Using variational methods and hyperbolic lattices to find the ground state of gapless systems [Poster]
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46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
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Results for “hyperbolic systems”
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Adaptive Uncertainty Quantification for Stochastic Hyperbolic Conservation Laws
Here, we propose a predictor-corrector adaptive method for the study of hyperbolic partial differential equations (PDEs) under uncertainty. Constructed around the framework of stochastic finite volume (SFV) methods, our approach circumvents sampling schemes or simulation ensembles while also preserving fundamental properties, in particular hyperbolicity of the resulting systems and conservation of the discrete solutions. Furthermore, we augment the existing SFV theory with a priori convergence results for statistical quantities, in particular push-forward densities, which we demonstrate through numerical experiments. By linking refinement indicators to regions of the physical and stochastic spaces, we drive anisotropic refinements of the discretizations, introducing new degrees of freedom where deemed profitable. To illustrate our proposed method, we consider a series of numerical examples for nonlinear hyperbolic PDEs based on Burgers’ and Euler’s equations.
97 MATHEMATICS AND COMPUTING↗
The Near-Sun Dust Environment: Initial Observations from Parker Solar Probe
The Parker Solar Probe (PSP) spacecraft has flown into the densest, previously unexplored, innermost region of our solar system's zodiacal cloud. While PSP does not have a dedicated dust detector, multiple instruments on the spacecraft are sensitive to the effects of meteoroid bombardment. Here, we discuss measurements taken during PSP's second orbit and compare them to models of the zodiacal cloud's dust distribution. Comparing the radial impact rate trends and the timing and location of a dust impact to an energetic particle detector, we find the impactor population to be consistent with dust grains on hyperbolic orbits escaping the solar system. Assuming PSP's impact environment is dominated by hyperbolic impactors, the total quantity of dust ejected from our solar system is estimated to be 0.5−10 tons/s. We expect PSP will encounter an increasingly intense impactor environment as its perihelion distance and semimajor axis are decreased.
J. R. Szalay↗
ZnO-Au x Cu 1-x Alloy and ZnO-Au x Al 1-x Alloy Vertically Aligned Nanocomposites for Low-Loss Plasmonic Metamaterials
Hyperbolic metamaterials are a class of materials exhibiting anisotropic dielectric function owing to the morphology of the nanostructures. In these structures, one direction behaves as a metal, and the orthogonal direction behaves as a dielectric material. Applications include subdiffraction imaging and hyperlenses. However, key limiting factors include energy losses of noble metals and challenging fabrication methods. In this work, self-assembled plasmonic metamaterials consisting of anisotropic nanoalloy pillars embedded into the ZnO matrix are developed using a seed-layer approach. Alloys of Au x Al 1-x or Au x Cu 1-x are explored due to their lower losses and higher stability. Optical and microstructural properties were explored. The ZnO-Au x Cu 1-x system demonstrated excellent epitaxial quality and optical properties compared with the ZnO-Au x Al 1-x system. Both nanocomposite systems demonstrate plasmonic resonance, hyperbolic dispersion, low losses, and epsilon-near-zero permittivity, making them promising candidates towards direct photonic integration.
36 MATERIALS SCIENCE↗
Stochastic finite volume method for uncertainty quantification of transient flow in gas pipeline networks
We develop a weakly intrusive framework to simulate the propagation of uncertainty in solutions of generic hyperbolic partial differential equation systems on graph-connected domains with nodal coupling and boundary conditions. The method is based on the Stochastic Finite Volume (SFV) approach and can be applied for uncertainty quantification (UQ) of the dynamical state of fluid flow over actuated transport networks. The numerical scheme has specific advantages for modeling intertemporal uncertainty in time-varying boundary parameters, which cannot be characterized by strict upper and lower (interval) bounds. We describe the scheme for a single pipe, and then formulate the controlled junction Riemann problem (JRP) that enables the extension to general network structures. In conclusion, we demonstrate the method's capabilities and performance characteristics using a standard benchmark test network.
97 MATHEMATICS AND COMPUTING↗
On resonance in linear conservation laws without source terms
A phenomena is described occuring in wave propagation for systems of conservation laws which are not hyperbolic. The nature of the wave propagation for linear systems of conservation laws which are degenerate in the sense that they are not equivalent to diagonal systems is examined. It is concluded that in the degenerate case, 'resonance' occurs, that is, the solutions are combinations of traveling waves and 'resonance waves'. Here resonance means that the solution may become unbounded even if the initial values are bounded. The solutions (waves) can be described as a superposition of 'packets' (groups) of 'resonance waves' traveling with the same speed. These are linear systems with constant coefficients which are self-exciting, which is what one would expect to encounter in nonlinear systems.
Gingold, H.↗
In situ compression artifact removal in scientific data using deep transfer learning and experience replay
The massive amount of data produced during simulation on high-performance computers has grown exponentially over the past decade, exacerbating the need for streaming compression and decompression methods for efficient storage and transfer of this data---key to realizing the full potential of large-scale computational science. Lossy compression approaches such as JPEG when applied to scientific simulation data realized as a stream of images can achieve good compression rates but at the cost of introducing compression artifacts and loss of information. This paper develops a unified framework for in situ compression artifact removal in which the fully convolutional neural network architectures are combined with scalable training, transfer learning, and experience replay to achieve superior accuracy and efficiency while significantly decreasing the storage footprint as compared with the traditional optimization-based approaches. We demonstrate the proposed approach and compare it with compressed sensing postprocessing and other baseline deep learning models using climate simulations and nuclear reactor simulations, both of which are driven by hyperbolic partial differential equations. Our approach when applied to remove the compression artifacts on the JPEG-compressed nuclear reactor simulation data (using a transfer-trained model that was pretrained on the climate simulation data and updated incrementally as the nuclear reactor simulation progressed), achieved a significant improvement---mean peak signal-to-noise ratio of 42.438 as compared with 27.725 obtained with the compressed sensing approach.
97 MATHEMATICS AND COMPUTING↗
Canonical-variables multigrid method for steady-state Euler equations
A novel approach for the solution of inviscid flow problems for subsonic compressible flows is described. The approach is based on canonical forms of the equations, in which subsystems governed by hyperbolic operators are separated from those governed by elliptic ones. The discretizations used as well as the iterative techniques for the different subsystems are inherently different. Hyperbolic parts, which describe, in general, propagation phenomena, are discretized using upwind schemes and are solved by marching techniques. Elliptic parts, which are directionally unbiased, are discretized using h-elliptic central discretizations, and are solved by pointwise relaxations together with coarse grid acceleration. The resulting discretization schemes introduce artificial viscosity only for the hyperbolic parts of the system; thus a smaller total artificial viscosity is used, while the multigrid solvers used are much more efficient. Solutions of the subsonic compressible Euler equations are achieved at the same efficiency as the full potential equation.
Taasan, Shlomo↗
Photogrammetry System and Method for Determining Relative Motion Between Two Bodies
A photogrammetry system and method provide for determining the relative position between two objects. The system utilizes one or more imaging devices, such as high speed cameras, that are mounted on a first body, and three or more photogrammetry targets of a known location on a second body. The system and method can be utilized with cameras having fish-eye, hyperbolic, omnidirectional, or other lenses. The system and method do not require overlapping fields-of-view if two or more cameras are utilized. The system and method derive relative orientation by equally weighting information from an arbitrary number of heterogeneous cameras, all with non-overlapping fields-of-view. Furthermore, the system can make the measurements with arbitrary wide-angle lenses on the cameras.
Miller, Samuel A.↗
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↗
Symmetry Determining Equations of the Euler Equations
This purpose of this document is to provide a clear derivation of the symmetry determining equations (SDEs) of the Euler equations to supplement the lecture document. The Euler equations are a coupled system of three first-order quasilinear hyperbolic partial differential equations (PDEs). The Euler equations are a system of partial differential equations (PDEs) for fluid velocity v(t, r), fluid density ρ(t, r), and fluid pressure P(t, r), where t is time and r is the spatial coordinate.
97 MATHEMATICS AND COMPUTING↗
The Delta x B = 0 Constraint Versus Minimization of Numerical Errors in MHD Simulations
The MHD equations are a system of non-strictly hyperbolic conservation laws. The non-convexity of the inviscid flux vector resulted in corresponding Jacobian matrices with undesirable properties. It has previously been shown by Powell et al. (1995) that an 'almost' equivalent MHD system in non-conservative form can be derived. This non-conservative system has a better conditioned eigensystem. Aside from Powell et al., the MHD equations can be derived from basic principles in either conservative or non-conservative form. The Delta x B = 0 constraint of the MHD equations is only an initial condition constraint, it is very different from the incompressible Navier-Stokes equations in which the divergence condition is needed to close the system (i.e., to have the same number of equations and the same number of unknown). In the MHD formulations, if Delta x B = 0 initially, all one needs is to construct appropriate numerical schemes that preserve this constraint at later time evolutions. In other words, one does not need the Delta x B condition to close the MHD system. We formulate our new scheme together with the Cargo & Gallice (1997) form of the MHD approximate Riemann solver in curvilinear grids for both versions of the MHD equations. A novel feature of our new method is that the well-conditioned eigen-decomposition of the non-conservative MHD equations is used to solve the conservative equations. This new feature of the method provides well-conditioned eigenvectors for the conservative formulation, so that correct wave speeds for discontinuities are assured. The justification for using the non-conservative eigen-decomposition to solve the conservative equations is that our scheme has a better control of the numerical error associated with the divergence of the magnetic condition. Consequently, computing both forms of the equations with the same eigen-decomposition is almost equivalent. It will be shown that this approach, using the non-conservative eigensystem when solving the conservative equations, also works well in the context of standard shock-capturing schemes.
Yee, H. C.↗
The Delta(dot) B = O Constraint vs. Minimization of Numerical Errors in MHD Simulations
The MHD equations are a system of non-strictly hyperbolic conservation laws. The non-convexity of the inviscid flux vector resulted in corresponding Jacobian matrices with undesirable properties. On the other hand, the MHD equations can be derived from basic principles in either conservative or non-conservative form. The non-conservative system has a better conditioned eigensystem. The Delta(dot)B = 0 constraint of the A4HD equations is only an initial condition constraint. One does not need the Delta(dot)B condition to close the MHD system. We formulate our new low dissipative high order scheme together with the Cargo & Gallice (1997) form of the MHD approximate Riemann solver in curvilinear grids for both versions of the MHD equations. A novel feature of our new method is that the well-conditioned eigen-decomposition of the non-conservative MHD equations is used to solve the conservative equations. This new feature of the method provides well-conditioned eigenvectors for the conservative formulation, so that correct wave speeds for discontinuities are assured. The justification for using the non-conservative eigen-decomposition to solve the conservative equations is that our scheme has a better control of the numerical error associated with the Delta(dot)B condition. Consequently, computing both forms of the equations with the same eigen-decomposition is almost equivalent. It will be shown that this approach, using the non-conservative eigensystem when solving the conservative equations, also works well in the context of standard shock-capturing schemes.
Yee, H. C.↗
MSDS sky reference and preamplifier study
The major goals in re-designing the Multispectral Scanner and Data System (MSDS) sky reference are: (1) to remove the sun-elevation angle and aircraft-attitude angle dependence from the solar-sky illumination measurement, and (2) to obtain data on the optical state of the atmosphere. The present sky reference is dependent on solar elevation and provides essentially no information on important atmospheric parameters. Two sky reference designs were tested. One system is built around a hyperbolic mirror and the reflection approach. A second approach to a sky reference utilizes a fish-eye lens to obtain a 180 deg field of view. A detailed re-design of the present sky reference around the fish-eye approach, even with its limitations, is recommended for the MSDS system. A preamplifier study was undertaken to find ways of improving the noise-equivalent reflectance by reducing the noise level for silicon detector channels on the MSDS.
Larsen, L.↗
Distributions of Orbital Elements for Meteoroids on Near-Parabolic Orbits According to Radar Observational Data
Some results of the International Heliophysical Year (IHY) Coordinated Investigation Program (CIP) number 65 Meteors in the Earth Atmosphere and Meteoroids in the Solar System are presented. The problem of hyperbolic and near-parabolic orbits is discussed. Some possibilities for the solution of this problem can be obtained from the radar observation of faint meteors. The limiting magnitude of the Kharkov, Ukraine, radar observation program in the 1970 s was +12, resulting in a very large number of meteors being detected. 250,000 orbits down to even fainter limiting magnitude were determined in the 1972-78 period in Kharkov (out of them 7,000 are hyperbolic). The hypothesis of hyperbolic meteors was confirmed. In some radar meteor observations 1 10% of meteors are hyperbolic meteors. Though the Advanced Meteor Orbit Radar (AMOR, New Zealand) and Canadian Meteor Orbit Radar (CMOR, Canada) have accumulated millions of meteor orbits, there are difficulties in comparing the radar observational data obtained from these three sites (New Zealand, Canada, Kharkov). A new global program International Space Weather Initiative (ISWI) has begun in 2010 (http://www.iswi-secretariat.org). Today it is necessary to create the unified radar catalogue of nearparabolic and hyperbolic meteor orbits in the framework of the ISWI, or any other different way, in collaboration of Ukraine, Canada, New Zealand, the USA and, possibly, Japan. Involvement of the Virtual Meteor Observatory (Netherlands) and Meteor Data Centre (Slovakia) is desirable too. International unified radar catalogue of near-parabolic and hyperbolic meteor orbits will aid to a major advance in our understanding of the ecology of meteoroids within the Solar System and beyond.
Kolomiyets, S. V.↗
South-North and radial traverses through the interplanetary dust cloud
Identical in situ dust detectors are flown on board the Galileo and Ulysses spacecraft. They record impacts of micrometeoroids in the ecliptic plane at heliocentric distances from 0.7 to 5.4 AU and in a plane almost perpendicular to the ecliptic from -79 deg to +79 deg ecliptic latitude. The combination of both Ulysses and Galileo measurements yield information about the radial and latitudinal distributions of micron and sub-micron sized dust in the solar system. Two types of dust particles were found to dominate the dust flux in interplanetary space: (1) Interplanetary micrometeoroids covering a wide mass range from 10(exp -16) to 10(exp -6) gr are mostly recorded inside 3 AU, and at latitudes below 30 deg; and (2) Interstellar grains with masses between 10(exp -14) and 10(exp -12) gr have been positively identified outside 3 AU near the ecliptic plane and outside 1.8 AU at high ecliptic latitudes (> 50 deg). Interstellar grains move on hyperbolic trajectories through the planetary system and constitute the dominant dust flux (1.5 x 10(exp -4)/ sq m sec) in the outer solar system and at high ecliptic latitudes. In order to compare and analyze the Galileo and Ulysses data sets, a new model is developed based on Divine's (1993) "Five populations of interplanetary meteoroids" model. By using this model, which takes into account the measured velocities and the effect of radiation pressure on small particles, we define four populations of meteoroids on elliptical orbits plus one population on hyperbolic orbits that all can fit the micrometeoroid flux observed by Galileo and Ulysses.
Gruen, E.↗
PEG Enhancement for EM1 and EM2+ Missions
NASA is currently building the Space Launch System (SLS) Block-1 launch vehicle for the Exploration Mission 1 (EM-1) test flight. The next evolution of SLS, the Block-1B Exploration Mission 2 (EM-2), is currently being designed. The Block-1 and Block-1B vehicles will use the Powered Explicit Guidance (PEG) algorithm. Due to the relatively low thrust-to-weight ratio of the Exploration Upper Stage (EUS), certain enhancements to the Block-1 PEG algorithm are needed to perform Block-1B missions. In order to accommodate mission design for EM-2 and beyond, PEG has been significantly improved since its use on the Space Shuttle program. The current version of PEG has the ability to switch to different targets during Core Stage (CS) or EUS flight, and can automatically reconfigure for a single Engine Out (EO) scenario, loss of communication with the Launch Abort System (LAS), and Inertial Navigation System (INS) failure. The Thrust Factor (TF) algorithm uses measured state information in addition to a priori parameters, providing PEG with an improved estimate of propulsion information. This provides robustness against unknown or undetected engine failures. A loft parameter input allows LAS jettison while maximizing payload mass. The current PEG algorithm is now able to handle various classes of missions with burn arcs much longer than were seen in the shuttle program. These missions include targeting a circular LEO orbit with a low-thrust, long-burn-duration upper stage, targeting a highly eccentric Trans-Lunar Injection (TLI) orbit, targeting a disposal orbit using the low-thrust Reaction Control System (RCS), and targeting a hyperbolic orbit. This paper will describe the design and implementation of the TF algorithm, the strategy to handle EO in various flight regimes, algorithms to cover off-nominal conditions, and other enhancements to the Block-1 PEG algorithm. This paper illustrates challenges posed by the Block-1B vehicle, and results show that the improved PEG algorithm is capable for use on the SLS Block 1-B vehicle as part of the Guidance, Navigation, and Control System.
Von der Porten, Paul↗
Canonical and noncanonical Hamiltonian operator inference
Here, a method for the nonintrusive and structure-preserving model reduction of canonical and noncanonical Hamiltonian systems is presented. Based on the idea of operator inference, this technique is provably convergent and reduces to a straightforward linear solve given snapshot data and gray-box knowledge of the system Hamiltonian. Examples involving several hyperbolic partial differential equations show that the proposed method yields reduced models which, in addition to being accurate and stable with respect to the addition of basis modes, preserve conserved quantities well outside the range of their training data.
97 MATHEMATICS AND COMPUTING↗