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DOE OSTI2023

Exploring finite temperature properties of materials with quantum computers

Abstract Thermal properties of nanomaterials are crucial to not only improving our fundamental understanding of condensed matter systems, but also to developing novel materials for applications spanning research and industry. Since quantum effects arise at the nano-scale, these systems are difficult to simulate on classical computers. Quantum computers can efficiently simulate quantum many-body systems, yet current quantum algorithms for calculating thermal properties of these systems incur significant computational costs in that they either prepare the full thermal state on the quantum computer, or they must sample a number of pure states from a distribution that grows with system size. Canonical thermal pure quantum (TPQ) states provide a promising path to estimating thermal properties of quantum materials as they neither require preparation of the full thermal state nor require a growing number of samples with system size. Here, we present an algorithm for preparing canonical TPQ states on quantum computers. We compare three different circuit implementations for the algorithm and demonstrate their capabilities in estimating thermal properties of quantum materials. Due to its increasing accuracy with system size and flexibility in implementation, we anticipate that this method will enable finite temperature explorations of relevant quantum materials on near-term quantum computers.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Advanced Quantum Poisson Solver in the NISQ era

The Poisson equation has many applications across the broad areas of science and engineering. Most quantum algorithms for the Poisson solver presented so far, either suffer from lack of accuracy and/or are limited to very small sizes of the problem, and thus have no practical usage. Here we present an advanced quantum algorithm for solving the Poisson equation with high accuracy and dynamically tunable problem size. After converting the Poisson equation to the linear systems through the finite difference method, we adopt the Harrow-Hassidim-Lloyd (HHL) algorithm as the basic framework. Particularly, in this work we present an advanced circuit that ensures the accuracy of the solution by implementing non-truncated eigenvalues through eigenvalue amplification as well as by increasing the accuracy of the controlled rotation angular coefficients, which are the critical factors in the HHL algorithm. We show that our algorithm not only increases the accuracy of the solutions, but also composes more practical and scalable circuits by dynamically controlling problem size in the NISQ devices. We present both simulated and experimental results, and discuss the sources of errors. Finally, we conclude that overall results on the quantum hardware are dominated by the error in the CNOT gates.

Robson, Walter↗

DOE OSTI2023

Adaptive variational quantum minimally entangled typical thermal states for finite temperature simulations

Scalable quantum algorithms for the simulation of quantum many-body systems in thermal equilibrium are important for predicting properties of quantum matter at finite temperatures. Here we describe and benchmark a quantum computing version of the minimally entangled typical thermal states (METTS) algorithm for which we adopt an adaptive variational approach to perform the required quantum imaginary time evolution. The algorithm, which we name AVQMETTS, dynamically generates compact and problem-specific quantum circuits, which are suitable for noisy intermediate-scale quantum (NISQ) hardware. We benchmark AVQMETTS on statevector simulators and perform thermal energy calculations of integrable and nonintegrable quantum spin models in one and two dimensions and demonstrate an approximately linear system-size scaling of the circuit complexity. We further map out the finite-temperature phase transition line of the two-dimensional transverse field Ising model. Finally, we study the impact of noise on AVQMETTS calculations using a phenomenological noise model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Solder Bond Fatigue is Insensitive to Module Size

In this article, we explore the influence of module size on the rate of interconnecting solder bond thermomechanical fatigue (TMF) damage. Structural mechanics models of crystalline silicon PV models are created to solve with the finite-element method. Results conclusively demonstrate that the rate of solder bond TMF damage is independent of module size, interconnect location across the cell and cell location across the module.

14 SOLAR ENERGY↗

DOE OSTI2021

Design Optimization of A-Type Heat Exchangers based on High Performance, Non-Round Tubes

Air-to-refrigerant heat exchangers (HXs) have been the topic of considerable research as they are the fundamental heat transfer components of HVAC&R systems. For residential and commercial applications, indoor heat exchangers are often in A-type configurations to reduce air-conditioner system footprint while still delivering the required cooling or heating. Classical HX design practices typically assume a uniform frontal air velocity profile to facilitate the use of conventional tube-fin airside heat transfer and pressure drop correlations for performance prediction. However, it is well-reported throughout the literature that A-type HXs experience significant airflow maldistribution which can severely degrade HX performance. Additionally, recent advancements in simulation software such as Computational Fluid Dynamics (CFD), Finite Element Analysis (FEA) and optimization algorithms have led researchers to consider primary heat transfer surface optimization to achieve highly compact HXs which do not require fins. In this paper, an A-type HX which utilizes shape-optimized non-round tubes is optimized for minimum duct size and airside pressure drop. This is achieved through coupling of an experimentally validated finite volume HX model with automated 2D CFD simulations of airflow through the HX for airside thermal-hydraulic performance evaluation. Preliminary results show that the optimal designs deliver similar capacity while achieving 20% reductions in airside pressure drop and duct cross-section area. Additionally, the optimal design apex angles in this study were similar to those from previous A-Type HX optimization studies for conventional tube-fin HX geometries, suggesting that the apex angle for optimal A-Type configuration performance may be independent of tube geometry.

42 ENGINEERING↗

DOE OSTI2023

Ultrastrong colloidal crystal metamaterials engineered with DNA

Lattice-based constructs, often made by additive manufacturing, are attractive for many applications. Typically, such constructs are made from microscale or larger elements; however, smaller nanoscale components can lead to more unusual properties, including greater strength, lighter weight, and unprecedented resiliencies. Here, solid and hollow nanoparticles (nanoframes and nanocages; frame size: ~15 nanometers) were assembled into colloidal crystals using DNA, and their mechanical strengths were studied. Nanosolid, nanocage, and nanoframe lattices with identical crystal symmetries exhibit markedly different specific stiffnesses and strengths. Unexpectedly, the nanoframe lattice is approximately six times stronger than the nanosolid lattice. Nanomechanical experiments, electron microscopy, and finite element analysis show that this property results from the buckling, densification, and size-dependent strain hardening of nanoframe lattices. Last, these unusual open architectures show that lattices with structural elements as small as 15 nanometers can retain a high degree of strength, and as such, they represent target components for making and exploring a variety of miniaturized devices.

42 ENGINEERING↗

DOE OSTI2021

On steady alternate bars forced by a localized asymmetric drag distribution in erodible channels

Studying the effect of different in-stream fluvial turbines siting on river morphodynamics allowed us to witness the onset of a time-averaged, large-scale, alternate distortion of bed elevations, which could not be exclusively related to the turbine rotor blockage. The longitudinal profiles of this two-dimensional bathymetric perturbation resemble those of steady fluvial bars. In this contribution we generalize the problem addressing a spatially impulsive, asymmetric distribution of drag force in the channel cross-section. Furthermore, this is experimentally investigated through the deployment of differently sized grids perpendicular to the flow, and analytically explored as a finite perturbation of an open channel flow over an erodible sediment layer, as described by a coupled flow–sediment shallow water equation. The steady solutions of this fluvial morphodynamic problem, physically represented by alternate bars scaling with the channel width, highlight the importance of the resonant conditions in defining the spatial extent of the bed deformation. The equations further suggest that in very shallow flows any asymmetric obstruction may lead to an upstream propagation of the steady bars, consistent with previous studies on the effects of channel curvature. In broad terms, this study provides the preliminary framework to control the onset of river meandering through imposed finite perturbations of the cross-section. In a more applied sense, it provides a tool to predict non-local scour–deposition patterns associated with the deployment of energy converters or other flow obstructions.

42 ENGINEERING↗

DOE OSTI2022

Role of Molecular Simulations in the Design of Metal–Organic Frameworks for Gas-Phase Thermocatalysis: A Perspective

Here, metal organic frameworks (MOFs) are highly tunable porous crystalline solids with spatially and electronically isolated catalytically active sites that have been demonstrated for a variety of thermo-, redox-, and photocatalytic reactions. Their tunable natures and relatively well-defined active sites make them advantageous for catalyst design, and molecular simulations have proven highly valuable in this endeavor. However, complexities in the MOF structure require advanced simulation strategies that accurately capture quantum chemistry at the strongly correlated transition metal cation active sites, compositional and structural changes caused by finite temperature and pressure reaction conditions, and transport effects in variously sized pore environments. Luckily, several groups have started using such simulation strategies, paving the way for rich opportunities to design MOF catalysts. Herein, we highlight such examples and provide a perspective on the needs for molecular simulations in the design of MOF catalysts moving forward.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

DESI DR2 Baryon Acoustic Oscillations from the Lyman Alpha Forest Multipoles

We present an alternative measurement of the Baryon Acoustic Oscillation (BAO) using the Legendre multipole representation of the Ly$α$ forest correlation functions from the second data release (DR2) of the Dark Energy Spectroscopic Instrument survey. Compressing the auto- and cross-correlation functions into Legendre multipoles yields a positive-definite covariance matrix without any smoothing -- unlike the baseline DR2 analysis -- thanks to a significantly reduced data vector size. We introduce the statistical corrections required to debias the finite-sample covariance matrix estimate and demonstrate that monopole and quadrupole terms for both auto- and cross-correlations can be used even when the correlation functions are distorted by continuum errors and contaminated by metals. This formalism has slightly diminished the constraining power of the BAO scale, while considerably weakening constraints on nuisance parameters. We measure the isotropic BAO scale with $0.93\%$ precision at $z_\mathrm{eff}=2.35$, the Hubble parameter $H(z_\mathrm{eff})=(239.5\pm3.4)~(147.09~\mathrm{Mpc}/r_d) ~\mathrm{km~s}^{-1}~\text{Mpc}^{-1}$, and the transverse comoving distance $D_M(z_\mathrm{eff})=(5.80 \pm 0.10)~(r_d/147.09~\mathrm{Mpc})$~Gpc for a given value of the sound horizon ($r_d$). Our BAO results are entirely consistent with the baseline DR2 analysis.

Karaçaylı, Naim Göksel [Chicago U., KICP; Ohio Sta↗

DOE OSTI2024

Thermal Management System for an Electric Machine With Additively Manufactured Hollow Conductors With Integrated Heat Pipes

Here, this paper discusses steps taken to develop a novel thermal management system for an aircraft propulsion electric machine containing additively manufactured coils integrated with heat pipes aimed at boosting its specific power. Experimental setups are used to size and characterize heat pipes for the application and 3D thermal finite element analysis is used to determine optimum heat transfer coefficient of the convective boundaries. For some of the convective boundaries, fin-based surface area enhancement is required to reach a target combined overall heat transfer coefficient and surface area performance (UA). This enhancement is worked out using a combination of the Engineering Equation Solver tool and 3D thermal FEA. The thermal management system's UA, and by extension its specific power, sensitivity to coolant temperature is explored. Temperature distribution plots of optimized machine components are also presented and discussed. Lastly, additional heat pipe testing is carried out to study its maximum heat transfer capability's sensitivity to condenser coolant temperature and configuration.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2021

Error estimates of finite difference methods for the Dirac equation in the massless and nonrelativistic regime

We present four frequently used finite difference methods and establish the error bounds for the discretization of the Dirac equation in the massless and nonrelativistic regime, involving a small dimensionless parameter 0 < ε &NestedLessLess; 1 inversely proportional to the speed of light. In the massless and nonrelativistic regime, the solution exhibits rapid motion in space and is highly oscillatory in time. Specifically, the wavelength of the propagating waves in time is at O(ε), while in space, it is at O(1) with the wave speed at O(ε -1 ). We adopt one leap-frog, two semi-implicit, and one conservative Crank-Nicolson finite difference methods to numerically discretize the Dirac equation in one dimension and establish rigorously the error estimates which depend explicitly on the time step τ, mesh size h, and the small parameter ε. The error bounds indicate that, to obtain the “correct” numerical solution in the massless and nonrelativistic regime, i.e., 0 < ε &NestedLessLess; 1, all these finite difference methods share the same ε-scalability as time step τ = O(ε 3/2 ) and mesh size h = O(ε 1/2 ). A large number of numerical results are reported to verify the error estimates.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Modeling and design of a separate effects irradiation test targeting fission gas release from Cr-doped UO 2

Fission gas release (FGR) from nuclear fuel during operation can diminish heat transfer properties across the pellet-cladding gap and increase the fuel rod internal pressure, thereby posing a concern to fuel reliability and safety during an accident. Enlarging the fuel grain size, which has been shown to improve fission gas retention, can be achieved by doping the fuel feedstock prior to sintering. In this work, the BISON fuel performance code was used to predict FGR from undoped and chromia-doped UO 2 (referred to as Cr-doped UO 2 ) fuel specimens with different grain sizes and across various temperatures. The BISON models identified the irradiation conditions for which FGR is most significant, and a separate effects irradiation experiment in the High Flux Isotope Reactor (HFIR) was then developed targeting those conditions. Further, the experiment leveraged the MiniFuel irradiation capability at Oak Ridge National Laboratory and consisted of 12 fuel specimens of varying grain size and Cr content. A coupling scheme between BISON FGR results and the ANSYS finite element thermal model used for experiment design was formulated to predict cumulative FGR from each fuel specimen based on expected irradiation temperature histories. The fuel samples were fabricated and characterized as a part of this work, and the fuel compositions modeled in BISON were representative of the specimens used in the experiment. This combined modeling and experimental effort aims to study the effect of fuel grain size and Cr content on FGR and to provide simulated BISON FGR results that can be used for future model validation activities.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2023

Design and Analysis of Multifidelity Finite Element Simulations

Abstract The numerical accuracy of finite element analysis (FEA) depends on the number of finite elements used in the discretization of the space, which can be varied using the mesh size. The larger the number of elements, the more accurate the results are. However, the computational cost increases with the number of elements. In current practice, the experimenter chooses a mesh size that is expected to produce a reasonably accurate result, and for which the computer simulation can be completed in a reasonable amount of time. Improvements to this approach have been proposed using multifidelity modeling by choosing two or three mesh sizes. However, mesh size is a continuous parameter, and therefore, multifidelity simulations can be performed easily by choosing a different value for the mesh size for each of the simulations. In this article, we develop a method to optimally find the mesh sizes for each simulation and satisfy the same time constraints as a single or a double mesh size experiment. A range of different mesh sizes used in the proposed method allows one to fit multifidelity models more reliably and predict the outcome when meshes approach infinitesimally small, which is impossible to achieve in actual simulations. We illustrate our approach using an analytical function and a cantilever beam finite element analysis experiment.

Engineering↗

DOE OSTI2020

Kirigami Engineering—Nanoscale Structures Exhibiting a Range of Controllable 3D Configurations

Abstract Kirigami structures provide a promising approach to transform flat films into 3D complex structures that are difficult to achieve by conventional fabrication approaches. By designing the cutting geometry, it is shown that distinct buckling‐induced out‐of‐plane configurations can be obtained, separated by a sharp transition characterized by a critical geometric dimension of the structures. In situ electron microscopy experiments reveal the effect of the ratio between the in‐plane cut size and film thickness on out‐of‐plane configurations. Moreover, geometrically nonlinear finite element analyses (FEA) accurately predict the out‐of‐plane modes measured experimentally, their transition as a function of cut geometry, and provide the stress–strain response of the kirigami structures. The combined computational–experimental approach and results reported here represent a step forward in the characterization of thin films experiencing buckling‐induced out‐of‐plane shape transformations and provide a path to control 3D configurations of micro‐ and nanoscale buckling‐induced kirigami structures. The out‐of‐plane configurations promise great utility in the creation of micro‐ and nanoscale systems that can harness such structural behavior, such as optical scanning micromirrors, novel actuators, and nanorobotics. This work is of particular significance as the kirigami dimensions approach the sub‐micrometer scale which is challenging to achieve with conventional micro‐electromechanical system technologies.

Zhang, Xu↗

DOE OSTI2022

Fast and scalable quantum Monte Carlo simulations of electron-phonon models

We introduce methodologies for highly scalable quantum Monte Carlo simulations of electron-phonon models, and report benchmark results for the Holstein model on the square lattice. The determinant quantum Monte Carlo (DQMC) method is a widely used tool for simulating simple electron-phonon models at finite temperatures, but incurs a computational cost that scales cubically with system size. Alternatively, near-linear scaling with system size can be achieved with the hybrid Monte Carlo (HMC) method and an integral representation of the Fermion determinant. Here, we introduce a collection of methodologies that make such simulations even faster. To combat "stiffness" arising from the bosonic action, we review how Fourier acceleration can be combined with time-step splitting. To overcome phonon sampling barriers associated with strongly-bound bipolaron formation, we design global Monte Carlo updates that approximately respect particle-hole symmetry. To accelerate the iterative linear solver, we introduce a preconditioner that becomes exact in the adiabatic limit of infinite atomic mass. Finally, we demonstrate how stochastic measurements can be accelerated using fast Fourier transforms. Here, these methods are all complementary and, combined, may produce multiple orders of magnitude speedup, depending on model details.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Confinement Controls the Bend Instability of Three-Dimensional Active Liquid Crystals

Spontaneous growth of long-wavelength deformations is a defining feature of active liquid crystals. We investigate the effect of confinement on the instability of 3D active liquid crystals in the isotropic phase composed of extensile microtubule bundles and kinesin molecular motors. When shear aligned, such fluids exhibit finite-wavelength self-amplifying bend deformations. By systematically changing the channel size we elucidate how the instability wavelength and its growth rate depend on the channel dimensions. Experimental findings are qualitatively consistent with a minimal hydrodynamic model, where the fastest growing deformation is set by a balance of active driving and elastic relaxation. Furthermore, our results demonstrate that confinement determines the structure and dynamics of active fluids on all experimentally accessible length scales.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2022

Multiscale and multiphysics FEA simulation and materials optimization for laser ultrasound transducers

In this study, the relationship between the nanocomposite design and the laser ultrasound transducer (LUT) characteristics was investigated through simulations in multiple scale levels for material behavior, device response, and acoustic wave propagation in media. First, the effects of the nanoparticle size and concentration on the effective properties of composites were quantitatively investigated with the finite element analysis (FEA) method. Second, the effective properties of the nanocomposite were assigned to the layer, which is modeled as a homogeneous material, in the FEA for the LUT simulating the energy conversion from the incident laser to the acoustic wave. Finally, the ultrasound propagation in the water was calculated by a theoretical wave propagation model. The FEA-based prediction was compared with the experimental data in the literature and a theoretical analysis for LUT based on Thermal-Acoustic coupling. As a result, the ultrasound waves on the transducer surface and at a distance in the water could be predicted. Based on the hierarchically integrated prediction procedure, the optimal conditions of the photoacoustic nanocomposites were investigated through the parametric study with the particle size and concentration as variables. The results guide the material designs optimized for different device characteristics, such as high pressure and broad bandwidth.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Population balance modeling of polyurethane foam formation with pressure‐dependent growth kernel

Abstract Polyurethane foams are widely used materials often chosen for their useful characteristics such as low thermal conductivity, ease of application, and high strength‐to‐weight ratios. Computational models are needed to predict the dynamics of the flow and expansion, and the resulting material properties, to improve manufacturing processes. In this paper, a model for PMDI, a water‐blown polyurethane foam, is presented. By extending a kinetics‐based approach by adding bubble‐scale information via a population balance equation (PBE) using the quadrature method of moments, we can track bubble size distributions during foaming. We present results from a three‐dimensional computational fluid dynamics model using arbitrary Lagrangian–Eulerian interface tracking implemented in finite element software. The model compares favorably with experimental data, including dynamics, bubble distributions measured by both camera and diffusion wave spectroscopy, and post‐test bubble size from scanning electron microscopy and density measurements from x‐ray computed tomography.

Ortiz, Weston↗