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Results for “Numerical approximation & analysis”

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NASA NTRS1998

Absolute Rovibrational Intensities of C-12O2-16 Absorption Bands in the 3090-3850/ CM Spectral Region

A multispectrum nonlinear least-squares fitting technique has been used to determine the absolute intensities for approximately 1500 spectral lines in 36 vibration - rotation bands Of C-12O2-16 between 3090 and 3850/ cm. A total of six absorption spectra of a high- purity (99.995% minimum) natural sample of carbon dioxide were used in the analysis. The spectral data (0.01/cm resolution) were recorded at room temperature and low pressure (1 to 10 Torr) using the McMath-Pierce Fourier transform spectrometer of the National Solar Observatory (NSO) on Kitt Peak. The absorption path lengths for these spectra varied between 24.86 and 385.76 m. The first experimental determination of the intensity of the theoretically predicted 2(nu)(sub 2, sup 2) + nu(sub 3) "forbidden" band has been made. The measured line intensities obtained for each band have been analyzed to determine the vibrational band intensity, S(sub nu), in /cm/( molecule/sq cm) at 296 K, square of the rotationless transition dipole moment |R|(exp 2) in Debye, as well as the nonrigid rotor coefficients. The results are compared to the values listed in the 1996 HITRAN database which are obtained using the direct numerical diagonalization (DND) technique as well as to other published values where available.

Devi, V. Malathy↗

NASA NTRS2010

Aero-Heating of Shallow Cavities in Hypersonic Freestream Flow

The purpose of these experiments and analysis was to augment the heating database and tools used for assessment of impact-induced shallow-cavity damage to the thermal protection system of the Space Shuttle Orbiter. The effect of length and depth on the local heating disturbance of rectangular cavities tested at hypersonic freestream conditions has been globally assessed using the two-color phosphor thermography method. These rapid-response experiments were conducted in the Langley 31-Inch Mach 10 Tunnel and were initiated immediately prior to the launch of STS-114, the initial flight in the Space Shuttle Return-To-Flight Program, and continued during the first week of the mission. Previously-designed and numerically-characterized blunted-nose baseline flat plates were used as the test surfaces. Three-dimensional computational predictions of the entire model geometry were used as a check on the design process and the two-dimensional flow assumptions used for the data analysis. The experimental boundary layer state conditions were inferred using the measured heating distributions on a no-cavity test article. Two test plates were developed, each containing 4 equally-spaced spanwise-distributed cavities. The first test plate contained cavities with a constant length-to-depth ratio of 8 with design point depth-to-boundary-layer-thickness ratios of 0.1, 0.2, 0.35, and 0.5. The second test plate contained cavities with a constant design point depth-to-boundary-layer-thickness ratio of 0.35 with length-to-depth ratios of 8, 12, 16, and 20. Cavity design parameters and the test condition matrix were established using the computational predictions. Preliminary results indicate that the floor-averaged Bump Factor (local heating rate nondimensionalized by upstream reference) at the tested conditions is approximately 0.3 with a standard deviation of 0.04 for laminar-in/laminar-out conditions when the cavity length-to-boundary-layer thickness is between 2.5 and 10 and for cavities in the depth-to-boundary-layer-thickness range of 0.3 to 0.8. Over this same range of conditions and parameters, preliminary results also indicate that the maximum Bump Factor on the cavity centerline falls between 2.0 and 2.75, as long as the cavity-exit conditions remain laminar. Cavities with length-to-boundary-layer-thickness ratio less than 2.5 can not be easily classified with this approach and require further analysis.

Everhart, Joel L.↗

DOE OSTI2020

Eigenmode analysis of the sheared-flow Z-pinch

Experiments have demonstrated that a Z-pinch can persist for thousands of times longer than the growth time of global magnetohydrodynamic (MHD) instabilities such as the m=0 sausage and m=1 kink modes. These modes have growth times on the order of ta=a/vi, where vi is the ion thermal speed and a is the pinch radius. Axial flows with duz/dr ≲ vi/a have been measured during the stable period, and the commonly accepted theory is that this amount of shear is sufficient to stabilize these modes as predicted by numerical studies using the ideal MHD equations. However, these studies only consider specific equilibrium profiles that typically have a modest magnitude for the logarithmic pressure gradient, qP≡d ln P/d ln r, and may not represent experimental conditions. Linear stability of the sheared-flow Z-pinch is studied here via a direct eigen-decomposition of the matrix operator obtained from the linear ideal MHD equations. Several equilibrium profiles with a large variation of qP are examined. Considering a practical range of k, 1/3 ≲ ka ≲ 10, it is shown that the shear required to stabilize m=0 modes can be expressed as duz/dr≥Cγ0/(ka)α. Here, γ0=γ0(ka) is the profile-specific growth rate in the absence of shear, which scales approximately with |qP|. Both C and α are profile-specific constants, but C is order unity and α≈1. It is further demonstrated that even a large value of shear, duz/dr=3vi/a, is not sufficient to provide linear stabilization of the m=1 kink mode for all profiles considered. This result is in contrast to the currently accepted theory predicting stabilization at much lower shear, duz/dr=0.1vi/a, and suggests that the experimentally observed stability cannot be explained within the linear ideal-MHD model.

Angus, J. R. (ORCID:0000000314740002)↗

DOE OSTI2020

Optically targeted search for gravitational waves emitted by core-collapse supernovae during the first and second observing runs of advanced LIGO and advanced Virgo

In this work, we present the results from a search for gravitational-wave transients associated with core-collapse supernovae observed within a source distance of approximately 20 Mpc during the first and second observing runs of Advanced LIGO and Advanced Virgo. No significant gravitational-wave candidate was detected. We report the detection efficiencies as a function of the distance for waveforms derived from multidimensional numerical simulations and phenomenological extreme emission models. Furthermore, the sources with neutrino-driven explosions are detectable at the distances approaching 5 kpc, and for magnetorotationally driven explosions the distances are up to 54 kpc. However, waveforms for extreme emission models are detectable up to 28 Mpc. For the first time, the gravitational-wave data enabled us to exclude part of the parameter spaces of two extreme emission models with confidence up to 83%, limited by coincident data coverage. Besides, using ad hoc harmonic signals windowed with Gaussian envelopes, we constrained the gravitational-wave energy emitted during core collapse at the levels of 4.27×10 -4 M ⊙ c 2 and 1.28×10 -1 M ⊙ c 2 for emissions at 235 and 1304 Hz, respectively. These constraints are 2 orders of magnitude more stringent than previously derived in the corresponding analysis using initial LIGO, initial Virgo, and GEO 600 data.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1993

Geologic mapping of Northern Atla Regio on Venus: Preliminary data

The Northern part of Atla Regio within the frame of C1-formate Magellan photo map 15N197 was mapped geologically at scale 1:8,000,000. This is a part of Russia's contribution into C1 geologic mapping efforts. The map is reproduced here being reduced about twice. The map shows that the Northern Atla area is predominantly a volcanic plain with numerous volcanic features: shield volcanoes, domes and hills with various morphology, corona-like constructions, radar bright and dark spots often with flow-like outlines. Relatively small areas of tessera occurred in the area are mainly semi-flooded with the plain material. Tesserae are considered to be the oldest terrains within the map sheet. There are many lineated terrains in the region. They are interpreted as the old, almost-buried tesserae (those with crossed lineaments) or partly buried ridge belts (those with parallel lineaments). These lineated terrains have an intermediate age between the young volcanic plains and the old tessera areas. Two prominent high volcanic shields are located within the region - Ozza Mons and Sapas Mona. The most prominent structure in Northern Atla is Ganis Chasma rift. The rift cuts volcanic plain and is considered to be under formation during approximately the same time with Ozza Mons shield. Ganis Chasma rift valley is highly fractured and bounded with fault scarps. Rift shoulder uplifts are typical for Ganis Chasma. There are few relatively young volcanic features inside the rift valley. The analysis of fracturing and rift valley geometry shows the rift originated due to 5-10 percent crustal extention followed by the crustal subsidence. The age sequence summary for the main terrain types in the region is (from older to younger ones): tesserae; lineated terrains with crossed lineaments; lineated terrains with parallel lineaments; volcanic plains; and prominent volcanic shields and Ganis Chasma rift valley. The geologic structure of Atla Regio as it appeared now with the Magellan high resolution images is very close to that of Beta Regio. Such conclusion coincide with the earlier ones based on the coarser data.

Nikishin, A. M.↗

NASA NTRS2020

Streak Instabilities on HIFiRE-5 Elliptic Cone

The Hypersonic International Flight Research and Experimentation (HIFiRE) 5 flight experiment by the Air Force Research Laboratories and Australian Defense Science and Technology Organization yielded inflight, hypersonic transition data for a canonical, 3D configuration in the form of an elliptic cone at various combinations of angle-of-attack and yaw. Previous analysis has shown that boundary-layer stability calculations for the as-flown, zero-yaw flight conditions are able to capture the second mode dominated transition along the attachment line as well as the crossflow induced transition in between the attachment line and the minor axis symmetry plane. However, there is still a need to understand the transition in the vicinity of the minor axis plane of symmetry, where the boundary layer thickness exhibits an azimuthally compact bulge due to the collision of the secondary flow approaching from the attachment lines on both sides. This paper reports a computational analysis of the stability of the boundary layer flow along the bulge regions on both the leeward and windward sides of the vehicle surface. At a representative flight condition corresponding to a time instant of t = 514.813 seconds, computations are performed to identify several different unstable modes within the bulge regions, with the eventual goal of developing a linear stability correlation for the transition onset near the minor axis symmetry plane. The most amplified flow instabilities in the pretransitional region correspond to a “stem” mode that is concentrated within a pair of nearly vertical shear layers below the cap of the mushroom shaped bulge in the mean velocity contours. An excellent agreement is found between the predictions of instability amplification based on the plane marching parabolized stability equations (PSE) and the direct numerical solutions (DNS). Given the large number of unstable modes within the bulge region, the observed agreement demonstrates, for first time, that the PSE can provide accurate predictions for the development of flow instabilities in streak-like flow features over three-dimensional bodies. The peak N-factor of approximately 15 at the transition location estimated from the thermocouple measurements along the leeward centerline is close to the transition N-factor for Mack mode transition during the HIFiRE-1 circular cone flight experiment with nearly zero degrees angle of attack.

Meelan Choudhari↗

DOE OSTI2020

An analysis of the spatio-temporal resolution of the immersed boundary method with direct forcing

The immersed boundary method (IBM) with direct forcing is very popular in the simulation of rigid particulate flows. In the IBM, an interaction force is introduced at the interface between fluid and particle in order to approximate the no-slip boundary condition. The interaction force is calculated through dividing the velocity difference (or error) between fluid and particle at the interface by the time step. Here, a dynamic equation for the velocity difference is derived. Additionally, analyses on the dynamic equation provide a few new findings: (i) The interaction force is the solution of a least-squares error problem, with the direct implication that the Lagrangian marker distribution has no effect on the large scale flow structure once the distribution of Lagrangian markers become saturated along the interface (i.e., each marker remains properly correlated with all its neighbors); (ii) The Lagrangian volume-weight is a relaxation factor to control how fast the velocity error decays to the ideal value of zero; (iii) The optimal choice of the Lagrangian volume-weight is the largest value permissible by a stability condition. A comprehensive convergence analysis with regard to the spatial and temporal resolution is presented for the velocity error and also for the shear-stress and surface pressure. In three simple canonical problems, it is analytically and numerically shown that the IBM results converge to the theoretical solutions obtained with precise imposition of no-slip and no-penetration boundary conditions. It is observed that it is not necessary to match the Lagrangian marker volume-weight to that of the local Eulerian cell volume and in fact this matching leads to lower than optimal computational efficiency. However, it is found that extremely high Eulerian grid resolution and small time step have to be used to obtain high precision simulation results. Especially, the time step should be inversely proportional to the particle Reynolds number for low Reynolds number flows. For high frequency oscillation problems, the grid size needs to be reduced by a factor of the square root of the frequency, and the time step to be reduced by a factor of the frequency. The theoretical findings here can be used to alleviate the technical difficulties in simulating non-spherical particles by not requiring the Lagrangian marker distribution to match the Eulerian grids and also in the implementation of IBM on non-uniform Eulerian grids. The present work also provides simple practical guidance on the choice of temporal and spatial resolution so as to control the simulation error a priori.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Evaluation of a quasi-steady-state approximation of the cloud droplet growth equation (QDGE) scheme for aerosol activation in global models using multiple aircraft data over both continental and marine environments

This research introduces a numerically efficient aerosol activation scheme and evaluates it by using stratus and stratocumulus cloud data sampled during multiple aircraft campaigns in Canada, Chile, Brazil, and China. The scheme employs a quasi-steady-state approximation of the cloud droplet growth equation (QDGE) to efficiently simulate aerosol activation, the vertical profile of supersaturation, and the activated cloud droplet number concentration (CDNC) near the cloud base. The calculated maximum supersaturation values using the QDGE scheme were compared with multiple parcel model simulations under various aerosol and environmental conditions. The differences are all below 0.18 %, indicating good performance and accuracy of the QDGE scheme. We evaluated the QDGE scheme by specifying observed environmental thermodynamic variables and aerosol information from 31 cloud cases as input and comparing the simulated CDNC with cloud observations. The average of mean relative error ($\overline{MRE}$) of the simulated CDNC for cloud cases in each campaign ranges from 17.30 % in Brazil to 25.90 % in China, indicating that the QDGE scheme successfully reproduces observed variations in CDNC over a wide range of different meteorological conditions and aerosol regimes. Additionally, we carried out an error analysis by calculating the maximum information coefficient (MIC) between the MRE and input variables for the individual campaigns and all cloud cases. MIC values were then sorted by aerosol properties, pollution level, environmental humidity, and dynamic condition according to their relative importance to MRE. Based on the error analysis, we found that the magnitude of MRE is more relevant to the specification of input aerosol pollution level in marine regions and aerosol hygroscopicity in continental regions than to other variables in the simulation.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS2016

Analysis of Summer-Time Ozone and Precursor Species in the Southeast United States

Ozone (O3) is a greenhouse gas and toxic pollutant which plays a major role in air quality and atmospheric chemistry. The understanding and ability to model the horizontal and vertical structure of O3 mixing ratios is difficult due to the complex formation/destruction processes and transport pathways that cause large variability of O3. The Environmental Protection Agency has National Ambient Air Quality Standards for O3 set at 75 ppb with future standards proposed to be as low as 65 ppb. These lower values emphasize the need to better understand/simulate the transport processes, emission sources, and chemical processes controlling precursor species (e.g., NOx, VOCs, and CO) which influence O3 mixing ratios. The uncertainty of these controlling variables is particularly large in the southeast United States (US) which is a region impacted by multiple different emission sources of precursor species (anthropogenic and biogenic) and transport processes resulting in complex spatio-temporal O3 patterns. During this work we will evaluate O3 and precursor species in the southeast US applying models, ground-based and airborne in situ data, and lidar observations. In the summer of 2013, the UAH O3 Differential Absorption Lidar (DIAL) (part of the Tropospheric Ozone Lidar Network (TOLNet)) measured vertical O3 profiles from the surface up to approximately 12 km. During this period, the lidar observed numerous periods of dynamic temporal and vertical O3 structures. In order to determine the sources/processes impacting these O3 mixing ratios we will apply the CTM GEOS-Chem (v9-02) at a 0.25 deg x 0.3125 deg resolution. Using in situ ground-based (e.g., SEARCH Network, CASTNET), airborne (e.g., NOAA WP-3D - SENEX 2013, DC-8 - SEAC4RS), and TOLNet lidar data we will first evaluate the model to determine the capability of GEOS-Chem to simulate the spatio-temporal variability of O3 in the southeast US. Secondly, we will perform model sensitivity studies in order to quantify which emission sources (e.g., anthropogenic, biogenic, lighting, wildfire) and transport processes (e.g., stratospheric, long-range, local scale) are contributing to these TOLNet-observed dynamic O3 patterns. Results from the evaluation of the model and the study of sources/processes impacting observed O3 mixing ratios will be presented.

Optical Radar↗

NASA NTRS1994

Generation of gear tooth surfaces by application of CNC machines

This study will demonstrate the importance of application of computer numerically controlled (CNC) machines in generation of gear tooth surfaces with new topology. This topology decreases gear vibration and will extend the gear capacity and service life. A preliminary investigation by a tooth contact analysis (TCA) program has shown that gear tooth surfaces in line contact (for instance, involute helical gears with parallel axes, worm gear drives with cylindrical worms, etc.) are very sensitive to angular errors of misalignment that cause edge contact and an unfavorable shape of transmission errors and vibration. The new topology of gear tooth surfaces is based on the localization of bearing contact, and the synthesis of a predesigned parabolic function of transmission errors that is able to absorb a piecewise linear function of transmission errors caused by gear misalignment. The report will describe the following topics: description of kinematics of CNC machines with six degrees of freedom that can be applied for generation of gear tooth surfaces with new topology. A new method for grinding of gear tooth surfaces by a cone surface or surface of revolution based on application of CNC machines is described. This method provides an optimal approximation of the ground surface to the given one. This method is especially beneficial when undeveloped ruled surfaces are to be ground. Execution of motions of the CNC machine is also described. The solution to this problem can be applied as well for the transfer of machine tool settings from a conventional generator to the CNC machine. The developed theory required the derivation of a modified equation of meshing based on application of the concept of space curves, space curves represented on surfaces, geodesic curvature, surface torsion, etc. Condensed information on these topics of differential geometry is provided as well.

Litvin, F. L.↗

NASA NTRS2023

An Analysis of Degradation in Low-Cost Particulate Matter Sensors

Low-cost sensors (LCSs) are increasingly being used to measure fine particulate matter (PM 2.5 ) concentrations in cities around the world. One of the most commonly deployed LCSs is PurpleAir with ∼15 000 sensors deployed in the United States, alone. PurpleAir measurements are widely used by the public to evaluate PM 2.5 levels in their neighborhoods. PurpleAir measurements are also increasingly being integrated into models by researchers to develop large-scale estimates of PM 2.5 . However, the change in sensor performance over time has not been well studied. It is important to understand the lifespan of these sensors to determine when they should be serviced or replaced, and when measurements from these devices should or should not be used for various applications. This paper fills this gap by leveraging the fact that: (1) each PurpleAir sensor is composed of two identical sensors and the divergence between their measurements can be observed, and (2) there are numerous PurpleAir sensors within 50 meters of regulatory monitors allowing for the comparison of measurements between these instruments. We propose empirically-derived degradation outcomes for the PurpleAir sensors and evaluate how these outcomes change over time. On average, we find that the number of ‘flagged’ measurements, where the two sensors within each PurpleAir sensor disagree, increases with time to ∼4% after 4 years of operation. Approximately, 2 percent of all PurpleAir sensors were permanently degraded. The largest fraction of permanently degraded PurpleAir sensors appeared to be in the hot and humid climate zone, suggesting that sensors in these locations may need to be replaced more frequently. We also find that the bias of PurpleAir sensors, or the difference between corrected PM2.5 levels and the corresponding reference measurements, changed over time by −0.12 μg m −3 (95% CI: −0.13 μg m −3 , −0.10 μg m −3 ) per year. The average bias increases dramatically after 3.5 years. Further, climate zone is a significant modifier of the association between degradation outcomes and time.

Priyanka deSouza↗

DOE OSTI2023

Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus

Abstract Variational quantum eigensolvers (VQEs) represent a powerful class of hybrid quantum-classical algorithms for computing molecular energies. Various numerical issues exist for these methods, however, including barren plateaus and large numbers of local minima. In this work, we consider the Adaptive, Problem-Tailored Variational Quantum Eiegensolver (ADAPT-VQE) ansätze, and examine how they are impacted by these local minima. We find that while ADAPT-VQE does not remove local minima, the gradient-informed, one-operator-at-a-time circuit construction accomplishes two things: First, it provides an initialization strategy that can yield solutions with over an order of magnitude smaller error compared to random initialization, and which is applicable in situations where chemical intuition cannot help with initialization, i.e., when Hartree-Fock is a poor approximation to the ground state. Second, even if an ADAPT-VQE iteration converges to a local trap at one step, it can still “burrow” toward the exact solution by adding more operators, which preferentially deepens the occupied trap. This same mechanism helps highlight a surprising feature of ADAPT-VQE: It should not suffer optimization problems due to barren plateaus and random initialization. Even if such barren plateaus appear in the parameter landscape, our analysis suggests that ADAPT-VQE avoids such regions by design.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1995

Rapid Numerical Simulation of Viscous Axisymmetric Flow Fields

A two-dimensional Navier-Stokes code has been developed for rapid numerical simulation of axisymmetric flow fields, including flow fields with an azimuthal velocity component. The azimuthal-invariant Navier-Stokes equations in a cylindrical coordinate system are mapped to a general body-fitted coordinate system, with the streamwise viscous terms then neglected by applying the thin-layer approximation. Turbulence effects are modeled using an algebraic model, typically the Baldwin-Lomax turbulence model, although a modified Cebeci-Smith model can also be used. The equations are discretized using central finite differences and solved using a multistage Runge-Kutta algorithm with a spatially varying time step and implicit residual smoothing. Results are presented for calculations of supersonic flow over a waisted body-of-revolution, transonic flow through a normal shock wave in a straight circular duct of constant cross sectional area, swirling supersonic (inviscid) flow through a strong shock in a straight radial duct, and swirling subsonic flow in an annular-to-circular diffuser duct. Comparisons between computed and experimental results are in fair to good agreement, demonstrating that the viscous code can be a useful tool for practical engineering design and analysis work.

Tweedt, Daniel L.↗

NASA NTRS2017

Online Visualization and Value Added Services of MERRA-2 Data at GES DISC

NASA climate reanalysis datasets from MERRA-2, distributed at the Goddard Earth Sciences Data and Information Services Center (GES DISC), have been used in broad research areas, such as climate variations, extreme weather, agriculture, renewable energy, and air quality, etc. The datasets contain numerous variables for atmosphere, land, and ocean, grouped into 95 products. The total archived volume is approximately 337 TB ( approximately 562K files) at the end of October 2017. Due to the large number of products and files, and large data volumes, it may be a challenge for a user to find and download the data of interest. The support team at GES DISC, working closely with the MERRA-2 science team, has created and is continuing to work on value added data services to best meet the needs of a broad user community. This presentation, using aerosol over Asia Monsoon as an example, provides an overview of the MERRA-2 data services at GES DISC, including: How to find the data? How many data access methods are provided? What are the best data access methods for me? How do download the subsetted (parameter, spatial, temporal) data and save in preferred spatial resolution and data format? How to visualize and explore the data online? In addition, we introduce a future online analytic tool designed for supporting application research, focusing on long-term hourly time-series data access and analysis.

Shen, Suhung↗

NASA NTRS1968

Predicted vibration responses of Apollo structure and effects of pressure correlation lengths on response

Progressive wove and reverberant acoustic fields ore often used in the laboratory for qualification testing of aerospace structures that are subjected to unsteady aerodynamic environments which occur during flight through the atmosphere. Acoustic simulation of these in-flight environments i s achieved i f the structural vibration response to acoustic excitation is equivalent, over the frequency range of interest, to the response caused by aerodynamic turbulence. To determine the degree of response simulation that could be expected for such qualification testing of the Apollo Spacecraft, responses of a segment of the Apollo structure were estimated theoretically for both acoustic and flight environments. The vibration analysis presented in this report was performed for the Spacecraft Lunar Module Adaptor; and the three environments treated are turbulence at Mach 1 and Mach 2, a reverberant acoustic field, and a modified acoustic progressive wave field. The progressive wave field is assumed to be generated within a specially designed shroud of sixteen axially oriented ducts which is constructed around and contoured to the external skin of the vehicle. Each duct is open on the side adjacent to the skin and is driven acoustically at one end by an independent noise source, thus allowing for different pressure correlation patterns around the circumference of the vehicle. The purpose of the analysis was to determine the effects of surface pressure correlation lengths on the response characteristics of representative Apollo structure, and to select on this basis, the optimum acoustic environment for structural vibration qualification tests of the Apollo in the Spacecraft Acoustic Laboratory at MSC. The method of analysis employed consists of determining, independently, the space average, mean-square acceleration spectral density for each of the significant modes of vibration of an equivalent cylindrical shell, and then expressing the total structural response as a linear summation of these modal responses. Approximately 570 classical modes of a pinned-end cylinder were used in order to find the spectral response characteristics of the structure throughout the frequency range of 10 - 1,000 Hz. The effective forcing functions or joint acceptances of the various modes of vibration were computed and are presented graphically for each of the pressure excitation environments. A brief development of the response equations used is presented in the report. Space average acceleration response spectra were computed for twelve different cases including aerodynamic turbulence at Mach 1 and Mach 2, reverberant acoustic field, five duct correlation patterns, two cases of an axially damped progressive wave field, and two cases in which the structural damping constant was varied from the expected value. The response spectra were computed and plotted by a high speed digital computer far a flat excitation pressure spectrum; and the response spectra were numerically integrated to give one-third octave bond average responses. A complete set of digital computer programs has been developed for both flat plate and cylindrical shell structures for the above environments, and each requires run times of three minutes or less. Thus, the work presented herein, along with the results, constitutes a practical advancement to the existing state-of-the-art of vibration prediction.

R W White↗

NASA NTRS1989

Space station contamination modeling

Current plans for the operation of Space Station Freedom allow the orbit to decay to approximately an altitude of 200 km before reboosting to approximately 450 km. The Space Station will encounter dramatically increasing ambient and induced environmental effects as the orbit decays. Unfortunately, Shuttle docking, which has been of concern as a high contamination period, will likely occur during the time when the station is in the lowest orbit. The combination of ambient and induced environments along with the presence of the docked Shuttle could cause very severe contamination conditions at the lower orbital altitudes prior to Space Station reboost. The purpose here is to determine the effects on the induced external environment of Space Station Freedom with regard to the proposed changes in altitude. The change in the induced environment will be manifest in several parameters. The ambient density buildup in front of ram facing surfaces will change. The source of such contaminants can be outgassing/offgassing surfaces, leakage from the pressurized modules or experiments, purposeful venting, and thruster firings. The third induced environment parameter with altitude dependence is the glow. In order to determine the altitude dependence of the induced environment parameters, researchers used the integrated Spacecraft Environment Model (ISEM) which was developed for Marshall Space Flight Center. The analysis required numerous ISEM runs. The assumptions and limitations for the ISEM runs are described.

Gordon, T. D.↗

DOE OSTI2021

Quantum phase transitions in long-range interacting hyperuniform spin chains in a transverse field

Hyperuniform states of matter are characterized by anomalous suppression of long-wavelength density fluctuations. While most of the interesting cases of disordered hyperuniformity are provided by complex many-body systems such as liquids or amorphous solids, classical spin chains with certain long-range interactions have been shown to demonstrate the same phenomenon. Such spin-chain systems are ideal models for exploring the effects of quantum mechanics on hyperuniformity. It is well-known that the transverse field Ising model shows a quantum phase transition (QPT) at zero temperature. Under the quantum effects of a transverse magnetic field, classical hyperuniform spin chains are expected to lose their hyperuniformity. High-precision simulations of these cases are complicated because of the presence of highly nontrivial long-range interactions. We perform an extensive analysis of these systems using density matrix renormalization group simulations to study the possibilities of phase transitions and the mechanism by which they lose hyperuniformity. Even for a spin chain of length 30, we see discontinuous changes in properties like the “τ order metric” of the ground state, the measure of hyperuniformity, and the second cumulant of the total magnetization along the x-direction, all suggestive of first-order QPTs. An interesting feature of the phase transitions in these disordered hyperuniform spin chains is that, depending on the parameter values, the presence of a transverse magnetic field may lead remarkably to an increase in the order of the ground state as measured by the “τ order metric,” even if hyperuniformity is lost. Therefore, it would be possible to design materials to target specific novel quantum behaviors in the presence of a transverse magnetic field. Our numerical investigations suggest that these spin chains can show no more than two QPTs. We further analyze the long-range interacting spin chains via the Jordan-Wigner mapping onto a system of spinless fermions, showing that under the pairwise-interaction approximation and a mean-field treatment, there can be at most two quantum phase transitions. Here, based on these numerical and theoretical explorations, we conjecture that for spin chains with long-range pair interactions that have convergent cosine transforms, there can be a maximum of two quantum phase transitions at zero temperature.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

A long short-term memory embedding for hybrid uplifted reduced order models

In this paper, we introduce an uplifted reduced order modeling (UROM) approach through the integration of standard projection based methods with long short-term memory (LSTM) embedding. Our approach has three modeling layers or components. In the first layer, we utilize an intrusive projection approach to model dynamics represented by the largest modes. The second layer consists of an LSTM model to account for residuals beyond this truncation. This closure layer refers to the process of including the residual effect of the discarded modes into the dynamics of the largest scales. However, the feasibility of generating a low rank approximation tails off for higher Kolmogorov n -width systems due to the underlying nonlinear processes. The third uplifting layer, called super-resolution, addresses this limited representation issue by expanding the span into a larger number of modes utilizing the versatility of LSTM. Therefore, our model integrates a physics-based projection model with a memory embedded LSTM closure and an LSTM based super-resolution model. In several applications, we exploit the use of Grassmann manifold to construct UROM for unseen conditions. We performed numerical experiments by using the Burgers and Navier-Stokes equations with quadratic nonlinearity. Finally, our results show robustness of the proposed approach in building reduced order models for parameterized systems and confirm the improved trade-off between accuracy and efficiency.

42 ENGINEERING↗