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At least 469 records · Page 26

Evaluation of image quality in a Cassegrain-type telescope with an oscillating secondary mirror

A ray-trace analysis is described of aberrations and extreme rays of a Cassegrain-type telescope with a tilted secondary mirror. The work was motivated by the need to understand the factors limiting image quality and to assist in the design of secondary mirrors for three telescopes with oscillating secondary mirrors (OSM) used at Ames Research Center for high altitude infrared astronomy. The telescopes are a 31-cm-diameter Dall-Kirkham (elliptical primary, spherical secondary) flown aboard a Lear jet, a 71-cm balloon-borne Dall-Kirkham flown on the AIROscope gondola, and a 91-cm true Cassegrain (parabolic primary, hyperbolic secondary) flown aboard a C-141 jet transport. The optics for these telescopes were not designed specifically for OSM operation, but all have OSM's and all must be used with various detector configurations; therefore, a facility that evaluates the performance of a telescope for a given configuration is useful. The analytical expressions are summarized and results for the above systems are discussed. Details of the calculation and a discussion of the computer program are given in the appendices.

Erickson, E. F.↗

Far field boundary conditions for computation over long time

A new class of computational far field boundary conditions for hyperbolic partial differential equations is developed. These boundary conditions combine properties of absorbing boundary conditions for transient solutions and properties of far field boundary conditions for steady-state problems. The conditions can be used to limit the computational domain when both traveling waves and evanescent waves are present. Boundary conditions for scalar wave equations are derived and analyzed. Extensions to systems of equations are discussed and results from numerical experiments are presented.

Engquist, Bjorn↗

Variable Step Integration Coupled with the Method of Characteristics Solution for Water-Hammer Analysis, A Case Study

One-dimensional water-hammer modeling involves the solution of two coupled non-linear hyperbolic partial differential equations (PDEs). These equations result from applying the principles of conservation of mass and momentum to flow through a pipe, and usually the assumption that the speed at which pressure waves propagate through the pipe is constant. In order to solve these equations for the interested quantities (i.e. pressures and flow rates), they must first be converted to a system of ordinary differential equations (ODEs) by either approximating the spatial derivative terms with numerical techniques or using the Method of Characteristics (MOC). The MOC approach is ideal in that no numerical approximation errors are introduced in converting the original system of PDEs into an equivalent system of ODEs. Unfortunately this resulting system of ODEs is bound by a time step constraint so that when integrating the equations the solution can only be obtained at fixed time intervals. If the fluid system to be modeled also contains dynamic components (i.e. components that are best modeled by a system of ODEs), it may be necessary to take extremely small time steps during certain points of the model simulation in order to achieve stability and/or accuracy in the solution. Coupled together, the fixed time step constraint invoked by the MOC, and the occasional need for extremely small time steps in order to obtain stability and/or accuracy, can greatly increase simulation run times. As one solution to this problem, a method for combining variable step integration (VSI) algorithms with the MOC was developed for modeling water-hammer in systems with highly dynamic components. A case study is presented in which reverse flow through a dual-flapper check valve introduces a water-hammer event. The predicted pressure responses upstream of the check-valve are compared with test data.

Turpin, Jason B.↗

A-Posteriori Error Estimation for Hyperbolic Conservation Laws with Constraint

This lecture considers a-posteriori error estimates for the numerical solution of conservation laws with time invariant constraints such as those arising in magnetohydrodynamics (MHD) and gravitational physics. Using standard duality arguments, a-posteriori error estimates for the discontinuous Galerkin finite element method are then presented for MHD with solenoidal constraint. From these estimates, a procedure for adaptive discretization is outlined. A taxonomy of Green's functions for the linearized MHD operator is given which characterizes the domain of dependence for pointwise errors. The extension to other constrained systems such as the Einstein equations of gravitational physics are then considered. Finally, future directions and open problems are discussed.

Barth, Timothy↗

Geometry and properties of the plasma in a quadrupole ion pump

The diameter of the plasma in a quadrupole ionization gauge and quadrupole ion pump has been measured as a function of pressure. The radio-frequency quadrupole systems are tuned in such a way that electrons remain on stable trajectories in the center of the tube. Being emitted at one end, the electrons encounter an inverted field at the other end so that they travel on spiral paths back and forth until they collide with the rest gas molecules, producing ions which are collected as an ion current at a cylinder surrounding the four hyperbolically shaped quadrupole electrodes.

Schwarz, H.↗

A comparative study of the parabolized Navier-Stokes code using various grid-generation techniques

The parabolized Navier-Stokes (PNS) equations are used to calculate the flow-field characteristics about the hypersonic research aircraft X-24C. A comparison of the results obtained using elliptic, hyperbolic, and algebraic grid generators is presented. The outer bow shock is treated as a sharp discontinuity, and the discontinuities within the shock layer are captured. Surface pressures and heat-transfer results at angles of attack of 6 deg and 20 deg, obtained using the three grid generators, are compared. The PNS equations are marched downstream over the body in both Cartesian and cylindrical base coordinate systems, and the results are compared. A robust marching procedure is demonstrated by successfully using large marching step sizes with the implicit shock fitting procedure. A correlation is found between the marching step size, Reynolds number, and the angle of attack at fixed values of smoothing and stability coefficients for the marching scheme.

Kaul, U. K.↗

A comparative study of the parabolized Navier-Stokes code using various grid-generation techniques

The parabolized Navier-Stokes (PNS) equations are used to calculate the flow-field characteristics about the hypersonic research aircraft X-24C. A comparison of the results obtained using elliptic, hyperbolic and algebraic grid generators is presented. The outer bow shock is treated as a sharp discontinuity, and the discontinuities within the shock layer are captured. Surface pressures and heat-transfer results at angles of attack of 6 deg and 20 deg, obtained using the three grid generators, are compared. The PNS equations are marched downstream over the body in both Cartesian and cylindrical base coordinate systems, and the results are compared. A robust marching procedure is demonstrated by successfully using large marching-step sizes with the implicit shock fitting procedure. A correlation is found between the marching-step size, Reynolds number and the angle of attack at fixed values of smoothing and stability coefficients for the marching scheme.

Kaul, U. K.↗

Insights on the continuous representations of piecewise-smooth nonlinear systems: limits of applicability and effectiveness

Dynamical systems subject to intermittent contact are often modeled with piecewise-smooth contact forces. However, the discontinuous nature of the contact can cause inaccuracies in numerical results or failure in numerical solvers. Representing the piecewise contact force with a continuous and smooth function can mitigate these problems, but not all continuous representations may be appropriate for this use. Here, five representations used by previous researchers (polynomial, rational polynomial, hyperbolic tangent, arctangent, and logarithm-arctangent functions) are studied to determine which ones most accurately capture nonlinear behaviors including super- and subharmonic resonances, multiple solutions, and chaos. The test case is a single-DOF forced Duffing oscillator with freeplay nonlinearity, solved using direct time integration. This work intends to expand on past studies by determining the limits of applicability for each representation and what numerical problems may occur.

42 ENGINEERING↗

The evolution of comet orbits

The origin of comets and the evolution of their orbits are discussed. Factors considered include: the law of survival of comets against ejection on hyperbolic orbits; short-period comets are not created by single close encounters of near-parabolic comets with Jupiter; observable long-period comets do not evolve into observable short-period comets; unobservable long-period comets with perihelia near Jupiter can evolve into observable short-period comets; long-period comets cannot have been formed or created within the planetary region of the solar system (excluding the effects of stellar perturbations); it is possible that some of the short-period comets could have been formed inside the orbit of Neptune; circularly-restricted three-body problem, and its associated Jacobi integral, are not valid approximations to use in studying origin and evolution of comets.

Everhart, E.↗

Thermal Protection System to Enable Ice Giant Aerocapture Mission for Delivering Both an Orbiter and an In Situ Probe

The Ice Giants have been identified as high priority science destinations in the last Decadal Survey [1] and could benefit from aerocapture as the primary method for orbit insertion [2]. A mass-efficient aerocapture system will enable the delivery of an orbiter along with an atmospheric probe (for in situ measurements to anchor global data collected by the orbiter) and possibly a lander at Triton [3]. Aerocapture could be executed either using low L/D rigid aeroshell with lift modulation (LMA) [4] or using deployable aeroshell using drag modulation (DMA) [3]. Nearly two decades ago, a NASA-funded team performed Neptune-Triton aerocapture studies with a mid-L/D lifting configuration [5] for achieving orbit using LMA. This study showed aerocapture challenges. Due to very high peak entry conditions combined with very high heat-load, a suite of TPS materials was required and this suite was deemed problematic from a qualification perspective, due test facility limitations. In the past 20 years, progress made in GN&C for lift-guided entry missions such as MSL, Orion EFT1, Mars 2020 and the upcoming Artemis missions, and the expertise in blunt body aerodynamics at large scale (~ 5m) has led the EDL community to conclude that aerocapture is a “go do” engineering activity and most technologies are in hand to propose missions with aerocapture [6] [7]. Aerocapture using DMA, currently in development, is an option for Ice Giant Missions. While DMA is simpler in some sense, due to ballistic entry and no need for lift-guided maneuvering, it has challenges and it’s maturity is lower. LMA and DMA both require one or more ablative Thermal Protection System (TPS) materials for the rigid aeroshell element. The ablative TPS needs to be robust and mass efficient due to the high heat loads and size of the rigid aeroshell. Currently, there are capable ablative thermal protection materials, e.g., Heatshield for Extreme Entry Environments Technology (HEEET), 3-D woven Mid-Density Carbon- Phenolic (3MDCP), and PICA (Phenolic-Impregnated Carbon Ablator) that are mature, i.e., at TRL 6 or higher. NASA also invested in Conformal PICA that was matured to TRL 5. Our goal is to evaluate the applicability of high TRL TPS and consider other design options. We first establish bounding aerocapture trajectories for a wide range of arrival conditions and the associated aerothermal environment. Based on the environments, we then determine the predicted TPS mass for the aeroshell [4]. In this presentation, we will outline the process by which we establish bounding aerocapture trajectories for hyperbolic excess velocities ranging from 27 km/s to 35 km/s, which are shown to be a range of velocities that can reduce the trip time from ~14 years to 8 years. The above velocity range translates to ~12 km/s to ~24 km/s arrival velocities at the planetary entry interface [2]. The velocity reduction required to achieve orbit ranges between ~2.5 km/s to 9.5 km/s for both Neptune and Triton. Propulsive insertion alone, due to the amount of fuel required to achieve the required velocity reduction, limits the science returned [2]. We establish the bounding aerocapture trajectories for a low L/D (~ 0.4) configuration for three different ballistic coefficients. The ballistic coefficient range is determined from three different aeroshell diameters of 3m, 4m and 5m and with an entry system mass of 2200 kg. With the above range of design parameters, we then determine conservative/bounding estimates of aerothermal environments by using a combination of CFD simulations and stagnation point heating estimates [7]. This engineering approach allows us to first assess the TPS need vs. TPS capability and determine the applicability of existing TPS. Once an applicable suite of TPS is determined, the TPS thickness and mass are computed. We show that the TPS mass fraction can be as low as 5% to as high as 20%, depending on total trip time reduction and other design parameters for a range of TPS. This is a large range for TPS mass fraction. We show PICA and HEEET can indeed enable aerocapture missions, but the missions incur a mass penalty. TPS mass savings, can be further reduced with the use of conformal PICA. Advancing the development of Conformal PICA to make it robust across the entire aerothermal environment (peak heat-flux, pressure and shear) range will result in TPS mass fractions of < 10% for Ice Giant aerocapture missions such as the Neptune-Triton mission. Aerocapture allows for not only shortening the trip time but enables larger mass to be placed in orbit. Furthermore, probes deployed from orbit will benefit in reduced entry environments allowing for a lower risk TPS implementation as compared to mission designs where the probe is released prior to orbit insertion. One of the challenges for the Ice Giant community is to ensure mission designs that maximize science and allow flexibility in the placement of the entry probe. The traditional approach to release the probe ahead of the orbiter may not optimize returned science. In this presentation, we will make the case for mature TPS such as HEEET and PICA. While these materials can enable aerocapture missions, completing the development of conformal PICA and extending Conformal PICA to be more robust, will have significant impact to TPS mass efficiency and significantly enhance science return for future Gas- and Ice-Giant missions.

E Venkatapathy↗

Spiral waves in externally excited neuronal network: Solvable model with a monotonically differentiable magnetic flux

Spiral waves are particular spatiotemporal patterns connected to specific phase singularities representing topological wave dislocations or nodes of zero amplitude, witnessed in a wide range of complex systems such as neuronal networks. The appearance of these waves is linked to the network structure as well as the diffusion dynamics of its blocks. We report a novel form of the Hindmarsh-Rose neuron model utilized as a square neuronal network, showing the remarkable multistructure of dynamical patterns ranging from characteristic spiral wave domains of spatiotemporal phase coherence to regions of hyperchaos. The proposed model comprises a hyperbolic memductance function as the monotone differentiable magnetic flux. Hindmarsh-Rose neurons with an external electromagnetic excitation are considered in three different cases: no excitation, periodic excitation, and quasiperiodic excitation. We performed an extensive study of the neuronal dynamics including calculation of equilibrium points, bifurcation analysis, and Lyapunov spectrum. We have found the property of antimonotonicity in bifurcation scenarios with no excitation or periodic excitation and identified wide regions of hyperchaos in the case of quasiperiodic excitation. Furthermore, the formation and elimination of the spiral waves in each case of external excitation with respect to stimuli parameters are investigated. We have identified novel forms of Hindmarsh-Rose bursting dynamics. Our findings reveal multipartite spiral wave formations and symmetry breaking spatiotemporal dynamics of the neuronal model that may find broad practical applications. © 2019 Author(s).

60 APPLIED LIFE SCIENCES↗

Quantum Ising model on (2+1)-dimensional anti–de Sitter space using tensor networks

We study the quantum Ising model on (2+1)-dimensional anti-de Sitter space using matrix product states (MPS) and matrix product operators (MPOs). We explore the bulk phase diagram of the theory on regular tessellations of hyperbolic space with coordination number seven and find disordered and ordered phases separated by a phase transition. We find that the boundary-boundary spin correlation function exhibits power law scaling deep in the disordered phase of the Ising model consistent with holography. At the critical point, we find the boundary entanglement entropy scales logarithmically with subsystem size but away from this, we see a linear scaling. In comparison, the full system exhibits a volume law scaling, which is expected in chaotic and/or highly connected systems. We also measure out of time ordered correlators (OTOCs) to explore the scrambling behavior of the theory.

Quantum spin models↗

Diagonalization and simultaneous symmetrization of the gas-dynamic matrices

The hyperbolic nature of the unsteady, inviscid, gas-dynamic equations implies the existence of a similarity transformation for diagonalizing an arbitrary linear combination of coefficient matrices. It is shown that the individual matrices are simultaneously symmetrized by the similarity transformation. The transformations and their norms can be applied to the well-posedness of the Cauchy problem, linear stability theory for finite-difference approximations, and simplification of block-tridiagonal systems that arise in implicit time-split algorithms.

Warming, R. F.↗

Multiple-Beam Communications Antenna

System has both fixed-spot and scanning coverage. Advanced offset-fed spacecraft antenna systems operating in 30/20 GHz frequency bands developed to provide multiple-radiating fixed-spot and regional-coverage scanning beams for use on communications satellites. Operating at higher frequencies, provides alternate frequency bands for expansion of existing satellite services and achieving frequency reuse capability for conservation of frequency spectrum. 20-GHz transmitting antenna is offset-fed, dual-reflector configuration. 30-GHz receiving antenna has orthogonal polarized feeds, hyperbolic reflectors, and two subreflectors.

Myhre, R. W.↗

Economical Third-Order Methods for Accurate Surface Heating Predictions on Simplex Element Meshes

A node-centered edge-based finite volume discretization of the compressible Navier-Stokes equations is presented with the heat flux reformulated as a first order system. A dissipation vector is derived for the reformulated system, such that the heat flux can be upgraded to O(h^3) on simplex element meshes in the same fashion as the inviscid fluxes. The method of manufactured solutions is used to demonstrate this uniform order property in heat flux. This new system is shown to efficiently produce accurate surface heating predictions on hypersonic hemisphere flow using an anisotropic simplex element mesh, achieving O(h^3) accuracy at relatively low computational cost compared to similar methods.

Computational Fluid Dynamics↗

Hyperbolic/parabolic development for the GIM-STAR code

Flow fields in supersonic inlet configurations were computed using the eliptic GIM code on the STAR computer. Spillage flow under the lower cowl was calculated to be 33% of the incoming stream. The shock/boundary layer interaction on the upper propulsive surface was computed including separation. All shocks produced by the flow system were captured. Linearized block implicit (LBI) schemes were examined to determine their application to the GIM code. Pure explicit methods have stability limitations and fully implicit schemes are inherently inefficient; however, LBI schemes show promise as an effective compromise. A quasiparabolic version of the GIM code was developed using elastical parabolized Navier-Stokes methods combined with quasitime relaxation. This scheme is referred to as quasiparabolic although it applies equally well to hyperbolic supersonic inviscid flows. Second order windward differences are used in the marching coordinate and either explicit or linear block implicit time relaxation can be incorporated.

Spradley, L. W.↗

Self-Assembled BaTiO 3 –Au x Ag 1– x Low-Loss Hybrid Plasmonic Metamaterials with an Ordered “Nano-Domino-like” Microstructure

Metallic plasmonic hybrid nanostructures have attracted enormous research interest due to the combined physical properties coming from different material components and the broad range of applications in nanophotonic and electronic devices. However, the high loss and narrow range of property tunability of the metallic hybrid materials have limited their practical applications. In this study, a metallic alloy-based self-assembled plasmonic hybrid nanostructure, i.e., a BaTiO 3 –Au x Ag 1– x (BTO) vertically aligned nanocomposite, has been integrated by a templated growth method for low-loss plasmonic systems. Comprehensive microstructural characterizations including high-resolution scanning transmission electron microscopy (HRSTEM), energy-dispersive X-ray spectroscopy (EDS), and three-dimensional (3D) electron tomography demonstrate the formation of an ordered “nano-domino-like” morphology with Au 0.4 Ag 0.6 nanopillars as cylindrical cores and BTO as square shells. By comparing with the BTO–Au hybrid thin film, the BTO–Au 0.4 Ag 0.6 alloyed film exhibits much broader plasmon resonance, hyperbolic dispersion, low-loss, and thermally robust features in the UV–vis–NIR wavelength region. This study provides a feasible platform for a complex alloyed plasmonic hybrid material design with low-loss and highly tunable optical properties toward all-optical integrated devices.

36 MATERIALS SCIENCE↗

A Parallel Non-Overlapping Domain-Decomposition Algorithm for Compressible Fluid Flow Problems on Triangulated Domains

This paper considers an algebraic preconditioning algorithm for hyperbolic-elliptic fluid flow problems. The algorithm is based on a parallel non-overlapping Schur complement domain-decomposition technique for triangulated domains. In the Schur complement technique, the triangulation is first partitioned into a number of non-overlapping subdomains and interfaces. This suggests a reordering of triangulation vertices which separates subdomain and interface solution unknowns. The reordering induces a natural 2 x 2 block partitioning of the discretization matrix. Exact LU factorization of this block system yields a Schur complement matrix which couples subdomains and the interface together. The remaining sections of this paper present a family of approximate techniques for both constructing and applying the Schur complement as a domain-decomposition preconditioner. The approximate Schur complement serves as an algebraic coarse space operator, thus avoiding the known difficulties associated with the direct formation of a coarse space discretization. In developing Schur complement approximations, particular attention has been given to improving sequential and parallel efficiency of implementations without significantly degrading the quality of the preconditioner. A computer code based on these developments has been tested on the IBM SP2 using MPI message passing protocol. A number of 2-D calculations are presented for both scalar advection-diffusion equations as well as the Euler equations governing compressible fluid flow to demonstrate performance of the preconditioning algorithm.

Barth, Timothy J.↗