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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Shock melting and the hcp-bcc phase boundary of Mg under dynamic loading

The high-temperature and high-pressure response of magnesium has been investigated through shock-release experiments performed up to shock melting. The longitudinal and bulk sound speeds of Mg are reported along the Hugoniot from 25 to 56 GPa and used to determine the elastic properties and Grüneisen parameter. The hexagonal close-packed (hcp)–body-centered cubic (bcc) phase transition is marked by a reduction in the determined shear wave speed. Thermal softening is observed to begin between 40 and 44 GPa, with incipient melt at 55.5 GPa, in close agreement with previous diffraction measurements under laser shock loading. Examination of the release profiles showed that two different responses were observed, depending on the peak stress. When plotted in a stress-energy phase diagram, the two responses are observed to form separate lines that intersect the static hcp-bcc phase transition and incipient melt. The results indicate that the hcp-bcc transition occurs on the Hugoniot at 28.4 GPa and place the hcp-bcc-liquid triple point ~20 GPa. In conclusion, a multiphase equation of state is developed which places the melt boundary below the previously reported static measurements.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Stochastic Price Generation for Evaluating Wholesale Electricity Market Bidding Strategies

This work presents a novel method for generating electricity price scenarios from statistical properties of past electricity prices using a hybrid statistical and reduced-form stochastic model. Previous work in applying stochastic differential equations (SDE) to model electricity prices has focused on daily average prices. To extend stochastic price generation methods to hourly or sub-hourly pricing, we address several weaknesses in the state-of-the-art: (1) we replace the mean-reversion component of the SDE with an ARIMA process that is better able to characterize the daily and weekly trends; (2) we extend the price-spike, or jump process to account for conditional probabilities of price spikes occurring in consecutive time steps by replacing the traditional Poisson process for modeling jumps with a generalized point process model inspired by brain neuron models; and (3) we replace the traditional method of estimating spike intensity with empirical variance with a Markov process based on observed price spike intensity transitions. The method is demonstrated with electricity prices from the US ERCOT market and a use-case example is provided for bidding an energy storage unit into the day-ahead and real-time energy markets of ERCOT using stochastic optimization methods. Results show that the the synthetic price model out performs a (naive) persistence forecast model by resulting in 24% to 47% more in profits over 168 simulated days.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2016

A Poisson method application to the assessment of the earthquake hazard in the North Anatolian Fault Zone, Turkey

North Anatolian Fault (NAF) is one from the most important strike-slip fault zones in the world and located among regions in the highest seismic activity. The NAFZ observed very large earthquakes from the past to present. The aim of this study; the important parameters of Gutenberg-Richter relationship (a and b values) estimated and this parameters taking into account, earthquakes were examined in the between years 1900-2015 for 10 different seismic source regions in the NAFZ. After that estimated occurrence probabilities and return periods of occurring earthquakes in fault zone in the next years, and is being assessed with Poisson method the earthquake hazard of the NAFZ. The Region 2 were observed the largest earthquakes for the only historical period and hasn’t been observed large earthquake for the instrumental period in this region. Two historical earthquakes (1766, M{sub S}=7.3 and 1897, M{sub S}=7.0) are included for Region 2 (Marmara Region) where a large earthquake is expected in the next years. The 10 different seismic source regions are determined the relationships between the cumulative number-magnitude which estimated a and b parameters with the equation of LogN=a-bM in the Gutenberg-Richter. A homogenous earthquake catalog for M{sub S} magnitude which is equal or larger than 4.0 is used for the time period between 1900 and 2015. The database of catalog used in the study has been created from International Seismological Center (ISC) and Boğazici University Kandilli observation and earthquake research institute (KOERI). The earthquake data were obtained until from 1900 to 1974 from KOERI and ISC until from 1974 to 2015 from KOERI. The probabilities of the earthquake occurring are estimated for the next 10, 20, 30, 40, 50, 60, 70, 80, 90 and 100 years in the 10 different seismic source regions. The highest earthquake occur probabilities in 10 different seismic source regions in the next years estimated that the region Tokat-Erzincan (Region 9) %99 with an earthquake occur probability for magnitude 6.5 which the return period 24.7 year, %92 with an earthquake occur probability for magnitude 7 which the return period 39.1 year, %80 with an earthquake occur probability for magnitude 7.5 which the return period 62.1 year, %64 with an earthquake occur probability for magnitude 8 which the return period 98.5 year. For the Marmara Region (Region 2) in the next 100 year estimated that %89 with an earthquake occur probability for magnitude 6 which the return period 44.9 year, %45 with an earthquake occur probability for magnitude 6.5 which the return period 87 year, %45 with an earthquake occur probability for magnitude 7 which the return period 168.6 year.

58 GEOSCIENCES↗
DOE OSTI2017

Magnetohydrodynamic motion of a two-fluid plasma

Here, the two-fluid Maxwell system couples frictionless electron and ion fluids via Maxwell’s equations. When the frequencies of light waves, Langmuir waves, and single-particle cyclotron motion are scaled to be asymptotically large, the two-fluid Maxwell system becomes a fast-slow dynamical system. This fast-slow system admits a formally-exact single-fluid closure that may be computed systematically with any desired order of accuracy through the use of a functional partial differential equation. In the leading order approximation, the closure reproduces magnetohydrodynamics (MHD). Higher order truncations of the closure give an infinite hierarchy of extended MHD models that allow for arbitrary mass ratio, as well as perturbative deviations from charge neutrality. The closure is interpreted geometrically as an invariant slow manifold in the infinite-dimensional two-fluid phase space, on which two-fluid motions are free of high-frequency oscillations. This perspective shows that the full closure inherits a Hamiltonian structure from two-fluid theory. By employing infinite-dimensional Lie transforms, the Poisson bracket for the all-orders closure may be obtained in closed form. Thus, conservative truncations of the single-fluid closure may be obtained by simply truncating the single-fluid Hamiltonian. Moreover, the closed-form expression for the all-orders bracket gives explicit expressions for a number of the full closure’s conservation laws. Notably, the full closure, as well as any of its Hamiltonian truncations, admits a pair of independent circulation invariants.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Evaluation of pressure reconstruction techniques for Model Order Reduction in incompressible convective heat transfer

This paper compares pressure reconstruction strategies in Model Order Reduction for incompressible flows with convective heat transfer. The Navier-Stokes equation are reduced along with the passive scalar transport equation for the temperature using the POD-Galerkin technique. Six different pressure reconstruction methods are evaluated, two of which are novel to the best of the authors’ knowledge. Accurate pressure reconstruction is key to avoid error buildup in when solving for the conservation of linear momentum at the reduced level. The six approaches are compared using Direct Numerical Simulations of convective heat exchange processes in a 3D Backward Facing Step with a heated cylinder. Additionally, when comparing time-averaged metrics, we observe that the reconstruction methods that approximate the reduced pressure field using techniques borrowed from full order models (mechanical analogy, pressure Poisson, and velocity supremizers) yield higher errors than the methods that seek to stabilize the reduced systems (reduced residual stabilization, artificial divergence, and Uzawa operator).

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
NASA NTRS2017

Preliminary Analysis of Two Years of the Massive Collision Monitoring Activity

It is hypothesized that the interactions between many of the most massive derelicts in low Earth orbit are more frequent than modeled by the traditional combination of kinetic theory of gases and Poisson probability distribution function. This is suggested by the fact that there are clusters of derelicts where members' inclinations are nearly identical and their apogees/perigees overlap significantly resulting in periodic synchronization of the objects' orbits. In order to address this proposition, an experiment was designed and conducted over the last two years. Results from this monitoring and characterization experiment are presented with implications for proposed debris remediation strategies. Four separate clusters of massive derelicts were examined that are centered around 775km, 850km, 975km, and 1500km, respectively. In aggregate, the constituents of these clusters contain around 500 objects and about 800,000kg of mass; this equates to a third of all derelict mass in LEO. Preliminary analysis indicates that encounter rates over this time period for these objects are greater than is estimated by traditional techniques. Hypothesized dependencies between latitude of encounter, relative velocity, frequency of encounters, inclination, and differential semi-major axis were established and verified. This experiment also identified specific repeatable cluster dynamics that may reduce the cost/risk and enhance the effectiveness of debris remediation activities and also enable new operational debris remediation options.

McKnight, Darren↗
NASA NTRS1987

Cell model and elastic moduli of disordered solids - Low temperature limit

The cell theory has been previously employed to compute the equation of state of a disordered condensed system. It is now generalized to include anisotropic stresses. The condition of affine deformation is adopted, transforming an orginally spherical into an ellipsoidal cell. With a Lennard-Jones n-m potential between nonbonded centers, the formal expression for the deformational free energy is derived. It is to be evaluated in the limit of the linear elastic range. Since the bulk modulus in this limit is already known, it is convenient to consider a uniaxial deformation. To begin with, restrictions are made to the low-temperature limit in the absence of entropy contributions. Young's modulus and Poisson's ratio then follow.

Peng, S. T. J.↗
DOE OSTI2016

Exploring the high-pressure behavior of superhard tungsten tetraboride

In this work, we examine the high-pressure behavior of superhard material candidate WB{sub 4} using high-pressure synchrotron x-ray diffraction in a diamond anvil cell up to 58.4 GPa. The zero-pressure bulk modulus, K{sub 0}, obtained from fitting the pressure-volume data using the second-order Birch-Murnaghan equation of state is 326 {+-} 3 GPa. A reversible, discontinuous change in slope in the c/a ratio is further observed at {approx}42 GPa, suggesting that lattice softening occurs in the c direction above this pressure. This softening is not observed in other superhard transition metal borides such as ReB{sub 2} compressed to similar pressures. Speculation on the possible relationship between this softening and the orientation of boron-boron bonds in the c direction in the WB{sub 4} structure is included. Finally, the shear and Young's modulus values are calculated using an isotropic model based on the measured bulk modulus and an estimated Poisson's ratio for WB{sub 4}.

Xie, Miao↗
NASA NTRS2023

Estimating the Subsolar Magnetopause Position from Soft X-Ray Images Using a Low-Pass Image Filter

The Lunar Environment heliospheric X-ray Imager (LEXI) and Solar wind Magnetosphere Ionosphere Link Explorer (SMILE) missions will image the Earth’s dayside magnetopause and cusps in soft X-rays after their respective launches in the near future, to specify global magnetic reconnection modes for varying solar wind conditions. To support the success of these scientific missions, it is critical to develop techniques that extract the magnetopause locations from the observed soft X-ray images. In this research, we introduce a new geometric equation that calculates the subsolar magnetopause position ( R s ) from a satellite position, the look direction of the instrument, and the angle at which the X-ray emission is maximized. Two assumptions are used in this method: (1) The look direction where soft X-ray emissions are maximized lies tangent to the magnetopause, and (2) the magnetopause surface near the subsolar point is almost spherical and thus R s is nearly equal to the radius of the magnetopause curvature. We create synthetic soft X-ray images by using the Open Geospace General Circulation Model (OpenGGCM) global magnetohydrodynamic model, the galactic background, the instrument point spread function, and Poisson noise. We then apply the fast Fourier transform and Gaussian low-pass filters to the synthetic images to remove noise and obtain accurate look angles for the soft X-ray peaks. From the filtered images, we calculate R 2 and its accuracy for different LEXI locations, look directions, and solar wind densities by using the OpenGGCM subsolar magnetopause location as ground truth. Our method estimates R s with an accuracy of <0.3 R E when the solar wind density exceeds >10 cm -3 . The accuracy improves for greater solar wind densities and during southward interplanetary magnetic fields. The method captures the magnetopause motion during southward interplanetary magnetic field turnings. Consequently, the technique will enable quantitative analysis of the magnetopause motion and help reveal the dayside reconnection modes for dynamic solar wind conditions. This technique will support the LEXI and SMILE missions in achieving their scientific objectives.

Hyangpyo Kim↗
DOE OSTI2020

Hot electrons between cold walls

We consider electron cooling in a collisionless plasma slab between two cold and freely emitting walls. Numerical calculations suggest a counterintuitive behavior of this system: the cooling rate slows down and eventually stops, leaving the system with a significant fraction of its initial thermal energy. Analytical treatment within the Vlasov–Poisson model reveals a set of steady-states with a two-component distribution of electrons: the primary electrons trapped within the potential wells and the secondary electrons forming the counterstreaming beams. We show that such steady-states are linearly stable with respect to one-dimensional perturbations. Establishment of a particular steady-state depends on initial conditions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Bringing Trimmed Serendipity Methods to Computational Practice in Firedrake

We present an implementation of the trimmed serendipity finite element family, using the open-source finite element package Firedrake. The new elements can be used seamlessly within the software suite for problems requiring H 1 , H (curl), or H (div)-conforming elements on meshes of squares or cubes. To test how well trimmed serendipity elements perform in comparison to traditional tensor product elements, we perform a sequence of numerical experiments including the primal Poisson, mixed Poisson, and Maxwell cavity eigenvalue problems. Overall, we find that the trimmed serendipity elements converge, as expected, at the same rate as the respective tensor product elements, while being able to offer significant savings in the time or memory required to solve certain problems.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1985

Vibrations of circular orthotropic plates in affine space

The vibration of an initially compressed plate having a circular geometry and orthotropy is examined in an affine space. The classical linear plate theory and Hamilton's principle are employed. The equations of motion of the plate are particularly simple in the chosen affine space, permitting a free-vibration study of the entire spectrum of composite materials with polar orthotropy. Approximate but very accurate standing-wave-type mode shapes are used in solving the essentially double eigenvalue problem to determine the effects of midplane forces on the vibration frequencies of the plate. The results indicate that the affine-space frequency increases with increasing stiffness ratio but decreases with increasing midplane compression. It is also discovered that, contrary to the trends observed for rectangular geometry and orthotropy by Oyibo (1981), Brunelle (1982), and Brunelle and Oyibo (1983), the affine-space frequency increases with increasing generalized Poisson's ratio.

Oyibo, G. A.↗
NASA NTRS1992

Stress concentrations for straight-shank and countersunk holes in plates subjected to tension, bending, and pin loading

A three dimensional stress concentration analysis was conducted on straight shank and countersunk (rivet) holes in a large plate subjected to various loading conditions. Three dimensional finite element analysis were performed with 20 node isoparametric elements. The plate material was assumed to be linear elastic and isotropic, with a Poisson ratio of 0.3. Stress concentration along the bore of the hole were computed for several ratios of hole radius to plate thickness (0.1 to 2.5) and ratios of countersink depth to plate thickness (0.25 to 1). The countersink angles were varied from 80 to 100 degrees in some typical cases, but the angle was held constant at 100 degrees for most cases. For straight shank holes, three types of loading were considered: remote tension, remote bending, and wedge loading in the hole. Results for remote tension and wedge loading were used to estimate stress concentration for simulated rivet in pin loading. For countersunk holes only remote tension and bending were considered. Based on the finite element results, stress concentration equations were developed. Whenever possible, the present results were compared with other numerical solutions and experimental results from the literature.

Shivakumar, K. N.↗
DOE OSTI2025

Elastic constants in monocrystalline tungsten under quasi-hydrostatic pressures to 11.3 GPa

Compressional (P) and shear (S) wave velocities of tungsten single crystals along the [100] and [110] directions were measured using ultrasonic interferometry at room temperature up to 11.3 GPa. Least-squares fitting of $V$$^{[100]}_{P}$, $V$$^{[100]}_{S}$, $V$$^{[110]}_{P}$, and pressure to finite strain (FS) equations yields the elastic constants: C 11 = 523.5(5) GPa, C 12 = 205.1(32) GPa, and C 44 = 160.8(4) GPa, along with their respective pressure derivatives: $C$$^{′}_{11}$ = 6.20(2), $C$$^{′}_{12}$ = 3.35(1), and $C$$^{′}_{44}$ = 1.65(6). Using the Voigt–Reuss–Hill approximation, the elastic moduli were derived as K S0 = 311.2(22) GPa and G 0 = 160.2(7)GPa, along with their respective pressure derivatives: $K$$^{′}_{S0}$ = 4.30(4) and $G$$^{′}_{0}$ = 1.56(1). The Debye temperature of tungsten was determined to be 380.7(8) K, showing good agreement with previous calorimetric measurements. The elastic anisotropy increases slightly from 1.01(1) at ambient pressure to 1.03(1) at 11.3 GPa, suggesting that tungsten remains nearly isotropic under compression. Poisson's ratio slightly increased from 0.281(3) to 0.288(3) with pressure. Additionally, Pugh's ratio decreased from 0.512(4) to 0.494(4), while Pettifor's ratio increased from 0.148(10) to 0.175(10) as pressure reached 11.3 GPa. These results suggest that tungsten is weakly ductile compared to the critical thresholds for ductile behavior (i.e., Pugh's ratio <0.6 and Pettifor's ratio >0, indicating ductile behavior), but that its ductility increases marginally under pressure.

Wang, Ran [Stony Brook University, NY (United Stat↗
DOE OSTI2017

Summer Proceedings 2016: The Center for Computing Research at Sandia National Laboratories

Solving sparse linear systems from the discretization of elliptic partial differential equations (PDEs) is an important building block in many engineering applications. Sparse direct solvers can solve general linear systems, but are usually slower and use much more memory than effective iterative solvers. To overcome these two disadvantages, a hierarchical solver (LoRaSp) based on H2-matrices was introduced in [22]. Here, we have developed a parallel version of the algorithm in LoRaSp to solve large sparse matrices on distributed memory machines. On a single processor, the factorization time of our parallel solver scales almost linearly with the problem size for three-dimensional problems, as opposed to the quadratic scalability of many existing sparse direct solvers. Moreover, our solver leads to almost constant numbers of iterations, when used as a preconditioner for Poisson problems. On more than one processor, our algorithm has significant speedups compared to sequential runs. With this parallel algorithm, we are able to solve large problems much faster than many existing packages as demonstrated by the numerical experiments.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Space charge induced beam instability in periodic focusing channel

The transverse evolution of the envelope of an intense, unbunched ion beam in a linear periodic transport channel can be modeled for the approximation of linear self-fields by the Kapchinskij-Vladimirskij envelope equation. The envelope mismatched modes, or the second order even mode [I. Hofmann, Phys. Rew. E 57, 4713 (1998)], are the lowest order of resonance leading to collective instability that the designer should avoid, which suggests that an accelerator system should be established in the parameter region where the zero beam current phase advance σ{sub 0} less than 90°. In this paper, we systemically studied the resonance mechanisms which result in confluent resonance in quadrupole Focusing-Defocusing (FD) channel and parametric resonance in solenoid channel. We propose that the mismatch modes cannot be exactly separated in FD channel; if one mode is excited, there is always some contribution of the other. To verify the influence of the confluent resonance and parametric resonance, the 2D Poissons solver in the self-consistent particle-in-cell simulation code TOPOPIC is adopted to study the beam evolution in both channels. Our simulations results show that the emittance show significant growth both in the confluent resonance stop band and parametric resonance stop band. The influences of the higher order of resonance are also discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Transport in Stochastic Media with Random Chord Length Distributions

Thermal radiation transport computations in binary Markovian random mixtures rely almost exclusively on the Levermore-Pomraning (LP) model which is obtained by applying a heuristic closure to the ensemble averaged random medium transport equation. The validity of this model has been extensively tested by comparing numerical results over a broad parameter range (material types and mixing parameters) against benchmark solutions in planar geometry. The conditions under which the LP-model provides useful results and when it breaks down are now well established, but work to date has been largely restricted to homogeneous mixing statistics, i.e., the mean chord lengths of both materials are taken to be spatially constant. In recent work, this limitation was relaxed by allowing the mean chord lengths and, in a consistent fashion, the volume fractions in the LP-model to vary spatially and in a follow-up investigation benchmark solutions were obtained by ensemble averaging results over material realizations sampled from a nonhomogeneous Poisson process (NHPP). Numerical experiments in rod geometry with specifically linear and quadratic spatial dependence of chord lengths showed that the material averaged radiation intensities vary nonmonotonically with depth into the medium, in stark contrast to solutions obtained assuming uniform chord lengths. Moreover, depending on the local optical thickness and strength of scattering, the LP-model results showed locally more nuanced deviations from the benchmark solutions than was the case with constant chord lengths. These limited numerical investigations highlight the nontrivial qualitative and quantitative consequences of nonhomogeneous mixing statistics, in particular that closure approximations may not be uniformly valid or invalid over the problem domain.

42 ENGINEERING↗
DOE OSTI2018

Experimental constraints on the sound velocities of cementite Fe 3 C to core pressures

Sound velocities of cementite Fe 3 C have been measured up to 1.5 Mbar and at 300 K in a diamond anvil cell using the nuclear resonant inelastic X-ray scattering (NRIXS) technique. From the partial phonon density of states (pDOS) and equation of state (EOS) of Fe 3 C, we derived its elastic parameters including shear modulus, compressional (V-p) and shear-wave (V-s) velocities to core pressures. A pressure-induced spin-pairing transition in the powdered Fe3C sample was found to occur gradually between 10 and 50 GPa by the X-ray Emission Spectroscopy (XES) measurements. Following the completion of the spin-pairing transition, the V p and V s of low-spin Fe 3 C increased with pressure at a markedly lower rate than its high-spin counterpart. Our results suggest that the incorporation of carbon in solid iron to form iron carbide phases, Fe 3 C and Fe 7 C 3 , could effectively lower the V s but respectively raise the Poisson's ratio by 0.05 and 0.07 to approach the seismically observed values for the Earth's inner core. In conclusion, the comparison with the preliminary reference Earth model (PREM) implies that an inner core composition containing iron and its carbon-rich alloys can satisfactorily explain the observed seismic properties of the inner core.

58 GEOSCIENCES↗