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NASA NTRS1991

Fragmentation in stellar collapse

A three dimensional Cartesian code was developed to model molecular cloud collapse and protostellar formation. The basic Eulerian scheme employs spatially second-order accurate, finite difference methods to advance the fluid variables in time. The hydrodynamic equations governing the collapse include the effects of self-gravity, rotation, and radiative transfer. Supplementary equations include Poisson's equation which relates the gravitational potential to the density distribution and a mean intensity equation derived with the Eddington approximation for radiative transfer. The gas pressures and internal energies are determined from equations of state derived for a molecular cloud composed of hydrogen, helium, and heavier elements.

Myhill, E. M.↗

NASA NTRS1987

Coupling finite element and spectral methods: First results

A Poisson equation on a rectangular domain is solved by coupling two methods: the domain is divided in two squares, a finite element approximation is used on the first square and a spectral discretization is used on the second one. Two kinds of matching conditions on the interface are presented and compared. In both cases, error estimates are proved.

Bernardi, Christine↗

NASA NTRS1990

Coupling finite element and spectral methods - First results

Bernardi, Christine↗

NASA NTRS1991

Statistical-mechanical selection of the shapes of disk galaxies

A new method is proposed for selecting steady state shapes of disk galaxies as 'most probable states' of a large number of stars, given only the total energy and total angular momentum. A partial differential equation is derived for the mean gravitational potential; it is closely related to the 'sinh-Poisson' equation for the mean-field description of a line vortex system or electrostatic guiding-center plasma. A 'water bag' approximation to the distribution function for bound stars renders the equation analytically tractable, but accurate solution of it may require numerical integration, in view of its general nonlinearity.

Montgomery, David↗

DOE OSTI2020

Technical Performance of Refractory Liners for Molten Chloride Salt Thermal Energy Storage Systems

A chloride-based molten-salt system that uses a ternary blend of MgCl2/KCl/NaCl is investigated to provide higher temperature thermal energy storage capability. Despite higher thermal stability, molten chlorides present several unique challenges, including the design of internal refractory-ceramic liners to prevent the corrosion and thermal stress of alloy tank shells. This work discusses issues and potential solutions related to containment of molten chloride salt, specifically the optimization of the refractory material at the molten salt interface (hot face). The down-selected hot face candidate limits permeation of salt through the material and forms a highly stable secondary surface phase in equilibrium with the molten salt. A mortar is created using the corrosion resistant hot face brick. Brick and mortar composite are subjected to mechanical stress/strain analysis, in order to calculate composite material properties and better inform thermomechanical models. The U.S. Department of Energy Generation 3 (DOE Gen3) program seeks to develop higher efficiency CSP plants that can provide cost-competitive, flexible power in the U.S. electric grid. The proposed Gen3 Liquid Pathway CSP plant closely resembles the configuration of current nitrate salt power towers with two-tank storage (Gen2). The differences between Gen2 and Gen3 include the types of compatible materials used in salt storage tank construction. Stainless steel loses strength at Gen3 temperatures, and although nickel superalloys would be capable of withstanding sustained high temperatures, these materials are prohibitively expensive at scale. Uninsulated tank shells also pose a significant risk as common steels are highly susceptible to chemical attack from molten chloride salt. To address these concerns, refractory-ceramic based containment materials are proposed to line the inside of the hot and cold storage tanks. In doing so, stainless or carbon steel shells may be used in construction depending on the level of insulation provided. The composition of the internal liner requires careful consideration to maximize the efficacy of multiple parameters including corrosion resistance, strength at operating temperature, durability, and cost. This is particularly true for the material at the interface with the salt, known as the "hot face", which is responsible for protecting the insulating layers between the tank shell and the hot face brick layer. The molten salt in this system is superheated over 300 °C above its freeze temperature. Therefore, unlike other industrial processes which use refractory-lined vessels, it is not expected that a freeze plane will develop in the hot face. Therefore, the hot face must be designed to withstand chemical corrosion and inhibit permeation of molten salt into the insulating layers. A down selection was performed to identify a hot face candidate best equipped to maintain thermal, mechanical, and chemical integrity when exposed to molten salt over extended periods of time. Long-duration chemical capability experiments were conducted with the down selected hot face refractory fully immersed in molten chloride salt for up to 3000 hours. The average salt penetration does not exceed 100 microns. When extrapolated to 20 and 30 years of continuous exposure, the expected salt penetration depth is approximately 2.0 mm and 2.9 mm, respectively. A magnesium-rich secondary phases develops at the salt/refractory interface. X-ray diffraction identifies the material as forsterite (Mg2SiO4), which is reported to form synthetically in molten chloride salt solutions. These results suggest the selected hot face will adequately inhibit salt permeation. While there is optimism that the hot face brick will inhibit salt permeation, mortar joints are typically the weakest point of a refractory brick liner. From a thermochemical perspective, differing thermal expansion coefficients may result in the mortar and brick to grow independent of each other, creating gaps through which molten salt can penetrate. To address this issue, NREL has developed an in-house mortar composed of the down selected hot face brick that has been shown to be compatible with the salt. Compressive stress/strain analyses have been performed on the brick/ mortar composites to generate stress/strain curves. Modulus of elasticity and Poisson's ratio of the composite may be calculated from the stress/strain curves, in order to provide more representative data to finite element mechanical models for accurate approximation of stress on the tank shell and the amount of thermal expansion expected within the tank liner.

41 EE - Solar Energy Technologies Office (EE-4S)↗

DOE OSTI2021

A weighted Shifted Boundary Method for free surface flow problems

The Shifted Boundary Method (SBM) belongs to the class of unfitted (or immersed, or embedded) finite element methods and was recently introduced for the Poisson, linear advection/diffusion, Stokes, Navier-Stokes, acoustics, and shallow-water equations. By reformulating the original boundary value problem over a surrogate (approximate) computational domain, the SBM avoids integration over cut cells and the associated problematic issues regarding numerical stability and matrix conditioning. Accuracy is maintained by modifying the original boundary conditions using Taylor expansions. Hence the name of the method, that shifts the location and values of the boundary conditions. In this article, we extend the SBM to the simulation of incompressible Navier-Stokes flows with moving free-surfaces, by appropriately weighting its variational form with the elemental volume fraction of active fluid. This approach prevents spurious pressure oscillations in time, which would otherwise be produced if the total active fluid volume were to change abruptly over a time step. In fact, the proposed weighted SBM method induces small mass (i.e., volume) conservation errors, which converge quadratically in the case of piecewise-linear finite element interpolations, as the grid is refined. Finally, we present an extensive set of two- and three-dimensional tests to demonstrate the robustness and accuracy of the method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Towards Automated Reasoning Chains for Verification of LLM-Generated Scientific Code

With the rise of Large Language Model (LLM) generated code, including in domains like scientific computing, ensuring not only syntactical, but also mathematical correctness, has become a critical task. Traditional formal methods approaches often struggle with the ambiguity of floating-point code, and full symbolic execution is extremely costly and limited. We propose a chain-of-reasoning approach that iteratively lifts basic semantics from code into the SPIRAL system and then establishes numerical equivalency to the desired mathematical operation. Here, we leverage the ample mathematical knowledge already formalized in SPIRAL to enable the system to recognize not just different implementations of the same algorithm but fully separate approaches to solving the given problem. The chain establishes tight error bounds on the output of given code with respect to the true continuous solution it approximates, quantifying all sources of error. We demonstrate this approach by establishing the correctness of a pseudospectral solver for a simple 1-dimensional Poisson problem.

Oschatz, Quentin [Carnegie Mellon University,Pitts↗

DOE OSTI2023

Voltage-Dependent First-Principles Simulation of Insertion of Chloride Ions into Al/Al 2 O 3 Interfaces Using the Quantum Continuum Approximation

Experiments have shown that pitting corrosion can develop in aluminum surfaces at potentials > − 0.5 V relative to the standard hydrogen electrode (SHE). Until recently, the onset of pitting corrosion in aluminum has not been rigorously explored at an atomistic scale because of the difficulty of incorporating a voltage into density functional theory (DFT) calculations. We introduce the Quantum Continuum Approximation (QCA) which self-consistently couples explicit DFT calculations of the metal-insulator and insulator-solution interfaces to continuum Poisson-Boltzmann electrostatic distributions describing the bulk of the insulating region. By decreasing the number of atoms necessary to explicitly simulate with DFT by an order of magnitude, QCA makes the first-principles prediction of the voltage of realistic electrochemical interfaces feasible. After developing this technique, we apply QCA to predict the formation energy of chloride atoms inserting into oxygen vacancies in Al(111)/α-Al 2 O 3 (0001) interfaces as a function of applied voltage. We predict that chloride insertion is only favorable in systems with a grain boundary in the Al 2 O 3 for voltages > − 0.2 V (SHE). Here our results roughly agree with the experimentally demonstrated onset of corrosion, demonstrating QCA's utility in modeling realistic electrochemical systems at reasonable computational cost.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1990

Average reflected power from a one-dimensional slab of discrete scatterers

Reflection from a one-dimensional random medium of discrete scatterers is considered. The discrete scattering medium is modeled by a Poisson impulse process with concentration lambda. By employing the Markov property of the Poisson impulse process, an exact functional integro-differential equation of the Kolmogorov-Feller type is found for the average reflected power. Approximate solutions to this equation are obtained by regular perturbation and two variable expansion techniques in the limit of small lambda. The regular perturbation results is valid for small slab thicknesses, while the two-variable result is uniformly valid for any thickness. The two-variable result shows that as the slab size becomes infinite all of the incident power is reflected on the average.

Saatchi, Sasan S.↗

DOE OSTI2024

Reassessment of Birch's Law on hcp‐Fe From Ultrasonic Sound Velocity Measurement and Implications on the Velocity Profiles of Earth's Inner Core

Here, we performed in situ X-ray diffraction and ultrasonic sound velocity measurements on hcp-Fe up to 15 GPa, 873 K in a multi-anvil apparatus. The elastic moduli and their pressure and temperature derivatives were determined by fitting the velocity and density data to the third-order finite strain equations, yielding K S0 = 169.0(57) GPa, K$^{′}_{S0}$ = 5.4(6), (∂K S /∂T) P = −0.031(3) GPa/K, G 0 = 104.5(27) GPa, G$^{′}_{0}$ = 1.7(2), (∂G/∂T) P = −0.060(2) GPa/K. Within the experimental P-T range, we find significant temperature effect on the density-velocity (ρ − V P or S ) relations and caution the use of the temperature-independent Birch's law for extrapolation to core conditions. Furthermore, temperature-induced velocity decrease is more significant in V S than in V P , offering a possible explanation for the high Poisson's ratio in the core. Extrapolations based on our results together with previous experimental data suggest that V P of hcp-Fe aligns with PREM at Earth's core conditions, while Vs and density are approximately 10% and 2.7% higher than PREM, respectively.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Near-zero photon bioimaging by fusing deep learning and ultralow-light microscopy

Enhancing the reliability and reproducibility of optical microscopy by reducing specimen irradiance continues to be an important biotechnology target. As irradiance levels are reduced, however, the particle nature of light is heightened, giving rise to Poisson noise, or photon sparsity that restricts only a few (0.5%) image pixels to comprise a photon. Photon sparsity can be addressed by collecting approximately 200 photons per pixel; this, however, requires long acquisitions and, as such, suboptimal imaging rates. Here, we introduce near-zero photon bioimaging, a method that operates at kHz rates and 10,000-fold lower irradiance than standard microscopy. To achieve this level of performance, we uniquely combined a judiciously designed epifluorescence microscope enabling ultralow background levels and AI that learns to reconstruct biological images from as low as 0.01 photons per pixel. We demonstrate that near-zero photon bioimaging captures the structure of multicellular and subcellular features with high fidelity, including features represented by nearly zero photons. Beyond optical microscopy, the near-zero photon bioimaging paradigm can be applied in remote sensing, covert applications, and biomedical imaging that utilize damaging or quantum light.

AI↗

NASA NTRS1990

Quadrature imposition of compatibility conditions in Chebyshev methods

This paper handles a problem encountered in the solution by way of Chebyshev spectral collocation discretization of the Poisson equation with homogeneous Neumann boundary conditions. When pseudospectral Chebyshev methodology is utilized to discretize the partial differential equation these integrals have to be approximated by an appropriate quadrature formula. The correct quadrature formula is developed for these problems, taking into account the degree of the polynomials involved. It is shown that this formula leads to a well-conditioned Chebyshev approximation to the differential equations and that the compatibility condition is automatically satisfied.

Gottlieb, D.↗

NASA NTRS2001

An Estimation of the Likelihood of Significant Eruptions During 2000-2009 Using Poisson Statistics on Two-Point Moving Averages of the Volcanic Time Series

Since 1750, the number of cataclysmic volcanic eruptions (volcanic explosivity index (VEI)>=4) per decade spans 2-11, with 96 percent located in the tropics and extra-tropical Northern Hemisphere. A two-point moving average of the volcanic time series has higher values since the 1860's than before, being 8.00 in the 1910's (the highest value) and 6.50 in the 1980's, the highest since the 1910's peak. Because of the usual behavior of the first difference of the two-point moving averages, one infers that its value for the 1990's will measure approximately 6.50 +/- 1, implying that approximately 7 +/- 4 cataclysmic volcanic eruptions should be expected during the present decade (2000-2009). Because cataclysmic volcanic eruptions (especially those having VEI>=5) nearly always have been associated with short-term episodes of global cooling, the occurrence of even one might confuse our ability to assess the effects of global warming. Poisson probability distributions reveal that the probability of one or more events with a VEI>=4 within the next ten years is >99 percent. It is approximately 49 percent for an event with a VEI>=5, and 18 percent for an event with a VEI>=6. Hence, the likelihood that a climatically significant volcanic eruption will occur within the next ten years appears reasonably high.

Wilson, Robert M.↗

NASA NTRS2010

Maximum Likelihood Time-of-Arrival Estimation of Optical Pulses via Photon-Counting Photodetectors

Many optical imaging, ranging, and communications systems rely on the estimation of the arrival time of an optical pulse. Recently, such systems have been increasingly employing photon-counting photodetector technology, which changes the statistics of the observed photocurrent. This requires time-of-arrival estimators to be developed and their performances characterized. The statistics of the output of an ideal photodetector, which are well modeled as a Poisson point process, were considered. An analytical model was developed for the mean-square error of the maximum likelihood (ML) estimator, demonstrating two phenomena that cause deviations from the minimum achievable error at low signal power. An approximation was derived to the threshold at which the ML estimator essentially fails to provide better than a random guess of the pulse arrival time. Comparing the analytic model performance predictions to those obtained via simulations, it was verified that the model accurately predicts the ML performance over all regimes considered. There is little prior art that attempts to understand the fundamental limitations to time-of-arrival estimation from Poisson statistics. This work establishes both a simple mathematical description of the error behavior, and the associated physical processes that yield this behavior. Previous work on mean-square error characterization for ML estimators has predominantly focused on additive Gaussian noise. This work demonstrates that the discrete nature of the Poisson noise process leads to a distinctly different error behavior.

Erkmen, Baris I.↗

NASA NTRS2004

Electron Density and Two-Channel Neutron Emission Measurements in Steady-State Spherical Inertial-Electrostatically Confined Plasmas, with Review of the 1-D Kinetic Model

Electron density measurements have been made in steady-state plasmas in a spherical inertial electrostatic confinement (IEC) discharge using microwave interferometry. Plasma cores interior to two cathodes, having diameters of 15 and 23 cm, respectively, were probed over a transverse range of 10 cm with a spatial resolution of about 1.4 cm for buffer gas pressures from 0.2 to 6 Pa in argon and deuterium. The transverse profiles are generally flat, in some cases with eccentric symmetric minima, and give mean densities of from approx. = 0.4 to 7x 10(exp 10)/cu cm, the density generally increasing with the neutral gas pressure. Numerical solutions of the 1-D Poisson equation for EC plasmas are reviewed and energy distribution functions are identified which give flat transverse profiles. These functions are used with the plasma approximation to obtain solutions which also give densities consistent with the measurements, and a double potential well solution is obtained which has minima qualitatively similar to those observed. Explicit consideration is given to the compatibility of the solutions interior and exterior to the cathode, and to grid transparency. Deuterium fusion neutron emission rates were also measured and found to be isotropic, to within the measurement error, over two simultaneous directions. Anisotropy was observed in residual emissions during operation with non-fusing hydrogen-1. The deuterium rates are consistent with predictions from the model.

Dobson, Chris C.↗

NASA NTRS2004

Electron Density and Two-Channel Neutron Emission Measurements in Steady-State Spherical Inertial-Electrostatically Confined Plasmas, with Review of the One-Dimensional Kinetic Model

Electron density measurements have been made in steady-state plasmas in a spherical inertial electrostatic confinement (IEC) discharge using microwave interferometry. Plasma cores interior to two cathodes, having diameters of 15 and 23 cm, respectively, were probed over a transverse range of 10 cm with a spatial resolution of about 1.4 cm for buffer gas pressures from 0.2 to 6 Pa in argon and deuterium. The transverse profiles are generally flat, in some cases with eccentric symmetric minima, and give mean densities of from approx. = 0.4 to 7 x 10(exp 10)/cu cm, the density generally increasing with the neutral gas pressure. Numerical solutions of the one-dimensional Poisson equation for IEC plasmas are reviewed and energy distribution functions are identified which give flat transverse profiles. These functions are used with the plasma approximation to obtain solutions which also give densities consistent with the measurements, and a double potential well solution is obtained which has minima qualitatively similar to those observed. Explicit consideration is given to the compatibility of the solutions interior and exterior to the cathode, and to grid transparency. Deuterium fusion neutron emission rates were also measured and found to be isotropic, to within the measurement error, over two simultaneous directions. Anisotropy was observed in residual emissions during operation with nonfusing hydrogen- 1. The deuterium rates are consistent with predictions from the model.

Dobson, Chris C.↗

NASA NTRS1973

On the effect of orthotropy in a cracked cylindrical shell

A pressurized cylindrical shell containing a longitudinal crack is considered. The shear modulus of the sheet may be evaluated from the measured Young's moduli and the Poisson's ratios rather than being an independent material constant. Two examples, one for a mildly orthotropic (titanium) and the other for a strongly orthotropic (graphite) material approximately satisfying the condition of special orthotropy are given. The results show that the stress intensity factors are rather strongly dependent on the degree of orthotropy.

Erdogan, F.↗

NASA NTRS1974

On the effect of orthotropy in a cracked cylindrical shell

A pressurized cylindrical shell containing a longitudinal crack is considered. It is assumed that the material has a special orthotropy - namely, that the shear modulus of the sheet may be evaluated from the measured Young's moduli and the Poisson's ratios and is not an independent material constant. Two examples, one for a mildly orthotropic (titanium) and the other for a strongly orthotropic (graphite) material approximately satisfying the condition of special orthotropy are given. The results show that the stress intensity factors are rather strongly dependent on the degree of orthotropy.

Erdogan, F.↗