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DBAS 1 computer program provides analyst with simple algorithms for exact rapid solutions of systems with planar, cylindrical, or spherical interfaces. Conventional solutions are complex and present convergence problems. Two algorithm types are figured for each geometry; one converges rapidly for short and the other for long diffusion times. DBAS 1 is written in FORTRAN IV for batch execution.
The paper constructs exact, nonlinear solutions for a horizontal, cylindrical, current-carrying prominence supported against solar gravity by the Lorentz force. The solutions incorporate the photosphere boundary condition, proposed by van Tend and Kuperus (1978), who analyzed it for line filaments. The solutions have a finite radius for the prominence material and satisfy the equations of magnetostatic equilibrium, and allow for the continuity of gas pressure and of the normal and tangential components of magnetic field across the circular prominence boundary. It is shown that an infinity of solutions is possible; a method is presented for constructing equilibrium fields for any horizontal prominence with arbitrary cross-section and with an arbitrary external magnetic field.
The paper presents exact analytical solutions which describe steady-state transport of relativistic electrons subject to diffusion, convection, and radiation losses. The diffusion coefficient is spatially and energy dependent; the bulk convection velocity is considered to be constant and directed outward from the galactic plane. The electron spectral behavior with respect to galactic height and energy indicates that convection provides a 'break' in the steady-state energy spectrum without recourse to distribution of sources. Radio observations of NGC 891 and NGC 4631 galaxies can be used to estimate their diffusion coefficient and its energy dependence. Application of analytical solutions to our Galaxy indicates that the diffusion coefficient and outflow velocity deduced from relativistic electron measurements and radio observations of their synchrotron radiation agree with values based on the transport of the cosmic ray nucleonic component.
Pressure drop data for six different cell geometries of various flow port, manifold, and cavity dimensions are presented. The redox/energy/storage system uses two fully soluble redox couples as anode and cathode fluids. Both fluids are pumped through a redox cell, or stack of cells, where the electrochemical reactions take place at porous carbon felt electrodes. Pressure drop losses are therefore associated with this system due to the continuous flow of reactant solutions. The exact pressure drop within a redox flow cell is directly dependent on the flow rate as well as the various cell dimensions. Pumping power requirements for a specific set of cell operating conditions are found for various cell geometries once the flow rate and pressure drop are determined. These pumping power requirements contribute to the overall system parasitic energy losses which must be minimized, the choice of cell geometry becomes critical.
The wavelength dependence of convection with a temperature-dependent viscosity is studied using two-dimensional finite difference models. A steady-state solution with a horizontal wavelength of eight times the depth is found to transport heat more efficiently than a solution with exactly the same parameters but with a wavelength of twice the depth. Only at the longer wavelengths is it possible for the top high viscosity boundary layer to participate more fully in the flow. Using models with a constant heat flux resulted in a decrease in the interior temperature of approximately 30% for the longer wavelength. It is also demonstrated that a parameterization using only a constant viscosity thermal structure and an interior viscosity is inadequate to parameterize the variable viscosity calculations described. This suggests that parameterized convection schemes may not accurately resolve the thermal evolution of planetary interior unless they can correctly include the effects of vertical viscosity structure.
The steady-state zonally averaged climate is perturbed by adding a latitude-dependent heat source to an energy balance equation of the simplified Budyko-Sellers type. The latitude of the ice edge, which is attached to an isotherm, becomes dependent on the strength of the perturbation. This dependence is given in terms of the well-known iceline-solar constant relation, and the latitude dependence of the perturbed temperature field is then uniquely determined. The exact analytical solution is linearized and expressed in terms of a superposition of line sources at various latitudes. The main features are: (1) The total temperature response is a sum of the direct effect of the perturbation and an indirect ice-albedo effect proportional to the solar ice-edge sensitivity; and (2) the indirect feedback effect produces an enhanced response in polar latitudes.
Exact analytic solutions are presented for equilibrium states of a self-gravitating one-dimensional cloud of gas, embedded in an external gravitational field due to a plane of 'stars' being heated at a rate proportional to the local gas density, and cooling by thermal conduction. It is found that the general topology of the solutions is such that the gas density has a minimum on the plane of 'stars', rising to an infinite but integrable peak away from the plane so that the total mass of gas in the cloud is finite. The results may be of interest in investigations of interstellar molecular clouds and of filamentary structures in supernova remnants as well as in the modeling of gas distributions around 'cocoon' protostars.
This paper presents an analytic model for a finite-size straight filament suspended horizontally in a steady state over a bipolar magnetic region. The equations of magnetostatic equilibrium are integrated exactly. The solution obtained illustrates the roles played by the electric current, magnetic field, pressure, and plasma weight in the balance of force everywhere in space. A specific example of a filament of diameter 50,000 km, with a density two orders of magnitude over the corona and supported by a magnetic field of about 4 gauss is included. The filament temperature can take values ranging from a small fraction to a few times the coronal temperature, depending on the internal electric current of the filament. To produce a cool filament, such as the quiescent prominence, the solution is required to have an internal field with a strong component along the filament, giving rise to helical structures. A hot filament such as the X-ray coronal loop can be produced as a twisted magnetic flux tube embedded in a strong background field aligned parallel to the filament and having lower density and temperature. The basic steps of construction can be used to develop models more realistic than the ones presented for their analytic simplicity.
The helical jet mode is modeled by an infinite helical vortex filament, and an exact analytical solution for the induced velocity field interior to the filament is derived. These expressions are then used to model the jet flow field and to analyze the high subsonic and supersonic jet noise generation. It is shown that noise will be generated directly if the helical mode convects or rotates. Reducing this noise by stabilizing the mode is difficult, since the self-induced velocities of the mode itself cause it to convect and rotate; the use of noncircular nozzles is suggested to eliminate the symmetry of the boundary condition. The helical mode can also generate noise indirectly by inducing time-dependent Coriolis accelerations on small-scale turbulence propagating in its induced velocity field. This suggests that any upstream turbulence generation has an enhanced potential for noise propagation when propagating in the presence of the helical mode.
The flow processes in rocket pump inducers are summarized. The experimental investigations were carried out with air as the test medium. The major characteristics features of the rocket pump inducers are low flow coefficient (0.05 to 0.2) large stagger angle (70 deg to 85 deg) and high solidity blades of little or no camber. The investigations are concerned with the effect of viscosity not the effects of cavitation. Flow visualization, conventional and hot wire probe measurement inside and at the exit of the blade passage, were the analytical methods used. The experiment was carried out using four three and two bladed inducers with cambered blades. Both the passage and the exit flow were measured. The basic research and boundary layer investigation was carried out using a helical flat plate (of some dimensions as the inducer blades tested), and flat plate helical inducer (four bladed). Detailed mean and turbulence flow field inside the passage as well as the exit of the rotor were derived from these measurement. The boundary layer, endwall, and other passage data reveal extremely complex nature of the flow, with major effects of viscosity present across the entire passage. Several analyses were carried out to predict the flow field in inducers. These included an approximate analysis, the shear pumping analysis, and a numerical solution of exact viscous equations with approximate modeling for the viscous terms.
By examining the exact analytic solution of a kinetic model of collisional interaction of ionospheric ions with atmospheric neutrals in the Bhatnagar-Gross-Krook approximation, we show that the onset of intense auroral electric fields in the topside ionosphere can produce the following kinetic effects: (1) heat the bulk ionospheric ions to approximately 2 eV, thus driving them up to higher altitudes where they can be subjected to collisionless plasma processes; (2) produce a non-Maxwellian superthermal tail in the distribution function; and (3) cause the ion distribution function to be anisotropic with respect to the magnetic field with the perpendicular average thermal energy exceeding the parallel thermal energy.
The effect of defects across the back-surface-field junction on the performance of high efficiency and thin solar cells, using a developed-perimeter device model for the three-dimensional defects is investigated. Significant degradation of open-circuit voltage can occur even if there are only a few defects distributed in the bulk of the solar cell. Two features in the thickness dependences of the fill factor and efficiency in impurity-doped back-surface-field solar cells are discovered in the exact numerical solution which are associated with the high injection level effect in the base and not predicted by the low-level analytical theory. What are believed to be the most accurate recombination parameters at the Ti center to date are also given and a theory is developed which is capable of distinguishing an acceptor-like deep level from a donor-like deep level using the measured values of the thermal emission and capture cross sections.
The shape of a gas bubble which rises through a quiescent incompressible, Newtonian fluid at intermediate Reynolds numbers is considered. Exact numerical solutions for the velocity and pressure fields, as well as the bubble shape, are obtained using finite difference techniques and a numerically generated transformation to an orthogonal, boundary-fitted coordinate system. No restriction is placed on the allowable magnitude of deformation.
Examination of the exact analytic solution of a kinetic model of collisional interaction of ionospheric fions with atmospheric neutrals in the Bhatnagar-Gross-Krook approximation, shows that the onset of intense auroral electric fields in the topside ionosphere can produce the following kinetic effects: (1) heat the bulk ionospheric ions to approximately 2 eV, thus driving them up to higher altitudes where they can be subjected to collisionless plasma processes; (2) produce a nonMaxwellian superthermal tail in the distribution function; and (3) cause the ion distribution function to be anisotropic with respect to the magnetic field with the perpendicular average thermal energy exceeding the parallel thermal energy.
A computer program was developed to calculate the three dimensional, steady, incompressible, inviscid, irrotational flow field at the propeller plane (propeller removed) located upstream of an arbitrary airframe geometry. The program uses a horseshoe vortex of known strength to model the wing. All other airframe surfaces are modeled by a network source panels of unknown strength which is exposed to a uniform free stream and the wing-induced velocity field. By satisfying boundary conditions on each panel (the Neumann problem), relaxed boundary conditions being used on certain panels to simulate inlet inflow, the source strengths are determined. From the known source and wing vortex strengths, the resulting velocity fields on the airframe surface and at the propeller plane are obtained. All program equations are derived in detail, and a brief description of the program structure is presented. A user's manual which fully documents the program is cited. Computer predictions of the flow on the surface of a sphere and at a propeller plane upstream of the sphere are compared with the exact mathematical solutions. Agreement is good, and correct program operation is verified.
The thin vertical filaments making up the quiescent prominence plasma, as revealed by fine spatial resolution H-alpha photographs, are characterized by a magnetostatic theory in which a horizontal row of long vertical filaments whose weights are supported by bowed magnetic field lines is described by a class of exact equilibrium solutions. The Kippenhahn-Schlueter (1957) solution for a long sheet without filamentary structures is a member of this class of solutions. In illustrating the role of the magnetic field in supporting and thermally shielding the filament plasma, it is found that the filament can have a sharp transition perpendicular to the local field, while the transition in the direction of the local field is diffuse. A consequence of the filamentary structure is that its support by the Lorentz force requires the electric current to have a component along the magnetic field.
A new approach is presented to diffraction problems involving plane strip barriers or slit apertures. These are problems that display the effects of multiple interacting edges. The approach taken here provides exact, compact solutions. The theory is introduced through a series of examples that are, in fact, the 'standard' problems of the subject, diffraction of a plane oblique wave by a slit, for example. In each case, the solutions are found to depend explicitly on a single 'special' function and its Fourier transform. These fundamental functions are described, with the emphasis placed on practical computational methods. The example problems are all couched in the language of acoustics.
Dual-shaped reflectors have been used for many years. Thus, these reflectors have been used as high gain antennas on Voyagers 1 and 2. The objectives of the geometrical optics (GO) dual shaped synthesis are considered. Concerning the synthesis of dual shaped reflectors, it has been shown for circular symmetric reflectors that an exact GO solution can be found to the problem of transforming, by two reflections, any feed pattern into any aperture distribution. This problem involves solving two simultaneous nonlinear ordinary differential equations. The same approach for offset geometry leads to two simultaneous nonlinear partial differential equations. It is shown that these equations could also be integrated numerically, except that in general these equations are not total and therefore, in general, they do not have a 'smooth' solution. It is further shown that the offset partial differentials often very nearly form a total differential in many cases of practical importance.