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At least 757 records · Page 42

The multichannel i -propyl + O2 reaction system: A model of secondary alkyl radical oxidation

The i-propyl + O2 reaction mechanism has been investigated by definitive quantum chemical methods to establish this system as a benchmark for the combustion of secondary alkyl radicals. Focal point analyses extrapolating to the ab initio limit were performed based on explicit computations with electron correlation treatments through coupled cluster single, double, triple, and quadruple excitations and basis sets up to cc-pV5Z. The rigorous coupled cluster single, double, and triple excitations/cc-pVTZ level of theory was used to fully optimize all reaction species and transition states, thus, removing some substantial flaws in reference geometries existing in the literature. The vital i-propylperoxy radical (MIN1) and its concerted elimination transition state (TS1) were found 34.8 and 4.4 kcal mol−1 below the reactants, respectively. Two β-hydrogen transfer transition states (TS2, TS2′) lie above the reactants by (1.4, 2.5) kcal mol−1 and display large Born–Oppenheimer diagonal corrections indicative of nearby surface crossings. An α-hydrogen transfer transition state (TS5) is discovered 5.7 kcal mol−1 above the reactants that bifurcates into equivalent α-peroxy radical hanging wells (MIN3) prior to a highly exothermic dissociation into acetone + OH. The reverse TS5 → MIN1 intrinsic reaction path also displays fascinating features, including another bifurcation and a conical intersection of potential energy surfaces. An exhaustive conformational search of two hydroperoxypropyl (QOOH) intermediates (MIN2 and MIN3) of the i-propyl + O2 system located nine rotamers within 0.9 kcal mol−1 of the corresponding lowest-energy minima.

Chemistry↗

Transfer Learning Trained LSTM Models for Household Load Profile Forecasting

Grid edge renewable energy resources, such as rooftop solar photovoltaics, closely interact with consumer load profiles. Therefore, forecasting future electricity demand, ideally at the individual household level, is indispensable. In this paper, we present a transfer learning enhanced household load profile forecasting method. First, we tune a long short-term memory forecasting model to perform day-ahead prediction of household electricity load profiles. Then we improve these individualized models using transfer learning, and we use k-means clustering to create optimal source data sets. We find average improvements of 4.38% (largest improvement of 10.71%) when the entire data set was used to train the source model and 2.45% (largest improvement of 11.57%) in the mean absolute error when households were first clustered and used to train separate source models for each cluster. We find that transfer learning with clustered data can effectively boost the forecasting performance of the LSTM models. We use realistic household power measurements for 148 real residential households in Austin, Texas.

deep learning↗

Comparison Study of Conventional and Adaptive Mesh Refinement in Organic Material Decomposition Models

This study compares conventional mesh refinement techniques, specifically Uniform Mesh Refinement (UMR), with a new Adaptive Mesh Refinement (AMR) method, applied to Organic Material Decomposition (OMD) models. The proposed benefit of AMR is that only areas that require refinement, based on minimizing a specific field gradient, are refined thus decreasing model wall time compared to conventional UMR methods. This work specifically focuses on comparing UMR and AMR methods on decomposing (both No-Flow and Porous-Flow material models) Polymeric Methylene Diisocyanate (PMDI) polyurethane foam. Throughout the work, the geometry increased in complexity to assess the refinement methods performance at varying levels geometric intricacy. While AMR has been shown to work well in a variety of applications, the UMR approach proved to be computationally faster, for many of the geometries and foam decomposition models, than AMR. However, it was observed that at higher levels of refinement, greater than 3 UMR, AMR begins to be computationally better. Additionally, the settings used to perform AMR greatly impact its performance, and lessons learned, in terms of OMD models, are shared. Due to physics involved in material decomposition, specifically the evolution of state variables, these problems don’t fully benefit from the advantages of AMR.

36 MATERIALS SCIENCE↗

Method for Measuring Dry Density of Compacted Bentonite Mixture Soil Using 3D Laser Scanner data - 19119

The bentonite mixture soil is planned to be used for the low-permeability layer of low-level radioactive waste (LLW) disposal facilities. The construction of the bentonite mixture soil is similar to that of normal soil construction, and the rolling pressure and/or vibration compaction are used. The quality control of construction is the same as normal soil work, and the construction management has to confirm that the compaction degree (that is ratio of the dry density to the modified proctor curve) is above specified value. As a method of measuring the dry density after construction, the conventional methods are the core cutter method and the sand replacement method. The measurement principle of these methods is simple and the reliability of the measurement value is high, but during measurements digging holes disturb the construction place, and the measurement duration is a disadvantage in these methods. Therefore, we developed a non-destructive method that can make measurements in a short time. The developed method uses the correlation between the density change and the layer thickness change before and after compaction, and estimates the density after compaction from the height change obtained from the survey results. However, since the material is compressed while the cross-sectional area spreads, this cross-sectional area change is also taken into consideration. By using the point cloud data of the 3D laser scanner surveying, it is possible to obtain almost continuous data in a short period of time. Corrected dry density values calculated by the above procedure ρ'{sub 3D} are generally consistent with dry density after compaction ρ{sub core} by the core cutter method. This method differs depending on the boundary conditions of the bottom and the side of the construction place. Then, the reliability of the method was evaluated by applying it to two boundary conditions and comparing it with the core cutter method. The proposed estimation method showed good agreement with the core cutter method. Therefore, it was confirmed that it is possible to estimate dry density with high reliability. Although this method needs to be used in set with core cutter method, the measurement frequency of the core cutter method can be reduced, and the measurement of a vast area can be done in a short time without disturbance. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Spatial DIC Errors due to Pattern-Induced Bias and Grey Level Discretization

Digital image correlation (DIC) is an optical metrology method widely used in experimental mechanics for full-field shape, displacement and strain measurements. The required strain resolution for engineering applications of interest mandates DIC to have a high image displacement matching accuracy, on the order of 1/100th of a pixel, which necessitates an understanding of DIC errors. In this paper, we examine two spatial bias terms that have been almost completely overlooked. They cause a persistent offset in the matching of image intensities and thus corrupt DIC results. We name them pattern-induced bias (PIB), and intensity discretization bias (IDB). We show that the PIB error occurs in the presence of an undermatched shape function and is primarily dictated by the underlying intensity pattern for a fixed displacement field and DIC settings. The IDB error is due to the quantization of the gray level intensity values in the digital camera. In this paper we demonstrate these errors and quantify their magnitudes both experimentally and with synthetic images.

47 OTHER INSTRUMENTATION↗

Luminaires for Advanced Lighting in Education

Evolving education methods and greater use of technology in the classroom are dictating the need to rethink facility designs, including classroom lighting. Advances in LED-based lighting technology have created the possibility of lighting systems that are not only cost effective and energy efficient, but also color-tunable and as durable as other facility infrastructures (a 20-30 year life expectancy). Thus, there is the opportunity that the modern lighting system can be used by educators as a tool in their teaching strategy. To meet this need, RTI International and Finelite, Inc. teamed to develop and test the Next Generation Integrated Classroom Lighting System (NICLS). The NICLS technology incorporates a high performance, color-tunable light engine into new luminaire designs (e.g., pendant, direct-indirect, downlight, troffers) that are acceptable for use in classrooms. During this project, we successfully demonstrated that the NICLS technology achieves exceptional performance and exceeds all DOE goals for the classroom of the future, including: Luminous efficacy value for NICLS luminaires in excess of 125 lpw at all CCT values; TWL range of 2,700 K to 6,500 K while maintaining a CRI of 82 or higher at all values; Capability for full-range dimming (100% to 1%) at all CCT values with flicker levels below industry guidelines; Performance of the lighting system in a classroom mock-up, incorporating daylight and occupancy sensing to provide automatic control of lighting zones to further reduce energy consumption; Rated lifetime on the system exceeding 50,000 hours with a lumen maintenance of at least 85% at 50,000 hours; and Teacher-focused UI located at the front of the classroom to operate the lighting system. A smartphone-based UI is also available to accommodate teacher movement in the classroom. A critical element of developing this technology is designing the user interface to be compatible with modern teaching methods, including increased use of icons and colors and intuitive appearance. The design of the NICLS technology and the user interface was modified with assistance from focus groups consisting of more than 80 teachers and educational professionals total. The focus groups were held in a full-sized classroom that served as a technology demonstration site for the NICLS. The NICLS technology is an advanced lighting system for educational settings that meets or exceeds all DOE photometric, electrical, and reliability goals for the COF. The NICLS technology has been demonstrated at the classroom level, and the feedback from the dozens of teachers and educational professionals who visited the demonstration site has been overwhelmingly positive. NICLS provides a state-of-the-art lighting environment that adjusts the lighting conditions—both color and illuminance levels—to the needs of students and teachers for the task at hand. Early research has suggested that such lighting conditions will improve not only teacher effectiveness but also a student’s ability to concentrate on learning activities.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

A search for microscopic black holes, string balls, and sphalerons in proton-proton collisions at $\sqrt{s}=13$ TeV

A search for microscopic black holes, string balls, and electroweak sphalerons using proton-proton collisions at $\sqrt{s}=13$ TeV recorded with the CMS detector at the CERN LHC during the 2016–2018 data taking, and corresponding to an integrated luminosity of 138 fb −1 , is presented. Two search strategies based on control samples in data are used. Model-independent limits on the cross section of physics phenomena with multiple energetic jets, leptons, and photons are set using a method that relies on the shape invariance of the scalar sum of the transverse momenta of all objects in the event. Model-dependent limits on black hole and sphaleron production are set using a newly introduced method that has been developed for the identification of collider events with distinct kinematic features by separating them into classes based on phase space proximity. In the context of models with large extra dimensions, semiclassical black holes and string balls with masses below 8.4–11.4 TeV and 9.0–10.7 TeV, respectively, are excluded at 95% confidence level, significantly extending the reach beyond previous searches. Results of a dedicated search for electroweak sphalerons are used to derive an upper limit of 0.0034 at 95% confidence level on the fraction of quark-quark interactions, with a center-of-mass energy above the nominal sphaleron transition energy threshold of 9 TeV, that result in a sphaleron transition.

Beyond Standard Model↗

Fungal drops: a novel approach for macro- and microscopic analyses of fungal mycelial growth

Abstract This study presents an inexpensive approach for the macro- and microscopic observation of fungal mycelial growth. The ‘fungal drops’ method allows to investigate the development of a mycelial network in filamentous microorganisms at the colony and hyphal scales. A heterogeneous environment is created by depositing 15–20 µl drops on a hydrophobic surface at a fixed distance. This system is akin to a two-dimensional (2D) soil-like structure in which aqueous-pockets are intermixed with air-filled pores. The fungus (spores or mycelia) is inoculated into one of the drops, from which hyphal growth and exploration take place. Hyphal structures are assessed at different scales using stereoscopic and microscopic imaging. The former allows to evaluate the local response of regions within the colony (modular behaviour), while the latter can be used for fractal dimension analyses to describe the hyphal network architecture. The method was tested with several species to underpin the transferability to multiple species. In addition, two sets of experiments were carried out to demonstrate its use in fungal biology. First, mycelial reorganization of Fusarium oxysporum was assessed as a response to patches containing different nutrient concentrations. Second, the effect of interactions with the soil bacterium Pseudomonas putida on habitat colonization by the same fungus was assessed. This method appeared as fast and accessible, allowed for a high level of replication, and complements more complex experimental platforms. Coupled with image analysis, the fungal drops method provides new insights into the study of fungal modularity both macroscopically and at a single-hypha level.

Buffi, Matteo↗

An investigation into factors affecting the precision of CT radiation dose profile width measurements using radiochromic films

Purpose: To investigate the impact of x-ray beam energy, exposure intensity, and flat-bed scanner uniformity and spatial resolution on the precision of computed tomography (CT) beam width measurements using Gafchromic XR-QA2 film and an off-the-shelf document scanner. Methods: Small strips of Gafchromic film were placed at isocenter in a CT scanner and exposed at various x-ray beam energies (80–140 kVp), exposure levels (50–400 mA s), and nominal beam widths (1.25, 5, and 10 mm). The films were scanned in reflection mode on a Ricoh MP3501 flat-bed document scanner using several spatial resolution settings (100 to 400 dpi) and at different locations on the scanner bed. Reflection measurements were captured in digital image files and radiation dose profiles generated by converting the image pixel values to air kerma through film calibration. Beam widths were characterized by full width at half maximum (FWHM) and full width at tenth maximum (FWTM) of dose profiles. Dependences of these parameters on the above factors were quantified in percentage change from the baselines. Results: The uncertainties in both FWHM and FWTM caused by varying beam energy, exposure level, and scanner uniformity were all within 4.5% and 7.6%, respectively. Increasing scanner spatial resolution significantly increased the uncertainty in both FWHM and FWTM, with FWTM affected by almost 8 times more than FWHM (48.7% vs 6.5%). When uncalibrated dose profiles were used, FWHM and FWTM were over-estimated by 11.6% and 7.6%, respectively. Narrower beam width appeared more sensitive to the film calibration than the wider ones (R{sup 2} = 0.68 and 0.85 for FWHM and FWTM, respectively). The global and maximum local background variations of the document scanner were 1.2%. The intrinsic film nonuniformity for an unexposed film was 0.3%. Conclusions: Measurement of CT beam widths using Gafchromic XR-QA2 films is robust against x-ray energy, exposure level, and scanner uniformity. With proper film calibration and scanner resolution setting, it can provide adequate precision for meeting ACR and manufacturer’s tolerances for the measurement of CT dose profiles.

60 APPLIED LIFE SCIENCES↗

SU-F-T-254: Dose Volume Histogram (DVH) Analysis of Breath Hold Vs Free Breathing Techniques for Esophageal Tumors

Purpose: Lung and heart doses and associated toxicity are of concern in radiotherapy for esophageal cancer. This study evaluates the dosimetry of deep-inspiration-breath-hold (DIBH) technique as compared to freebreathing( FB) using 3D-conformal treatment(3D-CRT) of esophageal cancer. Methods: Eight patients were planned with FB and DIBH CT scans. DIBH scans were acquired using Varian RPM system. FB and DIBH CTs were contoured per RTOG-1010 to create the planning target volume(PTV) as well as organs at risk volumes(OAR). Two sets of gross target volumes(GTV) with 5cm length were contoured for each patient: proximal at the level of the carina and distal at the level of gastroesophageal junction and were enlarged with appropriate margin to generate Clinical Target Volume and PTV. 3D-CRT plans were created on Eclipse planning system for 45Gy to cover 95% of PTV in 25 fractions for both proximal and distal tumors on FB and DIBH scans. For distal tumors celiac nodes were covered electively. DVH parameters for lung and heart OARs were generated and analyzed. Results: All DIBH DVH parameters were normalized to FB plan values. Average of heart-mean and heart-V40 was 0.70 and 0.66 for proximal lesions. For distal lesions ratios were 1.21 and 2.22 respectively. For DIBH total lung volume increased by 2.43 times versus FB scan. Average of lung-mean, V30, V20, V10, V5 are 0.82, 0.92, 0.76, 0.77 and 0.79 for proximal lesions and 1.17,0.66,0.87,0.93 and 1.03 for distal lesions. Heart doses were lower for breath-hold proximal lesions but higher for distal lesions as compared to free-breathing plans. Lung doses were lower for both proximal and distal breath-hold lesions except mean lung dose and V5 for distal lesions. Conclusion: This study showed improvement of OAR doses for esophageal lesions at mid-thoracic level utilizing DIBH vs FB technique but did not show consistent OAR sparing with DIBH for distal lesions.

60 APPLIED LIFE SCIENCES↗

Enhancing Least-Squares Finite Element Methods Through a Quantity-of-Interest

Here, we introduce an approach that augments least-squares finite element formulations with user-specified quantities-of-interest. The method incorporates the quantity-of-interest into the least-squares functional and inherits the global approximation properties of the standard formulation as well as increased resolution of the quantity-of-interest. We establish theoretical properties such as optimality and enhanced convergence under a set of general assumptions. Central to the approach is that it offers an element-level estimate of the error in the quantity-of-interest. As a result, we introduce an adaptive approach that yields efficient, adaptively refined approximations. Several numerical experiments for a range of situations are presented to support the theory and highlight the effectiveness of our methodology. Notably, the results show that the new approach is effective at improving the accuracy per total computational cost.

97 MATHEMATICS AND COMPUTING↗

Improved Guarantees for Optimal Nash Equilibrium Seeking and Bilevel Variational Inequalities

We consider a class of hierarchical variational inequality (VI) problems that subsumes VI-constrained optimization and several other problem classes, including the optimal solution selection problem and the optimal Nash equilibrium (NE) seeking problem. Our main contribution is threefold. (i) We consider bilevel VIs with monotone and Lipschitz continuous mappings and devise a single-timescale iteratively regularized extragradient method, named IR-EG 𝚖,𝚖 . We improve the existing iteration complexity results for addressing both bilevel VI and VI-constrained convex optimization problems. (ii) Under the strong monotonicity of the outer-level mapping, we develop a method named IR-EG 𝚜,𝚖 and derive faster guarantees than those in (i). We also study the iteration complexity of this method under a constant regularization parameter. These results appear to be new for both bilevel VIs and VI-constrained optimization. (iii) To our knowledge, complexity guarantees for computing the optimal NE in nonconvex settings do not exist. Motivated by this lacuna, we consider VI-constrained nonconvex optimization problems and devise an inexactly projected gradient method, named IPR-EG, where the projection onto the unknown set of equilibria is performed using IR-EG 𝚜,𝚖 with a prescribed termination criterion and an adaptive regularization parameter. We obtain new complexity guarantees in terms of a residual map and an infeasibility metric for computing a stationary point. Here, we validate the theoretical findings using preliminary numerical experiments for computing the best and the worst NEs.

bilevel optimization↗

Charged point defect benchmark of Hybrid and GGA-PBE

Data used by the publication "High-throughput calculations of charged point defect properties with semi-local density functional theory - performance benchmarks for materials screening applications." This work presented an in-depth benchmark analysis of automated, semi-local point defect calculations with a-posteriori corrections, compared to 245 “gold standard” hybrid calculations previously published. We considered three different a-posteriori correction sets for semi-local calculations, implemented in a fully automated workflow, and consider the qualitative and quantitative differences for four different categories of defect information: thermodynamic transition levels, formation energies, fermi levels, and dopability limits. We highlighted the type of qualitative information about point defect properties that can be extracted from high-throughput calculations based on semi-local DFT methods, while also demonstrating the limits of quantitative accuracy that can be achieved by these approaches.

Broberg, Danny↗

Fermilab Booster loss modelling and rebalancing using Bayesian methods

To meet PIP-II upgrade requirements, Fermilab Booster losses need to be reduced by 50% compared to present levels. So far, simulations are not good enough to predict loss patterns. Thus, an extensive Booster tune up will be necessary to achieve required performance. In this paper we present an effort to build a data-driven loss model using Bayesian techniques, and subsequently to rebalance losses for higher trip 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. Novel techniques of uncertainty constraints and approximate GP fitting were introduced to handle safety and timing requirements. We then performed single and multi-objective tuning using scalarized objectives comprised of critical beam loss locations. We achieved significant rebalancing of losses, increasing margins by 25%, as well as an overall improvement in transmission efficiency of 0.4%. Automated data collection is being developed so that more accurate surrogate models can be trained over time.

Kuklev, N. [Fermilab]↗

Dark Matter Constraints from a Unified Analysis of Strong Gravitational Lenses and Milky Way Satellite Galaxies

Joint analyses of small-scale cosmological structure probes have been relatively unexplored yet promise to advance measurements of microphysical dark matter properties using heterogeneous data. Here, we present a multidimensional analysis of dark matter substructure using strong gravitational lenses and the Milky Way (MW) satellite galaxy population, accounting for degeneracies in model predictions and using covariances in the constraining power of these individual probes for the first time. We simultaneously infer the projected subhalo number density and the half-mode mass describing the suppression of the subhalo mass function in thermal relic warm dark matter (WDM), $M_{\mathrm{hm}}$, using the semianalytic model \texttt{Galacticus} to connect the subhalo population inferred from MW satellite observations to the strong lensing host halo mass and redshift regime. Combining MW satellite and strong lensing posteriors in this parameter space yields $M_{\mathrm{hm}}<10^{7.0}\ M_{\mathrm{\odot}}$ (WDM particle mass $m_{\mathrm{WDM}}>9.7\ \mathrm{keV}$) at $95\%$ confidence and disfavors $M_{\mathrm{hm}}=10^{7.4}\ M_{\mathrm{\odot}}$ ($m_{\mathrm{WDM}}=7.4\ \mathrm{keV}$) with a 20:1 marginal likelihood ratio, improving limits on $m_{\mathrm{WDM}}$ set by the two methods independently by $\sim 30\%$. These results are marginalized over the line-of-sight contribution to the strong lensing signal, the mass of the MW host halo, and the efficiency of subhalo disruption due to baryons and are robust to differences in the disruption efficiency between the MW and strong lensing regimes at the $\sim 10\%$ level. This work paves the way for unified analyses of next-generation small-scale structure measurements covering a wide range of scales and redshifts.

79 ASTRONOMY AND ASTROPHYSICS↗

Monte Carlo Control Loops for Cosmic Shear Cosmology with DES Year 1

Weak lensing by large-scale structure is a powerful probe of cosmology and of the dark universe. This cosmic shear technique relies on the accurate measurement of the shapes and redshifts of background galaxies and requires precise control of systematic errors. The Monte Carlo Control Loops (MCCL) is a forward modelling method designed to tackle this problem. It relies on the Ultra Fast Image Generator (UFig) to produce simulated images tuned to match the target data statistically, followed by calibrations and tolerance loops. We present the first end-to-end application of this method, on the Dark Energy Survey (DES) Year 1 wide field imaging data. We simultaneously measure the shear power spectrum $C_{\ell}$ and the redshift distribution $n(z)$ of the background galaxy sample. The method includes maps of the systematic sources, Point Spread Function (PSF), an Approximate Bayesian Computation (ABC) inference of the simulation model parameters, a shear calibration scheme, and the fast estimation of the covariance matrix. We find a close statistical agreement between the simulations and the DES Y1 data using an array of diagnostics. In a non-tomographic setting, we derive a set of $C_\ell$ and $n(z)$ curves that encode the cosmic shear measurement, as well as the systematic uncertainty. Following a blinding scheme, we measure the combination of $\Omega_m$, $\sigma_8$, and intrinsic alignment amplitude $A_{\rm{IA}}$, defined as $S_8D_{\rm{IA}} = \sigma_8(\Omega_m/0.3)^{0.5}D_{\rm{IA}}$, where $D_{\rm{IA}}=1-0.11(A_{\rm{IA}}-1)$. We find $S_8D_{\rm{IA}}=0.895^{+0.054}_{-0.039}$, where systematics are at the level of roughly 60\% of the statistical errors. We discuss these results in the context of earlier cosmic shear analyses of the DES Y1 data. Our findings indicate that this method and its fast runtime offer good prospects for cosmic shear measurements with future wide-field surveys.

79 ASTRONOMY AND ASTROPHYSICS↗

Validation of Material Models For Automotive Carbon Fiber Composite Structures Via Physical And Crash Testing (VMM Composites Project)

As automotive fuel economy requirements increase, the push for reducing overall vehicle weight will likely include the consideration of materials that have not previously been part of mainstream vehicle design and manufacturing, including carbon fiber composites. Vehicle manufacturers currently rely on computer-aided engineering (CAE) methods as part of the design and development process, so going forward, the ability to accurately and predictably model carbon fiber composites will be necessary. If composites are to be used for structural components, this need applies to both, crash and quasi-static modeling. This final report covers the results of a five-year, $6.89M, 50% cost-shared research project between Department of Energy (DOE) and the US Advanced Materials Partnership (USAMP) under Cooperative Agreement DE-EE-0005661 known as “Validation of Material Models for Automotive Carbon Fiber Composite Structures Via Physical and Crash Testing (VMM).” The objective of the VMM Composites Project was to validate and assess the ability of physics-based material models to predict crash performance of automotive primary load-carrying carbon fiber composite structures. Simulation material models that were evaluated included micro-mechanics based meso-scale models developed by the University of Michigan (UM) and micro-plane models by Northwestern University (NWU) under previous collaborations with the DOE and Automotive Composites Consortium/USAMP, as well as five commercial crash codes: LS-DYNA, RADIOSS, VPS/PAM-CRASH, Abaqus, and GENOA-MCQ. CAE predictions obtained from seven organizations were compared with experimental results from quasi-static testing and dynamic crash testing of a thermoset carbon fiber composite front-bumper and crush-can (FBCC) system gathered under multiple loading conditions. This FBCC design was developed to demonstrate progressive crush, virtual simulation, tooling, fabrication, assembly, non-destructive evaluation and crash testing advances in order to assess the correlation of the predicted results to the physical tests. The FBCC was developed to meet a goal of 30-35% mass reduction while aiming for equivalent energy absorption as a steel component for which baseline experimental results were obtained from testing in the same crash modes. The project also evaluated crash performance of thermoplastic composite structures fabricated from commercial prepreg materials and low cost carbon fiber sourced from Oak Ridge National Laboratory. The VMM Project determined that no set of predictions from a CAE supplier were found to be universally accurate among all the six crash modes evaluated. In general, crash modes that were most dependent on the properties of the prepreg were more accurate than those that were dependent on the behavior of the joints. The project found that current CAE modeling methods or best practices for carbon fiber composites have not achieved standardization, and accuracy of CAE is highly reliant on the experience of its users. Coupon tests alone are not sufficient to develop an accurate material model, but it is necessary to bridge the gap between the coupon data and performance of the actual structure with a series of subcomponent level tests. Much of the unreliability of the predictions can be attributed to shortcomings in our ability to mathematically link the effects of manufacturing and material variability into the material models. This is a subject of ongoing research in the industry. The final report is organized by key technical tasks to describe how the validation project developed, modeled and compared crash data obtained on the composite FBCC to the multiple sets of CAE predictions. Highlights of the report include a discussion of the quantitative comparison between predictions and experimental data, as well as an in-depth discussion of remaining technological gaps that exist in the industry, which are intended to spur innovations and improvements in CAE technology.

36 MATERIALS SCIENCE↗

A solution framework for linear PDE-constrained mixed-integer problems

Abstract We present a general numerical solution method for control problems with state variables defined by a linear PDE over a finite set of binary or continuous control variables. We show empirically that a naive approach that applies a numerical discretization scheme to the PDEs to derive constraints for a mixed-integer linear program (MILP) leads to systems that are too large to be solved with state-of-the-art solvers for MILPs, especially if we desire an accurate approximation of the state variables. Our framework comprises two techniques to mitigate the rise of computation times with increasing discretization level: First, the linear system is solved for a basis of the control space in a preprocessing step. Second, certain constraints are just imposed on demand via the IBM ILOG CPLEX feature of a lazy constraint callback. These techniques are compared with an approach where the relations obtained by the discretization of the continuous constraints are directly included in the MILP. We demonstrate our approach on two examples: modeling of the spread of wildfire and the mitigation of water contamination. In both examples the computational results demonstrate that the solution time is significantly reduced by our methods. In particular, the dependence of the computation time on the size of the spatial discretization of the PDE is significantly reduced.

97 MATHEMATICS AND COMPUTING↗