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For certain dissipative systems, a comparison can be made between the Hamilton-Jacobi theory and the conformal invariance of action theory. The two concepts are not identical, but the conformal action theory covers the Hamilton-Jacobi theory.
The complete, exact exterior solution for a static, spherically symmetric source in locally conformal invariant Weyl gravity is presented. The solution includes the familiar exterior Schwarzschild solution as a special case and contains an extra gravitational potential term which grows linearly with distance. The obtained solution provides a potential explanation for observed galactic rotation curves without the need for dark matter. The solution also has some interesting implications for cosmology.
A general method for determining the structure of the gravitational equations of motion is presented in the fourth-order theory of gravity based on local conformal Weyl invariance of the gravitational action. The explicit structure for these equations is given for a time-dependent, spherically symmetric geometry.
Compact polarimetry has been shown to be an interesting alternative mode to full polarimetry when global coverage and revisit time are key issues. It consists on transmitting a single polarization, while receiving on two. Several critical points have been identified, one being the Faraday rotation (FR) correction and the other the calibration. When a low frequency electromagnetic wave travels through the ionosphere, it undergoes a rotation of the polarization plane about the radar line of sight for a linearly polarized wave, and a simple phase shift for a circularly polarized wave. In a low frequency radar, the only possible choice of the transmit polarization is the circular one, in order to guaranty that the scattering element on the ground is illuminated with a constant polarization independently of the ionosphere state. This will allow meaningful time series analysis, interferometry as long as the Faraday rotation effect is corrected for the return path. In full-polarimetric (FP) mode, two techniques allow to estimate the FR: Freeman method using linearly polarized data, and Bickel and Bates theory based on the transformation of the measured scattering matrix to a circular basis. In CP mode, an alternate procedure is presented which relies on the bare surface scattering properties. These bare surfaces are selected by the conformity coefficient, invariant with FR. This coefficient is compared to other published classifications to show its potential in distinguishing three different scattering types: surface, doublebounce and volume. The performances of the bare surfaces selection and FR estimation are evaluated on PALSAR and airborne data. Once the bare surfaces are selected and Faraday angle estimated over them, the correction can be applied over the whole scene. The algorithm is compared with both FP techniques. In the last part of the paper, the calibration of a CP system from the point of view of classical matrix transformation methods in polarimetry is proposed.
The state of the art in topology and flow geometry is presented. Solution techniques for partial differential equations are reviewed and included developments in coordinate transformations, conformal mapping, and invariant imbeddings. Applications of these techniques in fluid mechanics, flow geometry, boundary value problems, and fluidics are presented.
A new method is presented for obtaining the velocity potential of the flow about a body of revolution moving uniformly in the direction of its axis of symmetry in a fluid otherwise at rest. This method is based essentially on the fact that the form of the differential equation for the velocity potential is invariant with regard to conformal transformation of the meridian plane. By means of the conformal transformation of the meridian profile into a circle a system of orthogonal curvilinear coordinates is obtained, the main feature of which is that one of the coordinate lines is the meridian profile itself. The use of this type of coordinate system yields a simple expression of the boundary condition at the surface of the solid and leads to a rational process of iteration for the solution of the differential equation for the velocity potential. It is shown that the velocity potential for an arbitrary body of revolution may be expressed in terms of universal functions which, although not normal, are obtainable by means of simple quadratures. The general results are applied to a body of revolution obtained by revolving a symmetrical Joukowski profile about its axis of symmetry. A numerical example further serves to illustrate the theory.
In many real-world pollution chemical reaction problems, the rate of reaction problems, the rate of reaction may be greatly affected by unmixedness. An approximate closure scheme for a chemical kinetic submodel which conforms to the principles of invariant modeling and which accounts for the effects of inhomogeneous mixing over a wide range of conditions has been developed. This submodel has been coupled successfully with invariant turbulence and diffusion models, permitting calculation of two-dimensional diffusion of two reacting (isothermally) chemical species. The initial calculations indicate the ozone reactions in the wake of stratospheric aircraft will be substantially affected by the rate of diffusion of ozone into the wake, and in the early wake, by unmixedness.
Exterior differential ideals are discussed, and sets of invariant generators presented, for Reimannian, conformal and projective geometries, and for specializations such as Ricci-flat, self-dual and Einstein-Maxwell theories. The Cartan characteristic integers are explicitly calculated, and involutory basis forms found, for each of these (specialized to four dimensions), exposing their algebraic structure and showing how they generate well-posed sets of partial differential equations.
A whisker from a tin plated part was blamed for the loss of a commercial spacecraft in 1998. Although pure tin finishes are prohibited by NASA, tin plated parts, such as hybrids, relays and commercial off the shelf (COTS) parts, are something discovered to have been installed in NASA spacecraft. Invariably, the assumption is that a conformal coat will prevent the growth of, or short circuits caused by, tin whiskers. This study measures the effect a Uralane coating has on the initiation and growth of tin whiskers, on the ability of this coating to prevent a tin whisker from emerging from the coating, and on the ability to prevent shorting. A sample of fourteen brass substrates (1 inch by 4 inches by 1/16 inch) were plated by two separate processes: half of the specimens were 'bright' tin plated directly over the brass substrate and half received a copper flash over the brass substrate prior to 'bright' tin plating. Each specimen was coated on one half of the substrate with three bi-directional sprays of Uralane 5750 to a nominal thickness of 25 to 75 micrometers (1 to 3 mils). Several specimens of both types, Cu and non-Cu flashed, were placed in an oven maintained at 50 C as others' work suggests that this is the optimal temperature for whisker formation. The remaining specimens were maintained at room ambient conditions. The surfaces of each specimen have been regularly inspected using both optical (15 to 400x power) and Scanning Electronic Microscopy (SEM). Many types of growths, including needle-like whiskers, first appeared approximately three months after plating on the non-conformally coated sides of all specimens. At four months, 4 to 5 times more growth sites were observed on the coated side; however, the density of growth sites on the non-conformally coated side has since increased rapidly, and now, at one year, is about the same for both sides. The density of growth sites is estimated at 90/sq mm with 30 percent of the sites growing whiskers (needle-like forms) with the potential to cause short circuit bridging. The average growth rate of the needle-like whiskers on the non-conformally coated areas is about 130 micrometers per year with some outliers reaching 800 micrometers after one year. It is more difficult to make growth measurements under the conformal coat. As yet no whiskers have been observed to penetrate through the coating surface, however, a number of tin nodules appear on the verge of breaking through the thinner regions of the coating surface. These domes are developing sharper and sharper tips, as if a growing whisker is about to push its way through a tough skin. Our observations are that the specimens with copper flash show a much lower density of nucleation sites and significantly slower whisker growth compared to the specimens that have only bright tin plating over brass. The specimens kept at room temperature have a higher whisker density than those stored at 50 C. This is an unexpected result and does not agree with the published findings of others. All of the whiskers originate from small surface defects (thin, tiny scratches) that appear over the entire surface of each specimen.
A scalar-tensor-nonmetric theory of gravity without matter fields is shown to be equivalent to the scalar-tensor-torsion theory proposed by German, the only difference being in the source of the Weyl vector or torsion vector (for equivalently the scalar field) which remains arbitrary in the theory. General extended conformal transformations, which leave the curvature tensor invariant, are presented and their implications for metric-affine theories and scalar-tensor theories are discussed.
The problem considered is that of rectilinear motion with variable velocity. The paper gives, by an elementary construction, a system of coordinates which is conformal in a restricted region near the axis of the motion. In such coordinates the velocity of light remains invariant even for observers moving with variable velocity. By a particular choice of the scale relation the restricted conformal transformations can be made to reduce to the Lorentz transformation everywhere in the case of constant velocity and locally in the case of variable velocity.
The present work describes a mathematical model and numerical scheme for the computer-aided calculation of two- and three-dimensional transonic flow over an isolated yawed wing with oblique shock waves and a trailing vortex sheet. The flow is modeled by the potential equation for irrotational flow which is hyperbolic at supersonic points and elliptic at subsonic points. A coordinate-invariant difference scheme is used in which retarded difference formulas are constructed to conform with the local flow direction. The resulting 'rotated' difference scheme allows complete flexibility in the choice of a coordinate system. Shock waves are located automatically in the form of compression bands spread over a few mesh widths. The scheme has proven to be stable and convergent throughout the transonic range. Calculations have been performed for Mach number up to 1.2 and yaw angles up to 60 deg, the likely operating range of a yawed-wing transport designed to fly at supersonic speeds. Calculations becomes less accurate towards upper end of range, because the difference scheme is first-order accurate in the supersonic range.
Two approaches to an identification problem in hydrology are presented based upon concepts from modern control and estimation theory. The first approach treats the identification of unknown parameters in a hydrologic system subject to noisy inputs as an adaptive linear stochastic control problem; the second approach alters the model equation to account for the random part in the inputs, and then uses a nonlinear estimation scheme to estimate the unknown parameters. Both approaches use state-space concepts. The identification schemes are sequential and adaptive and can handle either time invariant or time dependent parameters. They are used to identify parameters in the Prasad model of rainfall-runoff. The results obtained are encouraging and conform with results from two previous studies; the first using numerical integration of the model equation along with a trial-and-error procedure, and the second, by using a quasi-linearization technique. The proposed approaches offer a systematic way of analyzing the rainfall-runoff process when the input data are imbedded in noise.
Cartan's methods of exterior differential forms are utilized to derive conformal and absolute conservation equations for various field quantities in relativistic hydromechanics. In particular, Fridman's results for the conservation of vector lines are extended to space time situations. The invariance concepts of Helmholtz and Bernoulli are formulated for arbitrary frames of reference, and the separate conservation concepts of total mass and total number in space time are distinguished and associated with the concept of turbulence.
A numerical method is presented for analyzing the transonic potential flow past a lifting, swept wing. A finite difference approximation to the full potential equation is solved in a coordinate system which is nearly conformally mapped from the physical space in planes parallel to the symmetry plane, and reduces the wing surface to a portion of one boundary of the computational grid. A coordinate invariant, rotated difference scheme is used, and the difference equations are solved by relaxation. The method is capable of treating wings of arbitrary planform and dihedral, although approximations in treating the tips and vortex sheet make its accuracy suspect for wings of small aspect ratio. Comparisons of calculated results with experimental data are shown for examples of both conventional and supercritical transport wings. Agreement is good for both types, but it was found necessary to account for the displacement effect of the boundary layer for the supercritical wing, presumably because of its greater sensitivity to changes in effective geometry.
Our previous analysis of the energetics of metabolism showed that both the biosynthesis of amino acids and lipids from sugars, and the fermentation of organic substrates, were energetically driven by electron transfer reactions resulting in carbon redox disproportionation (Weber, 1997). Redox disproportionation--the spontaneous (energetically favorable) direction of carbon group transformation in biosynthesis--is brought about and driven by the energetically downhill transfer of electron pairs from more oxidized carbon groups (with lower half-cell reduction potentials) to more reduced carbon groups (with higher half-cell reduction potentials). In this report, we compare the redox and kinetic properties of carbon groups in order to evaluate the relative biosynthetic capability of organic substrates, and to identify the optimal biosubstrate. This analysis revealed that sugars (monocarbonyl alditols) are the optimal biosynthetic substrate because they contain the maximum number of biosynthetically useful high energy electrons/carbon atom while still containing a single carbonyl group needed to kinetically facilitate their conversion to useful biosynthetic intermediates. This conclusion applies to aqueous life throughout the Universe because it is based on invariant aqueous carbon chemistry--primarily, the universal reduction potentials of carbon groups.
Maculopathy and retinitis pigmentosa (rp) are two vision defects which render the afflicted person with impaired ability to read and recognize visual patterns. For some time there has been interest and work on the use of image remapping techniques to provide a visual aid for individuals with these impairments. The basic concept is to remap an image according to some mathematical transformation such that the image is warped around a maculopathic defect (scotoma) or within the rp foveal region of retinal sensitivity. NASA/JSC has been pursuing this research using angle invariant transformations with testing of the resulting remapping using subjects and facilities of the University of Houston, College of Optometry. Testing is facilitated by use of a hardware device, the Programmable Remapper, to provide the remapping of video images. This report presents the results of studies of alternative remapping transformations with the objective of improving subject reading rates and pattern recognition. In particular a form of conformal transformation was developed which provides for a smooth warping of an image around a scotoma. In such a case it is shown that distortion of characters and lines of characters is minimized which should lead to enhanced character recognition. In addition studies were made of alternative transformations which, although not conformal, provide for similar low character distortion remapping. A second, non-conformal transformation was studied for remapping of images to aid rp impairments. In this case a transformation was investigated which allows remapping of a vision field into a circular area representing the foveal retina region. The size and spatial representation of the image are selectable. It is shown that parametric adjustments allow for a wide variation of how a visual field is presented to the sensitive retina. This study also presents some preliminary considerations of how a prosthetic device could be implemented in a practical sense, vis-a-vis, size, weight and portability.
A containment apparatus for containing a cloud of charged particles comprises a cylindrical vacuum chamber having a longitudinal axis. Within the vacuum chamber is a containment region. A magnetic field is aligned with the longitudinal axis of the vacuum chamber. The magnetic field is time invariant and uniform in strength over the containment region. An electric field is also aligned with the longitudinal axis of the vacuum chamber and the magnetic field. The electric field is time invariant, and forms a potential well over the containment region. One or more means are disposed around the cloud of particles for inducing a rotating electric field internal to the vacuum chamber. The rotating electric field imparts energy to the charged particles within the containment region and compress the cloud of particles. The means disposed around the outer surface of the vacuum chamber for inducing a rotating electric field are four or more segments forming a segmented ring, the segments conforming to the outer surface of the vacuum chamber. Each of the segments is energized by a separate alternating voltage. The sum of the voltages imposed on each segment establishes the rotating field. When four segments form a ring, the rotating field is obtained by a signal generator applying a sinusoidal signal phase delayed by 90,180 and 270 degrees in sequence to the four segments.