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All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

PolyPole-1: An accurate numerical algorithm for intra-granular fission gas release

This paper describes the development of a new numerical algorithm (called PolyPole-1) to efficiently solve the equation for intra-granular fission gas release in nuclear fuel. The work was carried out in collaboration with Politecnico di Milano and Institute for Transuranium Elements. The PolyPole-1 algorithms is being implemented in INL's fuels code BISON code as part of BISON's fission gas release model. The transport of fission gas from within the fuel grains to the grain boundaries (intra-granular fission gas release) is a fundamental controlling mechanism of fission gas release and gaseous swelling in nuclear fuel. Hence, accurate numerical solution of the corresponding mathematical problem needs to be included in fission gas behaviour models used in fuel performance codes. Under the assumption of equilibrium between trapping and resolution, the process can be described mathematically by a single diffusion equation for the gas atom concentration in a grain. In this work, we propose a new numerical algorithm (PolyPole-1) to efficiently solve the fission gas diffusion equation in time-varying conditions. The PolyPole-1 algorithm is based on the analytic modal solution of the diffusion equation for constant conditions, with the addition of polynomial corrective terms that embody the information on the deviation from constant conditions. The new algorithm is verified by comparing the results to a finite difference solution over a large number of randomly generated operation histories. Furthermore, comparison to state-of-the-art algorithms used in fuel performance codes demonstrates that the accuracy of the PolyPole-1 solution is superior to other algorithms, with similar computational effort. Finally, the concept of PolyPole-1 may be extended to the solution of the general problem of intra-granular fission gas diffusion during non-equilibrium trapping and resolution, which will be the subject of future work.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

Performance of high-order Godunov-type methods in simulations of astrophysical low Mach number flows

High-order Godunov methods for gas dynamics have become a standard tool for simulating different classes of astrophysical flows. Their accuracy is mostly determined by the spatial interpolant used to reconstruct the pair of Riemann states at cell interfaces and by the Riemann solver that computes the interface fluxes. In most Godunov-type methods, these two steps can be treated independently, so that many different schemes can in principle be built from the same numerical framework. Because astrophysical simulations often test out the limits of what is feasible with the computational resources available, it is essential to find the scheme that produces the numerical solution with the desired accuracy at the lowest computational cost. However, establishing the best combination of numerical options in a Godunov-type method to be used for simulating a complex hydrodynamic problem is a nontrivial task. In fact, formally more accurate schemes do not always outperform simpler and more diffusive methods, especially if sharp gradients are present in the flow. For this work, we used our fully compressible Seven-League Hydro (SLH) code to test the accuracy of six reconstruction methods and three approximate Riemann solvers on two- and three-dimensional (2D and 3D) problems involving subsonic flows only. We considered Mach numbers in the range from 10 −3 to 10 −1 , which are characteristic of many stellar and geophysical flows. In particular, we considered a well-posed, 2D, Kelvin–Helmholtz instability problem and a 3D turbulent convection zone that excites internal gravity waves in an overlying stable layer. Although the different combinations of numerical methods converge to the same solution with increasing grid resolution for most of the quantities analyzed here, we find that (i) there is a spread of almost four orders of magnitude in computational cost per fixed accuracy between the methods tested in this study, with the most performant method being a combination of a low-dissipation Riemann solver and a sextic reconstruction scheme; (ii) the low-dissipation solver always outperforms conventional Riemann solvers on a fixed grid when the reconstruction scheme is kept the same; (iii) in simulations of turbulent flows, increasing the order of spatial reconstruction reduces the characteristic dissipation length scale achieved on a given grid even if the overall scheme is only second order accurate; (iv) reconstruction methods based on slope-limiting techniques tend to generate artificial, high-frequency acoustic waves during the evolution of the flow; and (v) unlimited reconstruction methods introduce oscillations in the thermal stratification near the convective boundary, where the entropy gradient is steep.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Molecular dynamics force-field refinement against quasi-elastic neutron scattering data

Quasi-elastic neutron scattering (QENS) is one of the experimental techniques of choice for probing the dynamics at length and time scales that are also in the realm of full-atom molecular dynamics (MD) simulations. This overlap enables extension of current fitting methods that use time-independent equilibrium measurements to new methods fitting against dynamics data. We present an algorithm that fits simulation-derived incoherent dynamical structure factors against QENS data probing the diffusive dynamics of the system. We showcase the difficulties inherent to this type of fitting problem, namely, the disparity between simulation and experiment environment, as well as limitations in the simulation due to incomplete sampling of phase space. We discuss a methodology to overcome these difficulties and apply it to a set of full-atom MD simulations for the purpose of refining the force-field parameter governing the activation energy of methyl rotation in the octa-methyl polyhedral oligomeric silsesquioxane molecule. Our optimal simulated activation energy agrees with the experimentally derived value up to a 5% difference, well within experimental error. We believe the method will find applicability to other types of diffusive motions and other representation of the systems such as coarse-grain models where empirical fitting is essential. In addition, the refinement method can be extended to the coherent dynamic structure factor with no additional effort.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2002

Dynamics of Quantum Adiabatic Evolution Algorithm for Number Partitioning

We have developed a general technique to study the dynamics of the quantum adiabatic evolution algorithm applied to random combinatorial optimization problems in the asymptotic limit of large problem size n. We use as an example the NP-complete Number Partitioning problem and map the algorithm dynamics to that of an auxiliary quantum spin glass system with the slowly varying Hamiltonian. We use a Green function method to obtain the adiabatic eigenstates and the minimum exitation gap, gmin = O(n2(sup -n/2)), corresponding to the exponential complexity of the algorithm for Number Partitioning. The key element of the analysis is the conditional energy distribution computed for the set of all spin configurations generated from a given (ancestor) configuration by simultaneous flipping of a fixed number of spins. For the problem in question this distribution is shown to depend on the ancestor spin configuration only via a certain parameter related to the energy of the configuration. As the result, the algorithm dynamics can be described in terms of one-dimensional quantum diffusion in the energy space. This effect provides a general limitation of a quantum adiabatic computation in random optimization problems. Analytical results are in agreement with the numerical simulation of the algorithm.

Smelyanskiy, Vadius↗
NASA NTRS2002

Dynamics of Quantum Adiabatic Evolution Algorithm for Number Partitioning

We have developed a general technique to study the dynamics of the quantum adiabatic evolution algorithm applied to random combinatorial optimization problems in the asymptotic limit of large problem size n. We use as an example the NP-complete Number Partitioning problem and map the algorithm dynamics to that of an auxiliary quantum spin glass system with the slowly varying Hamiltonian. We use a Green function method to obtain the adiabatic eigenstates and the minimum excitation gap. g min, = O(n 2(exp -n/2), corresponding to the exponential complexity of the algorithm for Number Partitioning. The key element of the analysis is the conditional energy distribution computed for the set of all spin configurations generated from a given (ancestor) configuration by simultaneous flipping of a fixed number of spins. For the problem in question this distribution is shown to depend on the ancestor spin configuration only via a certain parameter related to 'the energy of the configuration. As the result, the algorithm dynamics can be described in terms of one-dimensional quantum diffusion in the energy space. This effect provides a general limitation of a quantum adiabatic computation in random optimization problems. Analytical results are in agreement with the numerical simulation of the algorithm.

Smelyanskiy, V. N.↗
NASA NTRS1995

Candle flames in microgravity

The candle flame in both normal and microgravity is non-propagating. In microgravity, however, the candle flame is also non-convective where (excepting Stefan flow) pure diffusion is the only transport mode. It also shares many characteristics with another classical problem, that of isolated droplet combustion. Given their qualitatively similar flame shapes and the required heat feedback to condensed-phase fuels, the gas-phase flow and temperature fields should be relatively similar for a droplet and a candle in reduced gravity. Unless the droplet diameter is maintained somehow through non-intrusive replenishment of fuel, the quasi-steady burning characteristics of a droplet can be maintained for only a few seconds. In contrast, the candle flame in microgravity may achieve a nearly steady state over a much longer time and is therefore ideal for examining a number of combustion-related phenomena. In this paper, we examine candle flame behavior in both short-duration and long-duration, quiescent, microgravity environments. Interest in this type of flame, especially 'candle flames in weightlessness', is demonstrated by very frequent public inquiries. The question is usually posed as 'will a candle flame burn in zero gravity', or, 'will a candle burn indefinitely (or steadily) in zero gravity in a large volume of quiescent air'. Intuitive speculation suggests to some that, in the absence of buoyancy, the accumulation of products in the vicinity of the flame will cause flame extinction. The classical theory for droplet combustion with its spherically-shaped diffusion flame, however, shows that steady combustion is possible in the absence of buoyancy if the chemical kinetics are fast enough. Previous experimental studies of candle flames in reduced and microgravity environments showed the flame could survive for at least 5 seconds, but did not reach a steady state in the available test time.

Dietrich, D. L.↗
NASA NTRS1994

Observations of Methane and Ethylene Diffusion Flames Stabilized Around a Blowing Porous Sphere Under Microgravity Conditions

This paper presents the experimental and theoretical results for expanding methane and ethylene diffusion flames in microgravity. A small porous sphere made from a low-density and low-heat-capacity insulating material was used to uniformly supply fuel at a constant rate to the expanding diffusion flame. A theoretical model which includes soot and gas radiation is formulated but only the problem pertaining to the transient expansion of the flame is solved by assuming constant pressure infinitely fast one-step ideal gas reaction and unity Lewis number. This is a first step toward quantifying the effect of soot and gas radiation on these flames. The theoretically calculated expansion rate is in good agreement with the experimental results. Both experimental and theoretical results show that as the flame radius increases, the flame expansion process becomes diffusion controlled and the flame radius grows as gamma t. Theoretical calculations also show that for a constant fuel mass injection rate a quasi-steady state is developed in the region surrounded by the flame and the mass flow rate at any location inside this region equals the mass injection rate.

Atreya, Arvind↗
DOE OSTI2015

Weak Necessary and Sufficient Stochastic Maximum Principle for Markovian Regime-Switching Diffusion Models

In this paper we prove a weak necessary and sufficient maximum principle for Markovian regime switching stochastic optimal control problems. Instead of insisting on the maximum condition of the Hamiltonian, we show that 0 belongs to the sum of Clarke’s generalized gradient of the Hamiltonian and Clarke’s normal cone of the control constraint set at the optimal control. Under a joint concavity condition on the Hamiltonian and a convexity condition on the terminal objective function, the necessary condition becomes sufficient. We give four examples to demonstrate the weak stochastic maximum principle.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Interface learning in fluid dynamics: Statistical inference of closures within micro–macro-coupling models

Many complex multiphysics systems in fluid dynamics involve using solvers with varied levels of approximations in different regions of the computational domain to resolve multiple spatiotemporal scales present in the flow. The accuracy of the solution is governed by how the information is exchanged between these solvers at the interface and several methods have been devised for such coupling problems. In this article, we construct a data-driven model by spatially coupling a microscale lattice Boltzmann method (LBM) solver and macroscale finite difference method (FDM) solver for reaction-diffusion systems. The coupling between the micro-macro solvers has one to many mapping at the interface leading to the interface closure problem, and we propose a statistical inference method based on neural networks to learn this closure relation. The performance of the proposed framework in a bifidelity setting partitioned between the FDM and LBM domain shows its promise for complex systems where analytical relations between micro-macro solvers are not available.

42 ENGINEERING↗
NASA NTRS1998

Global Studies of Molecular Clouds in the Galaxy, the Magellanic Cloud and M31

Over the past five years we have used our extensive CO surveys of the Galaxy and M31 in conjunction with spacecraft observations to address central problems in galactic structure and the astrophysics of molecular clouds. These problems included the nature of the molecular ring and its relation to the spiral arms and central bar, the cosmic ray distribution, the origin of the diffuse X-ray background, the distribution and properties of x-ray sources and supernova remnants, and the Galactic stellar mass distribution. For many of these problems, the nearby spiral M31 provided an important complementary perspective.

Thaddeus, Patrick↗
NASA NTRS1999

Global Studies of Molecular Clouds in the Galaxy, The Magellanic Clouds, and M31

Over the course of this grant we used various spacecraft surveys of the Galaxy and M31 in conjunction with our extensive CO spectral line surveys to address central problems in galactic structure and the astrophysics of molecular clouds. These problems included the nature of the molecular ring and its relation to the spiral arms and central bar, the cosmic ray distribution, the origin of the diffuse X-ray background, the distribution and properties of x-ray sources and supernova remnants, and the Galactic stellar mass distribution. For many of these problems, the nearby spiral M31 provided an important complementary perspective. Our CO surveys of GMCs (Galactic Molecular Clouds) were crucial for interpreting Galactic continuum surveys from satellites such as GRO (Gamma Ray Observatory), ROSAT (Roentgen Satellite), IRAS (Infrared Astronomy Satellite), and COBE (Cosmic Background Explorer Satellite) because they provided the missing dimension of velocity or kinematic distance. GMCs are a well-defined and widespread population of objects whose velocities we could readily measure throughout the Galaxy. Through various emission and absorption mechanisms involving their gas, dust, or associated Population I objects, GMCs modulate the galactic emission in virtually every major wavelength band. Furthermore, the visibility. of GMCs at so many wavelengths provided various methods of resolving the kinematic distance ambiguity for these objects in the inner Galaxy. Summaries of our accomplishments in each of the major wavelength bands discussed in our original proposal are given

Thaddeus, Patrick↗
DOE OSTI2016

Current transport mechanisms in mercury cadmium telluride diode

This paper reports the results of modelling of the current-voltage characteristics (I-V) of a planar mid-wave Mercury Cadmium Telluride photodiode in a gate controlled diode experiment. It is reported that the diode exhibits nearly ideal I-V characteristics under the optimum surface potential leading to the minimal surface leakage current. Deviations from the optimum surface potential lead to non ideal I–V characteristics, indicating a strong relationship between the ideality factor of the diode with its surface leakage current. Diode's I–V characteristics have been modelled over a range of gate voltages from −9 V to −2 V. This range of gate voltages includes accumulation, flat band, and depletion and inversion conditions below the gate structure of the diode. It is shown that the I–V characteristics of the diode can be very well described by (i) thermal diffusion current, (ii) ohmic shunt current, (iii) photo-current due to background illumination, and (iv) excess current that grows by the process of avalanche multiplication in the gate voltage range from −3 V to −5 V that corresponds to the optimum surface potential. Outside the optimum gate voltage range, the origin of the excess current of the diode is associated with its high surface leakage currents. It is reported that the ohmic shunt current model applies to small surface leakage currents. The higher surface leakage currents exhibit a nonlinear shunt behaviour. It is also shown that the observed zero-bias dynamic resistance of the diode over the entire gate voltage range is the sum of ohmic shunt resistance and estimated zero-bias dynamic resistance of the diode from its thermal saturation current.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

An Efficient Numerical Algorithm for Solving Data Driven Feedback Control Problems

The goal of this paper is to solve a class of stochastic optimal control problems numerically, in which the state process is governed by an Itô type stochastic differential equation with control process entering both in the drift and the diffusion, and is observed partially. The optimal control of feedback form is determined based on the available observational data. In this work, we call this type of control problems the data driven feedback control. The computational framework that we introduce to solve such type of problems aims to find the best estimate for the optimal control as a conditional expectation given the observational information. To make our method feasible in providing timely feedback to the controlled system from data, we develop an efficient stochastic optimization algorithm to implement our computational framework.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1952

Study of the Pressure Rise Across Shock Waves Required to Separate Laminar and Turbulent Boundary Layers

Results are presented of a dimensional study and an experimental investigation of the pressure rise across a shock wave which causes separation of the boundary layer on a flat plate. The experimental part of the investigation was conducted at a Mach number of 3.03 for a Reynolds number range of 2 x 10 (sup) 6 to 19 x 10 (sup) 6. The available experimental data are compared with the predictions of the present study, and the significance of the results obtained is discussed relative to certain practical design problems.

FLOW, SUPERSONIC↗
DOE OSTI2017

Detecting inter-aquifer leakage in areas with limited data using hydraulics and multiple environmental tracers, including {sup 4}He, {sup 36}Cl/Cl, {sup 14}C and {sup 87}Sr/{sup 86}Sr

The investigation of regionally extensive groundwater systems in remote areas is hindered by a shortage of data due to a sparse observation network, which limits our understanding of the hydrogeological processes in arid regions. The study used a multidisciplinary approach to determine hydraulic connectivity between the Great Artesian Basin (GAB) and the underlying Arckaringa Basin in the desert region of Central Australia. In order to manage the impacts of groundwater abstraction from the Arckaringa Basin, it is vital to understand its connectivity with the GAB (upper aquifer), as the latter supports local pastoral stations and groundwater-dependent springs with unique endemic flora and fauna. The study is based on the collation of available geological information, a detailed analysis of hydraulic data, and data on environmental tracers. Enhanced inter-aquifer leakage in the centre of the study area was identified, as well as recharge to the GAB from ephemeral rivers and waterholes. Throughout the rest of the study area, inter-aquifer leakage is likely controlled by diffuse inter-aquifer leakage, but the coarse spatial resolution means that the presence of additional enhanced inter-aquifer leakage sites cannot be excluded. This study makes the case that a multi-tracer approach along with groundwater hydraulics and geology provides a tool-set to investigate enhanced inter-aquifer leakage even in a groundwater basin with a paucity of data. A particular problem encountered in this study was the ambiguous interpretation of different age tracers, which is attributed to diffusive transport across flow paths caused by low recharge rates.

58 GEOSCIENCES↗
DOE OSTI2014

Particle acceleration at quasi-perpendicular shock waves: Theory and observations at 1 AU

The injection of particles into the diffusive shock acceleration mechanism at highly perpendicular (where θ {sub Bn} > 70°) interplanetary shocks is investigated. This extends the previous study of Neergaard Parker and Zank which focused on the injection problem at quasi-parallel interplanetary shocks. We use observations at 1 AU to construct upstream Maxwellian and κ-distributions that are then diffusively accelerated by the shock, thus yielding the downstream accelerated particle distribution. We compare the theoretical accelerated particle distribution to observations at 1 AU using Advanced Composition Explorer data. We classify our results for quasi-perpendicular shocks into three subcategories: those with ratios of the theoretical spectral index to observed power law of >1, ∼ 1, and <1, and compare the magnetic power spectral density plots of these categories. We find that in general the assumed upstream particle distribution that best fits the energetic particle observations is best represented by a κ-distribution, with κ = 4. The magnetic field fluctuations were representative of quasi-perpendicular shocks and showed no particular bias toward our spectral ratio subcategories. The subcategory with spectral ratio <0.9 yielded the largest injection energies for all groups. In all but two of the cases in this study, there were enough particles in the solar wind thermal core to account for the accelerated distribution, thereby giving a lower limit to the required injection energy needed to diffusively accelerate particles at a quasi-perpendicular interplanetary shock. In the remaining two cases, an additional population of particles was required to match the appropriate amplitude of the spectral index. For these cases, we used a low energy (1-50 keV) v {sup –5} spectrum advocated by Fisk and Gloeckler.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Conditional diffusion machine-learning framework for mapping valence electron distribution from convergent beam electron diffraction

Quantitative convergent beam electron diffraction (CBED) enables determination of aspherical valence electron distributions through refinement of low-order structure factors, which are highly sensitive to chemical bonding and charge density variations. However, conventional quantitative CBED (QCBED) requires solving a highly nonlinear inverse problem with many coupled parameters, and computationally intensive dynamical diffraction calculations, making it time-consuming and difficult to apply to complex systems. More broadly, reconstructing charge density and orbital electron distribution from diffraction data has long been a central challenge in both x-ray and electron crystallography. Here, in this study, we introduce an artificial-intelligence (AI)-based framework that replaces traditional refinement with a data-driven inverse solver. Using a large synthetic CBED dataset generated by Bloch-wave simulations, we train a conditional diffusion model to directly infer crystal structural parameters and multipole density formalism parameters, and hence valence electron distributions, from CBED patterns alone. By learning from forward simulations across realistic parameter space, the model effectively solves the inverse problem. Compared with direct regression approaches, the diffusion-based framework provides posterior parameter distributions for rigorous uncertainty quantification while preserving quantitative fidelity and reducing analysis time by orders of magnitude. By eliminating the need for external single-crystal x-ray diffraction data and complex nonlinear refinement, this approach enables practical, high-throughput, and in situ quantitative CBED, enabling real-time mapping of valence electron distributions and their correlation with functional responses in quantum and energy materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2017

Electric-field noise from carbon-adatom diffusion on a Au(110) surface: First-principles calculations and experiments

The decoherence of trapped-ion quantum bits due to heating of their motional modes is a fundamental science and engineering problem. This heating is attributed to electric-field noise arising from processes on the trap-electrode surfaces. In this work, we address the source of this noise by focusing on the diffusion of carbon-containing adsorbates on the surface of Au(110). We show by detailed scanned probe microscopy and density functional theory how the carbon adatom diffusion on the gold surface changes the energy landscape, and how the adatom dipole moment varies with the diffusive motion. Lastly, a simple model for the diffusion noise, which varies quadratically with the variation of the dipole moment, qualitatively reproduces the measured noise spectrum, and the estimate of the noise spectral density is in accord with measured values.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗