Showing papers on "Parabola published in 1985"

Parabolic reflector system

Abstract: A device to focus to a point parallel electromagnetic or sound waves, eg a solar power station, that consists of a reflector KLMN curved in one direction to a parabola, that reflects incoming waves onto a secondary reflector PQRS which is also curved to a parabola in one direction only. The two reflectors are so placed so as to concentrate the incoming parallel waves to a point focus F. The polar axis EG of the secondary reflector PCRS forms an acute angle theta with the axial plane ABCD of the primary reflector KLMN. The device may be mounted on a mechanism to allow the device to track the source of energy, eg in the case of a solar power station, the sun. The device can be mounted so that as it tracks the source of energy the focal point F remains stationary. The operation of the device can be reversed to create outgoing parallel waves of energy from a point source F.

The parabolic rule, the Pandya transformation, and the structure of 100 In

Abstract: The Pandya transformation and the Paar parabola rule are used to predict the level structure of particle-hole100In from the known levels of particle-particle92Nb.

A Rapid Method for Estimating Equivalent Parabolic Polars from Wind-Tunnel Tests.

Abstract: : A method for obtaining a 'best-fit' parabolic drag polar from measured force results is presented The method is used in estimating the blockage correction due to separated flow that must be applied to wind tunnel results An important part of the method is the use of computer graphics to identify the part of the measured drag polar that may best be described by a parabola, and thus used as the basis for a curve fit The method is fast, when compared to existing curve-fitting techniques, and suited to use with an online data reduction system

Gravitational oscillations in a rotating paraboloidal basin: A classical problem revisited

Abstract: The effect of ellipticity of the free surface on the frequencies of axisymmetric normal gravity modes in a rotating shallow layer of liquid contained in a circular cylinder with paraboloidal bottom is investigated. The classical shallow-water theory due to Lord Kelvin for the flat bottom case neglects the curvature of the free surface due to rotation. In 1962 Fultz and Platzman treated the flat-bottom case, taking into account the effect of this ellipticity. The present work is similar to that of Fultz and Platzman, but is more general and treats the flat bottom as a special case. Suitable nondimensional parameters are defined, namely a depth parameter, a rotation parameter, and a frequency parameter. The problem is formulated in terms of cylindrical polar coordinates. It is a Sturm-Liouville problem and the differential operator is self-adjoint. The problem is solved by the Galerkin method, but the solution thus obtained is not in a closed form. The problem is also solved in a closed form by making use of the Legendre functions, but since these functions are not tabulated very extensively the solution involving the Galerkin method is used for computational purposes. A discussion of these Legendre function solutions is given and the results are compared with those of the Galerkin method whenever possible. Poincare treated the gravity modes in a parabola without a cylinder and not taking the ellipticity into account. The writers treated this case including the effect of ellipticity obtained results that differ radically from those in which ellipticity is neglected. In particular, according to the present theory, rotation has not effect on the frequency of the fundamental mode

Curved Finite Elements and Curve Approximation

Abstract: The approximation of parameterized curves by segments of parabolas that pass through the endpoints of each curve segment arises naturally in all quadratic isoparametric transformations. While not as popular as cubics in curve design problems, the use of parabolas allows the introduction of a geometric measure of the discrepancy between given and approximating curves. The free parameters of the parabola may be used to optimize the fit, and constraints that prevent overspill and curve degeneracy are introduced. This leads to a constrained optimization problem in two varibles that can be solved quickly and reliably by a simple method that takes advantage of the special structure of the problem. For applications in the field of computer-aided design, the given curves are often cubic polynomials, and the coefficient may be calculated in closed form in terms of polynomial coefficients by using a symbolic machine language so that families of curves can be approximated with no further integration. For general curves, numerical quadrature may be used, as in the implementation where the Romberg quadrature is applied. The coefficient functions C sub 1 (gamma) and C sub 2 (gamma) are expanded as polynomials in gamma, so that for given A(s) and B(s) the integrations need only be done once. The method was used to find optimal constrained parabolic approximation to a wide variety of given curves.