Three-Dimensional Simulations of Machined Perturbation Profiles Subjected to the Richtmyer-Meshkov Instability: Mix Metrics Analysis and Comparison to Experiments
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Pellone, Samuel Louis↗
SEARCH · Engineering Papers
Results for “perturbation analysis”
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Finite element structural redesign by large admissible perturbations
In structural redesign, two structural states are involved; the baseline (known) State S1 with unacceptable performance, and the objective (unknown) State S2 with given performance specifications. The difference between the two states in performance and design variables may be as high as 100 percent or more depending on the scale of the structure. A Perturbation Approach to Redesign (PAR) is presented to relate any two structural states S1 and S2 that are modeled by the same finite element model and represented by different values of the design variables. General perturbation equations are derived expressing implicitly the natural frequencies, dynamic modes, static deflections, static stresses, Euler buckling loads, and buckling modes of the objective S2 in terms of its performance specifications, and S1 data and Finite Element Analysis (FEA) results. Large Admissible Perturbation (LEAP) algorithms are implemented in code RESTRUCT to define the objective S2 incrementally without trial and error by postprocessing FEA results of S1 with no additional FEAs. Systematic numerical applications in redesign of a 10 element 48 degree of freedom (dof) beam, a 104 element 192 dof offshore tower, a 64 element 216 dof plate, and a 144 element 896 dof cylindrical shell show the accuracy, efficiency, and potential of PAR to find an objective state that may differ 100 percent from the baseline design.
Bernitsas, Michael M.↗
The stability of tangential discontinuities
Intuition regarding the stability of MHD tangential discontinuities of solar wind has been borne out by a linear stability analysis of the MHD equations. In performing the calculation, the model used had no plasma flow and thus corresponded to the solar wind rest frame. The method calculated the change in total energy, plasma plus magnetic, due to the perturbation. This type of stability analysis is analogous to the test of the stability of an equilibrium point in a mechanical potential.
Birmingham, T.↗
Competition between Hydrogen and Chalcogen Bonding in Homodimers of Chalcogen Hydrides (H 2 X) 2 , X = O, S, Se, Te
The structural and chemical bonding motifs manifested by the competition between hydrogen and chalcogen bonding in the homodimers of chalcogen hydrides (H 2 X) 2 , where X = O, S, Se, Te have been characterized using high-level electronic structure calculations and analysis of the electron density based on Quasi-atomic orbital (QUAO) and the Symmetry-adapted perturbation theory (SAPT) methods. The QUAO analysis clearly identifies a three-center interaction responsible for either hydrogen or chalcogen bonds: in the former, the σ-bond connecting the donor and hydrogen atom participating in the hydrogen bond interacts with the lone pair on the nucleophile acceptor via the hydrogen atom, while in the latter this same σ-bond interacts with the nucleophile lone pair via the donor chalcogen. The number of minimum energy structures increase dramatically from one for (H 2 O) 2 , three for (H 2 S) 2 , four for (H 2 Se) 2 , and finally six for (H 2 Te) 2 . Furthermore, the emergence of the chalcogen-bonded arrangements appears for (H 2 S) 2 with their subsequent energetic stabilization over the hydrogen-bonded minima manifesting in (H 2 Se) 2 and (H 2 Te) 2 . In particular, one of the (H 2 S) 2 , two of the (H 2 Se) 2 , and three of the (H 2 Te) 2 dimers are chalcogen bonded. Induction plays a small but important role in stabilizing hydrogen over chalcogen-bonded structures, while dispersion is more important for chalcogen bonds.
Chemical structure↗
A Uniform Analysis of Debris Disks with the Gemini Planet Imager. I. An Empirical Search for Perturbations from Planetary Companions in Polarized Light Images
The Gemini Planet Imager (GPI) has excelled in imaging debris disks in the near-infrared. The GPI Exoplanet Survey imaged 24 debris disks in polarized H-band light, while other programs observed half of these disks in polarized J and/or K1 bands. Using these data, we present a uniform analysis of the morphology of each disk to find asymmetries suggestive of perturbations, particularly those due to planet–disk interactions. The multiwavelength surface brightness, disk color, and geometry permit the identification of any asymmetries such as warps or disk offsets from the central star. We find that 19 of the disks in this sample exhibit asymmetries in surface brightness, disk color, disk geometry, or a combination of the three, suggesting that for this sample, perturbations, as seen in scattered light, are common. The relationship between these perturbations and potential planets in the system is discussed. We also explore correlations among stellar temperatures, ages, disk properties, and observed perturbations. We find significant trends between the vertical aspect ratio and the stellar temperature, disk radial extent, and the dust grain size distribution power law, q. We also confirm a trend between the disk color and stellar effective temperature, where the disk becomes increasingly red/neutral with increasing temperature. Such results have important implications for the evolution of debris disk systems around stars of various spectral types.
79 ASTRONOMY AND ASTROPHYSICS↗
A Uniform Analysis of Debris Disks with the Gemini Planet Imager. I. An Empirical Search for Perturbations from Planetary Companions in Polarized Light Images
The Gemini Planet Imager (GPI) has excelled in imaging debris disks in the near-infrared. The GPI Exoplanet Survey imaged 24 debris disks in polarized H-band light, while other programs observed half of these disks in polarized J and/or K1 bands. Using these data, we present a uniform analysis of the morphology of each disk to find asymmetries suggestive of perturbations, particularly those due to planet–disk interactions. The multiwavelength surface brightness, disk color, and geometry permit the identification of any asymmetries such as warps or disk offsets from the central star. We find that 19 of the disks in this sample exhibit asymmetries in surface brightness, disk color, disk geometry, or a combination of the three, suggesting that for this sample, perturbations, as seen in scattered light, are common. The relationship between these perturbations and potential planets in the system is discussed. We also explore correlations among stellar temperatures, ages, disk properties, and observed perturbations. We find significant trends between the vertical aspect ratio and the stellar temperature, disk radial extent, and the dust grain size distribution power law, q. We also confirm a trend between the disk color and stellar effective temperature, where the disk becomes increasingly red/neutral with increasing temperature. Such results have important implications for the evolution of debris disk systems around stars of various spectral types.
Katie A Crotts↗
Non-linear analysis of vibrations of irregular plates
A numerical perturbation method is used to investigate the forced vibrations of irregular plates. Nonlinear terms associated with the midplane stretching are retained in the analysis. The numerical part of the method involves the use of linear, finite element techniques to determine the free oscillation mode shapes and frequencies and to obtain the linear midplane stress resultants caused by the midplane stretching. Representing the solution as an expansion in terms of these linear mode shapes, these modes and the resultants are used to determine the equations governing the time-dependent coefficients of this expansion. These equations are solved by using the method of multiple scales. Specific solutions are given for the main-resonant vibrations of an elliptical plate in the presence of internal resonances. The results indicate that modes other than the driven mode can be drawn into the steady state response. Though the excitation is composed of a single harmonic, the response may not be periodic. Moreover, the particular types of responses that can occur are highly dependent on the mode being excited and are sensitive to small geometrical changes.
Lobitz, D. W.↗
Unitarity bounds on effective field theories at the LHC
Effective Field Theory (EFT) extensions of the Standard Model are tools to compute observables (e.g. cross sections with partonic center-of-mass energy √s^) as a systematically improvable expansion suppressed by a new physics scale M. If one is interested in EFT predictions in the parameter space where M < √s^, concerns of self-consistency emerge, which can manifest as a violation of perturbative partial-wave unitarity. However, when we search for the effects of an EFT at a hadron collider with center-of-mass energy √s using an inclusive strategy, we typically do not have access to the event-by-event value of √s^. This motivates the need for a formalism that incorporates parton distribution functions into the perturbative partial-wave unitarity analysis. Developing such a framework and initiating an exploration of its implications is the goal of this work. Our approach opens up a potentially valid region of the EFT parameter space where M << √s. We provide evidence that there exist valid EFTs in this parameter space. The perturbative unitarity bounds are sensitive to the details of a given search, an effect we investigate by varying kinematic cuts.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Substructure Versus Property-Level Dispersed Modes Calculation
This paper calculates the effect of perturbed finite element mass and stiffness values on the eigenvectors and eigenvalues of the finite element model. The structure is perturbed in two ways: at the "subelement" level and at the material property level. In the subelement eigenvalue uncertainty analysis the mass and stiffness of each subelement is perturbed by a factor before being assembled into the global matrices. In the property-level eigenvalue uncertainty analysis all material density and stiffness parameters of the structure are perturbed modified prior to the eigenvalue analysis. The eigenvalue and eigenvector dispersions of each analysis (subelement and property-level) are also calculated using an analytical sensitivity approximation. Two structural models are used to compare these methods: a cantilevered beam model, and a model of the Space Launch System. For each structural model it is shown how well the analytical sensitivity modes approximate the exact modes when the uncertainties are applied at the subelement level and at the property level.
Stewart, Eric C.↗
A determination of the earth tidal amplitude and phase from the orbital perturbations of the Beacon Explorer C spacecraft
An analysis of the orbital inclination of the Beacon Explorer C spacecraft over a period of nearly five months in 1970 revealed a very clear and distinctive perturbation caused by the earth and ocean tides. The perturbation has a full amplitude of about 1.8 seconds of arc and a period of about 85 days. This amplitude is approximately 15% smaller than would be expected from the solid-earth tide alone and is shifted slightly in phase. The perturbation can be represented almost exactly by a Love number of k sub 2 = 0.245 with a phase lag of 3.2 degrees. The data used were laser range measurements obtained by a NASA Goddard Space Flight Center tracking system in Greenbelt, Maryland.
Smith, D. E.↗
Updated dispersion analysis for the first Orbital Flight Test (OFT-1) mission
A dispersion analysis considering 3-sigma uncertainties (or perturbations) in platform, vehicle, and environmental parameters was performed for the first orbital flight test (OFT-1) mission. The dispersion analysis is based on the nominal trajectory for the OFT-1 reference flight profile and was performed to determine state vector and performance dispersions (or variations) which result from the indicated 3 sigma uncertainties. The dispersions are determined at major mission events and fixed times from liftoff (time slices). Principal error contributors to the covariance matrix are listed. The dispersion data indicates that the largest position error occurs in the down range component. At main engine cutoff and circularization, the vehicle performance uncertainties are the major contributors to down range error.
Snow, L. S.↗
Linear stability analysis via simulated annealing and accelerated relaxation
Simulated annealing (SA) is a kind of relaxation method for finding equilibria of Hamiltonian systems. A set of evolution equations is solved with SA, which is derived from the original Hamiltonian system so that the energy of the system changes monotonically while preserving Casimir invariants inherent to noncanonical Hamiltonian systems. The energy extremum reached by SA is an equilibrium. Since SA searches for an energy extremum, it can also be used for stability analysis when initiated from a state where a perturbation is added to an equilibrium. The procedure of the stability analysis is explained, and some examples are shown. Because the time evolution is computationally time consuming, efficient relaxation is necessary for SA to be practically useful. An acceleration method is developed by introducing time dependence in the symmetric kernel used in the double bracket, which is part of the SA formulation described here. An explicit formulation for low-beta reduced magnetohydrodynamics (MHD) in cylindrical geometry is presented. In conclusion, since SA for low-beta reduced MHD has two advection fields that relax, it is important to balance the orders of magnitude of these advection fields.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Transverse energy–energy correlations of jets in the electron–proton deep inelastic scattering at HERA
We study the event shape variables, transverse energy–energy correlation TEEC (cosφ) and its asymmetry ATEEC (cosφ) in deep inelastic scattering (DIS) at the electron–proton collider HERA, where φ is the angle between two jets defined using a transverse-momentum (k T ) jet algorithm. At HERA, jets are defined in the Breit frame, and the leading nontrivial transverse energy–energy correlations arise from the 3-jet configurations. With the help of the NLOJET++, these functions are calculated in the leading order (LO) and the next-to-leading order (NLO) approximations in QCD at the electron–proton center-of-mass energy $\sqrt{s}$ = 314 GeV. We restrict the angular region to -0.8 ≤ cosφ ≤ 0.8, as the forward- and backward-angular regions require resummed logarithmic corrections, which we have neglected in this work. Following experimental jet-analysis at HERA, we restrict the DIS-variables x, y = Q 2 /(xs), where Q 2 = -q 2 is the negative of the momentum transfer squared q 2 , to 0 ≤ x ≤ 1, 0.2 ≤ y ≤ 0.6, and the pseudo-rapidity variable in the laboratory frame (η lab ) to the range -1 ≤ η lab ≤ 2.5. The TEEC and ATEEC functions are worked out for two ranges in Q 2 , defined by 5.5GeV 2 ≤ Q 2 ≤ 80GeV 2 , called the low-Q 2 -range, and 150GeV 2 ≤ Q 2 ≤ 1000GeV 2 , called the high-Q 2 -range. We show the sensitivity of these functions on the parton distribution functions (PDFs), the factorization (μ F ) and renormalization (μ R ) scales, and on α s (M$^2_Z$). Of these the correlations are stable against varying the scale μ F and the PDFs, but they do depend on μ R . For the choice of the scale μ R =$\sqrt{\langle ET \rangle^2+Q^2}$, advocated in earlier jet analysis at HERA, the shape variables TEEC and ATEEC are found perturbatively robust. These studies are useful in the analysis of the HERA data, including the determination of α s (M$^2_Z$) from the shape variables.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Comment on “Nonlocal nucleon matrix elements in the rest frame”
In a recent paper, “Nonlocal nucleon matrix elements in the rest frame” [1], it was observed that the next-to-leading order calculations of the renormalization factor can describe, to a few percent accuracy, the logarithm of the lattice quantum chromodynamics (QCD) rest frame matrix elements with separations up to distances of 0.6 fm on multiple lattice spacings. We argue that perturbative QCD breaks down at such a distance scale after resumming the associated large logarithms, while the Ansatz used in the analysis there is not justified in perturbation theory. Besides, we explain the observation in Ref. [1] and demonstrate that the Ansatz fails to describe the data for 𝑧 > 0.3 fm, showing an opposite trend. Finally, although Ref. [1] proposes multiplying the Ansatz by a Gaussian correction model, which is shown to reduce the discrepancy with the data, this does not legitimize the use of perturbative QCD at such distance scales.
Lattice QCD↗
Ensuring statistical reproducibility of ocean model simulations in the age of hybrid computing
Novel high performance computing systems that feature hybrid architectures require large scale code refactoring to unravel underlying exploitable parallelism. Such redesign can often be accompanied with machine-precision changes as the order of computation cannot always be maintained. For chaotic systems like climate models, these round-off level differences can grow rapidly. Systematic errors may also manifest initially as machine-precision differences. Isolating genuine round off level differences from such errors remains a challenge. Here, we apply two-sample equality of distribution tests to evaluate statistical reproducibility of the ocean model component of US Department of Energy's Energy Exascale Earth System Model (E3SM). A 2-year control simulation ensemble is compared to a modified ensemble as a test case - after a known non-bit-for-bit change in a model component is introduced - to evaluate the null hypothesis that the two ensembles are statistically indistinguishable. To quantify the false negative rates of these tests, we conduct a formal power analysis using a targeted suite of short simulation ensembles. The ensemble suite contains several perturbed ensembles, each with a progressively different climate than the baseline ensemble - obtained by perturbing the magnitude of a single model tuning parameter, the Gent and McWilliams κ, in a controlled manner. The null hypothesis is evaluated for each of perturbed ensembles using these tests. The power analysis informs on the detection limits of the tests for given ensemble size allowing model developers to evaluate the impact of an introduced non-bit-for-bit change to the model.
Mahajan, Salil↗
Random motion analysis of flexible satellite structures
A singular perturbation formulation is used to study the responses of a flexible satellite when random measurement errors can occur. The random variables, at different instants of time, are assumed to be uncorrelated. Procedures for obtaining maxima and minima are described, and a variation of the linear method is developed for the formal solution of the two-point boundary-value problems represented by the variational equations. Random and deterministic solutions for the structural position coordinates are studied, and an analytic algorithm for treating the force equation of motion is developed. Since the random system indicated by the variational equation will always be asymptotically unstable, any analysis of stability must be based on the deterministic system.
Huang, T. C.↗
Development of a spinning wave heat engine
A theoretical analysis and an experimental investigation were conducted to assess the feasibility of developing a spinning wave heat engine. Such as engine would utilize a large amplitude traveling acoustic wave rotating around a cylindrica chamber, and it should not suffer from the inefficiency, noise, and intermittent thrust which characterizes pulse jet engines. The objective of this investigation was to determine whether an artificially driven large amplitude spinning transverse wave could induce a steady flow of air through the combustion chamber under cold flow conditions. In the theoretical analysis the Maslen and Moore perturbation technique was extended to study flat cylinders (pancake geometry) with completely open side walls and a central opening. In the parallel experimental study, a test moel was used to determine resonant frequencies and radial pressure distributions, as well as oscillatory and steady flow velocities at the inner and outer peripheries. The experimental frequency was nearly the same as the theoretical acoustic value for a model of the same outer diameter but without a central hole. Although the theoretical analysis did not predict a steady velocity component, simulaneous measurements of hotwire and microphone responses have shown that the spinning wave pumps a mean flow radially outward through the cavity.
Zinn, B. T.↗
Dispersion analysis for baseline reference mission 1
A dispersion analysis considering 3 sigma uncertainties (or perturbations) in platform, vehicle, and environmental parameters was performed for the baseline reference mission (BRM) 1 of the space shuttle orbiter. The dispersion analysis is based on the nominal trajectory for the BRM 1. State vector and performance dispersions (or variations) which result from the indicated 3 sigma uncertainties were studied. The dispersions were determined at major mission events and fixed times from lift-off (time slices) and the results will be used to evaluate the capability of the vehicle to perform the mission within a 3 sigma level of confidence and to determine flight performance reserves. A computer program is given that was used for dynamic flight simulations of the space shuttle orbiter.
Kuhn, A. E.↗