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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Multi-level Monte Carlo methods in chemical applications with Lennard-Jones potentials and other landscapes with isolated singularities

We describe and compare outcomes of various Multi-Level Monte Carlo (MLMC) method variants, motivated by the potential of improved computational efficiency over rejection based Monte Carlo, which scales poorly with problem dimension. With an eye toward its application to computational chemical physics, we test MLMC's ability to sample trajectories on two problems — a familiar double-well potential, with known stationary distributions, and a Lennard-Jones solid potential (a Galton Board). By sampling Brownian motion trajectories, we are able to compute expectations of observable averages. These multi-basin potential energy problems capture the essence of the challenges with using MLMC, namely, maintaining correspondence of sample paths as time-resolution is varied. Addressing this challenge properly can lead to MLMC significantly outperforming standard Monte Carlo path sampling. We describe the essence of this problem and suggest strategies that circumvent diverging multilevel sample paths for an important class of problems. In the tests we also compare the computational cost of several, “adaptive,” variants of MLMC. Our results demonstrate that MLMC overcomes the collision, time scale limitation of the more familiar Brownian path MC samplers, and our implementation provides tunable error thresholds, making MLMC a promising candidate for application to larger and more complex molecular systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1974

Topics in structural dynamics: Nonlinear unsteady transonic flows and Monte Carlo methods in acoustics

The results are reported of two unrelated studies. The first was an investigation of the formulation of the equations for non-uniform unsteady flows, by perturbation of an irrotational flow to obtain the linear Green's equation. The resulting integral equation was found to contain a kernel which could be expressed as the solution of the adjoint flow equation, a linear equation for small perturbations, but with non-constant coefficients determined by the steady flow conditions. It is believed that the non-uniform flow effects may prove important in transonic flutter, and that in such cases, the use of doublet type solutions of the wave equation would then prove to be erroneous. The second task covered an initial investigation into the use of the Monte Carlo method for solution of acoustical field problems. Computed results are given for a rectangular room problem, and for a problem involving a circular duct with a source located at the closed end.

Haviland, J. K.↗
DOE OSTI2020

Using the Monte Carlo Method to Evaluate the Reliability of Screening Multifamily Housing for Radon

When screening for radon in a multifamily housing complex using a fixed sample density (e.g., testing 1 in 10 (10%) or 1 in 4 units (25%)), the statistical confidence is dependent upon the assumed elevated radon frequency. For example, testing 25% of units in a complex estimated to have eight units with elevated radon levels will provide 90% confidence. However, if it is assumed that, in the same complex, there are only three units with elevated radon levels, the confidence drops to around 58% for the same sample density. Furthermore, in the previous example, if elevated radon levels are not found during the screening, all that can be stated is that the screening provides 90% confidence that there are no more than seven units in the complex with elevated radon levels. To more fully illustrate this uncertainty, ten separate multifamily housing radon data sets with 1 to 10 units with radon levels ≥4 pCi/L (Table 1) were selected for analysis using the Monte Carlo statistical method. Unlike other mathematically based statistical approaches, the Monte Carlo statistical method relies on repeated analysis of randomly selected data. from a 100% sampled complex at various sample densities. Success for each simulation is defined as finding at least one unit with elevated radon levels. In this statistical method, confidence in the overarching conclusion can be greatly enhanced by repeating the simulated screening hundreds or even thousands of times. For this study, each of the ten data sets was simulated 1,000 times. For each simulation, the data set was randomized three times before the fixed percentage of data was selected.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2020

Fundamental gap of fluorographene by many-body GW and fixed-node diffusion Monte Carlo methods

Fluorographene (FG) is a promising graphene-derived material with a large bandgap. Currently existing predictions of its fundamental gap (Δ f ) and optical gap (Δ opt ) significantly vary when compared with experiment. We provide here an ultimate benchmark of Δ f for FG by many-body GW and fixed-node diffusion Monte Carlo (FNDMC) methods. Both approaches independently arrive at Δf ≈ 7.1 ± 0.1 eV. In addition, the Bethe–Salpeter equation enabled us to determine the first exciton binding energy, Eb = 1.92 eV. We also point to the possible misinterpretation problem of the results obtained for gaps of solids by FNDMC with single-reference trial wave functions of Bloch orbitals. We argue why instead of Δ opt , in the thermodynamic limit,

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Deep Neural Network Informed Markov Chain Monte Carlo Methods

In subsurface flow modeling, quantifying the uncertainty of model parameters and the corresponding uncertainly on output quantities is a crucial task for groundwater management. Markov chain Monte Carlo (MCMC) methods can take advantage of observed data to estimate parameters in a Bayesian setting. However, MCMC can be slow to converge and produce highly correlated samples when the dimensions of the parameters is high. Using gradients for the posterior distribution can help samplers explore the parameter space more efficiently, but obtaining gradients can be computationally challenging.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1990

Application of the direct simulation Monte Carlo method to the full shuttle geometry

A new set of programs has been developed for the application of the direct simulation Monte Carlo (or DSMC) method to rarefied gas flows with complex three-dimensional boundaries. The programs are efficient in terms of the computational load and also in terms of the effort required to set up particular cases. This efficiency is illustrated through computations of the flow about the Shuttle Orbiter. The general flow features are illustrated for altitudes from 170 to 100 km. Also, the computed lift-drag ratio during re-entry is compared with flight measurements.

Bird, G. A.↗
DOE OSTI2026

Scalable Quantum Monte Carlo Method for Polariton Chemistry via Mixed Block Sparsity and Tensor Hypercontraction Method

We present a reduced-scaling auxiliary-field quantum Monte Carlo (AFQMC) framework designed for large molecular systems and ensembles, with or without coupling to optical cavities. Our approach leverages the natural block sparsity of the Cholesky decomposition (CD) of electron repulsion integrals in molecular ensembles and employs tensor hypercontraction (THC) to efficiently compress low-rank Cholesky blocks. By representing the Cholesky vectors in a mixed format, keeping high-rank blocks in block-sparse form and compressing low-rank blocks with THC, we reduce the scaling of exchange-energy evaluation from quartic to robust cubic in the number of molecular orbitals N, while lowering memory from cubic toward quadratic. Benchmark analyses on one-, two-, and three-dimensional molecular ensembles (up to ∼1,200 orbitals) show that (a) the number of nonzeros in Cholesky tensors grows linearly with system size across dimensions; (b) the average numerical rank increases sublinearly and does not saturate at these sizes; and (c) rank heterogeneity─some blocks nearly full rank and many low rank, naturally motivates the proposed mixed block sparsity and THC scheme for efficient calculation of exchange energy. In conclusion, we demonstrate that the mixed scheme yields cubic wall-time scaling with favorable prefactors and preserves AFQMC accuracy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1984

Vectorized Monte Carlo methods for reactor lattice analysis

Some of the new computational methods and equivalent mathematical representations of physics models used in the MCV code, a vectorized continuous-enery Monte Carlo code for use on the CYBER-205 computer are discussed. While the principal application of MCV is the neutronics analysis of repeating reactor lattices, the new methods used in MCV should be generally useful for vectorizing Monte Carlo for other applications. For background, a brief overview of the vector processing features of the CYBER-205 is included, followed by a discussion of the fundamentals of Monte Carlo vectorization. The physics models used in the MCV vectorized Monte Carlo code are then summarized. The new methods used in scattering analysis are presented along with details of several key, highly specialized computational routines. Finally, speedups relative to CDC-7600 scalar Monte Carlo are discussed.

Brown, F. B.↗
DOE OSTI2023

Multi-fidelity microstructure-induced uncertainty quantification by advanced Monte Carlo methods

Quantifying uncertainty associated with the microstructure variation of a material can be a computationally daunting task, especially when dealing with advanced constitutive models and fine mesh resolutions in the crystal plasticity finite element method (CPFEM). Numerous studies have been conducted regarding the sensitivity of material properties and performance to the mesh resolution and choice of constitutive model. However, a unified approach that accounts for various fidelity parameters, such as mesh resolutions, integration time-steps and constitutive models simultaneously is currently lacking. Further, this paper proposes a novel uncertainty quantification (UQ) approach for computing the properties and performance of homogenized materials using CPFEM, that exploits a hierarchy of approximations with different levels of fidelity. In particular, we illustrate how multi-level sampling methods, such as multi-level Monte Carlo (MLMC) and multi-index Monte Carlo (MIMC), can be applied to assess the impact of variations in the microstructure of polycrystalline materials on the predictions of homogenized materials properties. We show that by adaptively exploiting the fidelity hierarchy, we can significantly reduce the number of microstructures required to reach a certain prescribed accuracy. Finally, we show how our approach can be extended to a multi-fidelity framework, where we allow the underlying constitutive model to be chosen from either a phenomenological plasticity model or a dislocation-density-based model.

36 MATERIALS SCIENCE↗
DOE OSTI2026

A lumped particle direct simulation Monte-Carlo method combined with the collisional-radiative model for simulations of non-equilibrium laser-induced plasma plumes

Collisional plasma plumes induced by laser irradiation of material targets exhibit large variations in local density as well as ionization and excitation states, making purely hydrodynamic or kinetic simulations inaccurate or infeasible. To address this challenge and capture non-equilibrium effects in laser-induced plasma plumes at arbitrary degrees of ionization, we develop a hybrid computational approach that combines the kinetic direct simulation Monte Carlo (DSMC) method with a collisional-radiative model (CRM). This ℓDSMC-CRM approach utilizes a lumped particle method to represent minor fractions of excited ions in particle-based simulations and a special coarse-graining technique for atomic spectra and photoionization rates, ensuring numerical convergence at reduced computational cost. The hybrid approach is applied to simulate spatially homogeneous relaxation as well as one- and two-dimensional expansions of plasma plumes induced by irradiation of a copper target by a nanosecond laser pulse in a vacuum or background gas. The comparison with an equilibrium model, where local Saha-Boltzmann equilibrium is enforced, shows that the non-equilibrium effects play a dominant role. The equilibrium model can fail to predict the flow structure and strongly underestimate the degree of absorption of laser radiation by the plume. The ℓDSMC-CRM approach is validated against experimental data demonstrating reasonable agreement with the experimental electron density and temperature, while the equilibrium model is found to dramatically underestimate electron density and temperature. The flexibility of the ℓDSMC-CRM approach allows for its seamless integration into existing DSMC frameworks, making it a valuable tool for high-fidelity plasma modeling in laser-material interactions, laser-based manufacturing, and beyond.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Toward improved property prediction of 2D materials using many-body quantum Monte Carlo methods

The field of 2D materials has grown dramatically in the past two decades. 2D materials can be utilized for a variety of next-generation optoelectronic, spintronic, clean energy, and quantum computing applications. These 2D structures, which are often exfoliated from layered van der Waals materials, possess highly inhomogeneous electron densities and can possess short- and long-range electron correlations. The complexities of 2D materials make them challenging to study with standard mean-field electronic structure methods such as density functional theory (DFT), which relies on approximations for the unknown exchange-correlation functional. To overcome the limitations of DFT, highly accurate many-body electronic structure approaches such as diffusion Monte Carlo (DMC) can be utilized. In the past decade, DMC has been used to calculate accurate magnetic, electronic, excitonic, and topological properties in addition to accurately capturing interlayer interactions and cohesion and adsorption energetics of 2D materials. Here, this approach has been applied to 2D systems of wide interest, including graphene, phosphorene, MoS 2 , CrI 3 , VSe 2 , GaSe, GeSe, borophene, and several others. In this review article, we highlight some successful recent applications of DMC to 2D systems for improved property predictions beyond standard DFT.

2D materials↗
DOE OSTI2020

Neutrino Transport with Monte Carlo Method. I. Toward Fully Consistent Implementation of Nucleon Recoils in Core-collapse Supernova Simulations

The small energy exchange via nucleon recoils in neutrino–nucleon scattering is now supposed to be one of the important factors for successful explosions of core-collapse supernovae (CCSNe), as they can change neutrino spectra through accumulation of a large number of scatterings. In deterministic methods employed for neutrino transport in CCSN simulations, we normally cannot afford to deploy a large enough number of energy bins needed to resolve this small energy exchange, and subgrid techniques are employed one way or another. In this paper, we study quantitatively with the Monte Carlo (MC) method how well such a treatment performs. We first investigate the effects of nucleon recoils on the neutrino spectra and confirm that the average energy is reduced by ~15% for heavy-lepton neutrinos and much smaller amounts for other types of neutrinos in a typical postbounce situation. It is also observed that the nucleon scattering dominates the electron scattering in the thermalization of neutrino spectra in all flavors. We then study possible artifacts that the coarse energy grid may produce in the deterministic methods. In order to mimic the latter calculation, we redistribute MC particles in each energy bin after a certain interval in a couple of ways and study how the results are affected, depending on the energy resolution. We also discuss the possible implications of our results for the deterministic methods.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Electronic band gaps from quantum Monte Carlo methods

We develop a method for calculating the fundamental electronic gap of semiconductors and insulators using grand canonical quantum Monte Carlo simulations. Further, we discuss the origin of the bias introduced by supercell calculations of finite size and show how to correct the leading and subleading finite size errors either based on observables accessible in the finite-sized simulations or from density-functional theory calculations. Our procedure is applied to carbon, silicon, and molecular hydrogen crystals, and compared to experiment for carbon and silicon.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Neutral band gap of carbon by quantum Monte Carlo methods

We present a method of calculating the energy gap of a charge-neutral excitation using only ground-state calculations. We report Quantum Monte Carlo calculations of Γ→ Γ and Γ → X particle-hole excitation energies in diamond carbon. We analyze the finite-size effect and find the same 1/L decay rate as that in a charged excitation, where L is the linear extension of the supercell. This slow decay is attributed to the delocalized nature of the excitation in supercells too small to accommodate excitonic binding effects. At larger system sizes, the apparent 1/L decay crosses over to a 1/L 3 behavior. Estimation of the scale of exciton binding can be used to correct finite-size effects of neutral gaps.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Application of Markov Chain Monte Carlo Methods for Uncertainty Quantification in Inverse Transport Problems

Determination of the components of a radioactive source/shield system using the system’s radiation signature is of great importance in homeland security, material safeguards, and waste management. Although significant progress has been made toward solving this inverse transport problem in recent years, work remains to be done to quantify the uncertainty in reconstructed results. In this article we apply two Markov chain Monte Carlo (MCMC) approaches, the delayed rejection adaptive metropolis (DRAM) and differential evolution adaptive metropolis (DREAM) methods, to solve inverse problems and quantify uncertainty. The DRAM method uses delayed rejection combined with global adaptation of the proposal covariance matrix. Furthermore, the DREAM method hybridizes MCMC sampling with the differential evolution (DE) algorithm. In numerical test cases, the DRAM and DREAM methods are shown to be superior to a first-order inverse Hessian approach for problems with noisy data and multiple unknown quantities, with DREAM converging to the posterior distribution more quickly than DRAM. The DREAM and DRAM results indicate that a full posterior distribution is required to quantify uncertainty in many inverse transport problems.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
DOE OSTI2025

Numerical analysis of gas exhaust in Wendelstein 7-X using the direct simulation Monte Carlo method

The present work is focused on a 3D numerical assessment of the Wendelstein 7-X (W7-X) particle exhaust. For all the numerical simulations the direct simulation Monte Carlo solver of the DIVGAS workflow, has been employed. The complex 3D geometry of the sub-divertor region includes the pumping gap panel, supporting structures, cooling pipes as well as the cryo-vacuum pump. All the considered flow simulations correspond to the Standard magnetic configuration of W7-X. The main conclusions, which can be extracted from the present numerical analysis could be summarized as follows; The coupling between EMC3-EIRENE and DIVGAS, which considers the fact that the incoming neutral particle flux at the sub-divertor is based on realistic plasma background, has been demonstrated. Three plasma scenarios have been considered, for which is clearly seen that by increasing the heating power, the neutral pressure as well as the resulting pumping efficiency is increased. The obtained numerical results of the neutral pressure in the sub-divertor lie within a more general scan matrix, which assumes a wider range of incoming particle flux, namely 10 19 –10 24 (s −1 ). It has been observed that, the sub-divertor neutral pressure is proportional to the incoming neutral particle flux, with the effective pumping speed to be a constant of proportionality. The influence of switching off the cryo-vacuum pump on the sub-divertor pressure is rather modest and a weak increase of the neutral pressure in the sub-divertor is expected. Correlations of the sub-divertor pressure with the total incoming particle flux as well as the individual pumped flux at each of the AEH and AEP sections have been deduced. Moreover, it has been demonstrated that the influence of the incoming neutral particle flux on the albedo coefficient at the AEH and AEP pumping gaps is rather weak. All the above numerical findings will actively support the optimization of the W7-X particle exhaust, in view of future experimental campaigns.

DSMC method↗
NASA NTRS1964

Applications of the method of Monte Carlo to problems in thermal radiation

A summary of the work involving the Monte Carlo method in the solution of problems in thermal radiation transfer is presented, which indicates general methods previously used for solving problems in which radiation is coupled with other modes of energy transfer. Previous work involving radiation in absorbing-emitting media is included. An example is outlined to indicate the use of the Monte Carlo method in the design of a space radiator. Suggestions are given for solution of a complex case incorporating the effects of coupled conduction, convection and radiation, wavelength dependent and selective surfaces, nonisothermal conditions, and strongly directional or nondiffuse emitting and reflecting surfaces. A discussion is given of the factors that may affect convergence, running time, and accuracy of the Monte Carlo solutions and of the advantages and disadvantages of this approach for practical problems. Also discussed are the case of programming for complex problems and the probable machine time requirements of the method.

THERMAL RADIATION↗
DOE OSTI2025

Scalable multilevel Monte Carlo methods exploiting parallel redistribution on coarse levels

Here, we study an element agglomeration coarsening strategy that requires data redistribution at coarse levels when the number of coarse elements becomes smaller than the number of MPI processes used on the finest level. The overall procedure generates coarse elements (general unstructured unions of fine grid elements) within the framework of element-based algebraic multigrid methods (or AMGe) studied previously. The AMGe-generated coarse spaces have the ability to exhibit approximation properties of the same order as the fine-level spaces since by construction they contain the piecewise polynomials of the same order as on the fine level. These approximation properties are key for the successful use of AMGe in multilevel solvers for nonlinear partial differential equations as well as for multilevel Monte Carlo (MLMC) simulations. The ability to coarsen without being constrained by the number of MPI processes, as described in the present paper, allows to improve the scalability of these solvers as well as the overall MLMC method. The paper illustrates this latter fact with detailed scalability study of MLMC simulations applied to model Darcy equations with a stochastic log-normal permeability field.

AMGe↗