voltage spectrum of the transmitted pulse divided by the power spectrum of the clutter. The synthesis of the optimum filter and various approximations to it are considered. The influence of these filters upon the signal‐to‐thermal‐noise ratio is also investigated. Finally, the influence of the second detector upon the signal‐to‐clutter or signal‐to‐noise ratio is considered.

ISSN:0021-8979    

DOI:10.1063/1.1721429

出版商:AIP    

年代:1953

数据来源: AIP

摘要:

A number of problems arising from the undesired overlapping or time coincidence of pulses from separate periodic pulse trains are considered. The coincidence time fraction is determined for two pulse trains with both a fixed initial phase and a randomly varying initial phase. The coincidence time fraction for these cases is then determined if only pulse coincidences equaling or exceeding a specified interval are considered. Finally, some problems involving more than two pulse trains are briefly discussed.

ISSN:0021-8979    

DOI:10.1063/1.1721430

出版商:AIP    

年代:1953

数据来源: AIP