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At least 1,063 records · Page 59

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DOE OSTI2013

Investigation of the possibility to use a fine-mesh solver for resolving coupled neutronics and thermal-hydraulics

The development of a fine-mesh coupled neutronic/thermal-hydraulic solver is touched upon in this paper. The reported work investigates the feasibility of using finite volume techniques to discretize a set of conservation equations modeling neutron transport, fluid dynamics, and heat transfer within a single numerical tool. With the long-term objective of developing fine-mesh computing capabilities for a few selected fuel assemblies in a nuclear core, this preliminary study considers an infinite array of a single fuel assembly having a finite height. Thermal-hydraulic conditions close to the ones existing in PWRs are taken as a first test case. The neutronic modeling relies on the diffusion approximation in a multi-energy group formalism, with cross-sections pre-calculated and tabulated at the sub-pin level using a Monte Carlo technique. The thermal-hydraulics is based on the Navier-Stokes equations, complemented by an energy conservation equation. The non-linear coupling terms between the different conservation equations are fully resolved using classical iteration techniques. Early tests demonstrate that the numerical tool provides an unprecedented level of details of the coupled solution estimated within the same numerical tool and thus avoiding any external data transfer, using fully consistent models between the neutronics and the thermal-hydraulics. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2018

A computationally efficient method for tempered fractional differential equations with application

This paper investigates the numerical approximation of the tempered fractional integral by using the Sinc-collocation scheme. The algorithm is extended to solve a class of tempered fractional differential equations that converges to the solution with exponential rate. Several numerical examples compare the numerical approximations with the exact solutions. The behavioral responses of the lumped capacitance model with tempered fractional order for transient conduction are investigated. The efficiency and accuracy of the proposed scheme are analyzed in the perspective of the L{sub 2}-norm error and convergence order.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

Analysis and Simulation of One-Dimensional Transport Models for Lithium Symmetric Cells

The main objective of this paper is to analyze transport models for lithium symmetric cells and arrive at an efficient model and code to simulate the same. Two one-dimensional models are considered. The first model uses the dilute solution Nernst–Planck equations in conjunction with the electroneutrality assumption (EN-NP model). For binary electrolytes, an analytical solution for electrolyte concentration is derived and compared with numerical solutions by an approximate finite volume method. The second approach relaxes the electroneutrality assumption by way of Poisson’s equation for the electrostatic potential (PNP model). The computational difficulties of the PNP model are tackled using the approximate finite volume method, with demonstrated convergence characteristics even with bulk dimensions several orders of magnitude larger than the characteristic double layer size. A robust code is developed for the PNP model. The computationally efficient transport models can facilitate simulations, physical understanding, and analysis. This is illustrated by a case study in which these models are coupled with modified kinetic models, which are then parameterized with experimental voltage response data using a systems-level approach. The estimated parameters provide further insight into the electrochemical phenomena underpinning voltage transitions in symmetric cells.

25 ENERGY STORAGE↗

DOE OSTI2020

A General Framework for Bounding Approximate Dynamic Programming Schemes

For years, there has been interest in approximation methods for solving dynamic programming problems, because of the inherent complexity in computing optimal solutions characterized by Bellman’s principle of optimality. A wide range of approximate dynamic programming (ADP) methods now exists. It is of great interest to guarantee that the performance of an ADP scheme be at least some known fraction, say ß , of optimal. This letter introduces a general approach to bounding the performance of ADP methods, in this sense, in the stochastic setting. The approach is based on new results for bounding greedy solutions in string optimization problems, where one has to choose a string (ordered set) of actions to maximize an objective function. This bounding technique is inspired by submodularity theory, but submodularity is not required for establishing bounds. Instead, the bounding is based on quantifying certain notions of curvature of string functions; the smaller the curvatures the better the bound. The key insight is that any ADP scheme is a greedy scheme for some surrogate string objective function that coincides in its optimal solution and value with those of the original optimal control problem. The ADP scheme then yields to the bounding technique mentioned above, and the curvatures of the surrogate objective determine the value ß of the bound. The surrogate objective and its curvatures depend on the specific ADP.

discrete event systems↗

DOE OSTI2021

Evaluating Space Object Conjunction Probabilities Using Characteristic Function Inversion

This report discusses an approach to computing the probability of a conjunction between two space objects in the short-term encounter scenario. A conjunction is defined here as an event where the miss distance between the objects is less than some specified value. The scenario assumptions are that the motion of the objects is linear, their positions are Gaussian distributed, and their velocities are known and constant. Under these assumptions, the squared-miss distance is shown to have the generalized chi-square distribution. An established statistical technique called characteristic function inversion is employed to evaluate the distribution and obtain conjunction probabilities. The method is closely related to a recent approach based on moment generating function inversion, and a qualitative comparison of the approaches is provided. Last, the method is tested on several benchmark test cases where it agrees with numerical integration on the cases with conjunction probabilities above 10 –12 . However, the exact probability in these cases is usually not needed and this probability can be bounded above using an independent Gaussian approximation. Overall, the report shows how to compute conjunction probabilities using a standard statistical method, though numerical integration seems to perform equally well.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Gradient Coding With Iterative Block Leverage Score Sampling

Gradient coding is a method for mitigating straggling servers in a centralized computing network that uses erasure-coding techniques to distributively carry out first-order optimization methods. Randomized numerical linear algebra uses randomization to develop improved algorithms for large-scale linear algebra computations. In this study, we propose a method for distributed optimization that combines gradient coding and randomized numerical linear algebra. The proposed method uses a randomized ℓ 2 -subspace embedding and a gradient coding technique to distribute blocks of data to the computational nodes of a centralized network, and at each iteration the central server only requires a small number of computations to obtain the steepest descent update. The novelty of our approach is that the data is replicated according to importance scores, called block leverage scores, in contrast to most gradient coding approaches that uniformly replicate the data blocks. Furthermore, we do not require a decoding step at each iteration, avoiding a bottleneck in previous gradient coding schemes. We show that our approach results in a valid ℓ 2 -subspace embedding, and that our resulting approximation converges to the optimal solution.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2014

Large Scale Computing and Storage Requirements for Basic Energy Sciences: Target 2017. Report of the NERSC Requirements Review Conducted October 8–9, 2013, Gathersburg, MD

The National Energy Research Scientific Computing Center (NERSC) is the primary computing center for the DOE Office of Science, serving approximately 5,000 users working on some 700 projects that involve nearly 600 codes in a wide variety of scientific disciplines. In addition to large-scale computing and storage resources NERSC provides support and expertise that help scientists make efficient use of its systems. The latest review revealed several key requirements, in addition to achieving its goal of characterizing BES computing and storage needs. high-level findings are: 1) Scientists will need access to significantly more computational and storage resources to achieve their goalds and reach BES research objectives; 2) Users will need assistance from NERSC to prepare for Cori (NERSC-8) and follow-on manycore systems; 3) Research teams need to run complex jobs of many different types and scales; 4) BES is a leader in innovative use of HPC and requires a diverse set of resources and services from NERSC; and 5) BES facilities need computational analysis and data storage resources beyond what they can provide. This report expands upon these key points and add others. The results are based upon representative samples, called "case studies," of the needs of science teams within BES. The case study topics were selected by the NERSC meeting coordinators and BES program managers to represent the BES production computing workload. Prepared by BES workshop participants, the case studies contain a summary of science goals, methods of solution, current and future computing requirements, and special software and support needs. Also included are strategies for computing in the highly parallel "many-core" environment that is expected to dominate HPC architectures over the next few years.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

A guide to the design of the virtual element methods for second- and fourth-order partial differential equations

Here we discuss the design and implementation details of two conforming virtual element methods for the numerical approximation of two partial differential equations that emerge in phase-field modeling of fracture propagation in elastic material. The two partial differential equations are: (i) a linear hyperbolic equation describing the momentum balance and (ii) a fourth-order elliptic equation modeling the damage of the material. Inspired by, we develop a new conforming VEM for the discretization of the two equations, which is implementation-friendly, i.e., different terms can be implemented by exploiting a single projection operator. We use C 0 and C 1 virtual elements for the second-and fourth-order partial differential equation, respectively. For both equations, we review the formulation of the virtual element approximation and discuss the details pertaining the implementation.

42 ENGINEERING↗

DOE OSTI2016

Feynman formulae and phase space Feynman path integrals for tau-quantization of some Lévy-Khintchine type Hamilton functions

Evolution semigroups generated by pseudo-differential operators are considered. These operators are obtained by different (parameterized by a number τ) procedures of quantization from a certain class of functions (or symbols) defined on the phase space. This class contains Hamilton functions of particles with variable mass in magnetic and potential fields and more general symbols given by the Lévy-Khintchine formula. The considered semigroups are represented as limits of n-fold iterated integrals when n tends to infinity. Such representations are called Feynman formulae. Some of these representations are constructed with the help of another pseudo-differential operator, obtained by the same procedure of quantization; such representations are called Hamiltonian Feynman formulae. Some representations are based on integral operators with elementary kernels; these are called Lagrangian Feynman formulae. Langrangian Feynman formulae provide approximations of evolution semigroups, suitable for direct computations and numerical modeling of the corresponding dynamics. Hamiltonian Feynman formulae allow to represent the considered semigroups by means of Feynman path integrals. In the article, a family of phase space Feynman pseudomeasures corresponding to different procedures of quantization is introduced. The considered evolution semigroups are represented as phase space Feynman path integrals with respect to these Feynman pseudomeasures, i.e., different quantizations correspond to Feynman path integrals with the same integrand but with respect to different pseudomeasures. This answers Berezin’s problem of distinguishing a procedure of quantization on the language of Feynman path integrals. Moreover, the obtained Lagrangian Feynman formulae allow also to calculate these phase space Feynman path integrals and to connect them with some functional integrals with respect to probability measures.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2026

Reduced-Cost Four-Component Relativistic Double Ionization Potential Equation-of-Motion Coupled-Cluster Approaches with 4-Hole–2-Particle Excitations and Three-Body Clusters

The double ionization potential (DIP) equation-ofmotion (EOM) coupled-cluster (CC) method with 4-hole−2- particle (4h-2p) excitations on top of the CC with singles, doubles, and triples calculation, abbreviated as DIP-EOMCCSDT(4h-2p), along with its perturbative DIP-EOMCCSD(T)(a)(4h-2p) approximation, are extended to a relativistic four-component (4c) framework. In addition, we introduce and test a new computationally practical DIP-EOMCC approach, which we call DIPEOMCCSD( T)(ã)(4h-2p), that approximates the treatment of 4h- 2p correlations within the DIP-EOMCCSD(T)(a)(4h-2p) method and reduces the $\mathcal{N}$ 8 scaling characterizing DIP-EOMCCSDT(4h- 2p) and DIP-EOMCCSD(T)(a)(4h-2p) to $\mathcal{N}$ 7 with the system size $\mathcal{N}$. Further improvements in computational efficiency are obtained using the frozen natural spinor (FNS) approximation to reduce the numbers of unoccupied spinors entering the correlated steps of the DIP-EOMCC calculations according to a well-defined occupation-number-based threshold. The resulting 4c-FNS-DIPEOMCC approaches are used to compute DIPs for the series of inert gas atoms from argon to radon as well as the vertical DIPs in Cl 2 , Br 2 , HBr, and HI, which have been experimentally examined in the past. We demonstrate that, when using complete basis set extrapolations and FNS truncation threshold of 10 −4.5 , the 4c-FNS-DIP-EOMCCSD(T)(ã)(4h-2p) calculations are capable of predicting DIPs in agreement with experimental data, improving upon their nonrelativistic and spin-free scalar-relativistic counterparts, particularly when examining DIPs characterized by stronger spin−orbit coupling effects.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2018

Fast Reactor Methods Development Plan

Fast reactor design and safety analysis methods (computer codes) have been under development for approximately sixty years. During the first forty years, code development was driven by the immediate needs of operational facilities such as Experimental Breeder Reactors I and II and the Fast Flux Test Facility. Development was further driven by programmatic needs to support advanced reactor programs such as the Clinch River Breeder Reactor Project and the Advanced Liquid Metal Reactor Program. By the early 1990s, design and safety analysis codes had been well established to addressed the unique characteristics of fast reactors. During the subsequent twenty years, however, development was nearly stagnant as a result of U.S. Government policy changes that abruptly canceled nearly all of the fast reactor research in the United States. As a result, the state of fast reactor design and safety analysis methods has deteriorated.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2015

Excitonic couplings between molecular crystal pairs by a multistate approximation

In this paper, we present a diabatization scheme to compute the excitonic couplings between an arbitrary number of states in molecular pairs. The method is based on an algebraic procedure to find the diabatic states with a desired property as close as possible to that of some reference states. In common with other diabatization schemes, this method captures the physics of the important short-range contributions (exchange, overlap, and charge-transfer mediated terms) but it becomes particularly suitable in presence of more than two states of interest. The method is formulated to be usable with any level of electronic structure calculations and to diabatize different types of states by selecting different molecular properties. These features make the diabatization scheme presented here especially appropriate in the context of organic crystals, where several excitons localized on the same molecular pair may be found close in energy. In this paper, the method is validated on the tetracene crystal dimer, a well characterized case where the charge transfer (CT) states are closer in energy to the Frenkel excitons (FE). The test system was studied as a function of an external electric field (to explore the effect of changing the relative energy of the CT excited state) and as a function of different intermolecular distances (to probe the strength of the coupling between FE and CT states). Additionally, we illustrate how the approximation can be used to include the environment polarization effect.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Mechanical properties of zeolite-templated carbons from approximate density functional theory calculations

Zeolite-templated carbon (ZTC) is a unique porous carbonaceous material whose structure is ordered at the nanometre scale, enabling a representative periodic description at the atomistic level. Utilizing an existing, well-defined reference model for ZTCs, a structural library of varying compositions was developed by refinement using density-functional tight-binding (DFTB) potentials parameterized for materials science applications. We first determined the quantum chemical-refined structures of models with CH, CHO, CHON, CHOB, and CHOBN compositions with various degrees of heteroatom substitution. These structural models comprise the characteristic morphological features of highly porous carbon materials, such as open-blade surfaces, edges, saddles, and closed-strut formations, spanning a range of curvatures and characteristic sizes. Second, we carried out alternating compression and expansion of the CHO model unit cell to determine the lowest energy structure as well as to obtain its bulk modulus in order to demonstrate a close connection between macroscopic observations and atomic-scale structures. Further, the agreement between experimental measurements and the computational model is remarkable and demonstrates the power of approximate density functional theory as a cost-effective computational tool with chemical accuracy for the investigation of structure/property relationships in real-world carbon-based solids.

03 NATURAL GAS↗

DOE OSTI2016

TU-AB-BRC-02: Accuracy Evaluation of GPU-Based OpenCL Carbon Monte Carlo Package (goCMC) in Biological Dose and Microdosimetry in Comparison to FLUKA Simulations

Purpose: One of the most accurate methods for radiation transport is Monte Carlo (MC) simulation. Long computation time prevents its wide applications in clinic. We have recently developed a fast MC code for carbon ion therapy called GPU-based OpenCL Carbon Monte Carlo (goCMC) and its accuracy in physical dose has been established. Since radiobiology is an indispensible aspect of carbon ion therapy, this study evaluates accuracy of goCMC in biological dose and microdosimetry by benchmarking it with FLUKA. Methods: We performed simulations of a carbon pencil beam with 150, 300 and 450 MeV/u in a homogeneous water phantom using goCMC and FLUKA. Dose and energy spectra for primary and secondary ions on the central beam axis were recorded. Repair-misrepair-fixation model was employed to calculate Relative Biological Effectiveness (RBE). Monte Carlo Damage Simulation (MCDS) tool was used to calculate microdosimetry parameters. Results: Physical dose differences on the central axis were <1.6% of the maximum value. Before the Bragg peak, differences in RBE and RBE-weighted dose were <2% and <1%. At the Bragg peak, the differences were 12.5% caused by small range discrepancy and sensitivity of RBE to beam spectra. Consequently, RBE-weighted dose difference was 11%. Beyond the peak, RBE differences were <20% and primarily caused by differences in the Helium-4 spectrum. However, the RBE-weighted dose agreed within 1% due to the low physical dose. Differences in microdosimetric quantities were small except at the Bragg peak. The simulation time per source particle with FLUKA was 0.08 sec, while goCMC was approximately 1000 times faster. Conclusion: Physical doses computed by FLUKA and goCMC were in good agreement. Although relatively large RBE differences were observed at and beyond the Bragg peak, the RBE-weighted dose differences were considered to be acceptable.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2020

Approximate quantum circuit synthesis using block encodings

One of the challenges in quantum computing is the synthesis of unitary operators into quantum circuits with polylogarithmic gate complexity. Exact synthesis of generic unitaries requires an exponential number of gates in general. We propose a novel approximate quantum circuit synthesis technique by relaxing the unitary constraints and interchanging them for ancilla qubits via block encodings. This approach combines smaller block encodings, which are easier to synthesize, into quantum circuits for larger operators. Due to the use of block encodings, our technique is not limited to unitary operators and can be applied for the synthesis of arbitrary operators. Overall, we show that operators which can be approximated by a canonical polyadic expression with a polylogarithmic number of terms can be synthesized with polylogarithmic gate complexity with respect to the matrix dimension.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Fast increased fidelity samplers for approximate Bayesian Gaussian process regression

Gaussian processes (GPs) are common components in Bayesian non-parametric models having a rich methodological literature and strong theoretical grounding. The use of exact GPs in Bayesian models is limited to problems containing several thousand observations due to their prohibitive computational demands. We develop a posterior sampling algorithm using H-matrix approximations that scales at O(n log 2 n). We show that this approximation’s Kullback-Leibler divergence to the true posterior can be made arbitrarily small. Though multidimensional GPs could be used with our algorithm, d-dimensional surfaces are modeled as tensor products of univariate GPs to minimize the cost of matrix construction and maximize computational efficiency. We illustrate the performance of this fast increased fidelity approximate GP, FIFA-GP, using both simulated and non-synthetic data sets

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Simulating a pulsed-power-driven plasma with ideal MHD

We describe a simple practical numerical method for simulating plasma driven within a vacuum chamber by a pulsed power generator. Typically, in this type of simulation, the vacuum region adjacent to the plasma is approximated as a highly resistive, light fluid; this involves computationally expensive solvers describing the diffusion of the magnetic field through this fluid. Instead, we provide a recipe for coupling pulsed power generators to the magnetohydrodynamics (MHD) domain by approximating the perfectly insulating vacuum as a light, perfectly conducting, inviscid MHD fluid and discuss the applicability of this counter-intuitive technique. This much more affordable ideal MHD representation is particularly useful in situations where a plasma exhibits interesting three-dimensional phenomena, either due to the design of the experiment or due to developing instabilities. We verified that this coupling recipe works by modeling an exactly solvable flux compression generator as well as a self-similar Noh-like solution and demonstrated convergence to the theoretical solution. We also showed examples of simulating complex three-dimensional pulsed power devices with this technique. We release our code implementation to the public.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2019

QAOA for Max-Cut requires hundreds of qubits for quantum speed-up

Computational quantum technologies are entering a new phase in which noisy intermediate-scale quantum computers are available, but are still too small to benefit from active error correction. Even with a finite coherence budget to invest in quantum information processing, noisy devices with about 50 qubits are expected to experimentally demonstrate quantum supremacy in the next few years. Defined in terms of artificial tasks, current proposals for quantum supremacy, even if successful, will not help to facilitate solutions to practical problems. In contrast, we believe that future users of quantum computers are interested in actual applications and that noisy quantum devices may still provide value by approximately solving hard combinatorial problems via hybrid classical-quantum algorithms. To lower bound the size of quantum computers with practical utility, we perform realistic simulations of the Quantum Approximate Optimization Algorithm and conclude that quantum speedup will not be attainable, at least for a representative combinatorial problem, until several hundreds of qubits are available.

97 MATHEMATICS AND COMPUTING↗