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DOE OSTI2021

Origin of the background absorption in carbon nanotubes: Phonon-assisted excitonic continuum

Excitonic effects in 1D semiconductors can be qualitatively different from those in higher dimensions. In particular, the Sommerfeld factor, the ratio of the above-band-edge excitonic continuum absorption to free electron-hole pair generation, has been shown to be less than 1 (suppressed) in 1D systems while it is larger than 1 (enhanced) in 2D and 3D systems. Strong continuum suppression indeed exists in semiconducting single-wall carbon nanotubes, a prototypical 1D semiconductor. However, absorption spectra for carbon nanotubes are typically fit with a combination of Lorentzians and a polynomial background baseline with little physical meaning. We performed absorption measurements in aligned single-chirality (6,5) carbon nanotube films. The obtained spectra were fit with our theoretical model obtained by solving the Boltzmann scattering equation involving fifty-nine different types of transitions among three different types of quasiparticles. Specifically, we took into account microscopic interactions between photons, phonons, and excitons, including their dispersions, which unambiguously demonstrated that the background absorption is due to phonon-assisted transitions from the semiconductor vacuum to finite-momentum continuum states of excitons. The excellent agreement we obtained between experiment and theory suggests that our numerical technique can be seamlessly extended to compute strongly out-of-equilibrium many-body dynamics and time-resolved spectra in low-dimensional materials.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Accelerating high-strain continuum-scale brittle fracture simulations with machine learning

Failure in brittle materials under dynamic loading conditions is a result of the propagation and coalescence of microcracks. Simulating this discrete crack evolution at the continuum level is computationally expensive or, in some cases, intractable, resulting in the need to make broad assumptions or neglect key physics. In this work, we have developed an approach using machine learning that overcomes the current inability to represent meso-scale physics at the macro-scale. Our approach leverages damage and stress data from a computationally expensive high-fidelity model that explicitly resolves microcrack behavior to build an inexpensive machine learning emulator. Once trained, the machine learning emulator is used to predict the evolution of crack length statistics, which then informs a continuum-scale constitutive model. This results in a significant speed-up of the workflow by four orders of magnitude. Both the machine learning emulator and the continuum-scale model are validated against the high-fidelity model and experimental data, respectively, showing excellent agreement. There are two key findings. The first is that we can reduce the dimensionality of the problem, establishing that the machine learning emulator only needs the length of the longest crack and one of the maximum stress components to capture the necessary physics. Another compelling finding is that the emulator can be trained in one experimental setting and transferred successfully to predict behavior in a different setting.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Modeling the dynamic response of rock masses with multiple compliant fluid saturated joint sets - Part II: Continuum modeling

Part I of this two-part paper describes enhancements of a mesoscale model to include: many non-persistent fluid saturated joints with finite area, normal compliance with hysteresis and the weakening effects of angular deviation in the joint sets and of fluid pressure in the joints. The objective of this Part II is to use the results of the mesoscale model as simulated data to inspire functional forms in a continuum model for rock masses with multiple compliant fluid saturated joint sets which include these enhancements. Also, an algorithm is proposed for reducing the number of joint sets being modeled. Examples are presented here which show that the continuum model can predict similar anisotropic response to that observed in mesoscale simulations. In contrast with the mesoscale model, the continuum model can be used for large scale simulations of real applications, smoothly transitioning from coupled inelastic thermomechanical response near an explosive source to orthotropic elastic response far from the source.

58 GEOSCIENCES↗

DOE OSTI2024

Radiative and continuum dampings of reversed shear Alfvén eigenmodes and perturbative analysis limitations for tokamaks

A careful theoretical analysis of the excitation of Alfvén eigenmodes (AEs), such as TAE (toroidicity-induced AE) and RSAE (reversed shear AE), by superalfvenic energetic particles is required for reliable predictions of energetic ion relaxation in present day fusion experiments. This includes the evaluation of different AE damping mechanisms including radiative and continuum dampings which are the focus of this study. A recent comprehensive benchmark of different eigenmode solvers including gyrokinetic, gyrofluid and hybrid magenetohydrodynamics (MHD) has shown that employed models may have deficiencies when addressing some of them (Taimourzadeh et al., Nucl. Fusion, vol. 59, 2019, 066006). Here, in this paper, we are studying the radiative and continuum dampings of RSAEs in details which were missing in hybrid NOVA/NOVA-C calculations to prepare a NOVA-C package with a substantial upgrade. Both dampings require the finite Larmor radius (FLR) corrections to AE mode structures to be accounted for. Accurately calculating different damping rates and understanding their parametric dependencies, we resolve the limitation coming out of the perturbative approach. In particular, here, the radiative damping is included perturbatively, whereas the continuum damping is computed non-perturbatively. Our comparison leads to the conclusion that the non-perturbative treatment of the unstable RSAE modes is needed to find the agreement with the gyrokinetic calculations. We expect that the RSAE mode structure modification plays a dominant role in determining the RSAE stability.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

A Review of Computational Models for the Flow of Milled Biomass Part II: Continuum-Mechanics Models

The design of efficient material-handling systems for milled lignocellulosic biomass is challenging due to their complex particle morphologies and frictional interactions. Computational modeling, including the discrete element method (DEM) and continuum-based finite-element/volume methods, may offer scientific insight and predictive capabilities for the flow of milled biomass in hoppers and feeders. Herein, this article (Part II) presents a review of current state-of-the-art continuum models for the flow of milled biomass, whereas DEM models are reviewed in a companion article (Part I). Advances of numerical methods to solve the global governing equations are discussed first, followed by a comprehensive review of constitutive models for granular materials, including Drucker–Prager, hypoplastic, Cambridge-type, inertial-rheology, and nonlocal granular fluidity models. Specifically, we provide in-depth discussion on the suitability of those models for milled lignocellulosic biomass materials in terms of nonlinear elasticity, dependence of flow strength on pressure, density and shear rate, and compaction (dilation) associated with hardening (softening). Furthermore, our study shows that, despite the recent advances in continuum granular flow modeling, the most suitable constitutive models still need further development to account for material parametrization, multiflow regimes, and multiscale behavior before they can be reliably used to optimize the design and operation of biomass handling systems.

09 BIOMASS FUELS↗

DOE OSTI2020

Fifth-degree elastic energy for predictive continuum stress–strain relations and elastic instabilities under large strain and complex loading in silicon

Materials under complex loading develop large strains and often phase transformation via an elastic instability, as observed in both simple and complex systems. Here, we represent a material (exemplified for Si I) under large Lagrangian strains within a continuum description by a 5th-order elastic energy found by minimizing error relative to density functional theory (DFT) results. The Cauchy stress—Lagrangian strain curves for arbitrary complex loadings are in excellent correspondence with DFT results, including the elastic instability driving the Si I → II phase transformation (PT) and the shear instabilities. PT conditions for Si I → II under action of cubic axial stresses are linear in Cauchy stresses in agreement with DFT predictions. Such continuum elastic energy permits study of elastic instabilities and orientational dependence leading to different PTs, slip, twinning, or fracture, providing a fundamental basis for continuum physics simulations of crystal behavior under extreme loading.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Benchmarking NIMROD continuum kinetic formulations through the steady-state poloidal flow

In this work, continuum kinetic formulations are employed as a mechanism to include closure physics in an extended magnetohydrodynamics model. Two continuum kinetic approaches have been implemented in the plasma fluid code NIMROD [Sovinec et al., “Nonlinear magnetohydrodynamics with high-order finite elements,” J. Comput. Phys. 195, 355 (2004)] including a Chapman–Enskog-like (CEL) formulation and a more conventional df approach. Ion kinetic closure schemes are employed to describe the neoclassical flow properties in axisymmetric toroidal geometry. In particular, predictions for steady-state values of poloidal flow profiles in tokamak geometry are provided using both the df formulation and two different solution techniques for the CEL approach. These results are benchmarked against analytic theory predictions as well as results from the drift kinetic code DK4D. The continuum kinetic formulations employed here show agreement with both the analytic theory and DK4D results, and offer a novel velocity space representation involving higher-order finite elements in pitch angle.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Anisotropic interactions for continuum modeling of protein–membrane systems

In this work, a model for anisotropic interactions between proteins and cellular membranes is proposed for large-scale continuum simulations. The framework of the model is based on dynamic density functional theory, which provides a formalism to describe the lipid densities within the membrane as continuum fields while still maintaining the fidelity of the underlying molecular interactions. Within this framework, we extend recent results to include the anisotropic effects of protein–lipid interactions. As applications, we consider two membrane proteins of biological interest: a RAS–RAF complex tethered to the membrane and a membrane embedded G protein-coupled receptor. A strong qualitative and quantitative agreement is found between the numerical results and the corresponding molecular dynamics simulations. Combining the scope of continuum level simulations with the details from molecular level particle simulations enables research into protein–membrane behaviors at a more biologically relevant scale, which crucially can also be accessed via experiment.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

What controls the UV-to-X-ray continuum shape in quasars?

ABSTRACT We present an investigation of the interdependence of the optical-to-X-ray spectral slope (αox), the He ii equivalent-width (EW), and the monochromatic luminosity at 2500 Å (L2500). The values of αox and He ii EW are indicators of the strength/shape of the quasar ionizing continuum, from the ultraviolet (UV; 1500–2500 Å), through the extreme ultraviolet (EUV; 300–50 Å), to the X-ray (2 keV) regime. For this investigation, we measure the He ii EW of 206 radioquiet quasars devoid of broad absorption lines that have high-quality spectral observations of the UV and 2 keV X-rays. The sample spans wide redshift (≈0.13–3.5) and luminosity (log(L2500) ≈ 29.2–32.5 erg s−1 Hz−1) ranges. We recover the well-known αox–L2500 and He ii EW–L2500 anticorrelations, and we find a similarly strong correlation between αox and He ii EW, and thus the overall spectral shape from the UV, through the EUV, to the X-ray regime is largely set by luminosity. A significant αox– He ii EW correlation remains after removing the contribution of L2500 from each quantity, and thus the emission in the EUV and the X-rays are also directly tied. This set of relations is surprising, since the UV, EUV, and X-ray emission are expected to be formed in three physically distinct regions. Our results indicate the presence of a redshift-independent physical mechanism that couples the continuum emission from these three different regions, and thus controls the overall continuum shape from the UV to the X-ray regime.

Timlin III, John D.↗

DOE OSTI2025

Non-Hermitian quantum mechanics approach for extracting and emulating continuum physics based on bound-state-like calculations: Detailed description

Here, this work applies a reduced basis method to study the continuum physics of a finite quantum system—either few or many-body. Specifically, I develop reduced-order models, or emulators, for the underlying inhomogeneous Schrödinger equation and train the emulators against the equation's bound-state-like solutions at complex energies. The emulators rapidly and accurately interpolate and extrapolate the matrix elements of the Hamiltonian resolvent operator (Green's function) across a parameter space that includes both complex energy and other real-valued physical inputs in the Schrödinger equation. The spectra, discretized and compressed as the result of emulation, and the associated resolvent matrix elements (or amplitudes), have the defining characteristics of non-Hermitian quantum mechanics calculations, featuring complex eigenenergies with negative imaginary parts and branch cuts moved below the real axis in the complex energy plane. Therefore, one now has a method that extracts continuum physics from bound-state-like calculations and emulates those extractions in the input parameter space. Building on a prior Letter [Zhang, Phys. Rev. Lett. 135, 242501 (2025)], this article provides the full theoretical details, a comprehensive analysis of the method's performance, and a brief discussion of how it can be coupled with existing continuum approaches to perform emulations in their input parameter spaces.

ab initio calculations↗

DOE OSTI2021

Situating the Vector Density Approach Among Contemporary Continuum Theories of Dislocation Dynamics

Abstract For the past century, dislocations have been understood to be the carriers of plastic deformation in crystalline solids. However, their collective behavior is still poorly understood. Progress in understanding the collective behavior of dislocations has primarily come in one of two modes: the simulation of systems of interacting discrete dislocations and the treatment of density measures of varying complexity that are considered as continuum fields. A summary of contemporary models of continuum dislocation dynamics is presented. These include, in order of complexity, the two-dimensional statistical theory of dislocations, the field dislocation mechanics treating the total Kröner–Nye tensor, vector density approaches that treat geometrically necessary dislocations on each slip system of a crystal, and high-order theories that examine the effect of dislocation curvature and distribution over orientation. Each of theories contain common themes, including statistical closure of the kinetic dislocation transport equations and treatment of dislocation reactions such as junction formation. An emphasis is placed on how these common themes rely on closure relations obtained by analysis of discrete dislocation dynamics experiments. The outlook of these various continuum theories of dislocation motion is then discussed.

Engineering↗

DOE OSTI2022

Genetic programming for interpretable, data-driven continuum damage models.

The damage mechanisms that lead to failure in engineering alloys have been studied extensively, but converting this knowledge into constitutive models that are suitable for engineering-scale analysis remains a challenge. Evolution laws for continuum damage have been developed in the past and have proven effective but suffer from many non-physical assumptions that inhibit the overall accuracy of the model. Further, the assumptions inherent in these existing models prevent them from being applicable to a broad class of materials. At the same time, computational models of fine-scale damage mechanisms continue to advance making it tractable to generate large training data sets through computer simulation. Data-driven machine learning approaches can leverage these data sets to avoid making limiting assumptions, and instead produce models directly from the results of microstructural simulations and/or experiments. Many of these machine learning approaches are rapid and accurate, but they offer little to no insight into the underlying relationships among state variables being discovered. Conversely, genetic programming symbolic regression (GPSR) is a machine learning method that produces analytic expressions relating the state variables, allowing maximal insight and interpretability. To that end, we propose using GPSR as a data-driven method of obtaining microstructurally informed continuum damage models. Data is generated using microstructural simulations of damage evolution, parameterized over microstructural statistics (i.e., pore shape) and nominally applied deformations. Analytic expressions for damage evolution are obtained from the data using GPSR, and these expressions are then utilized within a continuum constitutive model. Overall, this approach is a promising method of automatically obtaining analytic relations describing constitutive phenomena in a material.

Buche, Michael Robert↗

DOE OSTI2022

Development of a concurrent coupled Atomistic - Continuum model to predict the defect and grain structure for Additive Manufacturing process [Slides]

Development of a coupled atomistic-continuum model for metal AM process. Two-way coupling between atomistic (heat flux) and continuum (temperature) domain. Identification of grain and dislocation structure at the atomistic domain. Conversion of dislocation data from discrete atomistic to density form at the continuum. Obtain the spatial distribution of grain structure and dislocation density in additively manufactured metal polycrystal material.

36 MATERIALS SCIENCE↗

DOE OSTI2022

The Paschen Jump as a Diagnostic of the Diffuse Nebular Continuum Emission in Active Galactic Nuclei*

Photoionization modeling of active galactic nuclei (AGN) predicts that diffuse continuum (DC) emission from the broad-line region makes a substantial contribution to the total continuum emission from ultraviolet through near-infrared wavelengths. Evidence for this DC component is present in the strong Balmer jump feature in AGN spectra, and possibly from reverberation measurements that find longer lags than expected from disk emission alone. However, the Balmer jump region contains numerous blended emission features, making it difficult to isolate the DC emission strength. In contrast, the Paschen jump region near 8200 Å is relatively uncontaminated by other strong emission features. Here, we examine whether the Paschen jump can aid in constraining the DC contribution, using Hubble Space Telescope Space Telescope Imaging Spectrograph spectra of six nearby Seyfert 1 nuclei. The spectra appear smooth across the Paschen edge, and we find no evidence of a Paschen spectral break or jump in total flux. We fit multicomponent spectral models over the range 6800–9700 Å and find that the spectra can still be compatible with a significant DC contribution if the DC Paschen jump is offset by an opposite spectral break resulting from blended high-order Paschen emission lines. The fits imply DC contributions ranging from ~10% to 50% at 8000 Å, but the fitting results are highly dependent on assumptions made about other model components. These degeneracies can potentially be alleviated by carrying out fits over a broader wavelength range, provided that models can accurately represent the disk continuum shape, Fe ii emission, high-order Balmer line emission, and other components.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

New Measurements of the Lyα Forest Continuum and Effective Optical Depth with LyCAN and DESI Y1 Data

Abstract We present the Ly α Continuum Analysis Network (LyCAN), a convolutional neural network that predicts the unabsorbed quasar continuum within the rest-frame wavelength range of 1040–1600 Å based on the red side of the Ly α emission line (1216–1600 Å). We developed synthetic spectra based on a Gaussian mixture model representation of nonnegative matrix factorization (NMF) coefficients. These coefficients were derived from high-resolution, low-redshift ( z < 0.2) Hubble Space Telescope/Cosmic Origins Spectrograph (COS) quasar spectra. We supplemented this COS-based synthetic sample with an equal number of DESI Year 5 mock spectra. LyCAN performs extremely well on testing sets, achieving a median error in the forest region of 1.5% on the DESI mock sample, 2.0% on the COS-based synthetic sample, and 4.1% on the original COS spectra. LyCAN outperforms principal component analysis (PCA) and NMF-based prediction methods using the same training set by 40% or more. We predict the intrinsic continua of 83,635 DESI Year 1 spectra in the redshift range of 2.1 ≤ z ≤ 4.2 and perform an absolute measurement of the evolution of the effective optical depth. This is the largest sample employed to measure the optical depth evolution to date. We fit a power law of the form τ ( z ) = τ 0 ( 1 + z ) γ to our measurements and find τ 0 = (2.46 ± 0.14) × 10 −3 and γ = 3.62 ± 0.04. Our results show particular agreement with high-resolution, ground-based observations around z = 2, indicating that LyCAN is able to predict the quasar continuum in the forest region with only spectral information outside the forest.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Tree hydrodynamic modelling of the soil–plant–atmosphere continuum using FETCH3

Modelling the water transport along the soil–plant–atmosphere continuum is fundamental to estimating and predicting transpiration fluxes. A Finite-difference Ecosystem-scale Tree Crown Hydrodynamics model (FETCH3) for the water fluxes across the soil–plant–atmosphere continuum is presented here. The model combines the water transport pathways into one vertical dimension, and assumes that the water flow through the soil, roots, and above-ground xylem can be approximated as flow in porous media. This results in a system of three partial differential equations, resembling the Richardson–Richards equation, describing the transport of water through the plant system and with additional terms representing sinks and sources for the transfer of water from the soil to the roots and from the leaves to the atmosphere. The numerical scheme, developed in Python 3, was tested against exact analytical solutions for steady state and transient conditions using simplified but realistic model parameterizations. The model was also used to simulate a previously published case study, where observed transpiration rates were available, to evaluate model performance. With the same model setup as the published case study, FETCH3 results were in agreement with observations. Through a rigorous coupling of soil, root xylem, and stem xylem, FETCH3 can account for variable water capacitance, while conserving mass and the continuity of the water potential between these three layers. FETCH3 provides a ready-to-use open access numerical model for the simulation of water fluxes across the soil–plant–atmosphere continuum.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Fifth-degree elastic energy for predictive continuum stress-strain relations and elastic instabilities under large strain and complex loading in silicon

Levitas, Valery↗

DOE OSTI2022

Coupled continuum and network model framework to study catalyst layers of polymer electrolyte fuel cells

The nanostructured thin film (NSTF) catalyst layers which have demonstrated high power densities, mass activities, and exceptional metal and support stability can have limited operational robustness due to their thin thickness and the hydrophilicity of the metal-coated nano whiskers. The dispersed nanostructured thin film (dNSTF) catalyst layers have been developed by dispersing the NSTF Pt whiskers with ionomer and carbon support to increase the thickness and hydrophobicity. Continuum and network models (NM) are coupled through boundary conditions to study the polymer electrolyte fuel cell with a dNSTF cathode catalyst layer. The coupled model combines the computational efficiency of the continuum model with the pore-scale information in the dNSTF cathode catalyst layer of the NM. It captures the special morphology of the partially ionomer/water covered cylindrical whiskers, as well as water percolation through the pore structures and their impact on the cell performance. Here we observe optimal ionomer coverage on whiskers to be 0.5, ionomer to carbon ratio to be 0.9 and higher whisker to carbon ratios to be desired.

08 HYDROGEN↗