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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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At least 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Subcell limiting strategies for discontinuous Galerkin spectral element methods

Here, we present a general family of subcell limiting strategies to construct robust high-order accurate nodal discontinuous Galerkin (DG) schemes. The main strategy is to construct compatible low order finite volume (FV) type discretizations that allow for convex blending with the high-order variant with the goal of guaranteeing additional properties, such as bounds on physical quantities and/or guaranteed entropy dissipation. For an implementation of this main strategy, four main ingredients are identified that may be combined in a flexible manner: (i) a nodal high-order DG method on Legendre–Gauss–Lobatto nodes, (ii) a compatible robust subcell FV scheme, (iii) a convex combination strategy for the two schemes, which can be element-wise or subcell-wise, and (iv) a strategy to compute the convex blending factors, which can be either based on heuristic troubled-cell indicators, or using ideas from flux-corrected transport methods. By carefully designing the metric terms of the subcell FV method, the resulting methods can be used on unstructured curvilinear meshes, are locally conservative, can handle strong shocks efficiently while directly guaranteeing physical bounds on quantities such as density, pressure or entropy. We further show that it is possible to choose the four ingredients to recover existing methods such as a provably entropy dissipative subcell shock-capturing approach or a sparse invariant domain preserving approach. We test the versatility of the presented strategies and mix and match the four ingredients to solve challenging simulation setups, such as the KPP problem (a hyperbolic conservation law with non-convex flux function), turbulent and hypersonic Euler simulations, and MHD problems featuring shocks and turbulence.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

High-Accuracy Mesh-Free Quadrature for Trimmed Parametric Surfaces and Volumes

This work presents a high-accuracy, mesh-free, generalized Stokes theorem-based numerical quadrature scheme for integrating functions over trimmed parametric surfaces and volumes. The algorithm relies on two fundamental steps: (1) We iteratively reduce the dimensionality of integration using the generalized Stokes theorem to line integrals over trimming curves, and (2) we employ numerical antidifferentiation in the generalized Stokes theorem using high-order quadrature rules. Additionally, the scheme achieves exponential convergence up to trimming curve approximation error and has applications to computation of geometric moments, immersogeometric analysis, conservative field transfer between high-order curvilinear meshes, and initialization of multi-material simulations. We compare the quadrature scheme to commonly-used quadrature schemes in the literature and show that our scheme is much more efficient in terms of number of quadrature points used. We provide an open-source implementation of the scheme in MATLAB as part of QuaHOG, a software package for Quadrature of High-Order Geometries.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Semiconducting to Metallic Electronic Landscapes in Defects-Controlled 2D π-d Conjugated Coordination Polymer Thin Films

Two-dimensional coordination polymers (2DCPs) have been predicted to exhibit exotic properties such as superconductivity, topological insulating behavior, catalytic activity, and superior ion transport for energy applications; experimentally, these materials have fallen short of their expectation due to the lack of synthesis protocols that yield continuous, large crystallite domains, and highly ordered thin films with controllable physical and chemical properties. Herein, the fabrication of large-area, highly ordered 2DCP thin films with large crystallite domains using chemical vapor deposition (CVD) approaches is described. It is demonstrated that defects and the packing motifs of 2DCP thin films may be controlled by adjusting the vapor–vapor and vapor–solid interactions of the metal and organic linker precursors during the CVD fabrication process. Such control allows for the fabrication of defects-controlled 2DCP thin films that show either semiconducting or metallic behavior. The findings provide the first demonstration of tuning the electrical properties of sub 100 nm-thick continuous 2DCP thin films by controlling their electronic landscape through defect engineering. As such, it is determined that large-area, highly ordered 2DCP thin films may undergo a semiconducting to metallic transition that is correlated to changes in morphology, crystalline domain sizes, crystallite orientation, defect interactions, and electronic structure.

2D coordination polymers↗
DOE OSTI2025

A Particle-in-Cell Method for Plasmas with a Generalized Momentum Formulation, Part I: Model Formulation

Here, this paper formulates a new particle-in-cell method for the Vlasov–Maxwell system. Under the Lorenz gauge condition, Maxwell’s equations for the electromagnetic fields can be written as a collection of scalar and vector wave equations. The use of potentials for the fields motivates the adoption of a Hamiltonian formulation for particles that employs the generalized (conjugate) momentum. A notable advantage offered by the Hamiltonian formulation is the elimination of time derivatives in the Lorenz gauge formulation that are required by the standard Newton–Lorentz treatment of the particles. This allows the fields to retain the full time-accuracy guaranteed by the field solver. The resulting updates for particles require only knowledge of the fields and their spatial derivatives. An analytical method for constructing these spatial derivatives is presented that exploits the underlying integral solution used in the field solver for the wave equations. Moreover, these derivatives are demonstrated to converge at the same rate as the fields in both time and space. The Method of Lines Transpose field solver we consider in this work is globally first-order accurate in time and high-order accurate in space (e.g., fourth- and fifth-order) and belongs to a larger class of methods which are unconditionally stable, can address geometry, and leverage $\mathcal {O}(N)$ fast summation methods for efficiency. We demonstrate the method on several well-established benchmark problems on bounded domains, including a plasma sheath as well as a relativistic particle beam. The efficacy of the proposed formulation is established by comparing with a second-order accurate finite-difference time-domain method that employs a leapfrog time advance for particles and a charge conserving map suitable for bounded domains. The new method shows mesh-independent numerical heating properties even in cases where the plasma Debye length is smaller than the grid spacing. This is an important feature of the new method for problems defined on bounded domains, because it permits the use of coarser grids in space in the representation of the fields. Such a capability has significant implications for the simulation of plasmas in bounded domains with complex geometry, where the ratio between the largest and smallest cells can vary significantly. The use of high-order spatial approximations in the new method also means that fewer grid points are required in order to achieve a fixed accuracy. Our results also suggest that the new method can be used with fewer simulation particles per cell compared to the benchmark explicit method, which permits further computational savings.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

LA17-V-InverseRadTransportProblem-PD2Kb. Final Project Report

In the inverse radiation transport problem, a radiation signal emanating from an unknown object is used to reconstruct geometric and material parameters of the object , e.g., the mass of special nuclear material (SNM), the isotopic composition of the SNM (e.g., the enrichment of 235U), the thickness of shielding, etc. The inverse radiation transport problem is one of the most fundamental and important in the emergency response mission, and has been addressed in previous NA-22 and NA-42/84 investments by using derivative-free optimization methods. Our project was aimed at (i) consolidating previous work by applying polynomial chaos expansion (PCE) for reducing significantly the number of forward model simulations required by derivative-free optimization methods; (ii) developing a general-purpose framework and stand-alone software for solving the inverse radiation transport problem by applying a new “predictive modeling” methodology (predictive modeling of coupled multi-physics systems, PM_CMPS) which enables the fusing of experimental and computational information; and (iii) developing several benchmarks (for unscattered gamma rays) for demonstrating the quantification of non-Gaussian features (e.g., skewness and kurtosis, which characterize asymmetries and long tails) of response distributions by deterministically and efficiently propagating parameter uncertainties (covariances and higher-order moments, where available) using high-order sensitivities computed by the recently developed comprehensive adjoint sensitivity analysis methodology (C-ASAM). With regard to (i), application of PCE, the most significant accomplishment of this project was an implementation of PCE into INVERSE that significantly reduced computation time for the DiffeRential Evolution Adaptive Metropolis (DREAM) and Differential Evolution (DE) methods. For inverse transport problems with measurements of neutron leakage, neutron multiplication, and neutron-induced gamma-rays, the solution times for the DREAM and DE methods were reduced by factors of 30-300, reducing run times from hours to minutes while maintaining the same accuracy as the standard (non-PCE) DREAM and DE. Speedups were further improved by exploring sparse grid quadrature sets using the Toolkit for Adaptive Stochastic Modeling and Non-Intrusive ApproximatioN (Tasmanian) toolset. An initial exploration of sparse grids indicated that further speedups factors of 5-10 are obtainable. The implementation of PCE in INVERSE is not in a form that users can easily access. With regard to (ii), solving the inverse problem using a predictive modeling paradigm, the most significant accomplishment of this project were the derivation and implementation of adjoint-based second derivatives in neutron and photon transport theory. There are two codes that compute these derivatives. SENSPG computes them for uncollided gamma rays and SENSMG computes them for neutron leakage. SENSMG is open-source code available on github. Other significant accomplishments included a stand-alone code, MULTI-PRED, that implements the predictive modeling paradigm, along with a detailed manual. The code was implemented in the existing INVERSE code for inverse problems, but a head-to-head comparison of inverse methods was not achieved. We also derived and implemented the capability to compute sensitivities for multiplicity measurements into the SENSMG code, and this capability was used in a data assimilation application, but it was not used for solving inverse problems. With regard to (iii), developing benchmarks to demonstrate the importance of high-order sensitivity and uncertainty analysis, the most significant accomplishment of this project were two test problems that showed how important second-order sensitivities are.

07 ISOTOPE AND RADIATION SOURCES↗
DOE OSTI2020

Efficient discontinuous Galerkin implementations and preconditioners for implicit unsteady compressible flow simulations

This work presents and compares efficient implementations of high-order discontinuous Galerkin methods: a modal matrix-free discontinuous Galerkin (DG) method, a hybridizable discontinuous Galerkin (HDG) method, and a primal formulation of HDG, applied to the implicit solution of unsteady compressible flows. The matrix-free implementation allows for a reduction of the memory footprint of the solver when dealing with implicit time-accurate discretizations. HDG reduces the number of globally-coupled degrees of freedom relative to DG, at high order, by statically condensing element-interior degrees of freedom from the system in favor of face unknowns. The primal formulation further reduces the element-interior degrees of freedom by eliminating the gradient as a separate unknown. This paper introduces a p-multigrid preconditioner implementation for these discretizations and presents results for various flow problems. Benefits of the p-multigrid strategy relative to simpler, less expensive, preconditioners are observed for stiff systems, such as those arising from low-Mach number flows at high-order approximation. The p-multigrid preconditioner also shows excellent scalability for parallel computations. Finally, additional savings in both speed and memory occur with a matrix-free/reduced version of the preconditioner.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Classification of critical points in energy bands based on topology, scaling, and symmetry

A critical point of the energy dispersion is the momentum where electron velocity vanishes. At the corresponding energy, the density of states (DOS) exhibits nonanalyticity such as divergence. Critical points can be first classified as ordinary and high-order ones, and the ordinary critical points have been studied thoroughly by Léon van Hove, whose DOS is particle-hole symmetric and logarithmically divergent. In this work, we describe and classify high-order critical points based on topology, scaling, and symmetry. Specifically, we show that high-order critical points can have power-law-divergent DOS with particle-hole asymmetry, and can be realized at generic or symmetric momenta by tuning a few parameters such as twist angle, strain, pressure, and/or external fields.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
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 OSTI2021

Structure-preserving numerical discretizations for domains with boundaries

This SAND report documents Exploratory Express LDRD Project 223790, "Structure-preserving numerical discretizations for domains with boundaries", which developed a method to incorporate consistent treatment of domain boundaries and arbitrary boundary conditions in discrete exterior calculus (DEC) for arbitrary polygonal (2D) and tensor-product structure prism (3D) grids. The new DEC required the development of novel discrete exterior derivatives, boundary operators, wedge products and Hodge stars. This was accomplished through the use of boundary extension and the blending of known 2D operators on the interior with 1D operators on the boundary. The Hodge star was based on the Voronoi Hodge star, and retained the limitation of a triangular circumcentric primal or dual grid along with low-order accuracy. In addition to the new DEC, two related software packages were written: one for the study of DEC operators on arbitrary polygonal and polyhedral grids using both symbolic and numerical approaches and one for a (thermal) shallow water testbed using TRiSK-type numerics. Immediately relevant (already funded, through CANGA) followup work is the development of a high-order, geometrically flexible Hodge star and structure-preserving, high-order, oscillation-limiting transport operators (using WENO) for n-forms on arbitrary 2D and 3D grids. This will provide all of the machinery required for a high-order version of TRiSK with boundaries on arbitrary 2D and tensor-product 3D grids, which is applicable to both the atmospheric (CRM in E3SM-MMF) and oceanic (MPAS-O) components of E3SM.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Self-Assembly of 2D Gold Nanoparticle Superlattice in a Polymer Vesicle Layer Driven by Hydrophobic Interaction

We report self-assembly of gold nanoparticles (AuNPs) into highly ordered superstructures provides a promising route toward fabricating materials with new functionalities or enhanced physical properties. Although self-assembly of AuNPs has garnered significant research attention recently, a highly ordered superlattice of AuNPs under a low concentration in a confined geometry formed by nonfunctionalized materials has not been reported. Herein, we investigate the self-assembly of a 2D AuNPs superlattice in a polymer vesicle layer using hydrophobic interactions, which exhibits centered rectangular lattice symmetry. To create the highly ordered AuNPs superlattice, the P(EG x -b-iPGE y ) block copolymers that form the thickness of the hydrophobic vesicle layer comparable to the size of the AuNP are used as a template to control the AuNP degree of freedom. To the best of our knowledge, this study provides the first demonstration of a centered rectangular structure formation of AuNPs at the vesicle layer in 2D confined geometry.

self-assembly↗
DOE OSTI2022

Metrics for Intercomparison of Remapping Algorithms (MIRA) protocol applied to Earth system models

Abstract. Strongly coupled nonlinear phenomena such as those described by Earth system models (ESMs) are composed of multiple component models with independent mesh topologies and scalable numerical solvers. A common operation in ESMs is to remap or interpolate component solution fields defined on their computational mesh to another mesh with a different combinatorial structure and decomposition, e.g., from the atmosphere to the ocean, during the temporal integration of the coupled system. Several remapping schemes are currently in use or available for ESMs. However, a unified approach to compare the properties of these different schemes has not been attempted previously. We present a rigorous methodology for the evaluation and intercomparison of remapping methods through an independently implemented suite of metrics that measure the ability of a method to adhere to constraints such as grid independence, monotonicity, global conservation, and local extrema or feature preservation. A comprehensive set of numerical evaluations is conducted based on a progression of scalar fields from idealized and smooth to more general climate data with strong discontinuities and strict bounds. We examine four remapping algorithms with distinct design approaches, namely ESMF Regrid (Hill et al., 2004), TempestRemap (Ullrich and Taylor, 2015), generalized moving least squares (GMLS) (Trask and Kuberry, 2020) with post-processing filters, and WLS-ENOR (Li et al., 2020). By repeated iterative application of the high-order remapping methods to the test fields, we verify the accuracy of each scheme in terms of their observed convergence order for smooth data and determine the bounded error propagation using challenging, realistic field data on both uniform and regionally refined mesh cases. In addition to retaining high-order accuracy under idealized conditions, the methods also demonstrate robust remapping performance when dealing with non-smooth data. There is a failure to maintain monotonicity in the traditional L2-minimization approaches used in ESMF and TempestRemap, in contrast to stable recovery through nonlinear filters used in both meshless GMLS and hybrid mesh-based WLS-ENOR schemes. Local feature preservation analysis indicates that high-order methods perform better than low-order dissipative schemes for all test cases. The behavior of these remappers remains consistent when applied on regionally refined meshes, indicating mesh-invariant implementations. The MIRA intercomparison protocol proposed in this paper and the detailed comparison of the four algorithms demonstrate that the new schemes, namely GMLS and WLS-ENOR, are competitive compared to standard conservative minimization methods requiring computation of mesh intersections. The work presented in this paper provides a foundation that can be extended to include complex field definitions, realistic mesh topologies, and spectral element discretizations, thereby allowing for a more complete analysis of production-ready remapping packages.

58 GEOSCIENCES↗
DOE OSTI2021

On the numerical accuracy in finite-volume methods to accurately capture turbulence in compressible flows

The goal of the present article is to understand the impact of numerical schemes for the reconstruction of data at cell faces in finite-volume methods, and to assess their interaction with the quadrature rule used to compute the average over the cell volume. Here, third-, fifth- and seventh-order WENO-Z schemes are investigated. On a problem with a smooth solution, the theoretical order of convergence rate for each method is retrieved, and changing the order of the reconstruction at cell faces does not impact the results, whereas for a shock-driven problem all the methods collapse to first-order. Here, study of the decay of compressible homogeneous isotropic turbulence reveals that using a high-order quadrature rule to compute the average over a finite-volume cell does not improve the spectral accuracy and that all methods present a second-order convergence rate. However the choice of the numerical method to reconstruct data at cell faces is found to be critical to correctly capture turbulent spectra. In the context of simulations with finite-volume methods of practical flows encountered in engineering applications, it becomes apparent that an efficient strategy is to perform the average integration with a low-order quadrature rule on a fine mesh resolution, whereas high-order schemes should be used to reconstruct data at cell faces.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Enhancements to Overset Methods for Achieving Higher Accuracy and Solution Convergence: Preprint

Overset methods, when utilized within a multi-solver framework, provide a very flexible and powerful toolset for analyzing moving body problem. However, many overset framework suffer from several deficiencies such as (1) convergence degradation of the non-linear iterative schemes (2) difficulty in achieving higher-order accuracy and (3) high computational costs over long simulation times. In this work, we explore approaches that mitigate these deficiencies and provide a pathway for improved accuracy and fidelity of overset methods. A high-order, discontinuous Galerkin solver is integrated into an existing overset framework and applied to an unsteady ROBIN fuselage case. For convergence acceleration, an Overset-GMRES linear solver with a timestep controller is applied to a DLR-F6 aircraft steady simulation and an unsteady, notional rotor-fuselage. Finally the same rotor-fuselage case as well as the JVX rotor/wing case is simulated using a reduced-order aerodynamic model.

aerospace↗
DOE OSTI2024

Robust 3D multi-material hydrodynamics using discontinuous Galerkin methods

A high-order discontinuous Galerkin (DG) method is presented for nonequilibrium multi-material (m ≥ 2) flow with sharp interfaces. Material interfaces are reconstructed using the algebraic THINC approach, resulting in a sharp interface resolution. The system assumes stiff velocity relaxation and pressure nonequilibrium. The presented DG method uses Dubiner's orthogonal basis functions on tetrahedral elements. This results in a unique combination of sharp multimaterial interfaces and high-order accurate solutions in smooth single-material regions. A novel shock indicator based on the interface conservation condition is introduced to mark regions with discontinuities. Slope limiting techniques are applied only in these regions so that nonphysical oscillations are eliminated while maintaining high-order accuracy in smooth regions. A local projection is applied on the limited solution to ensure discrete closure law preservation. The effectiveness of this novel limiting strategy is demonstrated for complex three-dimensional multi-material problems, where robustness of the method is critical. The presented numerical problems demonstrate that more accurate and efficient multi-material solutions can be obtained by the DG method, as compared to second-order finite volume methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Two-Dimensional Binary Superlattice of BNNT-Surfactant Vesicle Complex Induced by Electrostatic Interaction

For a wide range of practical applications of boron nitride nanotubes (BNNTs), it is essential to achieve their highly ordered self-assembled structures. This study reports on a two-dimensional (2D) binary superlattice of individually exfoliated BNNTs with a negative surface charge (p-BNNT25) and cationic surfactant vesicles (CTAT/SDBS vesicles, prepared by mixing cetyltrimethylammonium tosylate (CTAT) and sodium dodecylbenzenesulfonate (SDBS)) complexes through electrostatic interactions. Depending on the surface charge density of the CTAT/SDBS vesicles and the mass ratio between the CTAT/SDBS vesicle and p-BNNT25, the CTAT/SDBS-BNNT complexes formed highly ordered superstructures. These structures include an intercalated lamellar phase with a centered rectangular structure (ICLP), in which a 2D array of p-BNNT25 is inserted into the multilamellar structure, and an AB 3 structure, in which the BNNTs are surrounded by surfactant micelles in a triangular arrangement. To the best of our knowledge, this is the first demonstration of the fabrication of highly ordered superstructures of individually exfoliated and negatively charged BNNTs with positively charged surfactant vesicles through electrostatic interactions. This approach for the 2D binary superlattices of CTAT/SDBS-BNNT complexes induced by electrostatic interactions is expected to be beneficial for a wide range of one-dimensional (1D) nanoparticle applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Scalability of high-performance PDE solvers

Performance tests and analyses are critical to effective high-performance computing software development and are central components in the design and implementation of computational algorithms for achieving faster simulations on existing and future computing architectures for large-scale application problems. In this article, we explore performance and space-time trade-offs for important compute-intensive kernels of large-scale numerical solvers for partial differential equations (PDEs) that govern a wide range of physical applications. We consider a sequence of PDE-motivated bake-off problems designed to establish best practices for efficient high-order simulations across a variety of codes and platforms. We measure peak performance (degrees of freedom per second) on a fixed number of nodes and identify effective code optimization strategies for each architecture. In addition to peak performance, we identify the minimum time to solution at 80% parallel efficiency. The performance analysis is based on spectral and p-type finite elements but is equally applicable to a broad spectrum of numerical PDE discretizations, including finite difference, finite volume, and h-type finite elements.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Effective field theory for dilute Fermi systems at fourth order

We discuss high-order calculations in perturbative effective field theory for fermions at low energy scales. The Fermi-momentum or k F a s as expansion for the ground-state energy of the dilute Fermi gas is calculated to fourth order, both in cutoff regularization and in dimensional regularization. For the case of spin one-half fermions we find from a Bayesian analysis that the expansion is well converged at this order for |k F a s |≲ 0.5. Furthermore, we show that Padé-Borel resummations can improve the convergence for |k F a s |≲ 1. Here, our results provide important constraints for nonperturbative calculations of ultracold atoms and dilute neutron matter.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

High-harmonic generation from artificially stacked 2D crystals

Here, we report a coherent layer-by-layer build-up of high-order harmonic generation (HHG) in artificially stacked transition metal dichalcogenides (TMDC) crystals in their various stacking configurations. In the experiments, millimeter-sized single crystalline monolayers are synthesized using the gold foil-exfoliation method, followed by artificially stacking on a transparent substrate. High-order harmonics up to the 19th order are generated by the interaction with a mid-infrared (MIR) driving laser. We find that the generation is sensitive to both the number of layers and their relative orientation. For AAAA stacking configuration, both odd- and even-orders exhibit a quadratic increase in intensity as a function of the number of layers, which is a signature of constructive interference of high-harmonic emission from successive layers. Particularly, we observe some deviations from this scaling at photon energies above the bandgap, which is explained by self-absorption effects. For AB and ABAB stacking, even-order harmonics remain below the detection level, consistent with the presence of inversion symmetry. Our study confirms our capability of producing nonperturbative high-order harmonics from stacked layered materials subjected to intense MIR fields without damaging samples. Our results have implications for optimizing solid-state HHG sources at the nanoscale and developing high-harmonics as an ultrafast probe of artificially stacked layered materials. Because the HHG process is a strong-field driven process, it has the potential to probe high-momentum and energy states in the bandstructure combined with atomic-scale sensitivity in real space, making it an attractive probe of novel material structures such as the Moiré pattern.

2D materials↗