Arbitrary Modifications Research Articles

Natural frequencies of plates with arbitrary concentrated mass and stiffness modifications

Vibration analysis of plates has been an active research subject and numerous technical papers have been accumulated. Though analytical solutions have been found for plates with specified forms of mass or stiffness modifications, the problem of plates with arbitrary mass and stiffness modifications has not been addressed to date despite its important practical implications. In this paper, a new and effective method has been developed to predict exactly the natural frequencies and mode shapes of plates with arbitrary mass, stiffness and damping modifications. Plate receptances are derived based on mode superposition and are then used to calculate the receptances of the modified plate. Natural frequencies and mode shapes of the modified plate are identified by analyzing the receptance data based on the concept of modal analysis. Numerical results are given to demonstrate the practical applicability of the proposed method.

Supersymmetric transformations of real potentials on the line

A systematic study of supersymmetric (or Darboux) factorizations on the line is performed. All possible pairs of supersymmetric transformations with the same factorization energy are reviewed; for such pairs, there is no condition on this energy. Iterations of single transformations and of pairs both allow arbitrary modifications of the bound spectrum. Different iterative methods lead to compact analytical equations depending on the initial potential and its solutions. Iterations of single transformations are able to transform an even potential into an even potential. Particular cases of a method based on iteration of pairs conserve either the reflection coefficient at all energies or the norming constants of bound states. These results are compared with previous methods established in other contexts. The most general supersymmetric transformation of a given potential is finally described, both with and without modifications of the bound spectrum.

Analysis of Plunge Shaving for Finishing Gears with Tooth Modifications.

A methodology based on space transformation matrices and the principle of conjugate movements has been developed to analyze three-dimensional gearing. The formulation for describing two moving conjugate rigid bodies is derived. Based on the manufacturing processes, relationships between the cutter parameters and the generated gear tooth profile are developed. Seven parameters of the cutter and finished gear coordinate system can be used to define arbitrary gear cutting and grinding machine conditions. An application of a plunge shaving cutting process is given to show the usefulness and accuracy of these formulas. An additional application shows the calculation method of the profile of shaving cutters which can finish helical on spur gears with arbitrary tooth modifications.

Most general form of phase-equivalent radial potentials for arbitrary modifications of the bound spectrum.

The most general form for radial potentials with the same phase shifts as a given real potential but arbitrarily different bound spectra is derived with a sequence of supersymmetric factorizations. The wave functions of the phase-equivalent potentials are expressed analytically in terms of the wave functions of the original potential.

Investigation of the shape of the imaginary part of the optical-model potential for electron scattering by rare gases

We present a comparative study of several empirical and nonempirical models for the absorption potential, which is the imaginary part of an optical-model potential, for electron scattering by rare gases. We show that the elastic differential cross section is most sensitive to the absorption potential for high-impact energy and large scattering angles. We compare differential cross sections calculated by several models for the absorption potential and by several arbitrary modifications of these model potentials. We are able to associate the effect of the absorption potential on the elastic differential cross section with its form at small electron-atom distances $r$, and we are able to deduce various qualitative features that the absorption potential must possess at small and large $r$ in order to predict both accurate differential cross sections and accurate absorption cross sections. Based on these observations, the Pauli blocking conditions of the quasifree scattering model for the absorption potential are modified empirically, thus producing a more accurate model that may be applied to other systems; e.g., electron-molecule scattering, with no adjustable parameters.

Enhancement of news photos

An image processing system for the enhancement and manipulation of news photographs is described. Capabilities implemented include cropping, enlarging, insertion of captions, unsharp masking, and arbitrary tone scale modifications. Primary advantages of this system include the reduction of processing time, greater flexibility and increased fidelity.

The dependence of the triton binding energy on the high-energy phase shift

An investigation of the dependence of the binding energy of the model triton on the highenergy part of the phase shift has been made for an interaction consisting of a second-rank separable potential. For this investigation we used our previous exact solution of the inverse scattering problem for a second-rank separable potential. It is shown that for input phase shifts obtained from either a standard separable potential or a local potential with a repuslive core this high-energy dependence of the binding energy is rather small. However arbitrary modifications in the standard phase shift at high energies produce large effects in the binding energy, presumably resulting from the “unphysical” nature of such changes. It is also found that separable potentials reproducing the same two-body data as a local potential generally produce much higher triton binding energies than the local potential. The effect of the interaction between the high-energy on-shell phase shift and the off-shell behaviour of the potential on the triton binding energy is also discussed.

Coma of Modified Gregorian and Cassegrainian Mirror Systems

The equivalence of the classical Newtonian, Cassegrainian, and Gregorian mirror systems with respect to the first two Seidel aberrations is rederived by means of a simple congruence. The effects of arbitrary small modifications of the two-mirror systems are then studied and general formulas are derived for the effects of such modifications on the spherical aberration and coma. Spherical aberration is corrected to the third order if the amount of glass removed from one surface is replaced at the corresponding zone of the other surface (approximate expression of Fermat’s principle). Modifications in which one surface is made spherical while the other is adjusted to eliminate spherical aberration result in large increases of coma for systems having the usual amplifying ratios.

Thin Films of Ferromagnetic Materials

Experimental observations are reported on the magnetic properties of thin evaporated films of nickel. The saturation magnetization follows the general prediction of Klein and Smith after somewhat arbitrary modifications on the basis of fitting the Weiss curve for bulk specimens, as suggested by Drigo. Qualitatively observed properties due to domain structure follow the predictions of Kittle. The surface roughness of the specimens has been carefully controlled. Measurements of temperature coefficient of resistance have led to modification of the theory of electron mean free path in thin films. The mean free path is found to vary at small thicknesses, rather than remaining constant as assumed by Fuchs and Sondheimer. The surface roughness has been estimated with the help of this theory. The films of nickel behave as if surface variations extend into the film approximately 3 angstroms from each surface.