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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Explicit Runge–Kutta Methods that Alleviate Order Reduction

Explicit Runge–Kutta (RK) methods are susceptible to a reduction in the observed order of convergence when applied to an initial boundary value problem with time-dependent boundary conditions. We study conditions on explicit RK methods that guarantee high order convergence for linear problems; we refer to these conditions as weak stage order conditions. We prove a general relationship between the method’s order, weak stage order, and number of stages. Furthermore, we derive explicit RK methods with high weak stage order and demonstrate, through numerical tests, that they avoid the order reduction phenomenon up to any order for linear problems and up to order three for nonlinear problems.

explicit Runge–Kutta↗
DOE OSTI2021

Spectral deferred correction methods for high-order accuracy in poroelastic problems

In this work, we investigate high-order accuracy in time integration by examining two operator splitting methods for poroelastic problems: the two-pass and the spectral deferred correction (SDC) methods. To enhance the order of accuracy, the two-pass method partitions a coupled operator symmetrically, whereas the SDC method corrects truncation errors by establishing an error equation. These high-order methods are applied to underlying solution strategies, i.e., monolithic, fixed-stress sequential, and undrained sequential methods. We observe that semi-discretized systems from spatial discretization have forms similar to those of index-1 differential algebraic equations (DAEs), causing order reduction against the two-pass method when it is used in conjunction with either the monolithic or sequential method. On the other hand, the SDC in conjunction with the monolithic method exhibits the desired second-order accuracy in poroelastic problems while increasing the order of accuracy for index-1 DAEs. However, the SDC in conjunction with either of the two sequential methods does not achieve the desired order of accuracy, and maintains first order because the flow equation for poroelasticity has an additional approximation associated with the volumetric strain rate term, which does not yield exactly the same forms as those of conventional DAEs. Thus, the monolithic SDC method can achieve higher-order accuracy, but may require higher computational costs because it involves solving matrix systems larger than those for the sequential methods.

02 PETROLEUM↗
DOE OSTI2020

Matrix-free preconditioning for high-order H (curl) discretizations

The greater arithmetic intensity of high-order finite element discretizations makes them attractive for implementation on next-generation hardware, but assembly of high-order finite element operators as matrices is prohibitively expensive. As a result, the development of general algebraic solvers for such operators has been an open research challenge. Fast matrix-free application of high-order operators has received significant attention in the literature in the context of Poisson-type problems, but preconditioners and solvers for inverting more general operators are not very well-developed. In this paper, we consider the problem of preconditioning a definite Maxwell operator at high polynomial order without assembling a matrix. We show that given efficient preconditioners for high-order H 1 finite element problems on the same mesh, efficient H(curl) preconditioners can be constructed in an auxiliary space framework. We demonstrate the resulting preconditioners in a practical setting with tensor-product basis functions on an unstructured mesh of quadrilaterals. Overall, our approach uses a sparsified H 1 solver constructed on a low-order mesh of the nodal points of the underlying high-order space, and we show that the resulting H(curl) preconditioner is effective at very high polynomial orders for two-dimensional model problems with complicated geometry, varying piecewise constant coefficients, and curved elements. The resulting preconditioner scales with nearly optimal O(p d+1 ) floating point operation count and optimal O(p d ) memory transfer requirements, outperforming existing Maxwell preconditioners in the high-order regime.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A second-order distributed memory parallel fast sweeping method for the Eikonal equation

The Eikonal equation is used to calculate wave propagation and distance fields, and due to its complexity requires numerical treatment for its solution. In this work, we present a second-order distributed memory parallel fast sweeping method. The second-order solution switches on a two-point stencil when two upwind points are available, and reverts to first-order otherwise. In all examples, the second-order method improves the solution over the first-order, allowing for significant savings in memory while achieving the same accuracy. Parallelization over distributed memory saw good weak scaling with optimal convergence. The computational time for second-order was approximately 2.5 times slower than first-order, where the largest amount of mesh points ran on 144 cores (512 GB) was ≈20 billion. The savings in memory from the second-order method combined with the distributed memory algorithm result in the ability to solve problems much larger than are possible with the serial first-order method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Absence of precursor incommensurate charge order in electronic nematic Ba 0.35 Sr 0.65 Ni 2 As 2

Recent discoveries of charge order and electronic nematic order in the iron-based superconductors and cuprates have pointed towards the possibility of nematic and charge fluctuations playing a role in the enhancement of superconductivity. The Ba 1–x Sr x Ni 2 As 2 system, closely related in structure to the BaFe 2 As 2 system, has recently been shown to exhibit both types of ordering without the presence of any magnetic order. We report single-crystal x-ray diffraction experiments on Ba 0.35 Sr 0.65 Ni 2 As 2 , providing evidence that the previously reported incommensurate charge order with wave-vector (0, 0.28, 0) tet in the tetragonal state of BaNi 2 As 2 vanishes by 65% Sr substitution together with nematic order. Furthermore, our measurements suggest that the nematic and incommensurate charge orders are closely tied in the tetragonal state and show that the (0, 0.33, 0) tri charge ordering in the triclinic phase of BaNi 2 As 2 evolves to become (0, 0.5, 0) tri charge ordering at x = 0.65 before vanishing at x = 0.71.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Hierarchy among the crystal lattice, charge density wave, and superconducting orders in transition metal dichalcogenides

Using high-energy x-ray scattering and large-scale three-dimensional (3D) structure modeling, in this study we investigate the relationship between the crystal lattice, charge density wave (CDW), and superconducting (SC) orders in transition metal dichalcogenides (TMDs). In particular, we systematically substitute Te for Se in Ta-Se-Te solid solutions, determine changes in their crystal lattice, and relate them to changes in the CDW transition temperature, $T_{CDW}$, and SC critical temperature, $T_c$ . We find that strong lattice distortions such as buckling of Ta layers are detrimental to the CDW and SC orders. The presence of a perfect lattice order in two dimensions is a prerequisite to the emergence of CDWs but insufficient to achieve a SC ordered state. For the SC order to emerge, the Ta sublattice should also appear periodic in 3D. Local chemical disorder may promote the SC order, and the perfectness of Ta coordination polyhedra is a factor contributing to its strength. A hierarchical relationship among the crystal lattice, CDW, and SC orders thus appears to exist in TMDs in a sense that different degrees of crystal lattice order-disorder promote and maintain the CDW and SC orders to a different extent, offering an opportunity to control the latter through modifying the former by rational design. Our findings are a step towards a better understanding of the correlation between lattice and electronic degrees of freedom in TMDs. We also demonstrate an efficient experimental approach to study them in fine detail.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Landau-Ginzburg theory of charge density wave formation accompanying lattice and electronic long-range ordering

Here we propose an analytical Landau-Ginzburg (LG) theory of the charge density waves coupled with lattice and electronic long-range order parameters. Examples of long-range order include the electronic wave function of superconducting Cooper pairs, structural distortions, electric polarization, and magnetization. We formulate the LG free energy density as a power expansion with respect to the charge density and other long-range order parameters as well as their spatial gradients and biquadratic coupling terms. We introduced a biquadratic coupling between the charge density gradient and long-range order parameters as well as nonlinear higher gradients of the long-range order parameters. The biquadratic gradient coupling is critical to the appearance of different spatially modulated phases in charge-ordered ferroics and high-temperature superconductors. We derived the thermodynamic conditions for the stability of the spatially modulated phases, which are the intertwined spatial waves of charge density and lattice/electronic long-range order. The analytical expressions for the energies of different phases, corresponding order parameters, charge density waves amplitudes, and modulation periods obtained in this paper can be employed to guide the comprehensive physical explanation, deconvolution, and Bayesian analysis of experimental data on quantum materials ranging from charge-ordered ferroics to high-temperature superconductors.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Coarsening dynamics of Ising-nematic order in a frustrated Heisenberg antiferromagnet

We study the phase ordering dynamics of the classical antiferromagnetic 𝐽 1 −𝐽 2 (nearest-neighbor and next-nearest-neighbor couplings) Heisenberg model on the square lattice in the strong frustration regime (𝐽 2 /𝐽 1 > 1/2). While thermal fluctuations preclude any long-range magnetic order at finite temperatures, the system exhibits a long-range spin-driven nematic phase at low temperatures. The transition into the nematic phase is further shown to belong to the two-dimensional Ising universality class based on the critical exponents near the phase transition. Our large-scale stochastic Landau-Lifshitz-Gilbert simulations find a two-stage phase ordering when the system is quenched from a high-temperature paramagnetic state into the nematic phase. In the early stage, collinear alignments of spins lead to a locally saturated Ising-nematic order. Once domains of well-defined Ising order are developed, the late-stage relaxation is dominated by curvature-driven domain coarsening, as described by the Allen-Cahn equation. The characteristic size of Ising-nematic domains scales as the square root of time, similar to the kinetic Ising model described by the time-dependent Ginzburg-Landau theory. Our results confirm that the late-stage ordering kinetics of the spin-driven nematic, which is a vestigial order of the frustrated Heisenberg model, belongs to the dynamical universality class of a nonconserved Ising order. Interestingly, the system shows no violation of the superuniversality hypothesis under weak bond disorder. The dynamic scaling invariance is preserved in the presence of weak bond disorder. Here, we also discuss possible applications of our results to materials for which vestigial Ising-nematic order is realized.

Antiferromagnets↗
DOE OSTI2025

Disentangling the intertwined orders in a magnetic kagome metal

Intertwined orders appear when multiple orders are strongly interacting, and kagome metals have emerged as new platforms to explore exotic phases. FeGe has been found to develop a charge density wave (CDW) order within magnetic phase, suggesting an intricate interplay of the lattice, charge, and spin degrees of freedom. Recently, postgrowth annealing has been proposed to tune the CDW order from long-range to complete suppression, offering a tuning knob for the CDW order. Here, by comparing the electronic structures of FeGe subjected to different annealing conditions and distinct CDW properties, we report spectral evolution associated with the lattice and spin degrees of freedom. We find band evolution linked to a spin density wave (SDW) order present in both samples with and without CDW order, and another evolution connected to the lattice distortions that onset with the long-range CDW order and revert with the SDW order. Our results reveal a rare competitive cooperation of the lattice, spin, and charge in FeGe.

Oh, Ji Seop↗
DOE OSTI2020

Comparison of Generation of Higher-Order Neutron Scattering Cross Sections

The generation of high-order neutron scattering cross sections consistent with high-fidelity simulations remains an area of active research. Popular options include generating cross sections from continuous energy Monte Carlo calculations or generating cross sections from a deterministic neutron transport calculation with high-fidelity tabulated cross sections. Both options present challenges. Monte Carlo simulations can naturally process continuous energy cross section data and allow for the general description of anisotropic neutron scattering given a scattering law. However, Monte Carlo simulations are inherently related to particle weighting and it has been suggested that this may be unacceptable for generating high-order neutron scattering cross sections. Deterministic neutron transport calculations can easily calculate high-order moments of the flux to appropriately calculate higher-order neutron scattering cross sections but are generally limited by discretization of space, energy, and angle. In this work, the trade-offs between generation of high-order neutron scattering cross sections via Monte Carlo and deterministic neutron transport methods are investigated. The methods implemented in the Monte Carlo computer program Serpent and the deterministic fast reactor neutron cross section generator MC2-3 are compared. Cross sections resulting from these methods are used in Rattlesnake, a deterministic neutron transport code developed by Idaho National Laboratory (INL), and results are compared to a reference continuous energy Monte Carlo calculation. Whereas previous work investigating the effects of anisotropic neutron scattering has focused on light water reactor (LWR) simulations, this work focuses on high-order neutron scattering cross sections as they relate to fast reactor simulations. To investigate the consequences of the Serpent and MC2-3 methodologies, a test problem is developed. The test problem is a one-dimensional geometry with fast reactor materials designed to demonstrate deep penetration and exacerbate the effects of high-order neutron scattering. Based on the results of the deep penetration test problem, it is concluded that P3 neutron scattering cross sections are sufficient to describe anisotropic scattering in fast reactor materials. Any neutron scattering of order higher than P3 offers negligible change in the eigenvalue of the test problem. Additionally, it is determined that the methodology as implemented in Serpent is applicable for generating high-order neutron scattering cross sections through at least P3 in fast reactor materials.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

Control oriented model order reduction for the hydraulic system of an autonomous wheel loader

Control design for an autonomous wheel loader requires a high-fidelity and low-order dynamics model. The objective of order reduction is to decrease the number of states in the model while maintaining performance comparable to the original model. Of all the power components in a wheel loader, the model order reduction for steering and working hydraulic systems is most demanding due to its nonlinear and stiff dynamical nature. This paper describes a physics-inspired model order reduction method that can reduce the model order by close to thirty percent. It is achieved by discarding orders with fast dynamics and consolidating multiple states into less new states. Furthermore, this method can also be extended to other types of off-road vehicles such as excavators, bulldozers, etc. Simulation results demonstrate that the reduced-order model exhibits very similar performance to the full-order model under typical operating conditions of wheel loaders, with an output error of less than six percent.

42 ENGINEERING↗
DOE OSTI2026

A fourth order sharp immersed method for the incompressible Navier-Stokes equations with stationary and moving boundaries and interfaces

We propose a fourth order Navier-Stokes solver based on the immersed interface method (IIM), for flow problems with stationary and one-way coupled moving boundaries and interfaces. Our algorithm employs a Runge-Kutta-based projection method that maintains high-order temporal accuracy in both velocity and pressure for steady and unsteady velocity boundary conditions. Fourth order spatial accuracy is achieved through a novel fifth order IIM discretization scheme for the advection term, as well as existing high-order interface-corrected finite difference schemes for the other differential operators. Using a set of manufactured flow problems with stationary and moving boundaries, we demonstrate fourth order convergence of velocity and pressure in the infinity norm, both inside the domain and on the immersed boundaries. The solver’s performance is further validated through a range of practical flow simulations, highlighting its efficiency over a second order scheme. Finally, we showcase the ability of our immersed discretization scheme to handle interface-coupled multiphysics problems by solving a conjugate heat transfer problem with multiple immersed solids. Overall, the proposed approach robustly combines the efficiency of high order discretization schemes with the flexibility of immersed discretizations for flow problems with complex, moving boundaries and interfaces.

42 ENGINEERING↗
DOE OSTI2025

Higher-order factorization machine for accurate surrogate modeling in material design

Efficient and robust optimization is important in material science for identifying optimal structural parameters and enhancing material performance. Surrogate-based active learning algorithms have recently gained great attention for their ability to efficiently navigate large, high-dimensional design spaces. Among surrogate models, 2 nd -order factorization machine (FM) models are widely employed as the surrogate model in active learning algorithms due to their balance between simplicity and effectiveness. However, their quadratic nature limits their capacity to capture complex, higher-order interactions among variables, often leading to suboptimal solutions. To overcome this limitation, we propose an active learning scheme integrating a 3 rd -order FM model, capable of modeling three-variable interactions and more intricate relationships in material systems. We comprehensively evaluate the surrogate modeling performance of the 3 rd -order FM case using various objective functions. Furthermore, we examine the optimization reliability and efficiency of the 3 rd -order FM-based active learning in a real-world material design task (e.g., nanophotonic structures for transparent radiative cooling). Our study shows that the 3 rd -order FM outperforms the 2 nd -order model in both surrogate accuracy and optimization performance, highlighting higher-order models’ promises for material design and optimization problems.

Factorization machine↗
DOE OSTI2021

Origin of the magnetic and orbital ordering in α-Sr 2 CrO 4

Motivated by recent experimental progress in transition metal oxides with the K 2 NiF 4 structure, in this study we investigate the magnetic and orbital ordering in α-Sr 2 CrO 4 . Using first principles calculations, first we derive a three-orbital Hubbard model, which reproduces the ab initio band structure near the Fermi level. The unique reverse splitting of t 2g orbitals in α-Sr 2 CrO 4 , with the 3d 2 electronic configuration for the Cr 4+ oxidation state, opens up the possibility of orbital ordering in this material. Using real-space Hartree-Fock for multi-orbital systems, we constructed the ground state phase diagram for the two dimensional compound α-Sr 2 CrO 4 . We found stable ferromagnetic, antiferromagnetic, antiferro-orbital, and staggered orbital stripe ordering in robust regions of the phase diagram. Furthermore, using the density matrix renormalization group method for two-leg ladders with the realistic hopping parameters of α-Sr 2 CrO 4 , we explore magnetic and orbital ordering for experimentally relevant interaction parameters. Again, we find a clear signature of antiferromagnetic spin ordering along with antiferro-orbital ordering at moderate to large Hubbard interaction strength. We also explore the orbital-resolved density of states with Lanczos, predicting insulating behavior for the compound α-Sr 2 CrO 4 , in agreement with experiments. Finally, an intuitive understanding of the results is provided based on a hierarchy between orbitals, with d xy driving the spin order, while electronic repulsion and the effective one dimensionality of the movement within the d xz and d yz orbitals driving the orbital order.

36 MATERIALS SCIENCE↗
DOE OSTI2025

A high-order computational framework for particle-resolved simulations of disperse multiphase flows

This work presents a high-order numerical approach for particle-resolved simulations of disperse multiphase flows, where the Navier-Stokes equations for fluid flow are solved using a high-order spectral element method in the Eulerian framework, and the particle phase is directly simulated with a discrete element method. The coupling between particles and fluids is explicitly handled using an adapted direct-forcing immersed boundary method. Unlike the conventional schemes, a high-order barycentric Lagrange interpolation method and a Gaussian projection kernel are used to ensure accurate momentum exchange between local boundary points and surrounding fluid nodes in the framework of high-order fluid solver. Benchmark tests of increasing complexity are conducted to demonstrate the accuracy and efficiency of our method. Here, it is found that our approach exhibits an excellent convergence performance, as the fluid element/grid is refined and the number of boundary points increases. Compared to conventional low-order methods, the proposed high-order framework enables the use of substantially larger fluid elements while maintaining high accuracy in modeling fluid-particle interactions, owing to the enhanced resolution of high-order basis functions. Moreover, since the primary unknowns are stored at element or grid nodes, the high-order approach offers improved efficiency in both CPU memory usage and total computational cost.

42 ENGINEERING↗
DOE OSTI2023

Orientational Order in Spin-Cast Lead-Iodide Perovskite Nanocrystal Solids

Combined synthetic control over size and composition renders colloidal lead-halide perovskite nanocrystals a tunable platform for high-efficiency optoelectronic applications. However, the properties and operational stability of devices based on nanocrystal solids are often dictated by the method of the evaporation-induced assembly. Ubiquitous slow evaporation techniques can produce highly ordered nanocrystal domains but limit the prospects for scalable fabrication of continuous device layers, calling for investigation of approaches to more rapidly form ordered perovskite nanocrystal solids. Here, we study orientationally ordered lead-iodide perovskite nanocrystal solids prepared by conventional spin coating with molecular additives (excess ligand) to enhance ordering within the arrays. In situ X-ray scattering measurements reveal that orientational ordering occurs rapidly upon solvent removal during spin coating and can be further enhanced by manipulating the spin speed. We vary the additive ligand length and explore trade-offs between ordering and layered perovskite impurity formation. Arrays treated with the intermediate-length octylamine ligand exhibit increased in-plane electronic conductivity, suggesting orientational ordering and internanocrystal electronic coupling can be enhanced by the treatment. In conclusion, these results highlight the prospects of establishing long-range order in lead-halide perovskite nanocrystal solids by using simple and fast coating methods.

14 SOLAR ENERGY↗
DOE OSTI2026

Orientation-dependent mutual crystalline and amorphous order in a single phase solid

Amorphous materials distinguish themselves from crystalline materials by lacking long-range order while retaining structural order at the local scale (2–5 Å). However, the complexity in topological and chemical order prevents current characterization tools from fully unveiling the structure in disordered materials. Consequently, the nature of medium-range order in amorphous materials has remained elusive. The Zachariasen and crystal competing models have been proposed to describe disordered phases and have both been verified through synthesis and characterization. The main difference between them is thought to be whether the amorphous phase shows medium-range order. Here we demonstrate a form of organized inorganic matter that is amorphous in two dimensions, while exhibiting long-range order and a high degree of crystallinity in the third. The structure consists of periodically stacked 2-dimensional amorphous Nb-W-O monolayers without long-range in-plane order. The unique periodic and therefore crystalline stacking along one principal axis enables direct imaging and revealed that the amorphous Nb-W-O monolayers formed in agreement with the Zachariasen model for 2 dimensions. Our findings show that the gap between crystalline and amorphous materials does not only depend on medium-range order but can also apply to principal dimensions within the same solid.

Nanowires↗
DOE OSTI2020

Spectroscopic fingerprint of charge order melting driven by quantum fluctuations in a cuprate

Copper oxide high-T C superconductors possess a number of exotic orders that coexist with or are proximal to superconductivity. Quantum fluctuations associated with these orders may account for the unusual characteristics of the normal state, and possibly affect the superconductivity. Yet, spectroscopic evidence for such quantum fluctuations remains elusive. Here in this paper, we use resonant inelastic X-ray scattering to reveal spectroscopic evidence of fluctuations associated with a charge order in nearly optimally doped Bi 2 Sr 2 CaCu 2 O 8+δ . In the superconducting state, while the quasielastic charge order signal decreases with temperature, the interplay between charge order fluctuations and bond-stretching phonons in the form of a Fano-like interference increases, an observation that is incompatible with expectations for competing orders. Invoking general principles, we argue that this behaviour reflects the properties of a dissipative system near an order–disorder quantum critical point, where the dissipation varies with the opening of the pseudogap and superconducting gap at low temperatures, leading to the proliferation of quantum critical fluctuations, which melt charge order.

36 MATERIALS SCIENCE↗