SEARCH · Search NASA
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
We establish the unique solvability of the first boundary value problem for a semilinear second order parabolic equation with varying time direction by using a modified Galerkin method and the regularization method. We obtain a priori error estimates for approximate solutions.
During the years of technology development by the Parabolic Dish program, the problems peculiar to tracking dishes have been explored in depth with particular emphasis on economics. Starting with the Precursor Concentrator, testing techniques and apparatus such as calorimeters and the flux mapper were developed. At the same time, mirrors were developed to have a long operating life as well as high performance. Commercially available equipment was evaluated as well. Building on all these elements, the Test Bed Concentrators were designed and built. With a peak intensity in the focal plane of over 17,500 suns and an average concentrator ratio over 3000 on an eight inch diameter aperture, they have proven to be the work horses of the technology. With a readily adjustable mirror array, they have proved to be an essential tool in the development of dish components, receivers, heat transport systems, instrumentation, controls, engines, and materials - all necessary to cost effective modules and plants. Utilizing the lessons learned from this technology, most cost effective systems were designed. These included Parabolic Dish Number 1 (PDC-1) and PDC-2 currently in final design by Acurex Corporation. Even more advanced concepts are being worked on, such as the Cassegranian systems by BDM Corporation.
Abstract This study focuses on addressing the inverse source problem associated with the parabolic equation. We rely on sparse boundary flux data as our measurements, which are acquired from a restricted section of the boundary. While it has been established that utilizing sparse boundary flux data can enable source recovery, the presence of a limited number of observation sensors poses a challenge for accurately tracing the inverse quantity of interest. To overcome this limitation, we introduce a sampling algorithm grounded in Langevin dynamics that incorporates dynamic sensors to capture the flux information. Furthermore, we propose and discuss two distinct dynamic sensor migration strategies. Remarkably, our findings demonstrate that even with only two observation sensors at our disposal, it remains feasible to successfully reconstruct the high-dimensional unknown parameters.
Nonlinear parabolic equations, considering existence, uniqueness theorems, abstract Cauchy problem, etc
The Q3DG is a computer program developed to perform a quasi-three-dimensional stress analysis for composite laminates which may contain delaminations. The laminates may be subjected to mechanical, thermal, and hygroscopic loads. The program uses the finite element method and models the laminates with eight-noded parabolic isoparametric elements. The program computes the strain-energy-release components and the total strain-energy release in all three modes for delamination growth. A rectangular mesh and data file generator, DATGEN, is included. The DATGEN program can be executed interactively and is user friendly. The documentation includes sections dealing with the Q3D analysis theory, derivation of element stiffness matrices and consistent load vectors for the parabolic element. Several sample problems with the input for Q3DG and output from the program are included. The capabilities of the DATGEN program are illustrated with examples of interactive sessions. A microfiche of all the examples is included. The Q3DG and DATGEN programs have been implemented on CYBER 170 class computers. Q3DG and DATGEN were developed at the Langley Research Center during the early eighties and documented in 1984 to 1985.
A new class of fully discrete Galerkin/Runge-Kutta methods is constructed and analyzed for semilinear parabolic initial boundary value problems. Unlike any classical counterpart, this class offers arbitrarily high, optimal order convergence. In support of this claim, error estimates are proved, and computational results are presented. Furthermore, it is noted that special Runge-Kutta methods allow computations to be performed in parallel so that the final execution time can be reduced to that of a low order method.
A compact range is a facility used for the measurement of antenna radiation and target scattering problems. Most presently available parabolic reflectors do not produce ideal uniform plane waves in the target zone. Design improvements are suggested to reduce the amplitude taper, ripple and cross polarization errors. The ripple caused by diffractions from the reflector edges can be reduced by adding blended rolled edges and shaping the edge contour. Since the reflected edge continues smoothly from the parabola onto the rolled surface, rather than being abruptly terminated, the discontinuity in the reflected field is reduced which results in weaker diffracted fields. This is done by blending the rolled edges from the parabola into an ellipse. An algorithm which enables one to design optimum blended rolled edges was developed that is based on an analysis of the continuity of the surface radius of curvature and its derivatives across the junction. Futhermore, a concave edge contour results in a divergent diffracted ray pattern and hence less stray energy in the target zone. Design equations for three-dimensional reflectors are given. Various examples were analyzed using a new physical optics method which eliminates the effects of the false scattering centers on the incident shadow boundaries. A Gregorian subreflector system, in which both the subreflector and feed axes are tilted, results in a substantial reduction in the amplitude taper and cross polarization errors. A dual chamber configuration is proposed to eliminate the effects of diffraction from the subreflector and spillover from the feed. A computationally efficient technique, based on ray tracing and aperture integration, was developed to analyze the scattering from a lossy dielectric slab with a wedge termination.
A family of five-stage fourth-order Runge-Kutta schemes is derived; these schemes required only two storage locations. A particular scheme is identified that has desirable efficiency characteristics for hyperbolic and parabolic initial (boundary) value problems. This scheme is competitive with the classical fourth-order method (high-storage) and is considerably more efficient and accurate than existing third-order low-storage schemes.
Vu-graphs are presented that show that point focus distributed receiver distributed generation systems are cost competitive with current utilities. System cost caveats and typical power module costs are described. Major problems inhibiting commercialization of the parabolic dish technology were reviewed.
A probabilistic representation is constructed for classical solution to the Cauchy problem for system of semilinear parabolic equations such that the second order terms with different coefficients enter in diagonal way, while the lower order terms enter in nondiagonal way. The systems of this kind arise as mathematical models of the parabolic conservation and balance laws and as mathematical models of dynamical systems with switching regimes.
Some results of the International Heliophysical Year (IHY) Coordinated Investigation Program (CIP) number 65 Meteors in the Earth Atmosphere and Meteoroids in the Solar System are presented. The problem of hyperbolic and near-parabolic orbits is discussed. Some possibilities for the solution of this problem can be obtained from the radar observation of faint meteors. The limiting magnitude of the Kharkov, Ukraine, radar observation program in the 1970 s was +12, resulting in a very large number of meteors being detected. 250,000 orbits down to even fainter limiting magnitude were determined in the 1972-78 period in Kharkov (out of them 7,000 are hyperbolic). The hypothesis of hyperbolic meteors was confirmed. In some radar meteor observations 1 10% of meteors are hyperbolic meteors. Though the Advanced Meteor Orbit Radar (AMOR, New Zealand) and Canadian Meteor Orbit Radar (CMOR, Canada) have accumulated millions of meteor orbits, there are difficulties in comparing the radar observational data obtained from these three sites (New Zealand, Canada, Kharkov). A new global program International Space Weather Initiative (ISWI) has begun in 2010 (http://www.iswi-secretariat.org). Today it is necessary to create the unified radar catalogue of nearparabolic and hyperbolic meteor orbits in the framework of the ISWI, or any other different way, in collaboration of Ukraine, Canada, New Zealand, the USA and, possibly, Japan. Involvement of the Virtual Meteor Observatory (Netherlands) and Meteor Data Centre (Slovakia) is desirable too. International unified radar catalogue of near-parabolic and hyperbolic meteor orbits will aid to a major advance in our understanding of the ecology of meteoroids within the Solar System and beyond.
A brief review of 2D PNS methodology is first presented which describes the specialized features of supersonic shock-capturing and subsonic pressure-split models required for the analysis of aircraft, rocket and scramjet jet mixing problems. These features include techniques for dealing with various types of embedded and interfacing subsonic regions, the inclusion of finite-rate chemistry and the direct-coupling with potential flow solutions. Preliminary 3D extensions of this PNS methodology geared to supersonic and subsonic rectangular free jet mixing problems are also reviewed. New 3D PNS work will be described which includes the development of a hybrid supersonic/subsonic free jet mixing model, and, a supersonic model geared to the analysis of turbulent mixing and combustion processes occurring in scramjet combustor/nozzle flowfields.
We have derived stability results for high-order finite difference approximations of mixed hyperbolic-parabolic initial-boundary value problems (IBVP). The results are obtained using summation by parts and a new way of representing general linear boundary conditions as an orthogonal projection. By slightly rearranging the analytic equations, we can prove strict stability for hyperbolic-parabolic IBVP. Furthermore, we generalize our technique so as to yield strict stability on curvilinear non-smooth domains in two space dimensions. Finally, we show how to incorporate inhomogeneous boundary data while retaining strict stability. Using the same procedure one can prove strict stability in higher dimensions as well.
A major problem in achieving significant speed-up on parallel machines is the overhead involved with synchronizing the concurrent process. Removing the synchronization constraint has the potential of speeding up the computation. The authors present asynchronous (AS) and corrected-asynchronous (CA) finite difference schemes for the multi-dimensional heat equation. Although the discussion concentrates on the Euler scheme for the solution of the heat equation, it has the potential for being extended to other schemes and other parabolic partial differential equations (PDEs). These schemes are analyzed and implemented on the shared memory multi-user Sequent Balance machine. Numerical results for one and two dimensional problems are presented. It is shown experimentally that the synchronization penalty can be about 50 percent of run time: in most cases, the asynchronous scheme runs twice as fast as the parallel synchronous scheme. In general, the efficiency of the parallel schemes increases with processor load, with the time level, and with the problem dimension. The efficiency of the AS may reach 90 percent and over, but it provides accurate results only for steady-state values. The CA, on the other hand, is less efficient, but provides more accurate results for intermediate (non steady-state) values.
Numerical instabilities often arise in the use of high-ordered collocation approximations for numerically solving parabolic partial differential equations. These problems may be reduced by formulations involving evaluation of collocation polynomials rather than combination of the polynomials into a power series. As an illustration, two formulations using shifted Legendre polynomials of order 26 and less are compared.
The presence of an unstable periodic classical orbit allows one to introduce the decay time as a purely classical magnitude: inverse of the Lyapunov index which characterizes the orbit instability. The Uncertainty Relation gives the corresponding resonance width which is proportional to the Planck constant. The more elaborate analysis is based on the parabolic equation method where the problem is effectively reduced to the multidimensional harmonic oscillator with the time-dependent frequency. The resonances form series in the complex energy plane which is equidistant in the direction perpendicular to the real axis. The applications of the general approach to various problems in atomic physics are briefly exposed.
A numerical method is devised to solve a class of linear boundary-value problems for one-dimensional parabolic equations degenerate at the boundaries. Feller theory, which classifies the nature of the boundary points, is used to decide whether boundary conditions are needed to ensure uniqueness, and, if so, which ones they are. The algorithm is based on a suitable preconditioned implicit finite-difference scheme, grid, and treatment of the boundary data. Second-order accuracy, unconditional stability, and unconditional convergence of solutions of the finite-difference scheme to a constant as the time-step index tends to infinity are further properties of the method. Several examples, pertaining to financial mathematics, physics, and genetics, are presented for the purpose of illustration.
An approximation framework is presented for computation (in finite dimensional spaces) of Riccati operators that can be guaranteed to converge to the Riccati operator in feedback controls for abstract evolution systems in a Hilbert space. It is indicated how these results may be used in the linear optimal regulator problem for a large class of parabolic systems.