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Results for “HYPERBOLIC CONFIGURATION”

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.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

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↗
DOE OSTI2018

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↗
DOE OSTI2018

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↗
DOE OSTI2014

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↗
DOE OSTI2013

Boundary uniqueness theorems for functions whose integrals over hyperbolic discs vanish

Sharp conditions are found describing the admissible rate of decrease of a nontrivial function whose integrals over all hyperbolic discs with fixed radius vanish. For the first time, the boundary behaviour of the function is investigated in a neighbourhood of a single point on the boundary of the domain of definition. Bibliography: 17 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

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↗
DOE OSTI2017

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↗
DOE OSTI2014

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↗
DOE OSTI2023

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↗
DOE OSTI2024

Mirror-centered representation of a focusing hyperbolic mirror for X-ray beamlines

Conic sections are commonly used in reflective X-ray optics. Hyperbolic mirrors can focus a converging light source and are frequently paired with elliptical or parabolic mirrors in Wolter type configurations. This paper derives the closed-form expression for a mirror-centered hyperbolic shape, with zero-slope at the origin. Combined with the slope and curvature, such an expression facilitates metrology, manufacturing and mirror-bending calculations. Previous works consider ellipses, parabolas, magnifying hyperbolas or employ lengthy approximations. Here, the exact shape function is given in terms of the mirror incidence angle and the source and image distances.

47 OTHER INSTRUMENTATION↗
DOE OSTI2024

Shearless effective barriers to chaotic transport induced by even twin islands in nontwist systems

For several decades now it has been known that systems with shearless invariant tori, nontwist Hamiltonian systems, possess barriers to chaotic transport. These barriers are resilient to breakage under perturbation and therefore regions where they occur are natural places to look for barriers to transport. Here we describe a kind of effective barrier that persists after the shearless torus is broken. Because phenomena are generic, for convenience we study the standard nontwist map (SNM), an area-preserving map that violates the twist condition locally in the phase space. The barrier occurs in nontwist systems when twin even period islands are present, which happens for a broad range of parameter values in the SNM. With a phase space composed of regular and irregular orbits, the movement of chaotic trajectories is hampered by the existence of shearless curves, total barriers, and a network of partial barriers formed by the stable and unstable manifolds of the hyperbolic points. Being a degenerate system, the SNM has twin islands and, consequently, twin hyperbolic points. We show that the structures formed by the manifolds intrinsically depend on period parity of the twin islands. For this even scenario the structure that we call a torus free barrier occurs because the manifolds of different hyperbolic points form an intricate chain atop a dipole configuration and the transport of chaotic trajectories through the chain becomes a rare event. This structure impacts the emergence of transport, the escape basin for chaotic trajectories, the transport mechanism, and the chaotic saddle. The case of odd periodic orbits is different: we find for this case the emergence of transport immediately after the breakup of the last invariant curve, and this leads to a scenario of higher transport, with intricate escape basin boundary and a chaotic saddle with nonuniformly distributed points.

classical mechanics↗
DOE OSTI2014

An instability of hyperbolic space under the Yang-Mills flow

We consider the Yang-Mills flow on hyperbolic 3-space. The gauge connection is constructed from the frame-field and (not necessarily compatible) spin connection components. The fixed points of this flow include zero Yang-Mills curvature configurations, for which the spin connection has zero torsion and the associated Riemannian geometry is one of constant curvature. We analytically solve the linearized flow equations for a large class of perturbations to the fixed point corresponding to hyperbolic 3-space. These can be expressed as a linear superposition of distinct modes, some of which are exponentially growing along the flow. The growing modes imply the divergence of the (gauge invariant) perturbative torsion for a wide class of initial data, indicating an instability of the background geometry that we confirm with numeric simulations in the partially compactified case. There are stable modes with zero torsion, but all the unstable modes are torsion-full. This leads us to speculate that the instability is induced by the torsion degrees of freedom present in the Yang-Mills flow.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2016

A compressible two-phase model for dispersed particle flows with application from dense to dilute regimes

Multiphase flows are present in many important fields ranging from multiphase explosions to chemical processing. An important subset of multiphase flow applications involves dispersed materials, such as particles, droplets, and bubbles. This work presents an Eulerian–Eulerian model for multiphase flows containing dispersed particles surrounded by a continuous media such as air or water. Following a large body of multiphase literature, the driving force for particle acceleration is modeled as a direct function of both the continuous-phase pressure gradient and the gradient of intergranular stress existing within the particle phase. While the application of these two components of driving force is well accepted in much of the literature, other models exist in which the particle-phase pressure gradient itself drives particle motion. The multiphase model treats all phases as compressible and is derived to ensure adherence to the 2nd Law of Thermodynamics. The governing equations are presented and discussed, and a characteristic analysis shows the model to be hyperbolic, with a degeneracy in the case that the intergranular stress, which is modeled as a configuration pressure, is zero. Finally, results from a two sample problems involving shock-induced particle dispersion are presented. The results agree well with experimental measurements, providing initial confidence in the proposed model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Quasinormal modes of naked singularities in presence of nonlinear scalar fields

We study linear perturbations against static spherically symmetric background configurations of general relativity with a real scalar field (SF), which is minimally coupled with gravity; it is nonlinear due to the presence of the self-action potential. The background solutions have a naked singularity at the center of the configuration. The focus is on the stability of the background and fundamental frequencies of the quasinormal modes (QNM) of the axial perturbations in the Regge-Wheeler gauge. The problem is reduced to one hyperbolic master equation with an effective potential 𝑊eff, which turns out to be positive for a general non-negative SF potential; this ensures the linear stability with respect to this kind of perturbations. For numerical simulations, the SF potential was chosen in the power-law form 𝑉⁡(𝜙) ∼ 𝜙 2⁢𝑛 with 2 < 𝑛 ≤40. We extracted the fundamental frequencies of QNM for different 𝑛 and various sets of the background configuration parameters. The results show that even for a small background SF, there is a significant difference between the fundamental frequencies and ones in case of the Schwarzschild background. Furthermore, the results are also compared with the case of the Fisher-Janis-Newman-Winicour background dealing with a massless linear scalar field.

General relativity↗
DOE OSTI2016

K-decompositions and 3d gauge theories

This paper combines several new constructions in mathematics and physics. Mathematically, we study framed flat PGL(K, C)-connections on a large class of 3-manifolds M with boundary. We introduce a moduli space $\mathcal{L}$ K (M) of framed flat connections on the boundary ∂M that extend to M. Our goal is to understand an open part of $\mathcal{L}$ K (M) as a Lagrangian subvariety in the symplectic moduli space X un K (∂M) of framed flat connections on the boundary — and more so, as a “K 2 -Lagrangian,” meaning that the K 2 -avatar of the symplectic form restricts to zero. We construct an open part of $\mathcal{L}$ K (M) from elementary data associated with the hypersimplicial K-decomposition of an ideal triangulation of M, in a way that generalizes (and combines) both Thurston’s gluing equations in 3d hyperbolic geometry and the cluster coordinates for framed flat PGL(K, C)-connections on surfaces. By using a canonical map from the complex of configurations of decorated flags to the Bloch complex, we prove that any generic component of $\mathcal{L}$ K (M) is K 2 -isotropic as long as ∂M satisfies certain topological constraints (theorem 4.2). In some cases this easily implies that $\mathcal{L}$ K (M) is K 2 -Lagrangian. For general M, we extend a classic result of Neumann and Zagier on symplectic properties of PGL(2) gluing equations to reduce the K 2 -Lagrangian property to a combinatorial statement. Physically, we translate the K-decomposition of an ideal triangulation of M and its symplectic properties to produce an explicit construction of 3d N = 2 superconformal field theories T K [M] resulting (conjecturally) from the compactification of K M5-branes on M. This extends known constructions for K = 2. Just as for K = 2, the theories T K [M] are described as IR fixed points of abelian Chern-Simons-matter theories. Changes of triangulation (2-3 moves) lead to abelian mirror symmetries that are all generated by the elementary duality between N f = 1 SQED and the XYZ model. In the large K limit, we find evidence that the degrees of freedom of T K [M] grow cubically in K.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2019

Characteristic path analysis of confinement influence on steady two-dimensional detonation propagation

Steady detonation in multi-dimensional flow is controlled by the chemical energy release that occurs in a subsonic elliptic flow region known as the detonation driving zone (DDZ). It is the region encompassing the detonation shock and sonic flow locus (in the frame of the detonation shock). A detonation that is strongly confined by material surrounding the explosive has the shock and sonic locus separated at the material interface. Information about the material boundary is traditionally believed to influence the DDZ structure via the subsonic flow on the boundary ahead of the sonic locus. A detonation that is weakly confined has the detonation shock and sonic locus intersecting at the material boundary. The sonic nature of the flow at the intersection point on the boundary is believed to isolate the DDZ structure from the material properties of the confinement. We examine the paths of characteristics propagating information about the confinement through the supersonic hyperbolic flow region that exists beyond the sonic locus, and determine whether these paths may impinge on the sonic locus and consequently influence the DDZ structure. Our configuration consists of a solid wall boundary deflected through a specified angle on detonation shock arrival, so that the streamline turning angle of the wall at the explosive edge is unambiguously defined. By varying the wall deflection angle from small through large values, we can systematically capture the evolution of the DDZ structure and the characteristic flow regions that influence its structure for strongly to weakly confined detonations. In all strong and weak confinement cases examined, we find that a subset of characteristics from the supersonic flow regions always impinge on the sonic locus. Limiting characteristics are identified that define the boundary between characteristics that impinge on the sonic surface and those that propagate information downstream of the sonic surface. In combination with an oblique-shock polar analysis, we show that the effects on the DDZ of characteristic impingement can be significant.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

On hyperbolicity violations in cosmological models with vector fields

Cosmological models with vector fields received much attention in recent years. Unfortunately, most of them are plagued with severe instabilities or other problems. In particular, it was noted in ref. [1] that the models with a non-linear function of the Maxwellian kinetic term do always imply violations of hyperbolicity somewhere in the phase space. In this work we make this statement more precise in several respects and show that those violations may not be present around spatially homogeneous configurations of the vector field.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Off-axis representation of hyperbolic mirror shapes for X-ray beamlines

Mirror-centered, closed-form expressions for hyperbolic surfaces used in X-ray beamlines have been derived. Hyperbolic mirrors create a virtual focus or source point and can be used to lengthen or shorten the effective focal distance of a compound optical system. The derivations here express off-axis segments of a hyperbolic surface in terms of the real and virtual focal distances and the incident glancing angle at the center of the mirror. Conventional mathematical expressions of hyperbolic shapes describe the surfaces in Cartesian or polar coordinates centered on an axis of symmetry, necessitating cumbersome rotation and translation to mirror-centered coordinates. The representation presented here, with zero slope and the origin at the central point, is most convenient for modeling, metrology, aberration correction, and general surface analysis of off-axis configurations. The direct derivation avoids the need for nested coordinate transforms. A series expansion provides a helpful approximation; the coefficients of the implicit equation are also provided.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗