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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 865 records · Page 48
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Engineering evaluations of nuclear material storage containers against the packaging requirements at TA-55 (FY22 Rules of Use Report)

A set of obligations in the yearly storage container surveillance program, ensures that a retrospective approach is applied with loaded containers in inventory to confirm compliance with all “users” to ensure nuclear material storage container requirements are being followed. Validation that packaged containers are properly used, within a specific set of container types prescribed “bounding conditions of use,” is based on meeting requirements as identified in operating procedures associated with TA55-DOP-091, TA-55 Nuclear Material Packaging, and PA-RD-01022, Nuclear Material Packaging Requirements. The surveillance plan obligation requires the application of local area nuclear material accountability software or (LANMAS) to produce queries. The data queries are used to assess attributes of containers in storage these investigations are conducted on a bi-annual basis. This rules of use (ROU) compliance process ensures proper usage of storage containers as containment systems and therefore provides effective worker protection. It is structured as a supporting effort by implementing aspects of PA-AP-01207, Nuclear Material Container Safety Management at TA-55.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Development of thinned silicon sensors on 8” wafers (CRADA FRA-2015-0015 Final Report)

Sensors fabricated from high resistivity, float zone, silicon material have been the basis of vertex detectors and trackers for the last 30 years. The areas of these devices have increased from a few square cm to >200 m 2 for the existing CMS tracker. CMS and ATLAS upgrades will each require more than 200 m 2 of silicon and the CMS High Granularity Calorimeter (HGC) will require more than 600 m 2 . Cost and complexity of assembly of these devices is related to the area of each module, which in turn is set by the area of the silicon sensors. A move from 4” and 6” wafers (the only sizes currently available) to 8” diameter in volume production has the potential for savings of tens of millions of dollars in the detector upgrade programs at the Large Hadron Collider (LHC) and future experiments. In addition to large area, the devices must be radiation hard, which can be achieved by the use of sensors thinned to 200 microns or less. The combination of wafer thinning and large wafer diameter is a significant technical challenge, and is the subject of this work.

43 PARTICLE ACCELERATORS↗
DOE OSTI2022

Ab Initio Structure Factors for Spin-Dependent Dark Matter Direct Detection

We present converged ab initio calculations of structure factors for elastic spin-dependent WIMP scattering off all nuclei used in dark matter direct-detection searches: 19 F, 23 Na, 27 Al, 29 Si, 73 Ge, 12 7I, and 129,131 Xe. From a set of established two- and three-nucleon interactions derived within chiral effective field theory, we construct consistent WIMP-nucleon currents at the one-body level, including effects from axial-vector two-body currents. We then apply the in-medium similarity renormalization group to construct effective valence-space Hamiltonians and consistently transformed operators of nuclear responses. Combining the recent advances of natural orbitals with three-nucleon forces expressed in large spaces, we obtain basis-space converged structure factors even in heavy nuclei. Generally results are consistent with previous calculations but large uncertainties in 127 I highlight the need for further study.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Role of consistent terminology in XPS reproducibility

The use of inconsistent and incorrect terminology in scientific publications contributes to misunderstanding, confusion, and erroneous results in the scientific literature. This issue is of particular importance in x-ray photoelectron spectroscopy (XPS) that is in widespread use for many different purposes by scientists with diverse backgrounds. A set of surface analysis terminology, approved through consensus by international experts, has been developed by International Organization for Standardization Technical Committee TC201 on Surface Chemical Analysis. To encourage wide use, the terminology is accessible at several web sites free of charge. This short overview provides examples to highlight the importance of agreed terminology in eliminating confusion between similar terms. Examples are provided of terms that are commonly misused or confused in the literature. Other examples highlight terminology that provides a common basis for comparing instrument parameters and performance. As science advances, it is important to clarify terminology for describing evolving concepts and developments important to XPS.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗
DOE OSTI2025

AI-Assisted Conceptual Development of a Pre-Geometric Cosmological Model - An Exercise in AI-Assisted Conceptual Framework Generation, Paper II: Local Geometry and Metric Structure

This paper develops the geometric sector of the replication-driven cosmogenesis framework introduced in Paper I. Starting from a pre-geometric spectral substrate and a minimal set of replication axioms, we show how coherent self-replicating units generate a spatial adjacency graph whose continuum limit acquires an effective Riemannian structure. The replication dynamics determines a characteristic correlation length that seeds the local metric, while overlap relations among coherent units produce an isotropic neighborhood geometry with an emergent dimensionality $d_{\rm eff}\simeq 3$ across a broad range of replication factors. As replication slows and causal order stabilizes, a limiting signal speed $c_\ast$ appears, providing the basis for the Lorentzian structure of spacetime without assuming a pre-existing light cone. We derive conditions under which the adjacency graph converges to a smooth three-dimensional manifold, describe the transition from Euclidean to Lorentzian propagation, and identify geometric invariants controlled by the replication parameters. This work establishes the geometric and causal layer of the replication cosmogenesis program, bridging the spectral axioms of Paper I to the cosmological dynamics explored in Paper III.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

$\mathrm{REX}$: An analytical tool for reactor operating envelope expansion through fuel-clad thermo-mechanics

Here REX, an analytical reactor design tool for the identification and expansion of reactor operating envelopes, is introduced and detailed. Written in MATLAB, REX takes core geometries and axially discretized detector and depletion output from the Serpent neutron transport code and performs full-core, pin-specific thermal-hydraulic and thermo-mechanical calculations. REX identifies the operating envelopes of advanced, solid-fuel nuclear reactors on the basis of their fuel-cladding, fuel-gas, and coolant-cladding interfacial thermo-mechanics. It iteratively pushes coolant inlet temperatures and modifies fuel pin geometries to induce mechanical failure in their original cladding materials at the fullest extent of their fuel cycle lengths and permissible coolant inlet temperatures. It then attempts to expand their operating envelopes by determining the mechanical responses of alternative cladding materials under the same geometric conditions. The result of the REX calculation sequence is a set of 5-D variables describing the temperatures, pressures, geometries, and mechanics of the core as functions of assembly, fuel pin, axial zone, depletion step, and coolant inlet temperature for each candidate cladding material with the limiting fuel pin geometry for the original material.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

Structural Tolerance Factor Approach to Defect-Resistant I 2 -II-IV-X 4 Semiconductor Design

Recent work on quaternary semiconductors Cu 2 BaSn(S,Se) 4 and Ag 2 BaSnSe 4 for photovoltaic and thermoelectric applications, respectively, has shown the promise of exploring the broader family of defect-resistant I 2 -II-IV-X 4 materials (where I, II, and IV refer to the formal oxidation state of the metal cations and X is a chalcogen anion) with tetrahedrally coordinated I/IV cations and larger II cations (i.e., Sr, Ba, Pb, and Eu) for optoelectronic and energy-related applications. Chemical dissimilarity among the II and I/IV atoms represents an important design motivation because it presents a barrier to antisite formation, which otherwise may act as electronically harmful defects. We herein show how all 31 experimentally reported I 2 -II-IV-X 4 examples (with large II cations and tetrahedrally coordinated smaller I/IV cations), which form within five crystal structure types, are structurally linked. Based on these structural similarities, we derive a set of tolerance factors that serve as descriptors for phase stability within this family. Despite common usage in the well-studied perovskite system, Shannon ionic radii are found to be insufficient for predicting metal–chalcogen bond lengths, pointing to the need for experimentally derived correction factors as part of an empirically driven learning approach to structure prediction. Here, we use the tolerance factors as a predictive tool and demonstrate that four new I 2 -II-IV-X 4 compounds, Ag 2 BaSiS 4 , Ag 2 PbSiS 4 , Cu 2 PbGeS 4 , and Cu 2 SrSiS 4 , can be synthesized in correctly predicted phases. One of these compounds, Ag 2 PbSiS 4 , shows potentially promising optoelectronic properties for photovoltaic applications.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Langevin dynamics of generalized spins as SU( N ) coherent states

Classical models of spin systems traditionally retain only the dipole moments, but a quantum spin state will frequently have additional structure. Spins of magnitude S have N = 2⁢S + 1 levels. Alternatively, the spin state is fully characterized by a set of N 2 - 1 local physical observables, which we interpret as generalized spin components. For example, a spin with S = 1 has three dipole components and five quadrupole components. Further, these components evolve under a generalization of the classical Landau-Lifshitz dynamics, which can be extended with noise and damping terms. In this paper, we reformulate the dynamical equations of motion as a Langevin dynamics of SU(N) coherent states in the Schrödinger picture. This viewpoint is especially useful as the basis for an efficient numerical method to sample spin configurations in thermal equilibrium and to simulate the relaxation and driven motion of topological solitons. To illustrate the approach, we simulate a nonequilibrium relaxation process that creates CP 2 skyrmions, which are topological defects with both dipole and quadrupole character.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Modifications to the JET Shattered Pellet Injector to Optimize Disruption Mitigation Experiments for Supporting ITER’s DMS Design

Shattered pellet injection (SPI) experiments on Joint European Torus (JET) are an important element in determining the physics basis for mitigating disruptions in ITER. Here, the initial design of the JET SPI system included three barrels to produce pellets with diameters of 4.5, 8.1, and 12.5 mm. The variability of the pellet speed by operating with and without a mechanical punch was limited and led to poor pellet integrity, so the mechanical punch was removed. Fragment size distribution is a function of pellet speed and the desire to change the resulting fragment size distribution was not originally a requirement. After the first set of SPI experiments on JET, different pellet sizes were considered to enable dual injection experiments with identical pellet diameters. It was also determined that speed control is necessary to improve experimental repeatability and to determine how the fragment size distribution impacts mitigation performance. Two barrels were fabricated to form pellets of 10 mm diameter and a third to form an 8.1 mm diameter pellet. New propellant valves were also fabricated and characterized to improve repeatability and overall performance. To have fine control of pellet speed, inserts to reduce the breech volume were fabricated and installed. Laboratory testing was conducted to ensure pellet release and provide a comparison of propellant gas delivered versus pellet speeds for a range of pellet types and mixtures. This article will also discuss how lessons learned from the JET SPI modifications can be applied to other SPI systems, such as the ITER SPI system, as controlling pellet release with the least amount of propellant gas is essential for optimal SPI effectiveness.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

AdS 3 orbifolds, BTZ black holes, and holography

Conical defects of the form (AdS 3 × S 3 )/Z k have an exact orbifold description in worldsheet string theory, which we derive from their known presentation as gauged Wess-Zumino-Witten models. The configuration of strings and fivebranes sourcing this geometry is well-understood, as is the correspondence to states/operators in the dual CFT 2 . One can analytically continue the construction to Euclidean AdS 3 (i.e. the hyperbolic ball $H$$^{+}_{3}$) and consider the orbifold by any infinite discrete (Kleinian) group generated by a set of elliptic elements γi ϵ SL(2, C), $γ$$^{ki}_{i}$ = 1, i = 1, . . . , K. The resulting geometry consists of multiple conical defects traveling along geodesics in $H$$^{+}_{3}$, and provides a semiclassical bulk description of correlation functions in the dual CFT involving the corresponding defect operators, which is nonperturbatively exact in α'. The Lorentzian continuation of these geometries describes a collection of defects colliding to make a BTZ black hole. We comment on a recent proposal to use such correlators to prepare a basis of black hole microstates, and elaborate on a picture of black hole formation and evaporation in terms of the underlying brane dynamics in the bulk.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Solving independent set problems with photonic quantum circuits

An independent set (IS) is a set of vertices in a graph such that no edge connects any two vertices. In adiabatic quantum computation [E. Farhi, et al ., Science 292, 472–475 (2001); A. Das, B. K. Chakrabarti, Rev. Mod. Phys. 80, 1061–1081 (2008)], a given graph G ( V , E ) can be naturally mapped onto a many-body Hamiltonian H IS G ( V , E ) , with edges E being the two-body interactions between adjacent vertices V . Thus, solving the IS problem is equivalent to finding all the computational basis ground states of H IS G ( V , E ) . Very recently, non-Abelian adiabatic mixing (NAAM) has been proposed to address this task, exploiting an emergent non-Abelian gauge symmetry of H IS G ( V , E ) [B. Wu, H. Yu, F. Wilczek, Phys. Rev. A 101, 012318 (2020)]. Here, we solve a representative IS problem G ( 8 , 7 ) by simulating the NAAM digitally using a linear optical quantum network, consisting of three C-Phase gates, four deterministic two-qubit gate arrays (DGA), and ten single rotation gates. The maximum IS has been successfully identified with sufficient Trotterization steps and a carefully chosen evolution path. Remarkably, we find IS with a total probability of 0.875(16), among which the nontrivial ones have a considerable weight of about 31.4%. Our experiment demonstrates the potential advantage of NAAM for solving IS-equivalent problems.

Science & Technology - Other Topics↗
DOE OSTI2020

Sources of Propane Consumed in California

Project Scope: The objective of this study is to specify the sources of propane consumed in California. It answers the questions, where does the propane used in California come from and how was it produced? The results of this study provide comprehensive, transparent, and verifiable estimates, based on the 2018 market. The information provided in this report is suitable for use to assess the life cycle carbon intensity of propane used as a transportation fuel in California. As the 2009 Low Carbon Fuel Standard (LCFS) aims to reduce California’s greenhouse gas (GHG) emissions and other smog-forming and toxic air pollutants, the appropriate designation of carbon intensity for propane as a transportation fuel is important for evaluating propane’s potential to contribute to GHG goals and understandings in the context of various actions. This study focuses on estimating the shares of total propane consumed in the state of California produced from petroleum refineries, natural gas plants, and bituminous sands sources inside California and elsewhere. Results: An estimated 590 million gallons of propane were consumed in California in 2018, of which, 59.5% originated from refinery production and 40.5% originated from natural gas plants. The majority of this was sourced from refinery production in California, 334 million gallons. Most of the propane imported to California for consumption was sourced from natural gas plants, 113 million gallons, with over half of the imported volume sourced from Canada. The volume sourced from bituminous sand upgrader and fractionator operations was negligible. Details from this analysis are presented in the table below which provides an overview of the propane flows estimated in this study by region and production method. The shares and volumes presented here represent a snapshot for 2018. A significant increase in propane demand, such as could be caused by increased use of propane as a transportation fuel in the state, would affect California’s propane production, imports, and exports. The method and data sources used for the estimates provided in this report also provide the framework which could be used for future updates. Key Method Considerations: The values presented here are based on a two-step approach where the first step was to determine the flows of propane into and out of California from different regions and the second step was to estimate the propane production methods in each region. A volume balance approach is used as the primary method for tracking the volume of propane in and out of California as propane production and import volumes are available by Petroleum Administration of Defense District (PADD) from EIA and neither inter-PADD propane transfers nor state-specific non-prime supplier consumption are available from a public data source. The volume balance performed for this study covered PADD 5 (the West Coast), which includes Arizona, California, Nevada, Oregon, and Washington. The volume balance used all available public datasets to determine propane production, imports, exports, and consumption. Volumes unaccounted for by these datasets were estimated using the resulting volume balance by assuming market equilibrium. Consumption within each state in PADD 5 was estimated based on known import, export, and production volumes and this amount was used to develop the volume balance. EIA only tracks consumption at the state level by prime supplier sales. The volume balance approach provides the basis to correct for additional propane consumed in-states where propane is transferred to California. To determine the California propane sources and trade in 2018. volume of propane consumed in California, the volume balance approach is again used where it was estimated all imported volumes not specifically flagged for re-export were consumed, and the remaining consumption was produced in-state. The California Energy Commission (CEC) provided the total volume of propane imported and exported from California in 2018; this volume data set along with commodity tracking from the Canada Energy Regulator (CER) and the International Trade Commission (ITC) which tracks port of entry and final destination was used to determine where propane originated from and where it was ultimately consumed. For example, the CER tracks propane leaving Canada and entering each state within the U.S. Imported propane from Canada to California – marked for California – is assumed to be consumed in California. When no further data were available, import volumes were assumed to be consumed in California without pass-through (i.e., no propane imported to California was directly sold and exported). In most cases, the production method for each propane source region was applied to the volume of propane transferred to California. In other words, the shares of propane sourced from natural gas and refineries for each production region was assigned to California imports based on their contribution to the total volume flows into California to determine the production method for propane consumed in-state. For volumes imported into California from PADD 4, Washington State, Canada, and the rest of the world (Argentina, Chile, Norway, Peru, South Korea, and Trinidad and Tobago), the volumes sourced from petroleum refineries and natural gas plants reflect the either production ratio for the region or, in cases where the sources specific to the amounts exported to California could be determined, the sources specific to the volumes transferred to California.

03 NATURAL GAS↗
DOE OSTI2024

Qudit Gate Decomposition Dependence for Lattice Gauge Theories

In this work, we investigate the effect of decomposition basis on primitive qudit gates on superconducting radio-frequency cavity-based quantum computers with applications to lattice gauge theory. Three approaches are tested: SNAP & Displacement gates, ECD & single-qubit rotations $R(\theta,\phi)$, and optimal pulse control. For all three decompositions, implementing the necessary sequence of rotations concurrently rather then sequentially can reduce the primitive gate run time. The number of blocks required for the faster ECD &$R_p(\theta)$ is found to scale $\mathcal{O}(d^2)$, while slower SNAP & Displacement set scales at worst $\mathcal{O}(d)$. For qudits with $d<10$, the resulting gate times for the decompositions is similar, but strongly-dependent on experimental design choices. Optimal control can outperforms both decompositions for small $d$ by a factor of 2-12 at the cost of higher classical resources. Lastly, we find that SNAP & Displacement are slightly more robust to a simplified noise model.

Kürkçüoglu, Doga Murat↗
DOE OSTI2020

Comparing event generator predictions and ab-initio calculations of $\nu$-$^{12}$C neutral current quasi-elastic scattering at 1 GeV

The measurement of neutrino oscillations and exotic physics searches are important parts of the physics program in the near future, with new state-of-the-art experiments planned within the next decade. Future and modern experiments in these fields will make use of nuclear targets. Event Generators (EGs) are software used in the analysis of neutrino oscillation experiments. EGs use to predict kinematic observables for a range of neutrino energies. These simulations may lack physics captured by more rigorous theoretical calculations. This work compares EG performance to nuclear theory calculations by comparing observables generated in the two frameworks. We provide a common set of definitions between theory and experiment and assess the physics contained in EG simulations. Neutral current quasi-elastic (NCQE) scattering events for neutrinos and anti-neutrinos on a $^{12}$C target are simulated with a specific EG, NEUT, used by the T2K experiment for its analysis. The simulated cross sections are compared to analytic calculations from nuclear theory within the factorization scheme. We compare the NEUT implementation of two different models on nuclear spectral functions: the Relativistic Fermi Gas (RFG) and the correlated basis spectral function (CBF) to analytic calculations of the same models in the factorization scheme. For both nuclear physics models, we compare the appearance of features in the distributions relevant to experimental analyses. Qualitatively, the shape of the simulated distribution is similar to the one obtained through theory calculations; however, there are some discrepancies between the theory calculations and the NEUT simulation. While the EG simulations and analytic calculations with the same model of nuclear dynamics show similar overall features, there are still differences between the two.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Mechanistic basis of post-treatment control of SIV after anti-α4β7 antibody therapy

Treating macaques with an anti-α4β7 antibody under the umbrella of combination antiretroviral therapy (cART) during early SIV infection can lead to viral remission, with viral loads maintained at < 50 SIV RNA copies/ml after removal of all treatment in a subset of animals. Depletion of CD8+ lymphocytes in controllers resulted in transient recrudescence of viremia, suggesting that the combination of cART and anti-α4β7 antibody treatment led to a state where ongoing immune responses kept the virus undetectable in the absence of treatment. A previous mathematical model of HIV infection and cART incorporates immune effector cell responses and exhibits the property of two different viral load set-points. While the lower set-point could correspond to the attainment of long-term viral remission, attaining the higher set-point may be the result of viral rebound. Here we expand that model to include possible mechanisms of action of an anti-α4β7 antibody operating in these treated animals. We show that the model can fit the longitudinal viral load data from both IgG control and anti-α4β7 antibody treated macaques, suggesting explanations for the viral control associated with cART and an anti-α4β7 antibody treatment. This effective perturbation to the virus-host interaction can also explain observations in other nonhuman primate experiments in which cART and immunotherapy have led to post-treatment control or resetting of the viral load set-point. Interestingly, because the viral kinetics in the various treated animals differed—some animals exhibited large fluctuations in viral load after cART cessation—the model suggests that anti-α4β7 treatment could act by different primary mechanisms in different animals and still lead to post-treatment viral control. This outcome is nonetheless in accordance with a model with two stable viral load set-points, in which therapy can perturb the system from one set-point to a lower one through different biological mechanisms.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2023

Fusion of Multiple Models for Improving Gross Primary Production Estimation With Eddy Covariance Data Based on Machine Learning

Abstract Terrestrial gross primary production (GPP) represents the magnitude of CO 2 uptake through vegetation photosynthesis, and is a key variable for carbon cycles between the biosphere and atmosphere. Light use efficiency (LUE) models have been widely used to estimate GPP for its physiological mechanisms and availability of data acquisition and implementation, yet each individual GPP model has exhibited large uncertainties due to input errors and model structure, and further studies of systematic validation, comparison, and fusion of those models with eddy covariance (EC) site data across diverse ecosystem types are still needed in order to further improve GPP estimation. We here compared and fused five GPP models (VPM, EC‐LUE, GOL‐PEM, CHJ, and C‐Fix) across eight ecosystems based on FLUXNET2015 data set using the ensemble methods of Bayesian Model Averaging (BMA), Support Vector Machine (SVM), and Random Forest (RF) separately. Our results showed that for individual models, EC‐LUE gave a better performance to capture interannual variability of GPP than other models, followed by VPM and GLO‐PEM, while CHJ and C‐Fix were more limited in their estimation performance. We found RF and SVM were superior to BMA on merging individual models at various plant functional types (PFTs) and at the scale of individual sites. On the basis of individual models, the fusion methods of BMA, SVM, and RF were examined by a five‐fold cross validation for each ecosystem type, and each method successfully improved the average accuracy of estimation by 8%, 18%, and 19%, respectively.

Environmental Sciences & Ecology↗
DOE OSTI2024

Exploration of signal processing methods for superconducting magnet and quench data

Quenching is the phenomenon of a superconducting magnetic material carrying current transitioning into a regular conducting material. This may cause severe and irreparable damage to the superconductor due to Joule heating. The Magnet Department at Fermi National Accelerator Laboratory (FNAL) has acquired experimental data through quench antenna arrays that are recorded when the quench is detected. These data are in terms of voltage signals that are sampled at 100kHz for several minutes. There are multiple channels and each channel provides a data set of more than 20 million observations, while there is one channel, called the trigger channel which shows the time when quench is detected. Despite some advancements that were made including machine learning, data complexity still shadows the progress. In this work, we studied a multi-resolution analysis of the quench antenna data through the Haar wavelet transform. In particular, we applied the maximally overlapped discrete w avelet transform (MODWT) of a suitable level L to the given data and then projected it onto the wavelet basis. This decomposes a given signal (Original data) $x ϵ \mathbb{R}^N$ into $L + 1$ subspaces of $\mathbb{R}^N$. One of the subspaces called the approximation, captures the trend of the signal, and the others, called the details, capture the fluctuations at different frequency bands. This decomposition provides a clear trend of the data at a suitable level and also various activities (spikes) are seen in the details of the decomposition at every level. These spikes might reveal some information about the quench under investigation but in any case, give information about magnet behavior. Also, this decomposition is seen to be very useful in removing noise present in the data due to the source or mechanism of the experiment.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

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↗