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At least 109 records · Page 6

Monte Carlo Second- and Third-Order Many-Body Green’s Function Methods with Frequency-Dependent, Nondiagonal Self-Energy

We fully develop the Monte Carlo many-body Green’s function (MC-GF) method with the following enhancements: (1) The truncation order of the perturbation expansion of the Dyson self-energy is raised from the second order (MC-GF2) to the third order (MC-GF3) with the aid of a computerized procedure to enumerate and transform all 84 third-order Goldstone diagrams into Monte Carlo integrable expressions and then into central processing unit (CPU)/graphical processing unit (GPU)-parallel computer codes. (2) An efficient algorithm is proposed that computes all off-diagonal and diagonal elements of the MC-GF2 and MC-GF3 self-energy matrices by common subexpression elimination. (3) The frequency-independent approximation is lifted by introducing a method that computes frequency derivatives of the MC-GF2 and MC-GF3 self-energies up to any arbitrarily high order at nearly no additional computational cost. (4) The imaginary-time integration in the Laplace-transformed expressions of the self-energy is carried out stochastically (instead of using a quadrature in the previous implementations), resulting in a 50- to 200-fold speedup. (5) The efficiency of the redundant-walker convergence acceleration scheme is analyzed numerically, and the guidelines are established to select an optimal number of walkers for maximal efficiency. When such an optimal number is used, the cost per sample is constant of molecular size on either many CPUs or many GPUs. (6) The computational cost to obtain a binding energy within a given statistical uncertainty is observed to increase as (tentatively) O(n 4 ) and O(n 5 ) of molecular size (n is the number of electrons) with and without the diagonal approximation, respectively, as opposed to O(n 5 ) and O(n 6 ) of the corresponding deterministic algorithms. With this method applied to the electron binding energies of C 60 , we show that the third-order corrections to the self-energies are much greater in electron binding energies than in ground-state energies. As a result, they display a sign of oscillatory convergence toward experimental results, not necessarily improving the agreement with increasing perturbation order, justifying MC-GF3 and motivating even higher-order methods.

Algorithms↗

Improving Solution Accuracy and Convergence for Stochastic Physics Parameterizations with Colored Noise

Stochastic parameterizations are used in numerical weather prediction and climate modeling to help capture the uncertainty in the simulations and improve their statistical properties. Convergence issues can arise when time integration methods originally developed for deterministic differential equations are applied naively to stochastic problems. In previous studies, it has been demonstrated that a correction term, known in stochastic analysis as the Itô correction, can help improve solution accuracy for various deterministic numerical schemes and ensure convergence to the physically relevant solution without substantial computational overhead. The usual formulation of the Itô correction is valid only when the stochasticity is represented by white noise. In this study, a generalized formulation of the Itô correction is derived for noises of any color. The formulation is applied to a test problem described by an advection–diffusion equation forced with a spectrum of fast processes. We present numerical results for cases with both constant and spatially varying advection velocities to show that, for the same time step sizes, the introduction of the generalized Itô correction helps to substantially reduce time integration error and significantly improve the convergence rate of the numerical solutions when the forcing term in the governing equation is rough (fast varying); alternatively, for the same target accuracy, the generalized Itô correction allows for the use of significantly longer time steps and, hence, helps to reduce the computational cost of the numerical simulation.

54 ENVIRONMENTAL SCIENCES↗

Assessment of the Geomechanical Risks Associated with CO 2 Injection at the FutureGen 2.0 Site: Application of the State of Stress Assessment Tool (SOSAT)

This report presents the results of the application of the State of Stress Assessment Tool (SOSAT) on the FutureGen 2.0 data set. SOSAT was developed as part of the National Risk Assessment Partnership (NRAP) project and provides a unique integrated framework for estimating the state of stress probability distribution at a given depth in the subsurface and evaluating the risk of induced shear and tensile failure resulting from the injection of carbon dioxide (CO 2 ). The approach implemented by SOSAT is based on two deterministic and widely used methods of determining the state of stress (i.e., stress polygon and one-dimensional tectonic-elastic approach). These methods have been modified using a probabilistic approach to account for uncertainties in the input parameters. The methodology proposed in SOSAT was demonstrated using the data obtained for the FutureGen 2.0 project located in the Illinois Basin. Although the FutureGen 2.0 project was suspended by the U.S. Department of Energy prior to the start of injection operations, the extensive characterization efforts undertaken at the storage site have yielded a considerable amount of valuable data about this part of the sedimentary basin. The FutureGen 2.0 storage site was designed to accommodate the injection of 1.1 million metric tons of CO 2 per year over a 20-year period. The injection of CO 2 and the associated pressure buildup in the reservoir is expected to alter the state of stress over the course of the injection. These changes in the initial stress state may affect fault stability and potentially lead to the unintentional creation of hydraulic fractures, which could pose a leakage risk if not contained within the reservoir. Assessing these risks is critical to making informed decisions about the characterization, management of the injection operation, and monitoring of the storage site. The data required by SOSAT for the geomechanical assessment of the FutureGen 2.0 site were identified, and the methodology proposed in SOSAT was followed to evaluate the probability of reactivating critically oriented faults or potentially creating hydraulic fractures in the reservoir. The results of the geomechanical analysis performed using the SOSAT led to the following conclusions. 1. The probability distribution of the state of stress indicates significant uncertainties in the magnitude of the maximum horizontal stress S Hmax , while the minimum horizontal stress S hmin is well constrained by the stress measurements conducted during the characterization efforts at the storage site. This uncertainty in the magnitude of S Hmax is a common challenge and has significant implications for geomechanical risk at sites like FutureGen 2.0 where a strike-slip tectonic regime exists. 2. The probability that the Mount Simon reservoir was initially critically stressed is relatively high—25%. When the pore pressure increases to the maximum allowable pressure permitted under the Underground Injection Control Class VI regulation of the FutureGen 2.0 project, the risk of shear failure approaches a probability of 43%. These relatively high probabilities reflect the current state of information about the geomechanical conditions in this part of the Illinois Basin. For future operations in this basin this should be a high characterization priority because it could significantly lower the risk of operations. 3. Based on the maximum injection pressure allowed in the UIC Class VI, the risk of unintentional hydraulic fracturing is limited. The risk of shear failure as determined by SOSAT is based on a very conservative approach assuming that critically oriented faults exist in the subsurface. While no faults have been formally identified at the FutureGen 2.0 site, the results obtained with SOSAT using the FutureGen 2.0 data set highlight the importance of integrating uncertainties in critical parameters to quantify geomechanical risks in a defensible way. Should SOSAT have been available at the time the characterization activities were being planned, more characterization efforts would have been implemented to reduce the uncertainties on the magnitude of the maximum horizontal stress, and to dismiss with confidence the potential existence of a critically-oriented fault in the reservoir (e.g., 3D seismic survey).

54 ENVIRONMENTAL SCIENCES↗

Diffusion Synthetic Acceleration for Heterogeneous Domains, Compatible with Voids

A standard approach to solving the S N transport equations is to use source iteration with diffusion synthetic acceleration (DSA). Although this approach is widely used and effective on many problems, there remain some practical issues with DSA preconditioning, particularly on highly heterogeneous domains. For large-scale parallel simulation, it is critical that both (a) preconditioned source iteration converges rapidly and (b) the action of the DSA preconditioner can be applied using fast, scalable solvers, such as algebraic multigrid (AMG). For heterogeneous domains, these two interests can be at odds. In particular, there exist DSA diffusion discretizations that can be solved rapidly using AMG, but they do not always yield robust/fast convergence of the larger source iteration. Conversely, there exist robust DSA discretizations where source iteration converges rapidly on difficult heterogeneous problems, but fast parallel solvers like AMG tend to struggle applying the action of such operators. Moreover, very few current methods for the solution of deterministic transport are compatible with voids. This paper develops a new heterogeneous DSA preconditioner based on only preconditioning the optically thick subdomains. The resulting method proves robust on a variety of heterogeneous transport problems, including a linearized hohlraum mesh related to inertial confinement fusion. Moreover, the action of the preconditioner is easily computed using O(1) AMG iterations, convergence of the transport iteration typically requires 2 to 5× fewer iterations than current state-of-the-art “full” DSA, and the proposed method is trivially compatible with voids. On the hohlraum problem, rapid convergence is obtained by preconditioning less than 3% of the mesh elements with five to ten AMG iterations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Projective Hedging Algorithms for Multistage Stochastic Programming, Supporting Distributed and Asynchronous Implementation

Here we propose a decomposition algorithm for multistage stochastic programming that resembles the progressive hedging method of Rockafellar and Wets but is provably capable of several forms of asynchronous operation. We derive the method from a class of projective operator splitting methods fairly recently proposed by Combettes and Eckstein, significantly expanding the known applications of those methods. Our derivation assures convergence for convex problems whose feasible set is compact, subject to some standard regularity conditions and a mild “fairness” condition on subproblem selection. The method’s convergence guarantees are deterministic and do not require randomization, in contrast to other proposed asynchronous variations of progressive hedging. Computational experiments described in an online appendix show the method to outperform progressive hedging on large-scale problems in a highly parallel computing environment.

97 MATHEMATICS AND COMPUTING↗

Intelligent multi-zone residential HVAC control strategy based on deep reinforcement learning

Residential heating, ventilation, and air conditioning (HVAC) has been considered as an important demand response resource. However, the optimization of residential HVAC control is no trivial task due to the complexity of the thermal dynamic models of buildings and uncertainty associated with both occupant-driven heat loads and weather forecasts. In this paper, we apply a novel model-free deep reinforcement learning (RL) method, known as the deep deterministic policy gradient (DDPG), to generate an optimal control strategy for a multi-zone residential HVAC system with the goal of minimizing energy consumption cost while maintaining the users’ comfort. Here, the applied deep RL-based method learns through continuous interaction with a simulated building environment and without referring to any prior model knowledge. Simulation results show that compared with the state-of-art deep Q network (DQN), the DDPG-based HVAC control strategy can reduce the energy consumption cost by 15% and reduce the comfort violation by 79%; and when compared with a rule-based HVAC control strategy, the comfort violation can be reduced by 98%. In addition, experiments with different building models and retail price models demonstrate that the well-trained DDPG-based HVAC control strategy has high generalization and adaptability to unseen environments, which indicates its practicability for real-world implementation.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

The collisional particle-in-cell method for the Vlasov–Maxwell–Landau equations

We introduce an extension of the particle-in-cell method that captures the Landau collisional effects in the Vlasov–Maxwell–Landau equations. The method arises from a regularisation of the variational formulation of the Landau equation, leading to a discretisation of the collision operator that conserves mass, charge, momentum and energy, while increasing the (regularised) entropy. The collisional effects appear as a fully deterministic effective force, thus the method does not require any transport–collision splitting. The scheme can be used in arbitrary dimension, and for a general interaction, including the Coulomb case. We validate the scheme on scenarios such as the Landau damping, the two-stream instability and the Weibel instability, demonstrating its effectiveness in the numerical simulation of plasma.

Bailo, Rafael (ORCID:0000000180183799)↗

An adaptive stochastic sequential quadratic programming with differentiable exact augmented lagrangians

In this study, we consider solving nonlinear optimization problems with a stochastic objective and deterministic equality constraints. We assume for the objective that its evaluation, gradient, and Hessian are inaccessible, while one can compute their stochastic estimates by, for example, subsampling. We propose a stochastic algorithm based on sequential quadratic programming (SQP) that uses a differentiable exact augmented Lagrangian as the merit function. To motivate our algorithm design, we first revisit and simplify an old SQP method Lucidi developed for solving deterministic problems, which serves as the skeleton of our stochastic algorithm. Based on the simplified deterministic algorithm, we then propose a non-adaptive SQP for dealing with stochastic objective, where the gradient and Hessian are replaced by stochastic estimates but the stepsizes are deterministic and prespecified. Finally, we incorporate a recent stochastic line search procedure Paquette and Scheinberg into the non-adaptive stochastic SQP to adaptively select the random stepsizes, which leads to an adaptive stochastic SQP. The global "almost sure" convergence for both non-adaptive and adaptive SQP methods is established. Numerical experiments on nonlinear problems in CUTEst test set demonstrate the superiority of the adaptive algorithm.

97 MATHEMATICS AND COMPUTING↗

Development and Application of a Risk Analysis Toolkit for Plant Resources Optimization

This report summarizes the R&D activities of the Risk Informed Asset Management (RIAM) project during fiscal year 2020 (FY20). This project focuses on the development of methods designed to optimize plant operations (e.g., maintenance/replacement schedule, optimal maintenance posture) provided system/component health/cost data. This project development lives in cooperation with the Plant Health Management (PHM) project which focuses on the development of methods that integrate component health data and propagate such information at the system level to evaluate most relevant sources of risk. This year’s activities for the RIAM project focused on the continuation of schedule optimization algorithms developed in FY19. While in FY19 we focused on both deterministic and stochastic capital budgeting methods, in FY20 we moved forward by implementing two versions of schedule optimization methods. The first one reformulates the capital budgeting problem in a distributionally robust form which allows the user to rely on data directly rather than proposing a distribution from the data itself. The second version reformulates the capital budgeting explicitly using risk measures as variables to maximize/minimize. Lastly, we focused on the development of methods designed to identify the optimal maintenance posture based on the Pareto Frontier analysis. Rather than performing a tradeoff analysis (i.e., identify the absolute best posture), the Pareto Frontier analysis performs a trade space exploration approach (i.e., identify value and costs of several postures and have the analyst perform the task of imposing desired value and cost constraints). This is performed by identifying maintenance postures that maximize value (e.g., system availability) and minimize operational costs, i.e., the Pareto frontier in a value-cost trade space.

97 MATHEMATICS AND COMPUTING↗

A hybrid Monte Carlo, discontinuous Galerkin method for linear kinetic transport equations

Here we present a hybrid method for time-dependent particle transport problems that combines Monte Carlo (MC) estimation with deterministic solutions based on discrete ordinates. For spatial discretizations, the MC algorithm computes a piecewise constant solution and the discrete ordinates use bilinear discontinuous finite elements. From the hybridization of the problem, the resulting problem solved by Monte Carlo is scattering free, resulting in a simple, efficient solution procedure. Between time steps, we use a projection approach to “relabel” collided particles as uncollided particles. In conclusion, from a series of standard 2-D Cartesian test problems we observe that our hybrid method has improved accuracy and reduction in computational complexity of approximately an order of magnitude relative to standard discrete ordinates solutions.

97 MATHEMATICS AND COMPUTING↗

On-the-fly response function generation method for composite coarse mesh

The hybrid stochastic deterministic transport code COMET, based on the incident response expansion theory, is used to model reactor cores with high fidelity and formidable computational speed. COMET models a reactor core using a library of incident flux response expansion coefficients that are pre computed for all the unique lattice cells (e.g., fuel assemblies, reflector blocks, etc.) in the core. In order to further improve its computational efficiency in pre-calculating the response library a new response function generation method is developed to compute the response functions for the composite coarse meshes made of a smaller set of unique lattices on the fly within the COMET's deterministic transport core sweep. The efficiency is achieved by eliminating a number of unique lattices that can be made up from the reduced set of unique meshes on the fly. The numerical process consists of the following steps. First, the boundary condition on composite coarse mesh boundaries is projected onto the expansion basis to compute the incident flux moments on external surfaces of all the basic (reduced set of unique) coarse meshes. Secondly, the deterministic sweeping solver in COMET is used to converge on the outgoing/incoming flux expansion moments crossing interfaces between the basic coarse meshes. Thirdly, the response functions for the composite coarse meshes are constructed as a superposition on the fly. The new response function generation method was tested on 88 composite coarse meshes consisting of CANDU fuel bundles and moderator blocks. It was found that response functions generated by the new method agree very well with those generated by direct Monte Carlo calculations. The average and maximum relative differences in the surface-to-surface response coefficients computed by the two methods are 0.10% and 0.20%, respectively. Similarly, the average and maximum relative differences in the response fission densities are 0.13% and 0.43%, respectively. These discrepancies are within one standard deviation of the stochastic uncertainties. The new method is five times faster than the original direct Monte Carlo method. The size of the response function library for the new method is five times smaller than that for the original method, leading to significantly less requirement for the computer hard drive space and memory. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Neutronics and Thermo-Fluids Simulation of Generic Pebble-Bed Fluoride-Salt-Cooled High-Temperature Reactor

The fluoride-salt-cooled high-temperature reactor (FHR) is one of the advanced reactors that has been attracting considerable interest from both the research community and the nuclear industry. To help facilitate the nuclear community's familiarity with the FHR, Kairos Power has developed a generic FHR (gFHR) benchmark. In the research performed here, this benchmark was used to assess innovative modeling methods that combine stochastic and deterministic computer codes to perform the design and analysis of the gFHR. Further, the Monte Carlo code Serpent 2 was used to generate few-group cross sections that were then used in the neutron diffusion and thermal-fluids code AGREE to perform full-core neutronics and thermal-fluids steady-state and transient core analysis. The Argonne National Laboratory code SAM was then used to model the gFHR system and to simulate the load-follow operation of the gFHR.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Hierarchical porous metals with deterministic 3D morphology and shape via de-alloying of 3D printed alloys

The present disclosure relates to a method for forming a three dimensional, hierarchical, porous metal structure with deterministically controlled 3D multiscale pore architectures. The method may involve providing a feedstock able to be applied in an additive manufacturing process, and using an additive manufacturing process to produce a three dimensional (3D) structure using the feedstock. The method may involve further processing the 3D structure through at least a de-alloying operation to form a metallic 3D structure having an engineered, digitally controlled macropore morphology with integrated nanoporosity.

Qi, Zhen↗

Uncertainty quantification methodology for hyperbolic systems with application to blood flow in arteries

We present a Stochastic Finite Volume - ADER (SFV-ADER) methodology for Uncertainty Quantification (UQ) in the general framework of systems of hyperbolic balance laws with uncertainty in parameters. The resulting method is weakly intrusive, meaning that deterministic solvers need minor modifications to include random contributions, and has no theoretical accuracy barrier. An illustration of the second-order version for the viscous Burgers equation with uncertain viscosity coefficient is first given in detail, under different deterministic initial conditions; the attainment of the theoretically expected convergence rate is demonstrated empirically; results and features of our scheme are discussed. We then extend the SFV-ADER method to a non-linear hyperbolic system with source terms that models one-dimensional blood flow in arteries, assuming uncertainties in a set of parameters of the problem. Results are then compared with measurements in a well-defined 1:1 experimental replica of the network of largest arteries in the human systemic circulation. For a 99%-confidence level, severe influence of parameter fluctuations is seen in pressure profiles, while secondary effects on flow rate profiles become visible, particularly in terminal branches. In conclusion, results suggest that the proposed methodology could successfully be applied to other physical problems involving hyperbolic balance laws.

60 APPLIED LIFE SCIENCES↗

Application of Genetic Algorithm (GA) Assisted Partial Least Square (PLS) Analysis on Trilinear and Non-trilinear Fluorescence Data Sets to Quantify the Fluorophores in Multifluorophoric Mixtures: Improving Quantification Accuracy of Fluorimetric Estimations of Dilute Aqueous Mixtures

Excitation-emission matrix fluorescence (EEMF) and total synchronous fluorescence spectroscopy (TSFS) are the 2 fluorescence techniques that are commonly used for the analysis of multifluorophoric mixtures. These 2 fluorescence techniques are conceptually different and provide certain advantages over each other. The manual analysis of such highly correlated large volume of EEMF and TSFS towards developing a calibration model is difficult. Partial least square (PLS) analysis can analyze the large volume of EEMF and TSFS data sets by finding important factors that maximize the correlation between the spectral and concentration information for each fluorophore. However, often the application of PLS analysis on entire data sets does not provide a robust calibration model and requires application of suitable pre-processing step. The present work evaluates the application of genetic algorithm (GA) analysis prior to PLS analysis on EEMF and TSFS data sets towards improving the precision and accuracy of the calibration model. The GA algorithm essentially combines the advantages provided by stochastic methods with those provided by deterministic approaches and can find the set of EEMF and TSFS variables that perfectly correlate well with the concentration of each of the fluorophores present in the multifluorophoric mixtures. The utility of the GA assisted PLS analysis is successfully validated using (i) EEMF data sets acquired for dilute aqueous mixture of four biomolecules and (ii) TSFS data sets acquired for dilute aqueous mixtures of four carcinogenic polycyclic aromatic hydrocarbons (PAHs) mixtures. In the present work, it is shown that by using the GA it is possible to significantly improve the accuracy and precision of the PLS calibration model developed for both EEMF and TSFS data set. Hence, GA must be considered as a useful pre-processing technique while developing an EEMF and TSFS calibration model.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Predicting the impact of particle-particle collisions on turbophoresis with a reduced number of computational particles

A common feature of wall-bounded turbulent particle-laden flows is enhanced particle concentrations in a thin layer near the wall due to a phenomenon known as turbophoresis. Even at relatively low bulk volume fractions, particle-particle collisions regulate turbophoresis in a critical way, making simulations sensitive to collisional effects. Lagrangian tracking of every particle in the flow can become computationally expensive when the physical number of particles in the system is large. Artificially reducing the number of particles in the simulation can mitigate the computational cost. When particle-particle collisions are an important aspect determining the simulation outcome, as in the case when turbophoresis plays an active role, simply reducing the number of particles in the simulation significantly alters the computed particle statistics. This paper introduces a computational particle treatment for particle-particle collisions which reproduces the results of a full simulation with a reduced number of particles. This is accomplished by artificially enhancing the particle collision radius based on scaling laws for the collision rates. The proposed method retains the use of deterministic collision models and is applicable for both low and high Stokes number regimes.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Accelerated radiation transport modeling techniques for pencil beam computed tomography using gamma rays

Monte Carlo radiation transport modeling studies were performed for a compact, and high-resolution gamma-ray computed tomography system designed for imaging irradiated nuclear fuel. The system comprises a 60 Co source – chosen for its highly penetrating 1173 keV and 1332 keV gamma rays – a pair of high-aspect-ratio pencil beam collimators, and an inorganic scintillator detector. Here two acceleration methods are proposed to rapidly model a transmission type gamma-ray tomography system. The first, a variance reduction technique, is based on performing Monte Carlo simulations with a monodirectionally-biased source, sampled from a characteristic sub-volume of the full source volume. The second acceleration method is based on the deterministic calculations using the Beer–Lambert law and detector response characteristics. Comparison of simulations using acceleration approaches with analog simulations of the fully isotropic, full-volume equivalent, show that the Monte Carlo variance reduction technique gives quantitatively accurate predictions for large collimator aspect ratios while the deterministic calculations are semi-quantitative but converge close to the correct result as the collimator aspect ratio increases. As such, these techniques can be used to reduce the computational cost in generating simulated radiographs and tomographs by several orders of magnitude. Experimental validation efforts are currently underway and will be demonstrated in future work.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Locally defined quantum emission from epitaxial few-layer tungsten diselenide

Recently, single photons have been observed emanating from point defects in two-dimensional (2D) materials including WSe 2 , WS 2 , hexagonal-BN, and GaSe, with their energy residing in the direct electronic bandgap. Here, we report single photon emission from a nominal weakly emitting indirect bandgap 2D material through deterministic strain induced localization. A method is demonstrated to create highly spatially localized and spectrally well-separated defect emission sites in the 750–800 nm regime in a continuous epitaxial film of few-layer WSe 2 synthesized by a multistep diffusion-mediated gas source chemical vapor deposition technique. To separate the effects of mechanical strain from the substrate or dielectric-environment induced changes in the electronic structure, we created arrays of large isotropically etched ultrasharp silicon dioxide tips with spatial dimensions on the order of 10 μm. We use bending based on the small radius of these tips—on the order of 4 nm—to impart electronic localization effects through morphology alone, as the WSe 2 film experiences a uniform SiO 2 dielectric environment in the device geometry chosen for this investigation. When the continuous WSe 2 film was transferred onto an array of SiO 2 tips, an ~87% yield of localized emission sites on the tips was observed. The outcomes of this report provide fundamental guidelines for the integration of beyond-lab-scale quantum materials into photonic device architectures for all-optical quantum information applications.

36 MATERIALS SCIENCE↗