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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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DOE OSTI2021

Toward simulating quantum field theories with controlled phonon-ion dynamics: A hybrid analog-digital approach

Quantum field theories are the cornerstones of modern physics, providing relativistic and quantum mechanical descriptions of physical systems at the most fundamental level. Simulating real-time dynamics within these theories remains elusive in classical computing. This provides a unique opportunity for quantum simulators, which hold the promise of revolutionizing our simulation capabilities. Trapped-ion systems are successful quantum-simulator platforms for quantum many-body physics and can operate in digital, or gate-based, and analog modes. Inspired by the progress in proposing and realizing quantum simulations of a number of relativistic quantum field theories using trapped-ion systems, and by the hybrid analog-digital proposals for simulating interacting boson-fermion models, we propose hybrid analog-digital quantum simulations of selected quantum field theories, taking recent developments to the next level. On one hand, the semi-digital nature of this proposal offers more flexibility in engineering generic model interactions compared with a fully-analog approach. On the other hand, encoding the bosonic fields onto the phonon degrees of freedom of the trapped-ion system allows a more efficient usage of simulator resources, and a more natural implementation of intrinsic quantum operations in such platforms. This opens up new ways for simulating complex dynamics of e.g., Abelian and non-Abelian gauge theories, by combining the benefits of digital and analog schemes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Scaling Limits and Generic Bounds for Exploration Processes

We consider exploration algorithms of the random sequential adsorption type both for homogeneous random graphs and random geometric graphs based on spatial Poisson processes. At each step, a vertex of the graph becomes active and its neighboring nodes become blocked. Given an initial number of vertices N growing to infinity, we study statistical properties of the proportion of explored (active or blocked) nodes in time using scaling limits. We obtain exact limits for homogeneous graphs and prove an explicit central limit theorem for the final proportion of active nodes, known as the jamming constant, through a diffusion approximation for the exploration process which can be described as a unidimensional process. We then focus on bounding the trajectories of such exploration processes on random geometric graphs, i.e., random sequential adsorption. As opposed to exploration processes on homogeneous random graphs, these do not allow for such a dimensional reduction. Instead we derive a fundamental relationship between the number of explored nodes and the discovered volume in the spatial process, and we obtain generic bounds for the fluid limit and jamming constant: bounds that are independent of the dimension of space and the detailed shape of the volume associated to the discovered node. Lastly, using coupling techinques, we give trajectorial interpretations of the generic bounds.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Analysis of the Spectral Stability of the Generalized Runge–Kutta Methods Applied to Initial-Boundary-Value Problems for Equations of the Parabolic Type. I. Explicit Methods

We develop a general algorithm for the analysis the spectral stability of generalized multistage Runge–Kutta methods of various orders of accuracy as applied to the numerical integration with respect to time of an initial-boundary-value problem for the second-order parabolic equation. The expression for the function of spectral stability is obtained in two alternative forms: on the basis of matrix relations and in the determinant form. We study specific realizations of various generalized explicit Runge–Kutta methods and their spectral stability. It is shown that all explicit generalized Runge–Kutta methods possess the property of conditional spectral stability and the property of conditional monotonicity of the numerical solution in time whose violation leads to the appearance of false oscillations of the approximate solution. The stability function for these methods is polynomial. It is shown that the application of two-stage generalized explicit Runge–Kutta methods leads to the appearance of predictor-corrector-type schemes. In the case of nonstationary one-dimensional heat-conduction problem, on the basis of a one-stage generalized Runge–Kutta method, we obtain the classical two-layer conditionally stable explicit finite-difference scheme on a four-point template. It is demonstrated that the five-stage generalized Runge–Kutta–Merson method is characterized by the weakest condition of spectral stability as compared with all investigated explicit generalized Runge–Kutta methods.

42 ENGINEERING↗
DOE OSTI2018

A variant nonmonotone smoothing algorithm with improved numerical results for large-scale LWCPs

This paper considers the linear weighted complementarity problem (denoted by LWCP) introduced by Potra (SIAM J Optim 22:1634–1654, 2012). Based on two weighted smoothing functions, we propose a new nonmonotone smoothing algorithm for solving the LWCP and establish its global and local quadratic convergence without the strict complementarity assumption. Compared to existing nonmonotone smoothing algorithms, the proposed algorithm solves the linear system only approximately which can save the computation work when one solves large-scale LWCPs. Moreover, the nonmonotone line search technique adopted in this paper includes the usual monotone line search and some existing nonmonotone line searches as special cases. Numerical results show that our algorithm is considerably efficient for solving large-scale LWCPs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

First-principles calculation of the configurational energy density of states for a solid-state ion conductor with a variant of the Wang and Landau algorithm

In this work, a variant of the Wang and Landau algorithm for calculation of the configurational energy density of states is proposed. The algorithm was developed for the purpose of using first-principles simulations, such as density functional theory, to calculate the partition function of disordered sublattices in crystal materials. The expensive calculations of first-principles methods make a parallel algorithm necessary for a practical computation of the configurational energy density of states within a supercell approximation of a solid-state material. The algorithm developed in this work is tested with the two-dimensional (2d) Ising model to bench mark the algorithm and to help provide insight for implementation to a materials science application. Tests with the 2d Ising model revealed that the algorithm has good performance compared to the original Wang and Landau algorithm and the 1/$\textit{t}$ algorithm, in particular the short iteration performance. Further, a proof of convergence is presented within an adiabatic assumption, and the analysis is able to correctly predict the time dependence of the modification factor to the density of states. The algorithm was then applied to the lithium and lanthanum sublattice of the solid-state lithium ion conductor Li 0.5 La 0.5 TiO 3 . This was done to help understand the disordered nature of the lithium and lanthanum. The results find, overall, that the algorithm performs very well for the 2d Ising model and that the results for Li 0.5 La 0.5 TiO 3 are consistent with experiment while providing additional insight into the lithium and lanthanum ordering in the material. The primary result is that the lithium and lanthanum become more mixed between layers along the c axis for increasing temperature. In part, the simulation of the disordered Li 0.5 La 0.5 TiO 3 system serves as a benchmark for what size systems are currently and in the near future practical to calculate with density functional theory methods.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2015

Determination of the effective diffusivity of water in a poly (methyl methacrylate) membrane containing carbon nanotubes using kinetic Monte Carlo simulations

A kinetic Monte Carlo (kMC) simulation algorithm is developed for computing the effective diffusivity of water molecules in a poly(methyl methacrylate) (PMMA) matrix containing carbon nanotubes (CNTs) at several loadings. The simulations are conducted on a cubic lattice to the bonds of which rate constants are assigned governing the elementary jump events of water molecules from one lattice site to another. Lattice sites belonging to PMMA domains of the membrane are assigned different rates than lattice sites belonging to CNT domains. Values of these two rate constants are extracted from available numerical data for water diffusivity within a PMMA matrix and a CNT pre-computed on the basis of independent atomistic molecular dynamics simulations, which show that water diffusivity in CNTs is 3 orders of magnitude faster than in PMMA. Our discrete-space, continuum-time kMC simulation results for several PMMA-CNT nanocomposite membranes (characterized by different values of CNT length L and diameter D and by different loadings of the matrix in CNTs) demonstrate that the overall or effective diffusivity, D{sub eff}, of water in the entire polymeric membrane is of the same order of magnitude as its diffusivity in PMMA domains and increases only linearly with the concentration C (vol. %) in nanotubes. For a constant value of the concentration C, D{sub eff} is found to vary practically linearly also with the CNT aspect ratio L/D. The kMC data allow us to propose a simple bilinear expression for D{sub eff} as a function of C and L/D that can describe the numerical data for water mobility in the membrane extremely accurately. Additional simulations with two different CNT configurations (completely random versus aligned) show that CNT orientation in the polymeric matrix has only a minor effect on D{sub eff} (as long as CNTs do not fully penetrate the membrane). We have also extensively analyzed and quantified sublinear (anomalous) diffusive phenomena over small to moderate times and correlated them with the time needed for penetrant water molecules to explore the available large, fast-diffusing CNT pores before Fickian diffusion is reached.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Acoustic Wave Propagation Modeling by a Two-dimensional Finite-difference Summation-by-parts Algorithm

Acoustic waveform modeling is a computationally intensive task and full three-dimensional simulations are often impractical for some geophysical applications such as long-range wave propagation and high-frequency sound simulation. In this study, we develop a two-dimensional high-order accurate finite-difference code for acoustic wave modeling. We solve the linearized Euler equations by discretizing them with the sixth order accurate finite difference stencils away from the boundary and the third order summation-by-parts (SBP) closure near the boundary. Non-planar topographic boundary is resolved by formulating the governing equation in curvilinear coordinates following the interface. We verify the implementation of the algorithm by numerical examples and demonstrate the capability of the proposed method for practical acoustic wave propagation problems in the atmosphere.

58 GEOSCIENCES↗
DOE OSTI2018

Accelerated Distributed Energy Management for Microgrids

This paper considers the optimal energy management for a microgrid. The goal of optimal energy management is to minimize the total generation cost while meeting total demand and satisfying individual generator output limits. To achieve this goal, we develop a distributed algorithm based on the consensus theory and gradient estimation technique. Compared to the existing algorithms with diminishing step-sizes, the proposed algorithm enjoys a faster convergence speed due to the fixed step-size, and thus increases the computation speed, and reduces the computation and communication burden. The proposed distributed algorithm is applicable to both fixed and time-varying directed communication networks. We show that the convergence of the proposed distributed algorithm is achieved if the fixed communication network is strongly connected, or if the time-varying communication network is uniformly jointly strongly connected. Numerical simulation results are used to illustrate and demonstrate the effectiveness of the proposed algorithm.

Du, Wen↗
DOE OSTI2022

Landau discriminants

Scattering amplitudes in quantum field theories have intricate analytic properties as functions of the energies and momenta of the scattered particles. In perturbation theory, their singularities are governed by a set of nonlinear polynomial equations, known as Landau equations, for each individual Feynman diagram. The singularity locus of the associated Feynman integral is made precise with the notion of the Landau discriminant, which characterizes when the Landau equations admit a solution. In order to compute this discriminant, we present approaches from classical elimination theory, as well as a numerical algorithm based on homotopy continuation. These methods allow us to compute Landau discriminants of various Feynman diagrams up to 3 loops, which were previously out of reach. For instance, the Landau discriminant of the envelope diagram is a reducible surface of degree 45 in the three-dimensional space of kinematic invariants. We investigate geometric properties of the Landau discriminant, such as irreducibility, dimension and degree. In particular, we find simple examples in which the Landau discriminant has codimension greater than one. Furthermore, we describe a numerical procedure for determining which parts of the Landau discriminant lie in the physical regions. In order to study degenerate limits of Landau equations and bounds on the degree of the Landau discriminant, we introduce Landau polytopes and study their facet structure. Finally, we provide an efficient numerical algorithm for the computation of the number of master integrals based on the connection to algebraic statistics.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Solving key challenges in collider physics with foundation models

Foundation models are neural networks that are capable of simultaneously solving many problems. Large language foundation models like ChatGPT have revolutionized many aspects of daily life, but their impact for science is not yet clear. In this paper, we use a new foundation model for hadronic jets to solve three key challenges in collider physics. In particular, we show how experiments can (1) save significant computing power when developing reconstruction algorithms, (2) perform a complete uncertainty quantification for high-dimensional measurements, and (3) search for new physics with model agnostic methods using low-level inputs. In each case, there are significant computational or methodological challenges with current methods that limit the science potential of deep learning algorithms. By solving each problem, we take jet foundation models beyond proof-of-principle studies and into the toolkit of practitioners.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2016

Particle-image Velocimetry Sensitivity through Automatic Differentiation

A commonly encountered difficulty in modern experimental fluid dynamics experiments is the need for full-flow visualization and measurement; traditional techniques such as hot-wire probes and laser Doppler velocimetry cannot provide such information without difficult scanning procedures. Particle-image velocimetry (PIV) is a measurement technique which can overcome this spatial limitation to provide real-time three-dimensional fluid velocity vectors for an entire plane within the flow, as opposed to a single point that is provided by other measurement techniques. To accomplish this, a PIV system seeds the fluid flow with tracer particles; these must have nearly the same density as that of the fluid and a high drag coefficient to ensure that they follow the fluid flow without deviation. A laser is sent through optics to expand its beam into a sheet which illuminates the plane of interest in the fluid. The particles reflect more light than the fluid, and their image is recorded using a high speed camera. Due to limitations in bandwidth, video cannot be taken fast enough to be useful, and instead pairs of images are captured with a known separation in time. The illuminated particles will move between the two images taken by the camera, and their relative motion can be used to compute the fluid velocity at that point. When a single camera is used, only two-dimensional velocity vectors can be computed, but with the addition of another camera this can be improved to full three-dimensional vectors. The flow's time evolution can be measured by taking series of image pairs and processing each pair to get the velocity field at the time between each image pair. Only the two-dimensional version will be considered in this work. To compute the velocity vectors of the flow, the images are broken up into interrogation regions, usually in a uniform grid. In the most basic PIV algorithm, corresponding regions in the image pairs are cross-correlated to compute the most likely displacement from one image to the next. This is used since the cross correlation will achieve a maximum value when the two interrogation regions line up the best. The location of the peak in the correlation map and scaling information for the optical setup is used to compute the particle displacement from one image to the next. This process is similar to holding two semi-transparent images and moving one until they match as well as possible. Sub-pixel displacements between images can be obtained by fitting a Gaussian function to the correlation peak. Knowing the displacement vector for each set of interrogation regions in the image pair, it is a simple matter to divide by the time gap between the two images to compute the fluid velocity at the point in time and space. Since there are many interrogation regions in each image pair, the velocity field for a sheet is sampled according to the arrangement of the interrogation regions. The sensitivity of the final computed vector to the input images is difficult to compute, and has led most considerations of uncertainty in the PIV field to apply Monte Carlo methods and correlations to quantify the systematic and random errors which result from application of various PIV algorithms. In this work, automatic differentiation (AD) has been used to trace the dependence of velocity vectors computed using the correlation-peak PIV algorithm back to the input values given to an artificial image generator. These initial results form the foundation for continued work in the application of AD to algorithms in PIV. They demonstrate that AD methods can be successfully applied to PIV algorithms without undue complexity. The derivatives of each individual vector with regard to the coefficients of the velocity field used to create the artificial images can be computed and the statistics of them considered collectively, or correlated between each other to quantify the effectiveness of a PIV algorithm. With the initial implementation complete, adding extra algorithms is relatively simple and considerable data can be generated for analysis. It is hoped that application of these methods can lead to improved PIV algorithms which demonstrate better sensitivity to small variations in particle displacement. While these methods can be used as an analysis tool for refinement of new algorithms, computation of actual resultant vector sensitivities to input images' individual pixels is the next logical step of this work. Such information will be analyzed with experimental data to produce a better understanding of how output vectors' uncertainty relates to the actual image pairs, and lead to automatic bad vector removal. (authors)

42 ENGINEERING↗
DOE OSTI2016

Reduced‐cost sparsity‐exploiting algorithm for solving coupled‐cluster equations

We present an algorithm for reducing the computational work involved in coupled‐cluster (CC) calculations by sparsifying the amplitude correction within a CC amplitude update procedure. We provide a theoretical justification for this approach, which is based on the convergence theory of inexact Newton iterations. We demonstrate by numerical examples that, in the simplest case of the CCD equations, we can sparsify the amplitude correction by setting, on average, roughly 90% nonzero elements to zeros without a major effect on the convergence of the inexact Newton iterations.

Brabec, Jiri↗
DOE OSTI2020

Quantum embedding for material chemistry based on domain separation and open subsystems

Our perspective considers two theories we recently proposed to perform quantum embedding calculations for chemical systems: domain-separated density functional theory (DSDFT) and locally coupled open subsystems (LCOS). The development includes both the fundamentals of each theory as well as potential applications, some technical aspects, and related challenges. DS-DFT is suited to study intramolecular effects, where one can apply a high level of theory (based on DFT or wave function theory) to a region of interest inside a molecule or solid, and lower level theory elsewhere, with smooth switching between the regions. LCOS, in contrast, is a fragment-based embedding which offers computational advantages to study intermolecular behavior such as electron hopping, spin-environment interaction, and charge transfer excitations. Yet, both theories can exchange roles when appropriate. In addition, these theories allow for control of computational scaling of their algorithms. We investigate paths to determine the charge-transfer operator used in LCOS, and suggest an auxiliary energy minimization that can provide a practical estimate to this operator. We also briefly discuss how to implement density fitting techniques in domain separation, and how domain separation can be used for pure wavefunction-based embedding.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2020

Characterization of Quantum States Based on Creation Complexity

Abstract The creation complexity of a quantum state is the minimum number of elementary gates required to create it from a basic initial state. The creation complexity of quantum states is closely related to the complexity of quantum circuits, which is crucial in developing efficient quantum algorithms that can outperform classical algorithms. A major question unanswered so far is what quantum states can be created with a number of elementary gates that scales polynomially with the number of qubits. In this work, it is first shown that for an entirely general quantum state it is exponentially hard (requires a number of steps that scales exponentially with the number of qubits) to determine if the creation complexity is polynomial. Then, it is shown that it is possible for a large class of quantum states with polynomial creation complexity to have common coefficient features such that, given any candidate quantum state, an efficient coefficient sampling procedure can be designed to determine if the state belongs to the class or not with arbitrarily high success probability. Consequently, partial knowledge of a quantum state's creation complexity is obtained, which can be useful for designing quantum circuits and algorithms involving such a state.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2016

Algorithms for Heterogeneous, Multiple Depot, Multiple Unmanned Vehicle Path Planning Problems

Unmanned vehicles, both aerial and ground, are being used in several monitoring applications to collect data from a set of targets. This article addresses a problem where a group of heterogeneous aerial or ground vehicles with different motion constraints located at distinct depots visit a set of targets. The vehicles also may be equipped with different sensors, and therefore, a target may not be visited by any vehicle. The objective is to find an optimal path for each vehicle starting and ending at its respective depot such that each target is visited at least once by some vehicle, the vehicle–target constraints are satisfied, and the sum of the length of the paths for all the vehicles is minimized. Two variants of this problem are formulated (one for ground vehicles and another for aerial vehicles) as mixed-integer linear programs and a branchand- cut algorithm is developed to compute an optimal solution to each of the variants. Computational results show that optimal solutions for problems involving 100 targets and 5 vehicles can be obtained within 300 seconds on average, further corroborating the effectiveness of the proposed approach.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2018

Finite Combinatorial Generation of Metabelian T-Ideal

In this work, we develop our idea on the construction of a system of combinatorial generators in a T-ideal of a free associative algebra, which is a full analogy of a Gröbner–Shirshov basis in a polynomial ideal. We prove a theorem on multilinear monomials that enables us to establish the existence of a finite set of combinatorial generators in a metabelian T-ideal.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Effect of Yagi–Uda nano-antenna element shape on the directivity and radiation efficiency

In this paper, different optimal designs of Yagi–Uda nano-antennas (NAs) are introduced and analyzed based on different element shapes to maximize the directivity and radiation efficiency. The studied element shapes include triangular, hexagonal, cube, square, rotated square, rectangular, ellipsoid, and elliptical cylinder shapes. The NAs parameters for each design are optimized using particle swarm optimization algorithm to achieve high directivity at a wavelength of 500 nm for wireless point-to-point applications. The designs are numerically analysed using 3-D finite difference time domain method (3-D FDTD) via Lumerical software package. To illustrate the performance of the proposed antennas, different radiation parameters such as radiation pattern, directivity, and radiation efficiency have been studied. Moreover, a tolerance of ± 5% is calculated to consider the imperfections that may appear in the fabrication process at a nanoscale. The optimized rectangular prism NA achieves the highest directivity of 24.21 with an efficiency of 50.74%. However, the optimized triangular prism NA has the highest efficiency of 73% with a directivity of 20.89. This enhancement is mainly attributed to the efficient coupling between array elements along with low side lobe level. However, a trade-off between directivity and radiation efficiency is obtained by the hexagonal prism NA with directivity of 21.9 and radiation efficiency of 69.1%.

77 NANOSCIENCE AND NANOTECHNOLOGY↗