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Initial boundary value problems for the general scalar singularly perturbed parabolic equation in a cylindrical domain are studied. The one-dimensional reaction-diffusion equation is considered in the absence of convection. Then, the general one-dimensional and N-dimensional reaction-convection-diffusion equations are analyzed.
A parallelized finite difference code based on the Newton method for systems of nonlinear elliptic boundary value problems in two dimensions is analyzed in terms of computational complexity and parallel efficiency. An approximate cost function depending on 15 dimensionless parameters is derived for algorithms based on stripwise and boxwise decompositions of the domain and a one-to-one assignment of the strip or box subdomains to processors. The sensitivity of the cost functions to the parameters is explored in regions of parameter space corresponding to model small-order systems with inexpensive function evaluations and also a coupled system of nineteen equations with very expensive function evaluations. The algorithm was implemented on the Intel Hypercube, and some experimental results for the model problems with stripwise decompositions are presented and compared with the theory. In the context of computational combustion problems, multiprocessors of either message-passing or shared-memory type may be employed with stripwise decompositions to realize speedup of O(n), where n is mesh resolution in one direction, for reasonable n.
Since a planet's magnetic field can sometimes provide a spacecraft with some protection against cosmic ray and solar flare particles, it is important to be able to quantify this protection. This is done by calculating cutoff rigidities. An alternate to the conventional method (particle trajectory tracing) is introduced, which is to treat the problem as a boundary value problem. In this approach trajectory tracing is only needed to supply boundary conditions. In some special cases, trajectory tracing is not needed at all because the problem can be solved analytically. A differential equation governing cutoff rigidities is derived for static magnetic fields. The presense of solid objects, which can block a trajectory and other force fields are not included. A few qualititative comments, on existence and uniqueness of solutions, are made which may be useful when deciding how the boundary conditions should be set up. Also included are topics on axially symmetric fields.
Red and near-infrared satellite data from the Advanced Very High Resolution Radiometer sensor have been processed over several days and combined to produce spatially continuous cloud-free imagery over large areas with sufficient temporal resolution to study green-vegetation dynamics. The technique minimizes cloud contamination, reduces directional reflectance and off-nadir viewing effects, minimizes sun-angle and shadow effects, and minimizes aerosol and water-vapor effects. The improvement is highly dependent on the state of the atmosphere, surface-cover type, and the viewing and illumination geometry of the sun, target and sensor. An example from southern Africa showed an increase of 40 percent from individual image values tothe final composite image. Limitations associated with the technique are discussed, and recommendations are given to improve this approach.
This paper states a conjecture which relates Lax-Richmyer stability to the algebraic test of the stability theory of Gustafsson, Kreiss, and Sundstrom (1972), developed for difference approximations to initial boundary value problems where the matrix size J increases linearly with n as n goes to infinity. This corresponds to mesh refinement in both space and time for t = n x delta t = constant.
A new approach for solving certain types of boundary value problems about complex configurations is presented. Numerical algorithms from such diverse fields as finite elements, preconditioned Krylov subspace methods, discrete Fourier analysis, and integral equations are combined to take advantage of the memory, speed and architecture of current and emerging supercomputers. Although the approach has application to many branches of computational physics, the present effort is concentrated in areas of Computational Fluid Dynamics (CFD) such as steady nonlinear aerodynamics, time harmonic unsteady aerodynamics, and aeroacoustics. The most significant attribute of the approach is that it can handle truly arbitrary boundary geometries and eliminates the difficult task of generating surface fitted grids.
Consider the first boundary value problem for a stationary Navier-Stokes system in a bounded three-dimensional region Omega with the boundary S: delta v = grad p+f, div v=0, v/s=0. Odqvist (1930) developed the potential theory and formulated the Green tensor for the above problem. The basic singular solution used by Odqvist to express the Green tensor is given. A theorem generalizing his results is presented along with four associated theorems. A specific problem associated with the study of the differential properties of the solution of stationary problems of magnetohydrodynamics is examined.
A computer simulation model of the measurement process for a ground-based Fabry-Perot interferometer (FPI) has been developed and used to study how variations of wind and temperature along the instrument line-of-sight affect the Doppler shift and width of the observed nightglow O(1D) emission line at high spectral resolution. Ground-based-derived temperatures in the nighttime sector of the winter hemisphere are found to give values that are representative of the peak O(1D) emission altitude. However, when the vertical temperature gradients are large, the ground-based FPI temperature measurement may differ by as much as about 12 percent from the temperature at the peak emission height. Simulations of the FPI measurement of nighttime thermospheric temperatures show that ground-based-derived temperatures may be lower by about 10 percent than the corresponding exospheric temperatures in the winter hemisphere and by about 15 percent in the summer hemisphere.
It is shown that Langmuir probes can have three different floating potentials in plasmas produced by a hot filament discharge in a multi-dipole device when the primary and secondary electron currents are comparable. The measured floating potential depends on the probe's initial condition - the most negative and the least negative potentials are found to be stable and the in-between value is found to be unstable. Results are compared to a simple theoretical model.
Deuterium on Mars has been detected by the resolution of several Doppler-shifted lines of HDO near 3.7 micrometers in the planet's spectrum. The ratio of deuterium to hydrogen is (9 + or - 4) x 10 to the -4th; the abundance of H2O was derived from lines near 1.1 micrometers. This ratio is enriched on Mars over the telluric value by a factor of 6 + or - 3. The enrichment implies that hydrogen escaped more rapidly from Mars in the past than it does now, consistent with a dense and warm ancient atmosphere on the planet.
In a study concerning the value of using radar imagery from systems with diverse parameters, X-band images of the Northern Louisiana Salt dome area generated by the airborne Goodyear electronic mapping system (GEMS) are analyzed in conjunction with imagery generated by the satelliteborne Seasat/SAR. The GEMS operated with an incidence angle of 75 to 85 deg and a resolution of 12 m, whereas the Seasat/SAR operated with an incidence angle of 23 deg and a resolution of 25 m. It is found that otherwise unattainable data on land management activities, improved delineation of the drainage net, better definition of surface roughness in cleared areas, and swamp identification, became accessible when adjustments for the time lapse between the two missions were made and supporting ground data concerning the physical and vegetative characteristics of the terrain were acquired.
Field equations yield overview of motions of many charged particles. Alternative approach developed for calculation of magnetic cutoff rigidities of electrically-charged particles in static magnetic field. New formulation involves partial differential field equation treated as boundary-value problem. Tracing of trajectories needed only to supply boundary conditions.
Initial results from the measurement conducted by the dust particle experiment on the lunar orbiting satellite Lunar Explorer 35 (LE 35) were reported with the data interpreted as indicating that the moon is a significant source of micrometeroids. Primary sporadic and stream meteoroids impacting the surface of the moon at hypervelocity was proposed as the source of micron and submicron particles that leave the lunar craters with velocities sufficient to escape the moon's gravitational sphere of influence. No enhanced flux of lunar ejecta with masses greater than a nanogram was detected by LE 35 or the Lunar Orbiters. Hypervelocity meteoroid simulation experiments concentrating on ejecta production combined with extensive analyses of the orbital dynamics of micron and submicron lunar ejecta in selenocentric, cislunar, and geocentric space have shown that a pulse of these lunar ejecta, with a time correlation relative to the position of the moon relative to the earth, intercepts the earth's magnetopause surface (EMPs). As shown, a strong reason exists for expecting a significant enhancement of submicron dust particles in the region of the magnetosphere between L values of 1.2 and 3.0. This is the basis for the proposal of a series of experiments to investigate the enhancement or even trapping of submicron lunar ejecta in this region. The subsequent interaction of this mass with the upper-lower atmosphere of the earth and possible geophysical effects can then be studied.
The ability of feed-forward neural net architectures to learn continuous-valued mappings in the presence of noise is demonstrated in relation to parameter identification and real-time adaptive control applications. Factors and parameters influencing the learning performance of such nets in the presence of noise are identified. Their effects are discussed through a computer simulation of the Back-Error-Propagation algorithm by taking the example of the cart-pole system controlled by a nonlinear control law. Adequate sampling of the state space is found to be essential for canceling the effect of the statistical fluctuations and allowing learning to take place.
Results of a preliminary investigation into a method which can be used to improve the results of an experimental force prediction analysis is presented. The method uses a singular value decomposition technique to reduce measurement noise present in the measured input data matrix. The fundamental theory for the method along with an experimental example is shown. The method is shown to provide encouraging force prediction improvements when the input data matrix contains high levels of measurement noise.
The stability of semi-discrete approximations for hyperbolic initial-boundary-value problems is considered. Asymptotic estimates of the eigenvalues of the finite-domain problem are given. These estimates are used to examine questions relating the normal mode analysis of the finite-domain problem and the normal mode quarter-plane analysis of the Gustafsson, Kreiss, and Sundstroem theory.
An explicit formula is obtained for the first-order eigenvector derivative that corresponds to the eigenvector of a repeated eigenvalue, in the case of the nonself-adjoint eigenvalue problem. This method applies to the class of nondefective problems whose first eigenvalue derivatives of the repeated eigenvalues are distinct. A singular-value decomposition approach is used to compute four requisite bases for eigenspaces, as well as to keep track of the dimensions of state variables and the conditioning of the state equations.
A general approach to solve boundary value problems numerically in a parallel environment is discussed. The basic algorithm consists of two steps: the local step where all the P available processors work in parallel, and the global step where one processor solves a tridiagonal linear system of the order P. The main advantages of this approach are two fold. First, this suggested approach is very flexible, especially in the local step and thus the algorithm can be used with any number of processors and with any of the SIMD or MIMD machines. Secondly, the communication complexity is very small and thus can be used as easily with shared memory machines. Several examples for using this strategy are discussed.