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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 451 records · Page 25
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Automated Adversary-in-the-Loop Cyber-Physical Defense Planning

Security of cyber-physical systems (CPS) continues to pose new challenges due to the tight integration and operational complexity of the cyber and physical components. To address these challenges, this article presents a domain-aware, optimization-based approach to determine an effective defense strategy for CPS in an automated fashion—by emulating a strategic adversary in the loop that exploits system vulnerabilities, interconnection of the CPS, and the dynamics of the physical components. Our approach builds on an adversarial decision-making model based on a Markov Decision Process (MDP) that determines the optimal cyber (discrete) and physical (continuous) attack actions over a CPS attack graph. The defense planning problem is modeled as a non-zero-sum game between the adversary and defender. We use a model-free reinforcement learning method to solve the adversary’s problem as a function of the defense strategy. We then employ Bayesian optimization (BO) to find an approximate best-response for the defender to harden the network against the resulting adversary policy. This process is iterated multiple times to improve the strategy for both players. We demonstrate the effectiveness of our approach on a ransomware-inspired graph with a smart building system as the physical process. Numerical studies show that our method converges to a Nash equilibrium for various defender-specific costs of network hardening.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Standardizing experimental approaches to investigate interactions between bacteria and ectomycorrhizal fungi

Bacteria and ectomycorrhizal fungi (EcMF) represent two of the most dominant plant root-associated microbial groups on Earth, and their interactions continue to gain recognition as significant factors that shape forest health and resilience. Yet, we currently lack a focused review that explains the state of bacteria-EcMF interaction research in the context of experimental approaches and technological advancements. To these ends, we illustrate the utility of studying bacteria-EcMF interactions, detail outstanding questions, outline research priorities in the field, and provide a suite of approaches that can be used to promote experimental reproducibility, field advancement, and collaboration. Though this review centers on the ecology of bacteria, EcMF, and trees, it by default offers experimental and conceptual insights that can be adapted to various subfields of microbiology and microbial ecology.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Systematic approach to define a prototype building model: Convenience Store

The US Department of Energy supports the development of commercial building energy codes and standards. To support commercial building energy research activities, continuous efforts have been made to convert 30 prototype building models, which cover 80% of commercial building floor space in the United States, into OpenStudio Standards prototype buildings. In this paper, we provide a systematic approach to define the building and system characteristics of a convenience store, which has the largest energy use intensity among the commercial building types not covered by current prototype models. This study will be used as a basis for developing the prototype convenience store building model.

Yoon, Yeobeom↗
DOE OSTI2026

ARM FY2026 Radar Plan

The U.S. Department of Energy (DOE) Atmospheric Radiation Measurement (ARM) User Facility maintains a suite of advanced atmospheric radar systems that serve as critical tools in ARM’s mission to provide continuous, high-quality observations for advancing the understanding and modeling of atmospheric processes. These radar systems enable detailed characterization of clouds, precipitation, and dynamic structures in the atmosphere, supporting a broad range of scientific applications. The number of deployed systems exceeds what current staffing levels can fully support for continuous 24/7/365 operation. As such, it is essential to have a clearly defined and community-informed plan that prioritizes radar operations and communicates ARM’s strategy for sustaining and evolving these observational assets. This FY2026 Radar Plan outlines ARM’s approach to managing its radar portfolio—balancing scientific impact, operational feasibility, and long-term sustainability. It reflects ARM’s continued commitment to delivering calibrated, well-documented radar data products that enable process-level studies and support the development and evaluation of weather and climate models. Through this plan, ARM aims to ensure transparency in decision-making, alignment with user needs, and support for innovative science across the facility’s fixed and mobile observatories. Given uncertainties around the Fiscal Year (FY) 2026 budget, this plan was developed to assume business as usual and will be updated as budgets and plans may change. It should be noted that, given the limited timeframe involved, this plan will be more succinct than previous plans.

47 OTHER INSTRUMENTATION↗
DOE OSTI2024

Artificial intelligence to unlock real-world evidence in clinical oncology: A primer on recent advances

Purpose: Real world evidence is crucial to understanding the diffusion of new oncologic therapies, monitoring cancer outcomes, and detecting unexpected toxicities. In practice, real world evidence is challenging to collect rapidly and comprehensively, often requiring expensive and time-consuming manual case-finding and annotation of clinical text. In this Review, we summarise recent developments in the use of artificial intelligence to collect and analyze real world evidence in oncology. Methods: We performed a narrative review of the major current trends and recent literature in artificial intelligence applications in oncology. Results: Artificial intelligence (AI) approaches are increasingly used to efficiently phenotype patients and tumors at large scale. These tools also may provide novel biological insights and improve risk prediction through multimodal integration of radiographic, pathological, and genomic datasets. Custom language processing pipelines and large language models hold great promise for clinical prediction and phenotyping. Conclusions: Despite rapid advances, continued progress in computation, generalizability, interpretability, and reliability as well as prospective validation are needed to integrate AI approaches into routine clinical care and real-time monitoring of novel therapies.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2025

Bottomonium properties in the quark-gluon plasma from a lattice-QCD informed 𝑇-matrix approach

Recent computations of bottomonium correlation functions with extended sources in lattice-discretized quantum chromodynamics (lQCD) provide new insights into heavy-quark dynamics at distance scales which are of the order of the inverse temperature. We analyze these results employing the thermodynamic 𝑇-matrix framework, in a continued effort to interpret lQCD data for quarkonium correlation functions in a nonperturbative and self-consistently solved quantum-many-body approach to a strongly coupled quark-gluon plasma (QGP). Its key inputs are the in-medium driving kernel (potential) of the scattering equation and an interference function which implements 3-body effects in the quarkonium coupling to the thermal medium. A simultaneous description of lQCD results for the bottomonium correlators with extended operators and the previously analyzed Wilson line correlators only requires minor refinements of the potential but calls for stronger interference effects at larger separation of the bottom quark and antiquark. We then analyze the poles of the self-consistent 𝑇 matrices on the real axis to assess the survival of the various bound states. Here, we estimate the pertinent temperatures where the poles disappear for the various bottomonium states and discuss the relation to the corresponding peaks in the bottomonium spectral functions. We also recalculate the spatial diffusion coefficient of the QGP and find it to be similar to that in our previous study.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Examining infrared thermography based approaches to rapid fatigue characterization of additively manufactured compression molded short fiber thermoplastic composites

A novel additive manufacturing (AM) methodology combined with a compression molding (CM) process has been developed to optimize the microstructure of short fiber thermoplastic composites (SFTs)with higher fiber alignment and lower porosity, yielding superior stiffness, strength, and structural integrity. Here, the current work examines the efficacy of the ‘passive’ infrared thermography (IRT) techniques for rapid fatigue characterization of SFTs that use the surface temperature evolution during cyclic loading due to self-heating as a fatigue indicator. A comparison of fatigue limits obtained from traditional stress-life (SN) (≈53.1%σ uts ) and IRT (≈54.1%σ uts ) shows a close match. However, the SN curve required 18 specimens and two weeks of continuous cyclic testing, while IRT used three specimens with 5 hours of testing. Thus, the IRT approach provides an accelerated testing framework for rapidly estimating the fatigue limit. Additionally, existing phenomenological approaches to IRT fatigue characterization have been examined.

42 ENGINEERING↗
DOE OSTI2026

Machine Learning-Enabled Wearable Piezoelectric Acoustic Sensor for Real-Time Breast Abnormality Detection

In contemporary society, breast health has become a significant public health concern, particularly among women. According to statistics from the World Health Organization, both the incidence and mortality rates of breast tumors have steadily increased in recent years. Therefore, effective early-stage screening and postoperative monitoring are essential for maintaining breast health. However, conventional clinical diagnostic modalities are typically bulky, operationally complex, and unsuitable for continuous real-time monitoring, which limits their use in portable and everyday health management applications. To address these limitations, this study proposes a machine learning-integrated wearable piezoelectric sensing platform as an auxiliary tool for breast health assessment. The device consists of a PDMS matching layer embedded with flexible silver nanowires, a P(VDF-TrFE) piezoelectric layer, and a multi-channel low-noise signal acquisition circuit. It is capable of acquiring acoustic echo signals from tissue-mimicking environments and automatically evaluating signal validity using a convolutional neural network (CNN). By integrating piezoelectric sensing with deep learning-based signal analysis, the proposed system achieves a signal-to-noise ratio exceeding 70 dB and a real-time classification accuracy above 96% under controlled conditions. These results demonstrate that the platform provides a compact, portable, and intelligent approach for wearable sensing of mechanical heterogeneity and highlight its potential for future development in continuous biomedical monitoring technologies.

He, Shuaitong↗
DOE OSTI2024

Effective Corrosion-Resistant Single-Atom Alloy Catalyst on HfO 2 -Passivated BiVO 4 Photoanode for Durable (≈800 h) Solar Water Oxidation

Green hydrogen (H 2 ) production from solar water splitting necessitates photoelectrodes with superior photoelectrochemical (PEC) activity and durability. However, surface defects and photocorrosion instability—especially at high potentials—limit PEC performance and stability. Herein, the prototypical bismuth vanadate (BiVO 4 ) photoanode is used to demonstrate a holistic approach to improve photocurrent density and long-term stability. In this approach, high surface-area nanostructuring of BiVO 4 is combined with barium (Ba) doping with semi-crystalline hafnium oxide (HfO 2 ) surface passivation and single-atom nickel platinum (NiPt) catalysts. The introduction of Ba 2+ ions into BiVO 4 increases the concentration of conductive V 4+ ions or the ratio of V 4+ ions to oxygen vacancies, avoiding V 5+ dissolution during water oxidation. The semi-crystalline HfO 2 , which serves as a passivation layer, prevents BiVO 4 photocorrosion by suppressing harmful chemical reactions when holes are transferred to the electrolyte. The synergistic use of isolated single-atom and Ni-Pt coordination improves charge transfer at the photoanode/electrolyte interface, leading to enhanced PEC kinetics and stability. As a result, a photoelectrode is demonstrated with ≈6.5 mA cm -2 at 1.23 V versus a reversible hydrogen electrode (RHE) and continuous operation for 800 h with a negligible degradation rate. This work provides a promising approach to improve photoanodes for PEC H 2 production.

08 HYDROGEN↗
DOE OSTI2026

A dendritic strontium river isoscape for fisheries applications in the Sacramento River basin, California, USA

Objective Understanding the origins and movements of fish is fundamental to effective conservation and fisheries management. Strontium isotope ratios ( 87 Sr/ 86 Sr) in otoliths provide a powerful tracer of natal origin and migratory pathways. However, existing 87 Sr/ 86 Sr isoscapes for the Sacramento River basin, an ecosystem that supports ecologically and economically important salmon populations, rely on discrete classification approaches that overlook unsampled habitats and do not incorporate spatial uncertainty. Our objective was to develop a continuous, network-explicit 87 Sr/ 86 Sr isoscape with quantified uncertainty to fill in data gaps and enable probabilistic assignments of fish origin and movement. Methods We used river water 87 Sr/ 86 Sr data from 106 sites (1997–2021) to develop spatial stream network models that use dendritic connectivity and watershed characteristics (lithology, bedrock age, and land cover) to predict river water 87 Sr/ 86 Sr throughout the basin. Models were fitted using maximum and restricted likelihood and were evaluated via Akaike’s information criterion and leave-one-out cross validation. We produced both historical (pre-dam) and present-day (below-dam) isoscapes, delineated uncertainty-informed isotopic ranges using k -means clustering, and applied a proof-of-concept Bayesian assignment to estimate natal origins and early rearing habitats for two endangered winter-run Chinook Salmon Oncorhynchus tshawytscha. Results Cross validation indicated strong performance of the 87 Sr/ 86 Sr model (leave-one-out cross validation: R 2 = 0.91; root mean square error = 0.0005). Uncertainty-informed clustering identified 19 isotopic “suites” (reaches with indistinguishable 87 Sr/ 86 Sr values) in present-day anadromous habitats and 25 suites in the historical network. Example natal and early rearing assignments included predictions that challenged expectations for juvenile salmon migration based on predicted river 87 Sr/ 86 Sr compositions. Conclusions This study developed a continuous, network-explicit 87 Sr/ 86 Sr isoscape that integrates existing river data to predict 87 Sr/ 86 Sr in unsampled reaches and the likely achievable range and resolution of otolith-based origin and life history inference. The resulting river isoscape provides a valuable tool to predict salmon movements and identify habitats supporting their survival and growth that otherwise might remain undetected. Coupling these predictions with complementary approaches that ground-truth juvenile presence (e.g., targeted fish surveys) represents an important step toward science-informed restoration and management of critical habitats throughout the Sacramento River basin.

Environmental sciences↗
DOE OSTI2020

Evaluation of Hybrid FPOG Applications in Regulated and Deregulated Markets Using HERON

Recent changes in the U.S. energy market, such as low natural gas prices and increased electricity production for variable renewable energy (VRE) sources, have led to an economic crisis for existing light-water reactor (LWR) nuclear power plants (NPP). Many owners and operators of LWRs have elected to decommission these plants rather than continue using them as consistent sources of clean baseload power. This has led to exploration of various possibilities to increase the economic viability of these units, including market restructuring to monetize benefits LWRs already provide to the grid through ancillary markets, load following and economic dispatch, and possible integration of secondary systems directly to the NPP for production of additional products through technologies such as hydrogen electrolysis or water desalination. Previous studies have considered the technologies associated with these Integrated Energy Systems (IES) activities, and the analysis of markets for these secondary products. To analyze the economic viability of various system configurations including IES, especially given the uncertainty surrounding load demand, electricity prices, and the availability of VRE resources, the stochastic technoeconomic analysis package HERON (Heuristic Energy Resource Optimization Network) was released earlier this year as an extension of the risk analysis framework RAVEN (Risk Analysis Virtual Environment). HERON focuses foremost on making the complex uncertainty quantification analysis tools approachable for energy systems analysts, also providing general dispatch optimization algorithms for those workflows. HERON continues to be improved and tested as a significant part of the IES viability analyses performed in this work. HERON is not a capacity expansion model. To consider market and grid energy system development in a variety of scenarios, HERON is best used in coupling with modelling tools such as US-REGEN, which sacrifice some of the uncertainty analysis and resolution of HERON's modelling for the ability to efficiently predict the change in the grid energy system's profile due to economic drivers over decades. HERON can then use this information to explore the economic viability of introducing changes to the predicted outcomes, such as the introduction of an IES. In this work, experts at EPRI using US-REGEN provide six projection scenarios for use in HERON stochastic technoeconomic analysis (STEA) in considering the options available for increasing LWR economic viability through introduction of a hydrogen-centric IES using a high-temperature steam electrolysis plant (HTSE), hydrogen storage, and a constant-rate contracted hydrogen consumer. The results obtained are differential in nature; they do not report expected profits for any configuration, but rather report on the possible increase in the NPV of a configuration with respect to a baseline no-IES configuration. Due to the uncertainty captured in the variable net load of the systems, there is likewise uncertainty in the mean values reported. We consider this viability both in terms of a regulated market, where the energy producers and IES are owned and operated by single entity, as well as a deregulated market, where the IES chooses its bid for electricity generation and is then dispatched by the grid system operator. Results indicate that for deregulated markets, the inclusion of the IES is often statistically beneficial. This is especially true in policies that are not favorable towards nuclear, as nuclear is less often dispatched and is forced to deal with frequent idle capacity. In the nominal case as well as the case of carbon tax policies, inclusion of the IES clearly benefited the economic performance of the NPP. In the regulated case, however, there was a trend towards minimizing the IES, likely due to the optimal sizing performed by US-REGEN of the NPP within the system as well as the lack of penalty for idle capacity at the NPP in the regulated market analyses.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2025

Instability of Nagaoka State and Quantum Phase Transition via Kinetic Frustration Control

We investigate the Nagaoka-Thouless (NT) ferromagnetic instability in the strongly interacting t-t' Hubbard model by continuously breaking particle-hole symmetry on a tunable square-triangular lattice geometry. We use an analytic approach to show that the fully spin-polarized state becomes unstable to a metastable spin-polaron when the kinetic frustration t'/t exceeds a critical, dimension-dependent value. Large-scale density matrix renormalization group (DMRG) simulations reveal a quantum phase transition from the NT ferromagnet to a spiral spin-density wave, which evolves continuously into the Haerter-Shastry antiferromagnet in the large-frustration limit. Remarkably, this transition remains robust at low but finite hole density, making it accessible in cold-atom and moiré Hubbard platforms under strong interactions. A variational analysis further captures the instability mechanism at finite density via frustration-induced magnon band deformation.

FOS: Physical sciences↗
DOE OSTI2023

An integrated data management and informatics framework for continuous drug product manufacturing processes: A case study on two pilot plants

The pharmaceutical industry continuously looks for ways to improve its development and manufacturing efficiency. In recent years, such efforts have been driven by the transition from batch to continuous manufacturing and digitalization in process development. To facilitate this transition, integrated data management and informatics tools need to be developed and implemented within the framework of Industry 4.0 technology. Here, in this regard, the work aims to guide the data integration development of continuous pharmaceutical manufacturing processes under the Industry 4.0 framework, improving digital maturity and enabling the development of digital twins. This paper demonstrates two instances where a data integration framework has been successfully employed in academic continuous pharmaceutical manufacturing pilot plants. Details of the integration structure and information flows are comprehensively showcased. Approaches to mitigate concerns in incorporating complex data streams, including integrating multiple process analytical technology tools and legacy equipment, connecting cloud data and simulation models, and safeguarding cyber-physical security, are discussed. Critical challenges and opportunities for practical considerations are highlighted.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

The Novel Hybrid Ab Initio Model of High-Performance Structural Alloys Design for Fossil Energy Power Plants

The current project developed a novel HT-CALPHAD/DFT approach, which can quickly design new high-performance structural alloys for the application of FE power plants. The PI will mainly take charge of high-throughput DFT simulations and computational thermodynamics of the selected multicomponent alloy systems for the FE power plant applications. At the end of the project, a novel hybrid model based on high throughput CALPHAD/DFT simulations and computational thermodynamics will be developed to provide guidance on how to identify multi-component new high-performance structural alloys with much less computational effort needed. It will address the extensive computation time needed for DFT on the new alloys design. In addition, it will also address the well-known headache of DFT, i.e. how to make the accurate prediction of the high-temperature equilibria. The novel hybrid model the PI proposed will not only be applied to the design of high-performance structural alloys in FE power plants but in many different applications, such as nuclear reactors. This hybrid modeling approach includes four sections: 1) HT-CALPHAD modeling of Al-Co-Cr-Ni-Fe system with FCC and BCC phase. In this section, 3561 non-equiatomic compositions were randomly generated in order to investigate the phase stability of single FCC and BCC phases. Meanwhile, we proposed a data screening procedure to screen out the good candidates within these compositions, considering the temperature range, average density, and melting temperature, etc. 2) Investigation of FCC-Cr lattice stability in Fe-Cr system. We systematically assessed the reliability of FCC-Cr lattice stability derived by DFT and CALPHAD approaches. Meanwhile, the Fe-Cr binary system was chosen as a case study to verify the Cr lattice stability obtained by both approaches. 3) High-throughput DFT modeling on elastic properties of Al-Co-Cr-Ni-Fe systems. We predicted and established the FCC quinary elastic constant database of the Al-Co-Cr-Fe-Ni systems at 0K by using special quasi-random structure (SQS) approach. The predictions will start with pure elements of Al-Co-Cr-Fe-Ni system and will be continued with binaries, ternaries, quaternaries, and finally the quinary compositions. 3) Modeling of temperature-dependent elastic properties in Al-Co-Cr-Ni-Fe systems. In this part, we predict the thermal expansion coefficient and elastic stiffness coefficient as a function of temperature by applying quasiharmonic approximation. With this approach, the elastic properties of HEAs at elevate temperature can be estimated.

01 COAL, LIGNITE, AND PEAT↗
DOE OSTI2024

2019 Budget Request for the DOE Computational Science Graduate Fellowship (CSGF) Grant

The Department of Energy Computational Science Graduate Fellowship (DOE CSGF) is necessary to meet the continual challenging national workforce needs that arise as computational science and engineering problems continue to grow in scope and complexity. Computational science and engineering (CSE) is a multidisciplinary approach that uses scientific computing to solve practical problems methods and to supply technical tools across the scientific discovery spectrum. In particular, the DOE CSGF emphasizes high-performance computing (HPC) that enables CSE that advances science and engineering in directions important to the DOE and the economy in general. Over the past half-century, HPC has been an essential tool for DOE’s success. During this period, important missions, such as nuclear stockpile stewardship, have turned to HPC as an essential technology. Entire science disciplines, such as biology and cosmology, have been transformed through the augmentation of scientific observation via HPC. At government laboratories and in industry, DOE CSGF alumni are helping push traditional HPC boundaries while contributing to discoveries in high-energy physics, renewable energy, fusion-reactor design, additive manufacturing, nanomaterials for next-generation batteries and transistors, and turbine and advanced nuclear reactor modeling. In addition, HPC is used to address national health needs that will eventually point to cures both by helping cancer researchers manage and analyze huge troves of data, by simulating biological mechanisms, and by accelerating drug development — including continuing to rise to the challenge of pandemic-related research. A 2023 report from the ASCAC Subcommittee on American Competitiveness and Innovation to the ASCR office, “Can the United States Maintain Its Leadership in High-Performance Computing?” says of the Program, “The CSGF program provides a barometer for disciplines that will be of interest to future DOE computing.” An explosion in scientific and technological data has driven the need for increasingly sophisticated HPC to transform those data into scientific understanding. With access to more and more data and the proliferation of HPC, Machine Learning and Artificial Intelligence are experiencing a renaissance, complementing the now well-established use of computational simulation. Indeed, in its September 2020 subcommittee report on “AI/ML, Data Intensive Science and High-Performance Computing”, the DOE Advanced Scientific Computing Advisory Committee (ASCAC) explicitly called for a fellowship program to train computational and data scientists to tackle exascale and data-intensive computing challenges. This collaboration of empirical and theory-based modeling will increasingly inform federal policymakers whose decisions affect American society and future generations, and it requires highly skilled and intellectually agile computational scientists who can support the fast-moving DOE National Laboratory research environment. In fact, the DOE CSGF program has explicitly and consistently addressed this need.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Lyapunov-Based Iterative Learning of Regions of Attraction for Autonomous Systems

This paper proposes a novel algorithm for estimating the region of attraction of equilibrium points for nonlinear discrete-time autonomous systems. The method iteratively expands an initial estimate of the region of attraction by constructing unions of sublevel sets of learned functions parametrized as neural networks. Unlike conventional techniques that rely on a single global Lyapunov function, the proposed approach provides a collection of local Lyapunov-like functions, enabling richer representations and potentially larger region of attraction estimates. These functions are trained using sampled state-space data, and their Lipschitz continuity ensures that desirable properties extend beyond the training samples. The devised strategy is tested via numerical simulations, demonstrating the effectiveness of the proposed approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Lyapunov-Based Iterative Learning of the Region of Attraction for Autonomous Systems

This presentation introduces a novel algorithm for estimating the region of attraction of equilibrium points for nonlinear discrete-time autonomous systems. The method iteratively expands an initial estimate of the region of attraction by constructing unions of sublevel sets of learned functions parametrized as neural networks. Unlike conventional techniques that rely on a single global Lyapunov function, the proposed approach provides a collection of local Lyapunov-like functions, enabling richer representations and potentially larger region of attraction estimates. These functions are trained using sampled state-space data, and their Lipschitz continuity ensures that desirable properties extend beyond the training samples. The devised strategy is tested via numerical simulations, demonstrating the effectiveness of the proposed approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Landau discriminants

Scattering amplitudes in quantum field theories have intricate analytic properties as functions of the energies and momenta of the scattered particles. In perturbation theory, their singularities are governed by a set of nonlinear polynomial equations, known as Landau equations, for each individual Feynman diagram. The singularity locus of the associated Feynman integral is made precise with the notion of the Landau discriminant, which characterizes when the Landau equations admit a solution. In order to compute this discriminant, we present approaches from classical elimination theory, as well as a numerical algorithm based on homotopy continuation. These methods allow us to compute Landau discriminants of various Feynman diagrams up to 3 loops, which were previously out of reach. For instance, the Landau discriminant of the envelope diagram is a reducible surface of degree 45 in the three-dimensional space of kinematic invariants. We investigate geometric properties of the Landau discriminant, such as irreducibility, dimension and degree. In particular, we find simple examples in which the Landau discriminant has codimension greater than one. Furthermore, we describe a numerical procedure for determining which parts of the Landau discriminant lie in the physical regions. In order to study degenerate limits of Landau equations and bounds on the degree of the Landau discriminant, we introduce Landau polytopes and study their facet structure. Finally, we provide an efficient numerical algorithm for the computation of the number of master integrals based on the connection to algebraic statistics.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗