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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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33 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Long-distance nuclear matrix elements for neutrinoless double-beta decay from lattice QCD

Neutrinoless double-beta ( 0 ν β β ) decay is a heretofore unobserved process which, if observed, would imply that neutrinos are Majorana particles. Interpretations of the stringent experimental constraints on 0 ν β β -decay half-lives require calculations of nuclear matrix elements. This work presents the first lattice quantum chromodynamics (LQCD) calculation of the matrix element for 0 ν β β decay in a multinucleon system, specifically the n n → p p e e transition, mediated by a light left-handed Majorana neutrino propagating over nuclear-scale distances. This calculation is performed with quark masses corresponding to a pion mass of m π = 806 MeV at a single lattice spacing and volume. The statistically cleaner Σ − → Σ + e e transition is also computed in order to investigate various systematic uncertainties. The prospects for matching the results of LQCD calculations onto a nuclear effective field theory to determine a leading-order low-energy constant relevant for 0 ν β β decay with a light Majorana neutrino are investigated. This work, therefore, sets the stage for future calculations at physical values of the quark masses that, combined with effective field theory and nuclear many-body studies, will provide controlled theoretical inputs to experimental searches of 0 ν β β decay. Published by the American Physical Society 2024

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Di-nucleons do not form bound states at heavy pion mass

We perform a high-statistics lattice QCD calculation of the low-energy two-nucleon scattering amplitudes. To address discrepancies in the literature, the calculation is performed at a heavy pion mass in the limit that the light quark masses are equal to the physical strange quark mass, 𝑚 𝜋 = 𝑚 𝐾 ≃ 714 MeV. Using a state-of-the-art momentum space method, we rule out the presence of a bound di-nucleon in both the isospin 0 (deuteron) and 1 (di-neutron) channels, in contrast with many previous results that made use of compact hexaquark creation operators. To diagnose the discrepancy, we add such hexaquark interpolating operators to our basis and find that they do not affect the determination of the two-nucleon finite-volume spectrum, and thus they do not couple to deeply bound di-nucleons that are missed by the momentum-space operators. Furthermore, we perform a high-statistics calculation of the HAL QCD potential on the same gauge ensembles and find qualitative agreement with our main results. We conclude that di-nucleons do not form bound states at heavy pion masses and that previous identification of deeply bound di-nucleons must have arisen from a misidentification of the spectrum from off-diagonal elements of a correlation function.

Physics - Physics of elementary particles and fiel↗
DOE OSTI2025

Di-nucleons do not form bound states at heavy pion mass

We perform a high-statistics lattice QCD calculation of the low-energy two-nucleon scattering amplitudes. In order to address discrepancies in the literature, the calculation is performed at a heavy pion mass in the limit that the light quark masses are equal to the physical strange quark mass, $m_π= m_K \simeq 714 $ MeV. Using a state-of-the-art momentum space method, we rule out the presence of a bound di-nucleon in both the isospin 0 (deuteron) and 1 (di-neutron) channels, in contrast with many previous results that made use of compact hexaquark creation operators. In order to diagnose the discrepancy, we add such hexaquark interpolating operators to our basis and find that they do not affect the determination of the two-nucleon finite volume spectrum, and thus they do not couple to deeply bound di-nucleons that are missed by the momentum-space operators. Further, we perform a high-statistics calculation of the HAL QCD potential on the same gauge ensembles and find qualitative agreement with our main results. We conclude that two-nucleons do not form bound states at heavy pion masses and that previous identification of deeply bound di-nucleons must have arisen from a misidentification of the spectrum from off-diagonal elements of a correlation function.

FOS: Physical sciences↗
DOE OSTI2024

A practical approach to calculating magnetic Johnson noise for precision measurements

Magnetic Johnson noise is an important consideration for many applications involving precision magnetometry, and its significance will only increase in the future with improvements in measurement sensitivity. The fluctuation–dissipation theorem can be utilized to derive analytic expressions for magnetic Johnson noise in certain situations, but when used in conjunction with finite element analysis tools, the combined approach is particularly powerful as it provides a practical means to calculate the magnetic Johnson noise arising from conductors of arbitrary geometry and permeability. In this paper, we demonstrate this method to be one of the most comprehensive approaches presently available to calculate thermal magnetic noise. In particular, its applicability is shown to not be limited to cases where the noise is evaluated at a point in space but also can be expanded to include cases where the magnetic field detector has a more general shape, such as a finite-size loop, a gradiometer, or a detector that consists of a polarized atomic species trapped in a volume. Furthermore, some physics insights gained through studies made using this method are discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Global Geo-processed Data of Aquifer Properties by 0.5° Grid, Country and Water Basins

This repository of global hydrogeologic datasets contains aquifer properties on 0.5° scale, including depth to groundwater (Fan et al., 2013), aquifer thickness (de Graaf et al., 2015), WHYMap aquifer classes (Richts et al., 2011), recharge (Döll and Fiedler, 2008; Gleeson et al., 2016), lakes (Messager et al., 2016), porosity and permeability (Gleeson et al., 2014), digitized and geo-processed from their respective sources. Globally gridded aquifer properties could be used independently to estimate global groundwater availability or used as critical inputs to the superwell model to simulate groundwater extraction and provide estimates of pumped volumes and unit costs under user-specific scenarios. Key resources related to this data are: Niazi, H., Ferencz, S. B., Graham, N. T., Yoon, J., Wild, T. B., Hejazi, M., Watson, D. J., & Vernon, C. R. (2025). Long-term hydro-economic analysis tool for evaluating global groundwater cost and supply: Superwell v1.1. Geoscientific Model Development, 18(5), 1737-1767. https://doi.org/10.5194/gmd-18-1737-2025 superwell model repository which uses this data to simulate groundwater extraction and provides estimates of the global extractable volumes and unit-costs ($/km3) of accessible groundwater production under user-specified extraction scenarios. Repository Overview Main output: aquifer_properties_rec.csv contains all processed outputs, including aquifer properties like porosity, permeability, recharge, lake areas, aquifer thickness, and depth to groundwater. shapefiles.zip: contains all digitized GIS databases and shapefile for all aquifer properties prep_inputs.R and prep_inputs_recharge_lakes.R: R scripts that process the shapefiles to produce the aquifer_properties_rec.csv file plot_inputs.R: R script for plotting the maps and conducting preliminary analysis on the available groundwater volume basin_to_country_mapping.csv, basin_country_region_mapping.csv and continent_county_mapping.csv provide the mapping between continents, 32 energy-economic macro regions, countries, and water basins for post-processing aquifer_properties_rec.csv Maps: Each map visualizes the spatial distribution of one of the aquifer properties across the globe map_in_Porosity.png map_in_Permeability.png map_in_Aquifer_thickness.png map_in_Depth_to_water.png map_in_Recharge.png map_in_Grid_area_km.png map_in_Lake_area_km.png map_in_WHYClass.png Sample inputs sample_inputs.py: this script samples inputs from the aquifer_properties_rec dataset, ensuring the sampled and original inputs maintain the same distributions sampled_data_100.csv contains 100 sampled data points and sampled_data_100.png compares their distributions Dataset Overview The main outputs are consolidated in a comprehensive aquifer_properties_rec.csv file and include the following fields: GridCellID: Unique identifier for each (roughly 0.5°) grid cell Continent: Continent name Country: Country name GCAM_basin_ID: Identifier for GCAM hydrologic basin Basin_long_name: Full name of the basin WHYClass: Hydrogeologic classification based on WHYMap aquifer classes (Richts et al., 2011) Porosity: Soil porosity (%) (Gleeson et al., 2014) Permeability: Soil permeability (in square meters; Gleeson et al., 2014) Aquifer_thickness: Thickness of the aquifer (in meters; de Graaf et al., 2015) Depth_to_water: Depth to groundwater (in meters; Fan et al., 2013) Recharge: long-term annual averaged recharge rates (in m/yr; Döll and Fiedler, 2008; Gleeson et al., 2016) Grid_area: Area of the grid cell (in square meters) Lakes_area: Area of inland lakes (in square meters; Messager et al., 2016) Key References The datasets are digitized versions of global hydrogeologic properties from the following key literature sources: Depth to Groundwater: Fan, Y., Li, H., & Miguez-Macho, G. (2013). Global Patterns of Groundwater Table Depth. Science, 339(6122), 940-943. https://doi.org/10.1126/science.1229881 Aquifer Thickness: de Graaf, I. E. M., Sutanudjaja, E. H., van Beek, L. P. H., & Bierkens, M. F. P. (2015). A high-resolution global-scale groundwater model. Hydrol. Earth Syst. Sci., 19(2), 823-837. https://doi.org/10.5194/hess-19-823-2015 Porosity and Permeability: Gleeson, T., Moosdorf, N., Hartmann, J., & van Beek, L. P. H. (2014). A glimpse beneath earth's surface: GLobal HYdrogeology MaPS (GLHYMPS) of permeability and porosity. Geophysical Research Letters, 41(11), 3891-3898. https://doi.org/10.1002/2014GL059856 Aquifer classes: Richts, A., Struckmeier, W. F., & Zaepke, M. (2011). WHYMAP and the Groundwater Resources Map of the World 1:25,000,000. In J. A. A. Jones (Ed.), Sustaining Groundwater Resources: A Critical Element in the Global Water Crisis (pp. 159-173). Springer Netherlands. https://doi.org/10.1007/978-90-481-3426-7_10 Recharge: Döll, P., & Fiedler, K. (2008). Global-scale modeling of groundwater recharge. Hydrol. Earth Syst. Sci., 12(3), 863-885. https://doi.org/10.5194/hess-12-863-2008; Gleeson, T., Befus, K. M., Jasechko, S., Luijendijk, E., & Cardenas, M. B. (2016). The global volume and distribution of modern groundwater. Nature Geoscience, 9(2), 161-167. https://doi.org/10.1038/ngeo2590 Inland Lakes: Messager, M. L., Lehner, B., Grill, G., Nedeva, I., & Schmitt, O. (2016). Estimating the volume and age of water stored in global lakes using a geo-statistical approach. Nature Communications, 7(1), 13603. https://doi.org/10.1038/ncomms13603 Cite as Niazi, H., Watson, D., Hejazi, M., Yonkofski, C., Ferencz, S., Vernon, C., Graham, N., Wild, T., & Yoon, J. (2024). Global Geo-processed Data of Aquifer Properties by 0.5° Grid, Country and Water Basins. MultiSector Dynamics-Living, Intuitive, Value-adding, Environment. https://doi.org/10.57931/2484226 Contact Reach out to Hassan Niazi or open an issue in the superwell repository for questions or suggestions.

aquifer thickness↗
DOE OSTI2023

Quantitative three-dimensional imaging of chemical short-range order via machine learning enhanced atom probe tomography

Abstract Chemical short-range order (CSRO) refers to atoms of specific elements self-organising within a disordered crystalline matrix to form particular atomic neighbourhoods. CSRO is typically characterized indirectly, using volume-averaged or through projection microscopy techniques that fail to capture the three-dimensional atomistic architectures. Here, we present a machine-learning enhanced approach to break the inherent resolution limits of atom probe tomography enabling three-dimensional imaging of multiple CSROs. We showcase our approach by addressing a long-standing question encountered in body-centred-cubic Fe-Al alloys that see anomalous property changes upon heat treatment. We use it to evidence non-statistical B 2 -CSRO instead of the generally-expected D0 3 -CSRO. We introduce quantitative correlations among annealing temperature, CSRO, and nano-hardness and electrical resistivity. Our approach is further validated on modified D0 3 -CSRO detected in Fe-Ga. The proposed strategy can be generally employed to investigate short/medium/long-range ordering phenomena in different materials and help design future high-performance materials.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Simulating Atmospheric Boundary Layer Turbulence with Nek5000/RS

We present large-eddy-simulation (LES) modeling approaches for the simulation of atmospheric boundary layer turbulence that are of direct relevance to wind energy production. In this report, we study a GABLS benchmark problem using high-order spectral element code Nek5000/RS, which is supported under the DOE’s Exascale Computing Project (ECP) Center for Efficient Exascale Discretizations (CEED) project, targeting application simulations on various acceleration-device based exascale computing platforms [1, 2]. We demonstrate our newly developed subgrid-scale (SGS) models based on high-pass filter (HPF), mean-field eddy viscosity (MFEV), and Smagorinsky (SMG) with no-slip and traction boundary conditions, provided with low-order statistics, convergence and turbulent structure analysis. The model fidelity and scaling performance of Nek5000/RS on DOE’s leadership computing platforms in comparison to those of AMR-Wind, a block-structured second-order finite-volume code with adaptive-mesh-refinement capabilities, are discussed in [3].

17 WIND ENERGY↗
DOE OSTI2025

MaTableGPT: GPT‐Based Table Data Extractor from Materials Science Literature

Abstract Efficiently extracting data from tables in the scientific literature is pivotal for building large‐scale databases. However, the tables reported in materials science papers exist in highly diverse forms; thus, rule‐based extractions are an ineffective approach. To overcome this challenge, the study presents MaTableGPT, which is a GPT‐based table data extractor from the materials science literature. MaTableGPT features key strategies of table data representation and table splitting for better GPT comprehension and filtering hallucinated information through follow‐up questions. When applied to a vast volume of water splitting catalysis literature, MaTableGPT achieves an extraction accuracy (total F1 score) of up to 96.8%. Through comprehensive evaluations of the GPT usage cost, labeling cost, and extraction accuracy for the learning methods of zero‐shot, few‐shot, and fine‐tuning, the study presents a Pareto‐front mapping where the few‐shot learning method is found to be the most balanced solution owing to both its high extraction accuracy (total F1 score >95%) and low cost (GPT usage cost of 5.97 US dollars and labeling cost of 10 I/O paired examples). The statistical analyses conducted on the database generated by MaTableGPT revealed valuable insights into the distribution of the overpotential and elemental utilization across the reported catalysts in the water splitting literature.

Yi, Gyeong Hoon [Computational Science Research Ce↗
DOE OSTI2022

Dynamic mode decomposition with core sketch

With the increase in collected data volumes, either from experimental measurements or high fidelity simulations, there is an ever-growing need to develop computationally efficient tools to process, analyze, and interpret these datasets. Modal analysis techniques have gained great interest due to their ability to identify patterns in the data and extract valuable information about the system being considered. Dynamic mode decomposition (DMD) relies on elements of the Koopman approximation theory to compute a set of modes, each associated with a fixed oscillation frequency and a decay/growth rate. Extracting these details from large datasets can be computationally expensive due to the need to implement singular value decomposition of the input data matrix. Sketching algorithms have become popular in numerical linear algebra where statistical theoretic approaches are utilized to reduce the cost of major operations. A sketch of a matrix is another matrix, which is significantly smaller, but still sufficiently approximates the original system. We put forth an efficient DMD framework, SketchyDMD, based on a core sketching algorithm that captures information about the range and corange (their mutual relationship) of input data. The proposed sketching-based framework can accelerate various portions of the DMD routines, compared to classical methods that operate directly on the raw input data. We conduct numerical experiments using the spherical shallow water equations as a prototypical model in the context of geophysical flows. In conclusion, we show that the proposed SketchyDMD is superior to existing randomized DMD methods that are based on capturing only the range of the input data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

A combined ensemble-volume average homogenization method for lattice structures with defects under dynamic and static loading

In the study of lattices structures, both experiments and numerical simulations are often conducted with small samples. Using combined ensemble and volume averaging, this work introduces a method to extract a macroscopic constitutive response of a lattice material from numerical simulations performed in periodic domains. The domain size needed to obtain statistically accurate results is investigated. Similar to molecular dynamics, the concept of the virial stress is introduced after homogenized equations are derived using the ensemble averaging method. Under static conditions, the virial stress is shown to agree with the volume averaged solid stress. Using the homogenization method, constitutive relations for this stress can be obtained from systems with uniform strains. Application of such obtained constitutive relations to more general cases results in an error proportional to the square of the ratio between the lattice length scale and the macroscopic length scale. Taking advantage of this property, numerical simulations are performed in systems with a uniform gradient of the average velocity. The volume average method is then used to accelerate convergence when studying lattices with defects. To avoid the artificial numerical time scale from the size of a representative volume element divided by the wave speed, a numerical scheme is developed to enforce a spatially uniform velocity gradient within the computational domain while allowing fluctuations of the velocity or displacement to develop naturally. To account for probability distribution of lattice defects, the stress is calculated as the ensemble-volume averaged value. For dynamic systems, energy dissipation properties are also studied.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Pion and kaon PDFs from lattice QCD via large momentum effective theory and short-distance factorization

In this paper, we present a first-principles lattice-QCD calculation of the unpolarized quark PDF for the pion and the kaon. The lattice data rely on matrix elements calculated for boosted mesons coupled to non-local operators containing a Wilson line. The calculations on this lattice ensemble correspond to two degenerate light, a strange, and a charm quark (𝑁 𝑓 = 2 + 1 + 1), using maximally twisted mass fermions with a clover term. The lattice volume is 32 3 × 64, with a lattice spacing of 0.0934 fm, and a pion mass of 260 MeV. Matrix elements are calculated for hadron boosts of |𝑃 3 | = 0, 0.41, 0.83, 1.25, 1.66, and 2.07 GeV. To match lattice QCD results to their light-cone counterparts, we employ two complementary frameworks: the large-momentum effective theory (LaMET) and the short-distance factorization (SDF). Using these approaches in parallel, we also test the lattice data to identify methodology-driven systematics. Results are presented for the standard quark PDFs, as well as the valence sector. Beyond obtaining the PDFs, we also explore the possibility of extracting information on SU(3) flavor-symmetry-breaking effects. For LaMET, we also parametrize the momentum dependence to obtain the infinite-momentum PDFs. Since the present calculation is performed on a single ensemble at a pion mass of 260 MeV and fixed lattice spacing, the uncertainties reported are statistical only, and systematic uncertainties remain to be addressed in future multi-ensemble studies.

Miller, Joshua [Temple University, Philadelphia, P↗
DOE OSTI2022

Using Direct Numerical Simulation of Pore-Level Events to Improve Pore-Network Models for Prediction of Residual Trapping of CO2

Direct numerical simulation and pore-network modeling are common approaches to study the physics of two-phase flow through natural rocks. For assessment of the long-term performance of geological sequestration of CO 2 , it is important to model the full drainage-imbibition cycle to provide an accurate estimate of the trapped CO 2 . While direct numerical simulation using pore geometry from micro-CT rock images accurately models two-phase flow physics, it is computationally prohibitive for large rock volumes. On the other hand, pore-network modeling on networks extracted from micro-CT rock images is computationally efficient but utilizes simplified physics in idealized geometric pore elements. This study uses the lattice-Boltzmann method for direct numerical simulation of CO 2 -brine flow in idealized pore elements to develop a new set of pore-level flow models for the pore-body filling and snap-off events in pore-network modeling of imbibition. Lattice-Boltzmann simulations are conducted on typical idealized pore-network configurations, and the interface evolution and local capillary pressure are evaluated to develop modified equations of local threshold capillary pressure of pore elements as a function of shape factor and other geometrical parameters. The modified equations are then incorporated into a quasi-static pore-network flow solver. The modified model is applied on extracted pore-network of sandstone samples, and saturation of residual trapped CO 2 is computed for a drainage-imbibition cycle. The modified model yields different statistics of pore-level events compared with the original model; in particular, the occurrence of snap-off in pore-throats is reduced resulting in a more frontal displacement pattern along the main injection direction. Compared to the original model, the modified model is in closer agreement with the residual trapped CO 2 obtained from core flow experiments and direct numerical simulation.

Kohanpur, Amir H.↗
DOE OSTI2025

Feasibility of Algal Biochar, a Byproduct of Biofuel Production, as a Supplemental Cementitious Material

Algal biochar, as the solid residue of biofuel production from algal biomass, is reported to explore disposition options, aiming to lessen the liability or obstacles to biofuel production processes. However, landfills and open combustion lead to adverse environmental impacts. One way to add value to such wastes is to use them as admixtures in cementitious construction materials. This study aims to investigate the feasibility of algae-derived biochar as supplementary cementitious materials (SCM) at different water contents and mixture ratios. Algal biochar-cement composites were prepared with different algal biochar content as well as different water-to-cement (w/c) ratios, and the surface area, morphology, elemental, and mineralogical composition were characterized. To compensate for the high-water absorption of algal biochar, a small concentration of a superplasticizer was used since higher w/c ratios negatively impact strength. The mechanical performance of algal biochar-cement composites is compared with control composites using commercial silica fume as a typical commercial SCM. The findings suggest that algal biochar is a promising candidate to replace commercial SCM, like silica fume, since algal biochar-cement composites can reach comparable compressive strength and Young’s modulus to commercial pozzolan-cement materials with the same w/c ratio, though at later curing times, 33 days. Although the tensile strength of algal biochar-cement composites is statistically similar at 7 days, it is significantly lower at later curing times, and further investigation is required to improve this property. Algal biochar-based cement binders showed comparable embodied carbon to silica fume-based cement binders based on a cradle-to-gate lifecycle analysis. However, the ability of algal biochar to absorb large volumes of CO 2 over short periods of time, as measured in this study, makes this novel SCM an excellent alternative to reduce the embodied carbon of concrete structures cradle-to-grave at 1/10 of the cost. In conclusion, valorization of algae-derived solid waste provides great potential to reduce embodied carbon and brings credit to biofuel production and concrete-based construction.

algae-derived↗
DOE OSTI2022

Muon track reconstruction in a segmented bolometric array using multi-objective optimization

Recent advances in segmented solid-state detector arrays for rare-event searches have allowed the technology to approach the ton-scale in detector mass and the scale of meters in size. Often focused around searches for neutrinoless double-beta decay or direct dark matter detection, such experiments also have the capability to search for exotic particles that leave track-like signatures across their volume. However, the segmented nature of such detector arrays often sets the spatial resolution and makes the problem of reconstructing track-like paths non-trivial. Here, in this paper, we present an algorithm that improves reconstruction of track-like events in segmented detectors using multi-objective optimization — a computational technique that optimizes more than one cost function at a time without specifying a quantitative weighting between them. Such a technique allows the reconstruction of tracks through a detector and the determination of path-lengths through individual elements. When combined with the reconstructed energy depositions in each element this allows for a calculation of the stopping power of track-like particles and opens the door to searches for particles with abnormal stopping power like monopoles or lightly-ionizing particles (LIPs). Results are presented which evaluate the precision of the reconstruction tools as they currently stand against Monte Carlo generated data. The algorithm is presented in the context of the CUORE experiment, but has applications to other segmented calorimeter detectors.

47 OTHER INSTRUMENTATION↗
DOE OSTI2022

A Micromorphic Length-Scale Coupling Framework for the Determination of Higher-Order Constitutive Models and the Multi-Scale Simulation of Heterogeneous Materials [Thesis]

Heterogeneous materials and materials with complex microstructures pose a unique challenge in the development of accurate models of their response to external stimuli. These difficulties principally arise due to the difficulty in characterizing and modeling the constituents and their interactions. It is usually possible, though non-trivial, to construct an explicit representation of the microstructure (a direct numeric simulation or DNS) but the method by which the complex modes of deformation and other processes can be homogenized to a reduced-order approximation is frequently unclear. Many homogenization approaches are ad-hoc and lack a strong justification beyond ease of computation. Furthermore, the homogenization approach can, in some cases, not utilize the full breadth of information available in the computation of the macro-scale stresses and deformation measures. It is also noteworthy that homogenization, by its very nature, will tend to obfuscate details of processes occurring at the lower length-scale. It is therefore of interest to include as much information as possible in the construction of the reduced-order model so as to be predictive in a variety of loading environments. We here present a length-scale bridging technique based upon the micromorphic continuum mechanics of Eringen which incorporates volume and surface area averages as a part of its construction. This approach enforces the balance equations at the micro-scale and then studies the effect of the spatially varying nature on the macro-scale. This leads, naturally, to further balance equations which are solved at the macro-scale. This work details a homogenization framework which arises naturally from the micromorphic construction of Eringen attempting to introduce no definitions beyond which are justifiable from micro-structural considerations. One of the results of this effort is the so-called “micromorphic filter” which has been developed and applied to several DNS to demonstrate its effectively. In order to determine the macroscopic degrees of freedom we utilize the special case of an overlap coupling technique where the macro-scale is fully constrained to the micro-scale. This enables us to study the resulting material properties as expected but also allows us to further study the boundary conditions on the additional degrees of freedom at the macro-scale.

42 ENGINEERING↗