Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “spatial constraints”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Utilizing Time Reversal Ultrasonics to Detect the Removal of Nuclear Materials from Geological Repositories (FY26 Mid-Year)

Detecting unauthorized nuclear material removal from storage environments, such as geological repositories, is a critical safeguards task essential to ensuring the integrity and non-diversion of nuclear materials. However, this process is fraught with significant technical challenges. Storage configurations often involve tightly packed nuclear material containers or obstructed environments, making detection of removal events exceedingly difficult. Optical surveillance cameras, which are commonly used for monitoring, suffer from substantial limitations, including restricted coverage, reliance on line-of-sight measurements, and vulnerability to environmental conditions in certain storage scenarios. As the global inventory of monitored nuclear materials increases and storage configurations become more complex— such as deep geological repositories, inaccessible storage vaults, and tightly packed containers—there is an urgent need for innovative detection technologies that can reliably identify unauthorized diversion events in these challenging environments. The challenge of detecting nuclear material removal in complex storage environments is both significant and urgent. Preventing unauthorized access, diversion, or tampering with nuclear materials is a cornerstone of global nuclear safeguards and nonproliferation efforts. Current detection methods are increasingly inadequate as storage configurations become more intricate and inaccessible. The limitations of existing technologies—such as their inability to detect changes behind obstructions, reliance on costly and labor-intensive processes, and vulnerability to environmental conditions—pose risks to the effectiveness of safeguards systems. Addressing this challenge is critical to maintaining international trust in nuclear safeguards frameworks and ensuring compliance with nonproliferation agreements. Our project builds on the proven concept of TRU technology that can address this unmet need. TRU has demonstrated exceptional spatial sensitivity and change detection capabilities in complex non-line-ofsight environments, making it uniquely suited for detecting unauthorized nuclear material removal in challenging storage configurations. Unlike optical methods, TRU is not limited by line-of-sight constraints or environmental conditions, enabling reliable detection of subtle alterations even behind obstructions. By leveraging TRU’s ability to identify removal or tampering events, we aim to develop a robust detection system that enhances safeguards in geological repositories, storage vaults, and other complex environments.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
DOE OSTI2022

Instrument design for an inertial confinement fusion ion temperature imager

A mix of contaminant mass is a known, performance-limiting factor for laser-driven inertial confinement fusion (ICF). It has also recently been shown that the contaminant mass is not necessarily in thermal equilibrium with the deuterium–tritium plasma. Contaminant mass temperature is one of the dominant uncertainties in contaminant mass estimates. The MixIT diagnostic is a new and potentially transformative diagnostic, capable of spatially resolving ion temperature. The approach combines principles of neutron time-of-flight and neutron imaging diagnostics. The information from the MixIT diagnostic can be used to optimize ICF target and laser drive designs as well as provide key constraints on ICF radiation-hydrodynamic simulations that are critical to contaminant mass estimates. This work details the design and optimization of the major components of the MixIT diagnostic: the neutron aperture, the neutron detector (scintillator), and the recording system.

47 OTHER INSTRUMENTATION↗
DOE OSTI2024

Wake forces in a background of quadratically coupled mediators

Two particles can exert forces on each other when embedded in a sea of weakly coupled particles. These “wake forces” occur whenever the source and target particles have quadratic interactions with the mediating particles; they are proportional to the ambient energy density and typically have a range of order the characteristic de Broglie wavelength of the background. The effect can be understood as source particles causing a disturbance in the background waves—a wake—which subsequently interacts with the target particles. Wake forces can be mediated by bosons or fermions, can have spin dependence, may be attractive or repulsive, and have a generally anisotropic spatial profile and range that depends on the phase-space distribution of the ambient particles. In this work, I investigate the application of wake forces to dark matter searches, recast existing limits on short-range forces into leading constraints on dark matter with quadratic couplings, and sketch out potential experimental modifications to optimize sensitivity. Wake forces occur in the Standard Model: the presence of the cosmic neutrino background induces a millimeter-range force about 22 orders of magnitude weaker than gravity. Wake forces may also be relevant in condensed-matter and atomic physics. Published by the American Physical Society 2024

Astronomy & Astrophysics↗
DOE OSTI2025

Fermilab Booster loss modelling and rebalancing using Bayesian methods

Fermilab Booster is being upgraded for the PIP-II project to support 20Hz ramp rate at higher intensities. Loss trip limits determine the achievable peak power. To meet PIP-II requirements, losses need to be halved as compared to current levels. Losses primarily occur at injection and transition crossing, with both gradually increasing and threshold-like intensity-dependent behaviors. The existing simulation models are not yet good enough for quantitative loss predictions. In practice, it will be necessary to tune up the Booster using iterative methods and operator intuition. In this paper we present an effort to systematically model Booster losses using active learning (Bayesian exploration) techniques, and subsequently to rebalance them for higher trip limit margins. We first created several sets of spatially and temporally isolated orbit and optics knobs, and trained Gaussian process models for each beam loss monitor as well as beam current. This is a complex task due to safety and timing requirements – we discuss mitigations such as uncertainty constraints and approximate fitting. Once models are stable, we perform large-scale single and multi-objective tuning using scalarized objectives made up of critical beam loss locations. Our results demonstrate significant rebalancing of losses, increasing trip margins, as well as an overall improvement in beam transmission efficiency. We are exploring how to combine existing simulations with experimental data and automate the collection procedure so that more advanced surrogate models can be created over time.

Kuklev, Nikita [Fermilab]↗
DOE OSTI2025

Perspectives on Systematic Cloud Microphysics Scheme Development With Machine Learning

Cloud microphysics—the collection of processes that govern the small‐scale formation, evolution, and interactions of liquid droplets and ice crystals in clouds and precipitation—remains a major source of uncertainty in weather and climate models. Although too small in scale to be explicitly resolved in any large‐eddy simulation, weather, or climate model, the representation of cloud microphysical processes has significant impact at the climate scale. Current microphysical schemes are limited by both parametric uncertainty, linked to uncertainty in physical parameter values, and structural uncertainty, arising from incomplete physical understanding of the processes at play or approximations made for computational efficiency. Recent advances in the application of machine learning (ML) to the physical sciences show significant potential for minimizing these limitations by leveraging high‐fidelity simulations and observations. Here we outline the challenges that must be addressed to apply ML toward cloud microphysics scheme development. This perspectives paper synthesizes recent progress in using data‐driven methods, including ML, to improve cloud microphysics parameterizations and highlights opportunities to address key uncertainties. We discuss the roles of aleatoric (irreducible, or statistical) and epistemic (reducible, or systematic) errors in contributing to microphysics parameterization uncertainty. ML can leverage observations to improve microphysical schemes via bottom‐up and top‐down constraints. Methods such as differentiable programming and ML‐enhanced sampling strategies and the creation of large scale benchmark data sets promise to bridge the gap between observations and models and to improve the consistency of cloud microphysical representation across temporal and spatial scales.

Lamb, Kara D. [Columbia Univ., New York, NY (Unite↗
DOE OSTI2023

Generation of entangled-photons by a quantum dot cascade source in polarized cavities: Using cavity resonances to boost signals and preserve the entanglements

Motivated by recent advances in the development of single photon emitters for quantum information sciences, here we design and formulate a quantum cascade model that describes cascade emission by a quantum dot (QD) in a cavity structure while preserving entanglement that stores information needed for single photon emission. The theoretical approach is based on a photonic structure that consists of two orthogonal cavities in which resonance with either the first or second of the two emitted photons is possible, leading to amplification and rerouting of the entangled light. The cavity–QD scheme uses a four-level cascade emitter that involves three levels for each polarization, leading to two spatially entangled photons for each polarization. By solving the Schrodinger equation, we identify the characteristic properties of the system, which can be used in conjunction with optimization techniques to achieve the “best” design relative to a set of prioritized criteria or constraints in our optical system. The theoretical investigations include an analysis of emission spectra in addition to the joint spectral density profile, and the results demonstrate the ability of the cavities to act as frequency filters for the photons that make up the entanglements and to modify entanglement properties. The results provide new opportunities for the experimental design and engineering of on-demand single photon sources.

Chemistry↗
DOE OSTI2026

Probing fundamental constant oscillation in the Galactic Center with S-Star Spectroscopy

Astrophysical spectroscopy provides a powerful probe of spacetime variations of fundamental constants, as atomic and ionic emission and absorption lines depend sensitively on the fine-structure constant. In particular, coherent temporal oscillations induced by an ultralight scalar background produce characteristic, time-resolved signatures that can be robustly disentangled from intrinsic variability. In the Galactic Center, such scalar backgrounds can be substantially enhanced, either through the formation of dense scalar clouds powered by black hole rotational energy extraction or as ultralight scalar dark matter forming a soliton-like core. These scalar configurations generically induce oscillations of the fine-structure constant, with periods set by the scalar mass and spatial profiles determined by the scalar wavefunction and its coupling to the electromagnetic sector. We show that precise, time-resolved spectroscopy of S-stars orbiting the supermassive black hole Sgr A^* provides a sensitive test of these effects, enabling constraints on quadratic scalar-photon couplings in the exceptionally high boson-density environment of the Galactic Center.

Bai, Zhaoyu [Weizmann Inst.] (ORCID:00000002075815↗
DOE OSTI2026

HostSub_GP: Precise Galaxy Background Subtraction in Transient Long-slit Spectroscopy with Gaussian Processes

We present a novel host galaxy subtraction technique in long-slit spectroscopy for extragalactic transients. Unlike classic methods which generally estimate the background using simple interpolation of local galaxy flux in the 2D spectrum, our approach leverages multi-band archival images of the host galaxies to model the background emission from the galaxy in the 2D spectrum. Such imaging encodes the wavelength-dependent galaxy profile along the slit, and is readily accessible through wide-field imaging surveys. We construct a smooth prior for the 2D galaxy profile with a Gaussian process (GP) based on these reference images, and use another GP to model the correlated deviations from the prior in the observed spectrum. This enables accurate inference of the galaxy flux blended with the transient. On synthetic long-slit data of a spiral galaxy extracted from a Multi Unit Spectroscopic Explorer hyper-spectral cube, the GP method remains robust as long as the host galaxy is spatially resolved and consistently outperforms classic methods. We apply the method to archival Keck spectra of two real transients, SN 2019eix and AT 2019qiz, to further demonstrate how the method uniquely recovers weak spectral features amid strong galaxy contamination, enabling refined constraints on the properties of both transients. We have released the software implementation, HostSub_GP, a scalable toolkit that leverages JAX, with an MIT license.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

The short ionizing photon mean free path at z = 6 in Cosmic Dawn III, a new fully coupled radiation-hydrodynamical simulation of the Epoch of Reionization

ABSTRACT Recent determinations of the mean free path of ionizing photons (mfp) in the intergalactic medium (IGM) at z = 6 are lower than many theoretical predictions. In order to gain insight, we investigate the evolution of the mfp in our new massive fully coupled radiation-hydrodynamics cosmological simulation of reionization: Cosmic Dawn III (CoDa III). CoDa III’s scale ($\rm 94^3 \, cMpc^3$) and resolution ($\rm 8192^3$ grid) make it particularly suitable to study the IGM during reionization. The simulation was performed with ramses-cudaton on Summit, and used 13 1072 processors coupled to 24 576 GPUs, making it the largest reionization simulation, and largest ever ramses simulation. A superior agreement with global constraints on reionization is obtained in CoDa III over Cosmic Dawn II (CoDa II), especially for the evolution of the neutral hydrogen fraction and the cosmic photoionization rate, thanks to an improved calibration, later end of reionization (z = 5.6), and higher spatial resolution. Analysing the mfp, we find that CoDa III reproduces the most recent observations very well, from z = 6 to z = 4.6. We show that the distribution of the mfp in CoDa III is bimodal, with short (neutral) and long (ionized) mfp modes, due to the patchiness of reionization and the coexistence of neutral versus ionized regions during reionization. The neutral mode peaks at sub-kpc to kpc scales of mfp, while the ionized mode peak evolves from 0.1 Mpc h−1 at z = 7 to ∼10 Mpc h−1 at z = 5.2. Computing the mfp as the average of the ionized mode provides the best match to the recent observational determinations. The distribution reduces to a single neutral (ionized) mode at z > 13 (z < 5).

Lewis, Joseph S. W. (ORCID:0000000179178474)↗
DOE OSTI2026

Soft X-ray reflection ptychography

Scanning transmission X-ray microscopy and ptychography have become mature tools for high-resolution, element-specific imaging of nanoscale structures. However, transmission geometries impose stringent constraints on sample thickness and preparation, thereby limiting investigations of extended or bulk specimens, especially in the soft X-ray region. Here, we demonstrate reflection-geometry soft X-ray ptychography as a robust imaging mode. Instrumental feasibility and spatial resolution are established using a lithographically defined Siemens star and barcode test pattern on a multilayer substrate. We empirically demonstrate a full-pitch spatial resolution of ca. 45 nm from Fourier ring correlation analysis of the reconstructed object. The results highlight the potential of the reflection geometry for nondestructive X-ray studies of materials without the need for transmissive samples.

Guenzing, Damian [Lawrence Berkeley National Labor↗
DOE OSTI2021

Nth-plant supply: corn stover supplies and costs in a fleet of biorefineries

Feedstock cost and cost variability is expected to increase with the number of biorefineries. To quantify this effect, this spatial-economic analysis simulates feedstock cost and cost variability of an industry based on corn stover as a function of the number of biorefineries. Results are reported for nine scenarios (a base case and sensitivity analysis of four variables – harvest efficiency, sustainability constraints, opportunity cost, and corn grain yield) under deterministic and stochastic simulations, assuming biorefineries using 658 000 Mg (725 000 tons) year- 1 of corn stover in 2019. The resulting supply curves are highly elastic (i.e. little change in cost) for the first 50 of the 121 biorefineries, with price increases in subsequent biorefineries depending on scenario. In the base-case deterministic scenario, weighted-average stover costs are $66 Mg -1 ($60 ton- 1 ), $69 Mg -1 ($62 ton -1 ), and $156 Mg -1 ($142 ton -1 ), at the first, 60th, and 121st biorefineries, respectively. The stochastic simulations, subject to observed 30-year corn yield variability, follow a similar pattern, with price distributions that vary by scenario. The base-case stochastic simulations illustrate minimal cost variability for the first 60 biorefineries, but rapid increases in cost variability in the second half of potential biorefineries, with similar patterns observed in the other scenarios. Of the four variables explored, price was most sensitive to harvest efficiency, followed by sustainability constraints, corn yield, and opportunity cost. Results suggest that, under conventional logistics, about half of the US corn stover resource is reliably available with minimum cost increase and variability. Interactive visualization is available at https://doi.org/10.11578/1828779.

09 BIOMASS FUELS↗
DOE OSTI2023

Directionally supervised cellular automaton for the initial peopling of Sahul

Reconstructing the patterns of Homo sapiens expansion out of Africa and across the globe has been advanced using demographic and travel-cost models. However, modelled routes are ipso facto influenced by migration rates, and vice versa. We combined movement ‘superhighways’ with a demographic cellular automaton to predict one of the world's earliest peopling events — Sahul between 75000 and 50000 years ago. Novel outcomes from the superhighways-weighted model include (i) an approximate doubling of the predicted time to continental saturation (~10,000 years) compared to that based on the directionally unsupervised model (~5000 years), suggesting that rates of migration need to account for topographical constraints in addition to rate of saturation; (ii) a previously undetected movement corridor south through the centre of Sahul early in the expansion wave based on the scenarios assuming two dominant entry points into Sahul; and (iii) a better fit to the spatially de-biased, Signor-Lipps-corrected layer of initial arrival inferred from dated archaeological material. Our combined model infrastructure provides a data-driven means to examine how people initially moved through, settled, and abandoned different regions of the globe.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2024

The Carousel Lens: A Well-modeled Strong Lens with Multiple Sources Spectroscopically Confirmed by VLT/MUSE

Over the past few years alone, the lensing community has discovered thousands of strong lens candidates, and spectroscopically confirmed hundreds of them. In this time of abundance, it becomes pragmatic to focus our time and resources on the few extraordinary systems, in order to most efficiently study the Universe. In this paper, we present such a system: DESI-090.9854-35.9683, a cluster-scale lens at z l = 0.49, with seven observed lensed sources around the core, and additional lensed sources further out in the cluster. From the number and the textbook configuration of the lensed images, a tight constraint on the mass potential of the lens is possible. This would allow for detailed analysis on the dark and luminous matter content within galaxy clusters, as well as a probe into dark energy and high-redshift galaxies. We present our spatially resolved kinematic measurements of this system from the Very Large Telescope Multi Unit Spectroscopic Explorer, which confirm five of these source galaxies (in ascending order, at z s = 0.962, 0.962, 1.166, 1.432, and 1.432). With previous Hubble Space Telescope imaging in the F140W and F200LP bands, we also present a simple flux-based lens model consisting of two power-law profiles that, for a cluster lens, well models the five lensed arc families with redshifts. We determine the mass to be M(< θ E ) = 4.78 × 10 13 M ⊙ for the primary mass potential. From the model, we extrapolate the redshift of one of the two source galaxies not yet spectroscopically confirmed to be at $z_s = 4.52^{+1.03}_{-0.71}$.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Sensitivities of subgrid-scale physics schemes, meteorological forcing, and topographic radiation in atmosphere-through-bedrock integrated process models: a case study in the Upper Colorado River basin

Abstract. Mountain hydrology is controlled by interacting processes extending from the atmosphere through the bedrock. Integrated process models (IPMs), one of the main tools needed to interpret observations and refine conceptual models of the mountainous water cycle, require meteorological forcing that simulates the atmospheric process to predict hydroclimate then subsequently impacts surface–subsurface hydrology. Complex terrain and extreme spatial heterogeneity in mountainous environments drive uncertainty in several key considerations in IPM configurations and require further quantification and sensitivity analyses. Here, we present an IPM using the Weather Research and Forecasting (WRF) model which forces an integrated hydrologic model, ParFlow-CLM, implemented over a domain centered over the East River watershed (ERW), located in the Upper Colorado River basin (UCRB). The ERW is a heavily instrumented 300 km2 region in the headwaters of the UCRB near Crested Butte, CO, with a growing atmosphere-through-bedrock observation network. Through a series of experiments in the water year 2019 (WY19), we use four meteorological forcings derived from commonly used reanalysis datasets, three subgrid-scale physics scheme configurations in WRF, and two terrain shading options within WRF to test the relative importance of these experimental design choices for key hydrometeorological metrics including precipitation and snowpack, as well as evapotranspiration, groundwater storage, and discharge simulated by the ParFlow-CLM. Our hypothesis is that uncertainty from synoptic-scale forcings produces a much larger spread in surface–subsurface hydrologic fields than subgrid-scale physics scheme choice. Results reveal that the WRF subgrid-scale physics configuration leads to larger spatiotemporal variance in simulated hydrometeorological conditions, whereas variance across meteorological forcing with common subgrid-scale physics configurations is more spatiotemporally constrained. Despite reasonably simulating precipitation, a delay in simulated discharge peak is due to a systematic cold bias across WRF simulations, suggesting the need for bias correction. Discharge shows greater variance in response to the WRF simulations across subgrid-scale physics schemes (26 %) rather than meteorological forcing (6 %). The topographic radiation option has minor effects on the watershed-average hydrometeorological processes but adds profound spatial heterogeneity to local energy budgets (±30 W m−2 in shortwave radiation and 1 K air temperature differences in late summer). This is the first presentation of sensitivity analyses that provide support to help guide the scientific community to develop observational constraints on atmosphere-through-bedrock processes and their interactions.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Constraining high-energy neutrinos from tidal disruption events with IceCube high-energy starting events

Tidal disruption events (TDEs) have been proposed as candidate sources of high-energy neutrinos. Successful and choked jets, as well as the accretion disk, corona, wind, and outflow regions in a TDE have been examined and shown to produce TeV - PeV neutrinos. In this work, we use the IceCube 12.5 year high energy starting events (HESE) dataset and perform a maximum likelihood analysis to investigate the spatial and temporal correlations between HESE dataset and a selected sample of 89 TDEs. Our results indicate that the currently observed data do not show any significant correlation and hence is consistent with the background only hypothesis. Using this result, we place constraints on the fraction of TDEs harboring intrinsic jets ($f_{\rm jet}$) and the corresponding isotropic-equivalent cosmic ray (CR) energy ($\mathcal{E}_{\rm CR}$). We note that even with limited statistics, we can constrain the parameter space as $\mathcal{E}_{\rm CR} \lesssim 3 \times 10^{53}$ erg for $f_{\rm jet} \gtrsim 0.6$ at more than 90% C.L. Finally, we discuss the theoretical implications of our results and the limits on the all-sky diffuse neutrino flux from TDEs. With more observational data in the electromagnetic band for TDEs and neutrino observations from IceCube and KM3NeT, our analysis can be used to place stringent constraints on physical parameters associated with TDEs.

Mukhopadhyay, Mainak [Fermilab; Chicago U., KICP; ↗
DOE OSTI2020

A cancellation problem in hybrid particle-in-cell schemes due to finite particle size

The quasi-neutral hybrid particle-in-cell algorithm with kinetic ions and fluid electrons is a popular model to study multi-scale problems in laboratory, space, and astrophysical plasmas. Here, it is shown that the different spatial discretizations of ions as finite-spatial-size particles and electrons as a grid-based fluid can lead to significant numerical wave dispersion errors in the long wavelength limit (kd i «1, where k is the wavenumber and di is the ion skin-depth). The problem occurs when high-order particle-grid interpolations, or grid-based smoothing, spreads the electric field experienced by the ions across multiple spatial cells and leads to inexact cancellation of electric field terms in the total (ion + electron) momentum equation. Practical requirements on the mesh spacing Δx/d i are suggested to bound these errors from above. The accuracy impact of not respecting these resolution constraints is shown for a non-linear shock problem.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

3D-printed sheet jet for stable megahertz liquid sample delivery at X-ray free-electron lasers

X-ray free-electron lasers (XFELs) can probe chemical and biological reactions as they unfold with unprecedented spatial and temporal resolution. A principal challenge in this pursuit involves the delivery of samples to the X-ray interaction point in such a way that produces data of the highest possible quality and with maximal efficiency. This is hampered by intrinsic constraints posed by the light source and operation within a beamline environment. For liquid samples, the solution typically involves some form of high-speed liquid jet, capable of keeping up with the rate of X-ray pulses. However, conventional jets are not ideal because of radiation-induced explosions of the jet, as well as their cylindrical geometry combined with the X-ray pointing instability of many beamlines which causes the interaction volume to differ for every pulse. This complicates data analysis and contributes to measurement errors. An alternative geometry is a liquid sheet jet which, with its constant thickness over large areas, eliminates the problems related to X-ray pointing. Since liquid sheets can be made very thin, the radiation-induced explosion is reduced, boosting their stability. These are especially attractive for experiments which benefit from small interaction volumes such as fluctuation X-ray scattering and several types of spectroscopy. Although their use has increased for soft X-ray applications in recent years, there has not yet been wide-scale adoption at XFELs. Here, gas-accelerated liquid sheet jet sample injection is demonstrated at the European XFEL SPB/SFX nano focus beamline. Its performance relative to a conventional liquid jet is evaluated and superior performance across several key factors has been found. This includes a thickness profile ranging from hundreds of nanometres to 60 nm, a fourfold increase in background stability and favorable radiation-induced explosion dynamics at high repetition rates up to 1.13 MHz. Its minute thickness also suggests that ultrafast single-particle solution scattering is a possibility.

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

Considering computational speed vs. accuracy: Choosing appropriate mesoscale RVE boundary conditions

Modeling a material’s microstructure using continuum theories allows for inspection of the relationship between coarse scale and fine scale behaviors. Computational limits generally require selection of a sub-volume from a bulk sample in order to directly model the microstructure. Boundary conditions are applied to the sub-volume to mimic the excluded bulk material. Appropriate selection of boundary conditions helps effectively determine the appropriate spatial scale required of the sub-volume. Applicable boundary conditions include direct displacement, periodic, and uniform traction. While direct displacement and periodic boundary conditions are commonly used, uniform traction boundary conditions have seen limited use due to rigid body stability issues in simulations of compression or shear deformation. A new application of uniform traction boundary conditions was developed through linear constraint equations, similar to approaches employed by direct displacement and periodic boundary conditions, to quench rigid body motions with minimal interference of the relative deformation of the model. These boundary conditions were tested by compressing several synthetically generated periodic microstructures using the finite element method. Evaluating the effective stiffness along the compression axis, the direct displacement boundary condition produced the stiffest response, whereas the uniform traction boundary condition produced the most compliant. Periodic boundary conditions produced the same response for all volumes analyzed and both the direct displacement and uniform traction boundary conditions trended toward the periodic response as the domain volume increased. Computational performance was also evaluated for each boundary condition using implicit and explicit solvers. Direct displacement boundary conditions presented the lowest computational cost of all of the boundary conditions followed by periodic then uniform traction. The computational expense of periodic and uniform traction boundary conditions limited the viable spatial scale and mesh resolutions able to be simulated. Selection of appropriate boundary conditions for specific uses need to be a balance between allowable computational expense and accuracy of the method. Techniques for evaluating which boundary conditions to use are discussed.

42 ENGINEERING↗