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Buckling of axially compressed circular cylindrical shells with localized or random axisymmetric imperfections, deriving asymptotic approximation formulas for stress calculation
Orthogonality and positive operators on space of almost periodic and quasi-periodic functions, using frequency-power formulas
An attempt was made to devise a simple expression or formula to describe radiative heating in the atmosphere by ozone absorption. Such absorption occurs in the Hartley, Huggins, and Chappuis bands and is only slightly temperature and pressure dependent.
Two types of formulas were obtained for (- dE/dx) and the number of collisions per unit of path length (dN/dx) = const, which depend on W sub m, with due account of the polarization effect of the medium.
A two transducer correction formula valid for both solid and liquid specimens is presented. Using computer simulations of velocity measurements, the accuracy and range of validity of the results are discussed and are compared with previous approximations.
The Poisson sum formula was applied to the problem of summing pairwise interactions between an observer molecule and a semi-infinite regular array of solid state molecules. The transformed sum is often much more rapidly convergent than the original sum, and forms a Fourier series in the solid surface coordinates. The method is applicable to a variety of solid state structures and functional forms of the pairwise potential. As an illustration of the method, the electric field above the (100) face of the CsCl structure is calculated and compared to earlier results obtained by direct summation.
Two FORTRAN computer programs for the interpretation of low resolution mass spectra were prepared and tested. One is for the calculation of the molecular isotopic distribution of any species from stored elemental distributions. The program requires only the input of the molecular formula and was designed for compatability with any computer system. The other program is for the determination of all possible combinations of atoms (and radicals) which may form an ion having a particular integer mass. It also uses a simplified input scheme and was designed for compatability with any system.
It has been suggested that if jet engines of aircraft were placed at above the wing instead of below it, the wing would provide a partial shielding of the noise generated by the engines relative to observers on the ground. The shielding effects of an idealized three-dimensional barrier in the presence of an idealized engine noise source was predicted by the Kirchoff formula. Based on the good agreement between experimental measurements and the numerical results of the current study, it was concluded that the Kirchoff approximation provides a good qualitative estimate of the acoustic shielding of a point source by a rectangular flat plate for measurements taken in the far field of the flat plate at frequencies ranging from 1 kHz to 20 kHz. At frequencies greater than 4 kHz the Kirchoff approximation provides accurate quantitative predictions of acoustic shielding.
Formulas are derived describing the gravitational waves produced by a stellar encounter of the following type. The two stars have stationary (i.e., nonpulsating) nearly Newtonian structures with arbitrary relative masses; they fly past each other with an arbitrary relative velocity; and their impact parameter is sufficiently large that they gravitationally deflect each other through an angle that is small as compared with 90 deg.
In isolated cases a pole may be encountered in a previously published solution for the fields in a klystron gap. Formulas, permitting the critical combinations of parameters to be defined, are presented. It is noted that the region of inaccuracy surrounding the pole is sufficiently small and that a 0.1% change in the field changing parameter is enough to avoid it.
The pressure distribution and resistance found by theory and experiment for simple quadrics fixed in an infinite uniform stream of practically incompressible fluid are calculated. The experimental values pertain to air and some liquids, especially water; the theoretical refer sometimes to perfect, again to viscid fluids. Formulas for the velocity at all points of the flow field are given. Pressure and pressure drag are discussed for a sphere, a round cylinder, the elliptic cylinder, the prolate and oblate spheroid, and the circular disk. The velocity and pressure in an oblique flow are examined.
A unified approach is used to derive many of the current formulations for calculation of discrete frequency noise for helicopter rotors and propellers. Both compact and noncompact source formulations are derived. The compact formulations are obtained as the limit of noncompact source results. In particular, the linearized acoustic equations by Hawkings and Lowson, Farassat, Hanson, Woan and Gregorek, Succi, and Jou are derived in this paper. An interesting thickness noise formula by Isom and its recent extension to the near field by Ffowcs Williams are also presented. The paper includes some comparisons of measured and calculated acoustic pressure signatures and spectra for an advanced propeller. The theoretical results are obtained using a computer program developed by the author and P. A. Nystrom.
Formulas and their approximation were developed to map geodetic position to an Earth tangent plane with an airport centered rectangular coordinate system. The transformations were developed for use in a terminal area air traffic model with deterministic aircraft traffic. The exact configured vehicle's approximation equations used in their precision microwave landing system navigation experiments.
An argument is presented for the validity of the quadrupole formula for gravitational radiation energy loss in the far field of nearly Newtonian (e.g., binary stellar) systems. This argument differs from earlier ones in that it determines beforehand the formal accuracy of approximation required to describe gravitationally self-interacting systems, uses the corresponding approximate equation of motion explicitly, and evaluates the appropriate asymptotic quantities by matching along the correct space-time light cones.
Elastohydrodynamic film thickness was measured for a 20-mm ball bearing using the capacitance technique. The bearing was thrust loaded to 90, 448, and 778 N. The corresponding maximum stresses on the inner race were 1.28, 2.09, and 2.45 GPa. Test speeds ranged from 400 to 14,000 rpm. Film thickness measurements were taken with four different lubricants: (a) synthetic paraffinic, (b) synthetic paraffinic with additives, (c) neopentylpolyol (tetra) ester meeting MIL-L-23699A specifications, and (d) synthetic cycloaliphatic hydrocarbon traction fluid. The test bearing was mist lubricated. Test temperatures were 300, 338, and 393 K. The measured results were compared to theoretical predictions using the formulas of Grubin, Archard and Cowking, Dowson and Higginson, and Hamrock and Dowson. There was good agreement with theory at low dimensionless speed, but the film was much smaller than theory predicts at higher speeds. This was due to kinematic starvation and inlet shear heating effects.
Corrections for the theory of polarization of second harmonic plasma emission are proposed. The nontransversality of the magnetoionic waves was not taken into account correctly and is here corrected. The corrected and uncorrected results are compared for two simple cases of parallel and isotropic distributions of Langmuir waves. It is found that whereas with the uncorrected formula plausible values of the coronal magnetic fields were obtained from the observed polarization of the second harmonic, the present results imply fields which are stronger by a factor of three to four.
Previous work in this area is surveyed and the mathematics involved in determining the quantitative intensity measurements in triplet bands is presented. Explicit expressions for the intensity distribution in the branches of the 3 Sigma-3 Pi and 1 Sigma-3Pi bands valid for all values of the coupling constant Y of the 3 Pi terms are given. The intensity distribution calculated according to the formulas given is compared with measurements of PH, 3 Pi-3 Sigma. Good quantitative agreement is obtained.
A way of considering a small but often used class of reliability model and approximating algebraically the systems reliability is shown. The models considered are appropriate for redundant reconfigurable digital control systems that operate for a short period of time without maintenance, and for such systems the method gives a formula in terms of component fault rates, system recovery rates, and system operating time.