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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Quantifying uncertainty in analysis of shockless dynamic compression experiments on platinum. I. Inverse Lagrangian analysis

Absolute measurements of solid-material compressibility by magnetically driven shockless dynamic compression experiments to multi-megabar pressures have the potential to greatly improve the accuracy and precision of pressure calibration standards for use in diamond anvil cell experiments. Here, to this end, we apply characteristics-based inverse Lagrangian analysis (ILA) to 11 sets of ramp-compression data on pure platinum (Pt) metal and then reduce the resulting weighted-mean stress–strain curve to the principal isentrope and room-temperature isotherm using simple models for yield stress and Grüneisen parameter. We introduce several improvements to methods for ILA and quasi-isentrope reduction, the latter including calculation of corrections in wave speed instead of stress and pressure to render results largely independent of initial yield stress while enforcing thermodynamic consistency near zero pressure. More importantly, we quantify in detail the propagation of experimental uncertainty through ILA and model uncertainty through quasi-isentrope reduction, considering all potential sources of error except the electrode and window material models used in ILA. Compared to previous approaches, we find larger uncertainty in longitudinal stress. Monte Carlo analysis demonstrates that uncertainty in the yield-stress model constitutes by far the largest contribution to uncertainty in quasi-isentrope reduction corrections. We present a new room-temperature isotherm for Pt up to 444 GPa, with 1-sigma uncertainty at that pressure of just under ±1.2%; the latter is about a factor of three smaller than uncertainty previously reported for multi-megabar ramp-compression experiments on Pt. The result is well represented by a Vinet-form compression curve with (isothermal) bulk modulus K 0 = 270.3 ± 3.8 GPa, pressure derivative K$^{'}_{0}$= 5.66 ± 0.10, and correlation coefficient $R_{K_{0},K^{'}_{0}}$= –0.843.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Lagrangian analysis for turbulent transport in variable-density turbulence

In this report Lagrangian analysis of materially conserved scalars is applied to the problem of turbulent transport in variable-density flows. The consequences of an additional material conserved quantity, the density, is generally not acknowledged and leads to significant and meaningfully different expressions for turbulent transport in the moment equations. The formal Lagrangian analysis produces gradient transport expressions substantially different from those obtained by the physically intuitive “argument by analogy” method used in computational models. Various intuitive arguments, in Favre and Reynolds averaged settings, are contrasted to the formal Lagrangian results. Using expressions from the formal analysis, we derive consistent gradient transport closures for the turbulent transport terms that appear in the first- and second-order Favre moment equations. Results for coupled multispecies turbulent transport are given. The analysis is limited to variable-density turbulence in which the dilatation of the fluctuating velocity is small. The results are applicable to turbulent combustion and to stellar convection problems in which the density fluctuations are on the order of the mean density.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

A Lagrangian analysis of pockets of open cells over the southeastern Pacific

Abstract. Pockets of open cells (POCs) have been shown to develop within closed-cell stratocumulus (StCu), and a large body of evidence suggests that the development of POCs result from changes in small-scale processes internal to the boundary layer rather than large-scale forcings. Precipitation is widely viewed as a key process important to POC development and maintenance. In this study, GOES-16 satellite observations are used in conjunction with MERRA-2 winds to track and compare the microphysical and environmental evolution of two populations of closed-cell StCu selected by visual inspection over the southeastern Pacific Ocean: one group that transitions to POCs and another comparison group (CLOSED) that does not. The high spatiotemporal resolution of the new GOES-16 data allows for a detailed examination of the temporal evolution of POCs in this region. We find that POCs tend to develop near the coast, last tens of hours, are larger than 104 km2, and often (88 % of cases) do not re-close before they exit the StCu deck. Most POCs are observed to form at night and tend to exit the StCu during the day when the StCu is contracting in area. Relative to the CLOSED trajectories, POCs have systematically larger effective radii, lower cloud drop number concentrations, a comparable conditional in-cloud liquid water path, and a higher frequency of more intense precipitation. Meanwhile, no systematic environmental differences other than boundary layer height are observed between POC and CLOSED trajectories. Interestingly, there are no differences in reanalysis aerosol optical depth between both sets of trajectories, which may lead one to the interpretation that differences in aerosol concentrations are not influencing POC development or resulting in a large number that re-close. However, this largely depends on the reanalysis treatment of aerosol–cloud interactions, and the product used in this study has no explicit handling of these important processes. These results support the consensus view regarding the importance of precipitation on the formation and maintenance of POCs and demonstrate the utility of modern geostationary remote sensing data in evaluating the POC life cycle.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Quantifying uncertainty in analysis of shockless dynamic compression experiments on platinum. II. Bayesian model calibration

Dynamic shockless compression experiments provide the ability to explore material behavior at extreme pressures but relatively low temperatures. Typically, the data from these types of experiments are interpreted through an analytic method called Lagrangian analysis. Here, in this work, alternative analysis methods are explored using modern statistical methods. Specifically, Bayesian model calibration is applied to a new set of platinum data shocklessly compressed to 570 GPa. Several platinum equation-of-state models are evaluated, including traditional parametric forms as well as a novel non-parametric model concept. The results are compared to those in Paper I obtained by inverse Lagrangian analysis. The comparisons suggest that Bayesian calibration is not only a viable framework for precise quantification of the compression path, but also reveals insights pertaining to trade-offs surrounding model form selection, sensitivities of the relevant experimental uncertainties, and assumptions and limitations within Lagrangian analysis. The non-parametric model method, in particular, is found to give precise unbiased results and is expected to be useful over a wide range of applications. The calibration results in estimates of the platinum principal isentrope over the full range of experimental pressures to a standard error of 1.6%, which extends the results from Paper I while maintaining the high precision required for the platinum pressure standard.

Brown, Justin Lee↗
DOE OSTI2019

Non-iterative characteristics analysis for high-pressure ramp loading

Here in the canonical ramp compression experiment, a smoothly increasing load is applied to the surface of the sample, and the particle velocity history is measured at two or more different distances into the sample, at interfaces where the surface of the sample can be probed. The velocity histories are used to deduce a stress-density relation, usually using iterative Lagrangian analysis to account for the perturbing effect of the impedance mismatch at the interface. In that technique, a stress-density relation is assumed in order to correct for the perturbation and is adjusted until it becomes consistent with the deduced stress-density relation. This process is subject to the usual difficulties of nonlinear optimization, such as the existence of local minima (sensitivity to the initial guess), possible failure to converge, and relatively large computational effort. We show that, by considering the interaction of successive characteristics reaching a free surface, the stress-density relation can be deduced directly by recursion rather than iteration. This calculation is orders of magnitude faster than iterative analysis and does not require an initial guess. Direct recursion may be less suitable for very noisy data, but it was robust when applied to trial data. The stress-density relation deduced was identical to the result from iterative Lagrangian analysis.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Pressure Gain, Stability, and Operability of Methane/Syngas Based RDEs Under Steady and Transient Conditions (Final Project Report)

The scope of this work addresses key issues associated with losses associated with the detonation wave and other processes internal to the RDE operation, as well as it develops modeling tools for the evaluation of these losses and exhaust emissions in RDEs. The main challenge in studying RDEs is that RDE performance is highly reliant on the specifics of the design so much so that simple/canonical systems alone cannot provide useful engineering information, but practical RDE designs are sufficiently complex and involve extreme operational environments that detailed access either experimentally (laser diagnostics, for instance) or computationally (direct numerical simulations) are as yet to become practical. To overcome this challenge, we have conducted a combined experimental/simulation/analytical study investigating key phenomena that control the characteristics of operation of RDEs. As a result, the study has developed tools and methods that can be used to evaluate performance and design approaches using reduced-physics models, with the assumptions validated using detailed simulations, and the model prediction tested using experimental observations. The specific objectives of the research were: (1) Develop and demonstrate a low-loss fully axial injection concept, taking advantage of stratification effects to alter the detonation structure and position the wave favorably within the combustor; (2) Obtain stability and operability characteristics of an RDE across operating conditions to aid in the development of operability and performance rules for the operations of other systems; and (3) Develop quantitative metrics for performance gain as well as quantitative description of the loss mechanisms through a combination of diagnostics development, reduced-order modeling, and detailed simulations. The work conducted here has made contribution on design of low-loss inlets that has broad application within the power generation industry for use with pressure gain combustion. The operability and stability of different designs, while focusing on axial air inlet designs, has been analyzed. The effect of nozzle and injection conditions was studied. Models and simulations of exhaust emissions, focusing on NOx emission has been developed and used to investigate how operation of the RDE affect NOx production using Lagrangian analysis of RDE simulations. This work has built on previous programs, with the goal of further understanding operation of RDEs and elevate the readiness of design consideration. In addition, a suite of diagnostic and modeling tools have been developed to obtain quantitative metrics on performance based on measurements, which can be readily transferred to other experimental configurations.

08 HYDROGEN↗
DOE OSTI2025

Ergodic Lagrangian dynamics in a superhero universe

We present a fictional scenario that, while undeniably whimsical, provides the foundation for a unique exercise in extended problem solving, physics analysis, and quantitative model development. Starting with the foundational premise of the Wild Cards shared-world superhero universe, we demonstrate how a variety of concepts appropriate to the advanced undergraduate level—ergodicity, functional analysis, Lagrangian mechanics, and the ever-important simplifying approximation—can be combined into a rich, coherent mathematical model. The goal of this case study is to develop a useful pedagogical exercise in exploring an open-ended research question that presents, at first glance, no clear path forward. Being both eclectic and lengthy, this exercise offers a unique way for students to apply their core physics and mathematics education. It is perhaps best used within a senior honors seminar or within a brief (e.g., January term) elective class.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Phase transitions in Zr at sub-nanosecond time scales

Here solid-solid phase transitions are investigated in Zr thin films using shock compression induced by a short laser pulse (<1 ns). Shock wave profiles are measured at free surfaces for films of different thicknesses (a few micrometers) using chirped-pulse line velocimetry with 10 ps time resolution. Experiments are performed at pressures up to ~50 GPa, which is sufficient to reach the ω and β phases under equilibrium conditions. The shock wave structures are analyzed using a general Lagrangian analysis method, which allows for the calculation of stress–strain paths and assessments of phase transition behavior. In agreement with recent short laser pulse experiments using ultra-fast x-ray diffraction, we do not find any clear evidence of the α–ω transition, though this would be expected from the phase diagram. Instead, we infer a direct transformation to a metastable β-phase at lower shock pressures (<20 GPa) and equilibrium β at higher pressures. Through the velocimetry analysis, we find α–β transformation onset times of less than ~100 ps and completion times of less than ~200 ps.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Temperature response and brine availability to heated boreholes in bedded salt

Abstract There is a growing need for disposal of high‐level nuclear waste. To reduce uncertainty associated with brine availability to repository excavations in salt formations, a collaboration between Sandia, Los Alamos, and Lawrence Berkeley National Laboratories is performing a series of borehole‐scale coupled process tests. Here, we report on the first round of the Brine Availability Test in Salt (BATS) project, a “shakedown” experiment called Phase 1s. Experimental testing included placing a resistive heater, a 260‐W radiative heater, and a 750‐W radiative heater within previously drilled horizontal boreholes at the Waste Isolation Pilot Plant (WIPP) while monitoring temperature and water inflow. The experiments successfully achieved the targeted temperature of 120 °C when using the 750‐W radiative heater. Simulations using FEHM (Finite Element Heat and Mass transfer code) and TOUGH‐FLAC (Transport Of Unsaturated Groundwater and Heat–Fast Lagrangian Analysis of Continua) were able to accurately predict the coupled thermo–hydro–mechanical–chemical response of salt, matching the observed temperature and brine production. Due to the extremely low permeability of salt, these systems take many years to reach steady state when perturbed by mining activities. Long‐term numerical simulations are used to develop the initial pressure and saturation conditions. The inclusion of a damaged rock zone with higher permeability around the borehole also affects the saturation and pressure distributions and plays an important role in dissipating the potential for thermal pressurization. Knowledge gained from this round of experimentation and simulation will be used to conduct the next BATS project experiment in new boreholes at WIPP.

58 GEOSCIENCES↗
DOE OSTI2022

Reduced scale stripline platform to extend accessible pressures on the Z machine: Shockless compression of platinum to 650 GPa

Reaching astrophysically relevant high energy density (HED) material states in the laboratory is an ongoing effort at multiple experimental facilities. We have developed a new dynamic compression platform for the Z Pulsed Power Facility that allows for sample sizes 100s of [Formula: see text]m in thickness that accommodate multiple grains in order to fully capture bulk properties, such as material strength. A pair of experiments compressed platinum (Pt) to HED conditions and conventional inverse Lagrangian analysis as well as a recent Bayesian calibration technique were used to determine the principal isentrope to 650 GPa with density uncertainties of <2%. These low uncertainties are calculated for single sample experiments, presenting the possibility of even smaller experimental uncertainties with multiple samples the platform allows. Our new platform extends the accessible Pt ramp pressures achievable on the Z machine to over 80% of the pressure recently achieved using the National Ignition Facility planar Hohlraum platform. This new capability, the next generation evolution of the stripline platform, was made possible by advancements in both our understanding of the Z pulsed power driver and our overall magnetohydrodynamic modeling capabilities.

Porwitzky, Andrew↗
DOE OSTI2022

Towards sharp error analysis of extended Lagrangian molecular dynamics

The extended Lagrangian molecular dynamics (XLMD) method provides a useful framework for reducing the computational cost of a class of molecular dynamics simulations with constrained latent variables. The XLMD method relaxes the constraints by introducing a fictitious mass ε for the latent variables and solving a set of singularly perturbed ordinary differential equations. While favorable numerical performance of XLMD has been demonstrated in several different contexts in the past decade, mathematical analysis of the method remains scarce. Here, we propose the first error analysis of the XLMD method in the context of a classical polarizable force field model. While the dynamics with respect to the atomic degrees of freedom are general and nonlinear, the key mathematical simplification of the polarizable force field model is that the constraints on the latent variables are given by a linear system of equations. We prove that when the initial value of the latent variables is compatible in a sense that we define, XLMD converges as the fictitious mass ε is made small with $\mathscr{O}$(ε) error for the atomic degrees of freedom and with $\mathscr{O}$($\sqrt{ε}$) error for the latent variables, when the dimension of the latent variable d' is 1. Furthermore, when the initial value of the latent variables is improved to be optimally compatible in a certain sense, we prove that the convergence rate can be improved to $\mathscr{O}$(ε) for the latent variables as well. Numerical results verify that both estimates are sharp not only for d'=1, but also for arbitrary d'. In the setting of general d', we do obtain convergence, but with the non-sharp rate of $\mathscr{O}$($\sqrt{ε}$) for both the atomic and latent variables.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2025

Stability analysis of the Eulerian–Lagrangian finite volume methods for nonlinear hyperbolic equations in one space dimension

In this paper, we construct a novel Eulerian–Lagrangian finite volume (ELFV) method for nonlinear scalar hyperbolic equations in one space dimension. It is well known that the exact solutions to such problems may contain shocks though the initial conditions are smooth, and direct numerical methods may suffer from restricted time step sizes. To relieve the restriction, we propose an ELFV method, where the space-time domain was separated by the partition lines originated from the cell interfaces whose slopes are obtained following the Rakine–Hugoniot junmp condition. Unfortunately, to avoid the intersection of the partition lines, the time step sizes are still limited. To fix this gap, we detect effective troubled cells (ETCs) and carefully design the influence region of each ETC, within which the partitioned space-time regions are merged together to form a new one. Then with the new partition of the space-time domain, we theoretically prove that the proposed first-order scheme with Euler forward time discretization is total-variation-diminishing and maximum-principle-preserving with at least twice larger time step constraints than the classical first order Eulerian method for Burgers’ equation. Numerical experiments verify the optimality of the designed time step sizes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Meshfree simulation and experimental validation of extreme thermomechanical conditions in friction stir extrusion

Abstract Friction stir extrusion (FSE) is a novel solid-phase processing technique that consolidates and extrudes metal powders, flakes, chips, or billets into high-performance parts by plastic deformation, which has the potential to save substantial processing time and energy. Currently, most studies on FSE are experimental and only a few numerical models have been developed to explain and predict the complex physics of the process. In this work, a meshfree simulation framework based on smoothed particle hydrodynamics (SPH) was developed for FSE. Unlike traditional grid-based methods, SPH is a Lagrangian particle-based method that can handle severe material deformations, capture moving interfaces and surfaces, and monitor the field variable histories explicitly without complicated tracking schemes. These aspects of SPH make it attractive for the FSE process, where in situ evolution of field variables is difficult to observe experimentally. To this end, a 3-D, fully thermomechanically coupled SPH model was developed to simulate the FSE of aluminum wires. The developed model was thoroughly validated by comparing the numerically predicted material flow, strain, temperature history, and extrusion force with experimental results for a certain set of process parameters. The validated SPH model can serve as an effective tool to predict and better understand the extreme thermomechanical conditions during the FSE process.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2022

Demonstrating the viability of Lagrangian in situ reduction on supercomputers

Performing exploratory analysis and visualization of large-scale time-varying computational science applications is challenging due to inaccuracies that arise from under-resolved data. In recent years, Lagrangian representations of the vector field computed using in situ processing are being increasingly researched and have emerged as a potential solution to enable exploration. However, prior works have offered limited estimates of the encumbrance on the simulation code as they consider “theoretical” in situ environments. Further, the effectiveness of this approach varies based on the nature of the vector field, benefitting from an in-depth investigation for each application area. With this study, an extended version of Sane et al. (2021), we contribute an evaluation of Lagrangian analysis viability and efficacy for simulation codes executing at scale on a supercomputer. We investigated previously unexplored cosmology and seismology applications as well as conducted a performance benchmarking study by using a hydrodynamics mini-application targeting exascale computing. Here, to inform encumbrance, we integrated in situ infrastructure with simulation codes, and evaluated Lagrangian in situ reduction in representative homogeneous and heterogeneous HPC environments. To inform post hoc accuracy, we conducted a statistical analysis across a range of spatiotemporal configurations as well as a qualitative evaluation. Additionally, our study contributes cost estimates for distributed-memory post hoc reconstruction. In all, we demonstrate viability for each application — data reduction to less than 1% of the total data via Lagrangian representations, while maintaining accurate reconstruction and requiring under 10% of total execution time in over 90% of our experiments.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Developing a Lagrangian Frame Transformation on Satellite Data to Study Cloud Microphysical Transitions in Arctic Marine Cold Air Outbreaks

Abstract Arctic marine cold air outbreaks (CAOs) generate distinct and dynamic cloud regimes due to intense air‐sea interactions. To understand the temporal evolution of CAO cloud properties and compare different CAO events, a Lagrangian perspective is particularly useful. We developed a novel technique that enables the conversion of inherently Eulerian satellite data into a Lagrangian framework, combining the broad spatiotemporal coverage of satellite observations with the advantages of Lagrangian tracking. This technique was applied to eight CAO cases associated with a recent field campaign. Our results reveal a striking contrast among the cases in terms of cloud‐top phase transitions, providing new insights into the evolution of CAO cloud properties.

Lagrangian analysis↗
DOE OSTI2022

Insights on sources and formation mechanisms of liquid-bearing clouds over MOSAiC examined from a Lagrangian framework

Understanding Arctic stratiform liquid-bearing cloud life cycles and properly representing these life cycles in models is crucial for evaluations of cloud feedbacks as well as the faithfulness of climate projections for this rapidly warming region. Examination of cloud life cycles typically requires analyses of cloud evolution and origins on short time scales, on the order of hours to several days. Measurements from the recent Multidisciplinary drifting Observatory for the Study of Arctic Climate (MOSAiC) expedition provide a unique view of the current state of the central Arctic over an annual cycle. Here, we use the MOSAiC radiosonde measurements to detect liquid-bearing cloud layers over full atmospheric columns and to examine the cloud-generating air masses’ properties. We perform 5-day (120 h) back-trajectory calculations for every detected cloud and cluster them using a unique set of variables extracted from these trajectories informed by ERA5 reanalysis data. This clustering method enables us to separate between the air mass source regions such as ice-covered Arctic and midlatitude open water. We find that moisture intrusions into the central Arctic typically result in multilayer liquid-bearing cloud structures and that more than half of multilayer profiles include overlying liquid-bearing clouds originating in different types of air masses. Finally, we conclude that Arctic cloud formation via prolonged radiative cooling of elevated stable subsaturated air masses circulating over the Arctic can occur frequently (up to 20% of detected clouds in the sounding data set) and may lead to a significant impact of ensuing clouds on the surface energy budget, including net surface warming in some cases.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Analysis of DESI × DES using the Lagrangian effective theory of LSS

In this work we use Lagrangian perturbation theory to analyze the harmonic space galaxy clustering signal of the Bright Galaxy Survey (BGS) and luminous red galaxies (LRGs) targeted by the dark energy spectroscopic instrument (DESI), combined with the galaxy-galaxy lensing signal measured around these galaxies using Dark Energy Survey Year 3 source galaxies. The BGS and LRG galaxies are extremely well characterized by DESI spectroscopy and, as a result, lens galaxy redshift uncertainty and photometric systematics contribute negligibly to the error budget of our “2 × 2-point” analysis. On the modeling side, this work represents the first application of the SPINOSAURUS code, implementing an effective field theory model for galaxy intrinsic alignments, and we additionally introduce a new scheme ( MAIAR ) for marginalizing over the large uncertainties in the redshift evolution of the intrinsic alignment signal. Furthermore, this is the first application of a hybrid effective field theory model for galaxy bias based on the A emulus 𝜈 simulations. Our main result is a measurement of the amplitude of the lensing signal, 𝑆 8 = 𝜎 8 ⁢(Ω 𝑚 /0.3) 0.5 = 0.85⁢0$^{+0.042}_{−0.050}$, consistent with values of this parameter derived from the primary cosmic microwave background. This constraint is artificially improved by a factor of 51% if we assume a more standard, but restrictive parametrization for the redshift evolution and sample dependence of the intrinsic alignment signal, and 63% if we additionally assume the nonlinear alignment model. Furthermore, we show that when fixing the cosmological model to the best-fit values from Planck PR4 there is > 5⁢𝜎 evidence for a deviation of the evolution of the intrinsic alignment signal from the functional form that is usually assumed in cosmic shear and galaxy-galaxy lensing studies.

79 ASTRONOMY AND ASTROPHYSICS↗