Successive occurrences of quasi-circular ribbon flares in a fan-spine-like configuration involving hyperbolic flux tube
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Prabir K Mitra↗
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The potential use of satellites in hyperbolic position finding.
Configurations of hyperbolic position-fixing systems using synchronous satellites, showing Loran-like networks on earth resulting from these configurations
HYPERBOLIC POSITION LINE↗
Central configurations and hyperbolic-elliptic motion in the three-body problem
A refined classification of motion for the planar three-body problem with zero-sum total energy is presented. The structure and dimensions of the sets of initial conditions leading to parabolic expansion or hyperbolic-elliptic motion are found. Attention is given to the use of the Hamiltonian of the system and to the two- and three-dimensional problem. It is verified that the new coordinates of position and linear momentum approaches limits as t (time) approaches infinity, and that these limits constitute equilibrium solutions to the three-body problem representing control configurations.
Hulkower, N. D.↗
Contact Problem of Wear of the Elastic Half Plane with Winkler’s Coating Caused by Punches of Canonical Shapes
The problem of contact interaction of punches of canonical shapes (cylindrical, elliptic, and hyperbolic) with elastic half planes covered with protective coatings is solved with regard for the wear of the material. We propose a method for the solution of the singular integrodifferential equation of the problem. The numerical analysis of contact pressure is performed for different times, and some specific features of wear of the material by the punches of different shapes are discovered. The time for which the coating is totally worn out at a given point of the contact zone is determined.
42 ENGINEERING↗
A comparative design analysis of three configurational families for manned earth entry at hyperbolic speeds.
Optimum entry vehicle design using aerobreaking for manned earth entry at hyperbolic speeds, examining blunted conic, biconic and tetrahedral configurations
SPACECRAFT DESIGN↗
Solution of Boundary Value Problems in Cylinders with Two-Layer Film Inclusions
We consider the class of boundary value problems for elliptic, parabolic, and hyperbolic equations in cylinders separated by a two-layer film into two half-cylinders. We prove the existence and uniqueness theorem and express the solutions in terms of solutions to analogous classical problems in cylinders without films.
97 MATHEMATICS AND COMPUTING↗
Characteristically Closed Domains for First Order Strictly Hyperbolic Systems in the Plane
We consider a first order strictly hyperbolic system of n equations with constant coefficients in a bounded domain. It is assumed that the domain is strictly convex relative to characteristics, so that the projection along each characteristic is an involution having two fixed singular points. The natural statement of boundary value problems for such systems requires that singular points go to singular points under such transformations. We present a necessary and sufficient condition for the existence of such domains, called characteristically closed.
97 MATHEMATICS AND COMPUTING↗
Fluctuational electrodynamics of hyperbolic metamaterials
We give a detailed account of equilibrium and non-equilibrium fluctuational electrodynamics of hyperbolic metamaterials. We show the unifying aspects of two different approaches; one utilizes the second kind of fluctuation dissipation theorem and the other makes use of the scattering method. We analyze the near-field of hyperbolic media at finite temperatures and show that the lack of spatial coherence can be attributed to the multi-modal nature of super-Planckian thermal emission. We also adopt the analysis to phonon-polaritonic super-lattice metamaterials and describe the regimes suitable for experimental verification of our predicted effects. The results reveal that far-field thermal emission spectra are dominated by epsilon-near-zero and epsilon-near-pole responses as expected from Kirchoff's laws. Our work should aid both theorists and experimentalists to study complex media and engineer equilibrium and non-equilibrium fluctuations for applications in thermal photonics.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Light Scattering by a Periodically Corrugated Boundary of a Hyperbolic Medium
The scattering features of radiation incident on a periodically modulated boundary of a hyperbolic medium (HM) are studied numerically. An optimal (in a certain class of functions)—sawtooth—profile shape is found that provides minimum reflection in a wide range of wavelengths. It is shown that, for a certain orientation of the optical axes of the HM, “hot points” appear on the sawtooth boundary, that are responsible for the subwavelength field localization. A generalization is implemented of the numerical method based on the Green’s second identity for the field calculation.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Kepler motion on single-sheet hyperboloid
The classical Kepler–Coulomb problem on the single-sheeted hyperboloid H{sup 3}{sub 1} is solved in the framework of the Hamilton–Jacobi equation. We have proven that all the bounded orbits are closed and periodic. The paths are ellipses or circles for finite motion.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
An investigation of liquid-hydrogen stratification in a large cylindrical tank of the saturn configuration.
Liquid hydrogen stratification test data for large cylindrical tank of Saturn configuration, using hyperbolic temperature profile and boundary layer considerations in analysis
TEMPERATURE GRADIENT↗
A comparative design analysis of three configurational families for manned earth entry at hyperbolic speeds.
Optimum entry vehicle design using aerobreaking for manned Earth entry at hyperbolic speeds, examining blunted conic, biconic and tetrahedral configurations
ATMOSPHERIC ENTRY↗
Computation of three-dimensional inviscid flow over hypersonic missile configurations using the GIM code
A three-dimensional computational technique was used to obtain flowfield solutions to the Euler equations over selected hypersonic missile configurations. The General Interpolants Method (GIM) computer code was used with interpolation functions in an algebraic approach to generate a discrete computational grid for each configuration. The spatial marching version of the GIM code, which treats the parabolized Navier-Stokes (PNS) equations or the Euler equations with a shock capturing, 'MacCormack-like' scheme, was used to advance the solution hyperbolically over each configuration. The inviscid flowfield solutions over the two three-dimensional missile configurations, calculated using the GIM hyperbolic scheme, are presented here. The flow field over a wing/body configuration at zero degree angle of attack is presented. Flow over the fuselage of a tactical missile, termed the TAME 10, at both zero degree and 7.5 degree angles of attack is presented. In addition, an inviscid, two-dimensional analysis of an inlet configuration designed to mount on the TAME 10 is included. Contour maps of velocity and pressure are included for each configuration. Comparison of calculation and data show good agreement.
Xiques, K. E.↗
1997 May 12 Coronal Mass Ejection Event. I. A Simplified Model of the Preeruptive Magnetic Structure
A simple model of the coronal magnetic field prior to the coronal mass ejection (CME) eruption on 1997 May 12 is developed. First, the magnetic field is constructed by superimposing a large-scale background field and a localized bipolar field to model the active region (AR) in the current-free approximation. Second, this potential configuration is quasi-statically sheared by photospheric vortex motions applied to two flux concentrations of the AR. Third, the resulting force-free field is then evolved by canceling the photospheric magnetic flux with the help of an appropriate tangential electric field applied to the central part of the AR. To understand the structure of the modeled configuration, we use the field line mapping technique by generalizing it to spherical geometry. We demonstrate that the initial potential configuration contains a hyperbolic flux tube (HFT) which is a union of two intersecting quasi-separatrix layers. This HFT provides a partition of the closed magnetic flux between the AR and the global solar magnetic field. Such a partition is approximate since the entire flux distribution is perfectly continuous. The vortex motions applied to the AR inter-lock the field lines in the coronal volume to form additionally two new HFTs pinched into thin current layers. Reconnection in these current layers helps to redistribute the magnetic flux and current within the AR in the flux-cancellation phase. In this phase, a magnetic flux rope is formed together with a bald patch separatrix surface wrapping around the rope. Other important implications of the identified structural features of the modeled configuration are also discussed.
Titov, V. S.↗
Temporal evolution of the magnetic topology of the NOAA active region 11158
We studied the temporal evolution of the magnetic topology of the active region (AR) 11158 based on the reconstructed three-dimensional magnetic fields in the corona. The non-linear force-free field extrapolation method was applied to the 12 minute cadence data obtained with the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory during 5 days. By calculating the squashing degree factor Q in the volume, the derived quasi-separatrix layers (QSLs) show that this AR has an overall topology, resulting from a magnetic quadrupole, including a hyperbolic flux tube (HFT) configuration that is relatively stable at the timescale of the flare (∼1-2 hr). A strong QSL, which corresponds to some highly sheared arcades that might be related to the formation of a flux rope, is prominent just before the M6.6 and X2.2 flares, respectively. These facts indicate the close relationship between the strong QSL and the high flare productivity of AR 11158. In addition, with a close inspection of the topology, we found a small-scale HFT that has an inverse tear-drop structure above the aforementioned QSL before the X2.2 flare. It indicates the existence of magnetic flux rope at this place. Even though a global configuration (HFT) is recognized in this AR, it turns out that the large-scale HFT only plays a secondary role during the eruption. In conclusion, we dismiss a trigger based on the breakout model and highlight the central role of the flux rope in the related eruption.
79 ASTRONOMY AND ASTROPHYSICS↗
Hyperbolic Methods for Surface and Field Grid Generation
This chapter describes the use of hyperbolic partial differential equation methods for structured surface grid generation and field grid generation. While the surface grid generation equations are inherently three dimensional, the field grid generation equations can be formulated in two or three dimensions. The governing equations are derived from orthogonality relations and cell area/volume constraints; and are solved numerically by marching from an initial curve or surface. The marching step size and marching distance can be prescribedly the user. Exact specifications of the side and outer boundaries are not possible with a one sweep marching scheme but limited control is achievable. Excellent orthogonality and grid clustering characteristics are provided by hyperbolic methods with one to two orders of magnitude savings in time over typical elliptic methods. Since hyperbolic grid generation methods do not require the exact specifications of the side and outer boundaries of a grid, these methods are particularly well suited for the overlapping grid approach for solving problems on complex configurations. Grid generation software based on hyperbolic methods and their applications on several complex configurations will be described.
Chan, William M.↗
Use of a hyperbolic grid generation scheme in simulating supersonic viscous flow about three-dimensional winged configuration
The present paper describes a numerical mesh generation technique to be used with an implicit finite difference method for simulating visous supersonic flow about low-aspect-ratio wing body configurations using a single grid strategy. The computational domain is segmented into multiple regions, with borders located in supersonic areas to avoid the otherwise costly interfacing procedure between adjacent segments. The numerical procedure is applied to calculate the turbulent flow around the shuttle orbiter and a canard projectile at supersonic free stream Mach number.
Rizk, Y. M.↗
Arrhenian to non-Arrhenian crossover in glass melt viscosity
The activation energy for glass melt viscosity is a function of temperature, i.e., non-Arrhenian, within a middle range of viscosity values (typically, between 10 2 and 10 10 Pa s) and constant, i.e., Arrhenian, outside this range. At the low-viscosity end, the Arrhenian to non-Arrhenian transition (termed the crossover) falls within the glass processing range: glass melting and fining occur within the Arrhenian range while glass forming occurs within the non-Arrhenian range. By the Adam-Gibbs equation, the configuration entropy is nearly constant at high temperatures (low viscosities), where the glass melt turns into a simple liquid, and decreases with decreasing temperature (increasing viscosity) as the glass is increasingly polymerized. In the present study, the power-law function and hyperbolic tangent function are used to express the configuration entropy as a function of temperature. The viscosity crossover is defined as the point at which onset of structural grouping is causing the configuration entropy to deviate from its high-temperature value. In conclusion, it appears that the limited range of the configuration entropy of the fully depolymerized melt imposes a restriction on the crossover viscosity; for well-defined glass families, such as float glasses or nuclear waste glasses, the crossover point can be defined using a fixed, i.e., composition-independent, viscosity value.
36 MATERIALS SCIENCE↗