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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Problem-tailored Simulation of Energy Transport on Noisy Quantum Computers

The transport of conserved quantities like spin and charge is fundamental to characterizing the behavior of quantum many-body systems. Numerically simulating such dynamics is generically challenging, which motivates the consideration of quantum computing strategies. However, the relatively high gate errors and limited coherence times of today's quantum computers pose their own challenge, highlighting the need to be frugal with quantum resources. In this work we report simulations on quantum hardware of infinite-temperature energy transport in the mixed-field Ising chain, a paradigmatic many-body system that can exhibit a range of transport behaviors at intermediate times. We consider a chain with L = 12 sites and find results broadly consistent with those from ideal circuit simulators over 90 Trotter steps, containing up to 990 entangling gates. To obtain these results, we use two key problem-tailored insights. First, we identify a convenient basis – the Pauli Y basis – in which to sample the infinite-temperature trace and provide theoretical and numerical justifications for its efficiency relative to, e.g., the computational basis. Second, in addition to a variety of problem-agnostic error mitigation strategies, we employ a renormalization strategy that compensates for global nonconservation of energy due to device noise. We discuss the applicability of the proposed sampling approach beyond the mixed-field Ising chain and formulate a variational method to search for a sampling basis with small sample-to-sample fluctuations for an arbitrary Hamiltonian. This opens the door to applying these techniques in more general models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Kinetics of the benzyl + HO 2 and benzoxyl + OH barrierless association reactions: fate of the benzyl hydroperoxide adduct under combustion and atmospheric conditions

Radical–radical association reactions are challenging to address theoretically due to difficulties finding the bottleneck that variationally minimizes the reactive flux. For this purpose, the variable reaction coordinate (VRC) formulation of the variational transition state theory (VTST) represents an appropriate tool. Here, we revisited the kinetics of two radical–radical association reactions of importance in combustion modelling and poly-aromatic hydrocarbon (PAH) chemistry by performing VRC calculations: benzyl + HO 2 and benzoxyl + OH, both forming the adduct benzyl hydroperoxide. Our calculated rate constants are significantly lower than those previously reported based on VTST calculations, which results from a more efficient minimization of the reactive flux through the bottleneck achieved by the VRC formulation. Both reactions show different trends in the variation of their rate constants with temperature. We observed that if the pair of single occupied molecular orbitals (SOMOs) of the associating radicals show a similar nature, i.e. similar character, and thereby a small energy gap, a highly stabilized transition state structure is formed as the result of a very efficient SOMO–SOMO overlap, which may cancel out the free energy bottleneck for the formation of the adduct and result in large rate constants with a negative temperature dependence. This is the case of the benzoxyl and OH radical pair, whose SOMOs show O 2p nature with an energy gap of 20.2 kcal mol –1 . On the other hand, the benzyl and HO 2 radical pair shows lower rate constants with a positive temperature dependence due to the larger difference between both SOMOs (a 28.9 kcal mol –1 energy gap) as a consequence of the contribution of the multiple resonance structures of the benzyl radical. The reverse dissociation rate constants were also calculated using multi-structural torsional anharmonicity partition functions, which were not included in previous work, and the results show a much slower dissociation of benzyl hydroperoxide. Our work may help to improve kinetic models of interest in combustion and PAH formation, as well as to gain further understanding of radical–radical association reactions, which are ubiquitous in different environments.

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

On the convexity of phase-field fracture formulations: Analytical study and comparison of various degradation functions

Efficient and accurate fracture modeling is of great importance in applications where catastrophic outcomes under extreme scenarios are possible. The phase-field (PF) approach to fracture received significant attention over the past decade, due to its capability to capture complicated fracture patterns (e.g., crack merging and branching). Specifically, crack initiation and propagation are modeled via minimization of the total energy functional, which is regularized with the aid of a phase field. Despite the promising results and modeling capabilities of the PF method in many applications, the solution of fracture problems remains computationally challenging mainly due to the non-convexity of the total energy functional with respect to the combined unknown (phase field and displacement) fields. Understanding the effects of their coupling on convexity is crucial in order to address frequently encountered hurdles in fracture modeling (e.g., inefficient solvers and non-physical crack nucleation). In this paper, we develop convexity criteria for a wide class of PF fracture formulations. For this class of formulations, the second variation of the total energy functional is expressed in terms of Hessian matrices (evaluated at individual material points). Depending on the choice of geometric crack functions and degradation functions, we classify the formulations into three categories and analytically study each one separately. To study the sign of the second variation, we derive inequalities which are satisfied at material points when the Hessian matrix is locally positive semi-definite. These inequalities provide objective criteria for comparing degradation functions. Finally, the applicability of the proposed convexity criteria is demonstrated in the context of a one-dimensional problem, solved using a conventional monolithic solver.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Dual-cone variational calculation of the two-electron reduced density matrix

The computation of strongly correlated quantum systems is challenging because of its potentially exponential scaling in the number of electron configurations. Variational calculation of the two-electron reduced density matrix (2-RDM) without the many-electron wave function exploits the pairwise nature of the electronic Coulomb interaction to compute a lower bound on the ground-state energy with polynomial computational scaling. Recently, a dual-cone formulation of the variational 2-RDM calculation was shown to generate the ground-state energy, albeit not the 2-RDM, at a substantially reduced computational cost, especially for higher $\textit{N}$-representability conditions such as the T2 constraint. Here we generalize the dual-cone variational 2-RDM method to compute not only the ground-state energy but also the 2-RDM. The central result is that we can compute the 2-RDM from a generalization of the Hellmann-Feynman theorem. Specifically, we prove that in the Lagrangian formulation of the dual-cone optimization the 2-RDM is the Lagrange multiplier. Further, we apply the method to computing the energies and properties of strongly correlated electrons—including atomic charges, electron densities, dipole moments, and orbital occupations—in an illustrative hydrogen chain and the nitrogen-fixation catalyst FeMoco. The dual variational computation of the 2-RDM with T2 or higher N -representability conditions provides a polynomially scaling approach to strongly correlated molecules and materials with significant applications in atomic and molecular and condensed-matter chemistry and physics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Variational design principles for nonequilibrium colloidal assembly

Using large deviation theory and principles of stochastic optimal control, we show that rare molecular dynamics trajectories conditioned on assembling a specific target structure encode a set of interactions and external forces that lead to enhanced stability of that structure. Such a relationship can be formulated into a variational principle, for which we have developed an associated optimization algorithm and have used it to determine optimal forces for targeted self-assembly within nonequilibrium steady-states. We illustrate this perspective on inverse design in a model of colloidal cluster assembly within linear shear flow. We find that colloidal clusters can be assembled with high yield using specific short-range interactions of tunable complexity. Shear decreases the yields of rigid clusters, while small values of shear increase the yields of nonrigid clusters. The enhancement or suppression of the yield due to shear is rationalized with a generalized linear response theory. Furthermore, by studying 21 unique clusters made of six, seven, or eight particles, we uncover basic design principles for targeted assembly out of equilibrium.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Variational quantum solver employing the PDS energy functional

In our previous work (J. Chem. Phys. 2020, 153, 201102),we reported a new class of quantum algorithms that are based on the quantum computation of the connected moment expansion to find the ground and excited state energies. In particular, the Peeters-Devreese-Soldatov (PDS) formulation is found variational and bearing the potential for further combining with the existing variational quantum infrastructure. Following this direction, here we propose a variational quantum solver employing the PDS energy gradient. In comparison with the usual variational quantum eigensolver (VQE) and the original static PDS approach, the proposed variational quantum solver offers an effective approach to achieve high ac-curacy at finding the ground state and its energy through the rotation of the trial wave function of modest quality guided by the low order PDS energy gradients, thus improves the ac-curacy and efficiency of the quantum simulation. We demonstrate the performance of the proposed variational quantum solver for toy models, H2molecule, and strongly correlated planar H4system in some challenging situations. In all the case studies, the proposed variational quantum approach out-performs the usual VQE and static PDS calculations even at the lowest order.

Peng, Bo↗
DOE OSTI2020

Self-consistent effective Hamiltonian theory for fermionic many-body systems

Using a separable many-body variational wavefunction, we formulate a self-consistent effective Hamiltonian theory for fermionic many-body system. The theory is applied to the two-dimensional (2D) Hubbard model as an example to demonstrate its capability and computational effectiveness. Most remarkably for the Hubbard model in 2D, a highly unconventional quadruple-fermion non-Cooper pair order parameter is discovered.

Physics↗
DOE OSTI2022

Isogeometric large-eddy simulations of turbulent particle-laden flows

In recent years, isogeometric analysis (IGA) has attracted significant attention from the computational mechanics community due to its ability to integrate design and analysis. Besides, IGA is also a higher-order discretization technique for solving partial differential equations, showing high approximation capability per degree of freedom. In this paper, we extend the application realm of IGA to particle-laden flows based on Eulerian–Eulerian description that couples Navier–Stokes equations with a density transport equation through a Boussinesq approximation. The coupled systems are solved by using quadratic non-uniform rational B-spline (NURBS) functions and a recently developed residual-based variational multiscale (VMS) formulation, which introduces coupling between the fine velocity scales and density equation residuals. We deploy the proposed approach to perform large-eddy simulations (LES) of dilute particle-laden flows over a flat surface at Reynolds number = 10,000. We compare the simulation results against direct numerical simulation (DNS) results from the literature. We find that combining VMS and IGA, the proposed approach enables accurate prediction of a wide range of flow/particle statistics with a relatively lower mesh resolution.

Mathematics↗
DOE OSTI2021

Modeling of Lithium Nucleation and Plating Kinetics Under Fast Charge Conditions

The onset of lithium nucleation and subsequent plating on the graphite particles is a challenging problem in the design of fast charging batteries. Here, a variational phase field formulation has been developed to initiate the nucleation of lithium particles based on the local plating overpotential conditions and allowing to predict the lithium plating under fast charge conditions. The model demonstrates that (1) at small charging current density, there is no nucleation and plating of metallic lithium, and no effect on the intercalation kinetics; (2) at intermediate charging current densities, initially a stagnated growth from isolated lithium nuclei is observed followed by a continuous growth of metallic lithium; (3) at large charging current densities, a continuous growth of metallic lithium resulting from coalescence of small nuclei into large nuclei decreases the excess interfacial energy, which in turn slows down the intercalation kinetics. The formulation sets the stage for predicting and evaluating the influence of various electrolyte compositions, graphite particle morphologies and electrode loadings on the nucleation and plating dynamics under fast charge conditions.

25 ENERGY STORAGE↗
DOE OSTI2026

A 3D-Printed Millimeter-Wave Inline Waveguide-to-Coplanar-Waveguide Transition to Enable Dense Spectrometer Arrays for Intensity Mapping Surveys

We present a 3D-printed millimeter-wave, octave-bandwidth, in-line waveguide-to-coplanar-waveguide transition designed to enable focal planes with dense arrays of on-chip spectrometers. These arrays will enable compelling surveys of the large-scale structure of the universe through millimeter-wave intensity mapping. The transition consists of a four-step ridge-waveguide transformer that couples light from a rectangular waveguide onto a coplanar waveguide via an electrical connection made with indium bump bonds. We develop a tolerance-aware optimization approach to identify high-performance transition geometries that are robust to manufacturing variations; the same formulation can be applied to other tolerance-sensitive design problems. We also describe the implementation of a custom apparatus and procedure for bump-bonding a silicon chip to a metallized 3D-printed component. We detail the fabrication of the coplanar waveguide chip and three-dimensional waveguide structure, simulations and metrology of a test device, and room temperature reflectance measurements of this device. The room temperature metrology and reflection measurements are consistent with a model that predicts a coupling efficiency of $\mathord{\sim} 95\%$ at cryogenic temperatures in the 85-170 GHz frequency range.

Stover, Austin [Chicago U.; Chicago U., KICP] (ORC↗
DOE OSTI2025

VitriEdge: Repairable & Durable Vitrimer Coatings for Wind Turbine Blade Leading Edges

The primary goal of this Level 1b incubator project was to explore the use of vitrimer coatings for repair of leading-edge erosion on end-of-life wind turbine blade surfaces, beyond coating strength of adhesion which has previously been demonstrated in the Level 1a project. Uniform vitrimer coatings (thickness: 400 µm) were applied to two end-of-life wind turbine blades for flexural, fatigue, and laminate tensile testing where the addition of the coating did not produce any statistical variation in tensile properties with minor drops in flexural strength for some laminate formulations. However, a <2% variation in storage modulus was measured for laminate structures (i.e., blade samples with vitrimer coatings) across 100,000 flexural cycles and upon laminate tensile failure, the vitrimer coatings displayed no visible signs of delamination. In addition, three methods to heal vitrimer coating damage was displayed: oven heating, addition of hot water, and a forced convection heat gun. All three heating and healing mechanisms demonstrated significant healing with scratch depths decreasing between 79-91% at healing times ranging between 1-min and 10-minutes. Finally, a water jet machine was used to simulate rain erosion for both the blade surfaces and vitrimer-coated blade surfaces where the diameter and depth of the damage was recorded as a function of exposure time, water pressure, height of exposure, and angle of exposure. Of interest, while the vitrimer coating did not significantly lessen the damage experienced during rain erosion, the addition of vitrimer composite coatings(5 wt.% mica addition) did result in a crack-resistant, durable coating capable of self-healing behavior and in all cases the angle of rain exposure was the most critical parameter explored. It is crucial to continue exploring this space where vitrimer coatings are of interest for both their self-healing properties and potential use as reversible adhesives.

17 WIND ENERGY↗
DOE OSTI2025

Analysis of the weighted shifted boundary method for the Poisson and Stokes problems

The Shifted Boundary Method (SBM) belongs to the class of unfitted (or immersed, or embedded) finite element methods, and relies on reformulating the original boundary value problem over a surrogate (approximate) computational domain. Accuracy is maintained by properly shifting the location and values of the boundary conditions. This avoids integration over cut cells and the associated implementation issues. Recently, the Weighted SBM (WSBM) was proposed for the Navier-Stokes equations with free surfaces and the Stokes flow with moving boundaries. The attribute “weighted” in the name WSBM stems from the fact that its variational form is weighted with the elemental volume fraction of active fluid. The motivation for the development of the WSBM was the preservation of the volume of active fluid to a higher degree of accuracy, which in turn resulted in improved stability and robustness characteristics in moving-boundary, time-dependent simulations. In this article, we present the numerical analysis of the WSBM formulations for the Poisson and Stokes problems. We give mathematical conditions under which the bilinear forms defining the discrete variational formulations are uniformly coercive (Poisson problem) or inf-sup stable (Stokes problem). By these results, stability and optimal convergence is proven in the natural norm; L2-error estimates can also be derived.

Approximate domain boundaries↗
DOE OSTI2024

A phase-field diffraction model for thermo-hydro-mechanical propagating fractures

This paper introduces a novel diffraction based thermo-hydraulic–mechanical (THM) model for fracture propagation using a phase-field fracture (PFF) approach. The key innovation of the THM-PFF model lies in its integrated treatment of four solution variables—displacements, phase-field, pressure, and temperature—each governed by a combination of conservation of momentum (mechanics problem), a variational inequality (constrained minimization problem), mass conservation (pressure problem), and energy conservation (temperature problem). This leads to a new formulation of a coupled variational inequality system. A major advancement is the development of an extended fixed-stress algorithm, where displacements, phase-field, pressures, and temperatures are solved in a staggered sequence. An important aspect of this work is the global coupling of pressures and temperatures across the domain using diffraction systems, with diffraction coefficients defined by material parameters weighted by the diffusive phase-field variable. To ensure robust local mass conservation, we employ enriched Galerkin finite elements (EG) for both pressure and temperature diffraction equations. By enriching the continuous Galerkin basis functions with discontinuous piecewise constants, EG accurately represents solution and parameter discontinuities while preserving local mass and energy conservation—crucial aspects for THM problems and realistic behavior. Moreover, the use of a predictor–corrector local mesh adaptivity scheme is employed, allowing the model to handle small phase-field length-scale parameters while maintaining high numerical accuracy and reasonable computational cost. Furthermore, these new model and algorithmic developments represent significant advances in the field and have been substantiated through rigorous numerical tests.

Diffraction systems↗
DOE OSTI2021

A moving discontinuous Galerkin finite element method with interface condition enforcement for compressible flows

A variation of moving discontinuous Galerkin finite element method with interface condition enforcement (MDG-ICE) is developed for solving the compressible Euler equations. The MDG-ICE method, originating from the work of Corrigan et al. [1], [2], [3], [4], is based on the space-time DG formulation, where both flow field and grid geometry are considered as independent variables and the conservation laws are enforced both on discrete elements and element interfaces. The element conservation laws are solved in the standard discontinuous solution space to determine conservative quantities, while the interface conservation is enforced using a variational formulation in a continuous space to determine discrete grid geometry. The resulting over-determined system of nonlinear equations arising from the MDG-ICE formulation can then be solved in a least-squares sense, leading to an unconstrained nonlinear least-squares problem that is regularized and solved by Levenberg-Marquardt method. A number of numerical experiments for both 1D unsteady and 2D steady state compressible flow problems are conducted to assess the accuracy and robustness of the MDG-ICE method. Numerical results obtained indicate that the MDG-ICE method is able to implicitly detect and track all types of discontinuities via interface conservation enforcement and satisfy the conservation law on both elements and interfaces via grid movement and grid management, demonstrating that an exponential rate of convergence for Sod and Lax-Harden shock tube problems can be achieved and highly accurate solutions without overheating to both double-rarefaction wave and Noh problems can be obtained.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

hp -VPINNs: Variational physics-informed neural networks with domain decomposition

We formulate a general framework for hp-variational physics-informed neural networks (hp-VPINNs) based on the nonlinear approximation of shallow and deep neural networks and hp-refinement via domain decomposition and projection onto the space of high-order polynomials. The trial space is the space of neural network, which is defined globally over the entire computational domain, while the test space contains piecewise polynomials. Specifically in this study, the hp-refinement corresponds to a global approximation with a local learning algorithm that can efficiently localize the network parameter optimization. Here, we demonstrate the advantages of hp-VPINNs in both accuracy and training cost for several numerical examples of function approximation and in solving differential equations.

42 ENGINEERING↗
DOE OSTI2023

High-Order Mesh hr-adaptivity for Surface Fitting to Implicit Geometries

We present an ℎ𝑟-adaptivity framework for morphing a given mesh to fit a target surface prescribed as the zero isocontour of a discrete function. In this framework, high-order meshing is posed as a variational minimization problem that depends on the mesh quality prescribed via the target matrix optimization paradigm (TMOP) and position of a subset of mesh nodes with respect to the target surface. The proposed formulation ensures that the variational problem is converged and mesh quality degradation near the surface is limited, even when the mesh topology is incompatible with the target surface. Additionally, a mesh subset-based approach and ℎ-refinement is introduced to efficiently increase fitting accuracy while reducing the computational cost of the mesh morphing problem. The ℎ𝑟-adaptivity technique extends to different element types in two- and three-dimensions, and can be used in existing finite element and spectral element frameworks to obtain high-order body-fitted meshes. Various numerical experiments demonstrate the robustness and accuracy of the fitting approach for problems of practical interest such as Lagrangian hydrodynamics and topology optimization.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Fully variational incremental CASSCF

We report the complete-active-space self-consistent field (CASSCF) method is a canonical electronic structure theory that holds a central place in conceptualizing and practicing first principles simulations. For application to realistic molecules, however, the CASSCF must be approximated to circumvent its exponentially scaling computational costs. Applying the many-body expansion - also known as the method of increments - to CASSCF (iCASSCF) has been shown to produce a polynomially scaling method that retains much of the accuracy of the parent theory and is capable of treating full valence active spaces. Due to an approximation made in the orbital gradient, the orbital parameters of the original iCASSCF formulation could not be variationally optimized, which limited the accuracy of its nuclear gradient. Herein, a variational iCASSCF is introduced and implemented, where all parameters are fully optimized during energy minimization. This method is able to recover electronic correlations from the full valence space in large systems, produce accurate gradients, and optimize stable geometries as well as transition states. Demonstrations on challenging test cases, such as the oxoMn(salen)Cl complex with 84 electrons in 84 orbitals and the automerization of cyclobutadiene, show that the fully variational iCASSCF is a powerful tool for describing challenging molecular chemistries.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗