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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 163 records · Page 9

Nuclear Physics Network Requirements Review (Final Report)

The Energy Sciences Network (ESnet) is the high-performance network user facility for the US Department of Energy (DOE) Office of Science (SC) and delivers highly reliable data transport capabilities optimized for the requirements of data-intensive science. In essence, ESnet is the circulatory system that enables the DOE science mission by connecting all its laboratories and facilities in the US and abroad. ESnet is funded and stewarded by the Advanced Scientific Computing Research (ASCR) program and managed and operated by the Scientific Networking Division at Lawrence Berkeley National Laboratory (LBNL). ESnet is widely regarded as a global leader in the research and education networking community. ESnet interconnects DOE national laboratories, user facilities, and major experiments so that scientists can use remote instruments and computing resources as well as share data with collaborators, transfer large datasets, and access distributed data repositories. ESnet is specifically built to provide Between July 2023 and October 2023, ESnet and the Nuclear Physics program (NP) of the DOE SC organized an ESnet requirements review of NP-supported activities. Preparation for these events included identification of key stakeholders: program and facility management, research groups, and technology providers. Each stakeholder group was asked to prepare formal case study documents about its relationship to the NP program to build a complete understanding of the current, near-term, and long-term status, expectations, and processes that will support the science going forward.

97 MATHEMATICS AND COMPUTING↗

Robotic Planning under Uncertainty in Spatiotemporal Environments in Expeditionary Science

In the expeditionary sciences, spatiotemporally varying environments -- hydrothermal plumes, algal blooms, lava flows, or animal migrations -- are ubiquitous. Mobile robots are uniquely well-suited to study these dynamic, mesoscale natural environments. We formalize expeditionary science as a sequential decision-making problem, modeled using the language of partially-observable Markov decision processes (POMDPs). Solving the expeditionary science POMDP under real-world constraints requires efficient probabilistic modeling and decision-making in problems with complex dynamics and observational models. Previous work in informative path planning, adaptive sampling, and experimental design have shown compelling results, largely in static environments, using data-driven models and information-based rewards. However, these methodologies do not trivially extend to expeditionary science in spatiotemporal environments: they generally do not make use of scientific knowledge such as equations of state dynamics, they focus on information gathering as opposed to scientific task execution, and they make use of decision-making approaches that scale poorly to large, continuous problems with long planning horizons and real-time operational constraints. In this work, we discuss these and other challenges related to probabilistic modeling and decision-making in expeditionary science, and present some of our preliminary work that addresses these gaps. We ground our results in a real expeditionary science deployment of an autonomous underwater vehicle (AUV) in the deep ocean for hydrothermal vent discovery and characterization. Our concluding thoughts highlight remaining work to be done, and the challenges that merit consideration by the reinforcement learning and decision-making community.

Preston, Victoria↗

Granger causal inference for climate change attribution

Abstract Climate change detection and attribution (D&A) is concerned with determining the extent to which anthropogenic activities have influenced specific aspects of the global climate system. D&A fits within the broader field of causal inference, the collection of statistical methods that identify cause and effect relationships. There are a wide variety of methods for making attribution statements, each of which require different types of input data and focus on different types of weather and climate events and each of which are conditional to varying extents. Some methods are based on Pearl causality (direct experimental interference) while others leverage Granger (predictive) causality, and the causal framing provides important context for how the resulting attribution conclusion should be interpreted. However, while Granger-causal attribution analyses have become more common, there is no clear statement of their strengths and weaknesses relative to Pearl-causal attribution and no clear consensus on where and when Granger-causal perspectives are appropriate. In this prospective paper, we provide a formal definition for Granger-based approaches to trend and event attribution and a clear comparison with more traditional methods for assessing the human influence on extreme weather and climate events. Broadly speaking, Granger-causal attribution statements can be constructed quickly from observations and do not require computationally-intesive dynamical experiments. These analyses also enable rapid attribution, which is useful in the aftermath of a severe weather event, and provide multiple lines of evidence for anthropogenic climate change when paired with Pearl-causal attribution. Confidence in attribution statements is increased when different methodologies arrive at similar conclusions. Moving forward, we encourage the D&A community to embrace hybrid approaches to climate change attribution that leverage the strengths of both Granger and Pearl causality.

Risser, Mark D. (ORCID:0000000319561783)↗

A novel matching formulation for startup costs in unit commitment

Here we present a novel formulation for startup cost computation in the unit commitment problem (UC). Both our proposed formulation and existing formulations in the literature are placed in a formal, theoretical dominance hierarchy based on their respective linear programming relaxations. Our proposed formulation is tested empirically against existing formulations on large-scale UC instances drawn from real-world data. While requiring more variables than the current state-of-the-art formulation, our proposed formulation requires fewer constraints, and is empirically demonstrated to be as tight as a perfect formulation for startup costs. This tightening can reduce the computational burden in comparison to existing formulations, especially for UC instances with large reserve margins and high penetration levels of renewables.

97 MATHEMATICS AND COMPUTING↗

Non-linear relationships between daily temperature extremes and US agricultural yields uncovered by global gridded meteorological datasets

Global agricultural commodity markets are highly integrated among major producers. Prices are driven by aggregate supply rather than what happens in individual countries in isolation. Furthermore, estimating the effects of weather-induced shocks on production, trade patterns and prices hence requires a globally representative weather data set. Recently, two data sets that provide daily or hourly records, GMFD and ERA5-Land, became available. Starting with the US, a data rich region, we formally test whether these global data sets are as good as more fine-scaled country-specific data in explaining yields and whether they estimate similar response functions. While GMFD and ERA5-Land have lower predictive skill for US corn and soybeans yields than the fine-scaled PRISM data, they still correctly uncover the underlying non-linear temperature relationship. All specifications using daily temperature extremes under any of the weather data sets outperform models that use a quadratic in average temperature. Correctly capturing the effect of daily extremes has a larger effect than the choice of weather data. In a second step, focusing on Sub Saharan Africa, a data sparse region, we confirm that GMFD and ERA5-Land have superior predictive power to CRU, a global weather data set previously employed for modeling climate effects in the region.

54 ENVIRONMENTAL SCIENCES↗

Is stochastic thermodynamics the key to understanding the energy costs of computation?

The relationship between the thermodynamic and computational properties of physical systems has been a major theoretical interest since at least the 19th century. It has also become of increasing practical importance over the last half-century as the energetic cost of digital devices has exploded. Importantly, real-world computers obey multiple physical constraints on how they work, which affects their thermodynamic properties. Moreover, many of these constraints apply to both naturally occurring computers, like brains or Eukaryotic cells, and digital systems. Most obviously, all such systems must finish their computation quickly, using as few degrees of freedom as possible. This means that they operate far from thermal equilibrium. Furthermore, many computers, both digital and biological, are modular, hierarchical systems with strong constraints on the connectivity among their subsystems. Yet another example is that to simplify their design, digital computers are required to be periodic processes governed by a global clock. None of these constraints were considered in 20th-century analyses of the thermodynamics of computation. The new field of stochastic thermodynamics provides formal tools for analyzing systems subject to all of these constraints. We argue here that these tools may help us understand at a far deeper level just how the fundamental thermodynamic properties of physical systems are related to the computation they perform.

computation↗

Detector R&D needs for the next generation $e^+e^-$ collider

The 2021 Snowmass Energy Frontier panel wrote in its final report "The realization of a Higgs factory will require an immediate, vigorous and targeted detector R&D program". Both linear and circular $e^+e^-$ collider efforts have developed a conceptual design for their detectors and are aggressively pursuing a path to formalize these detector concepts. The U.S. has world-class expertise in particle detectors, and is eager to play a leading role in the next generation $e^+e^-$ collider, currently slated to become operational in the 2040s. It is urgent that the U.S. organize its efforts to provide leadership and make significant contributions in detector R&D. These investments are necessary to build and retain the U.S. expertise in detector R&D and future projects, enable significant contributions during the construction phase and maintain its leadership in the Energy Frontier regardless of the choice of the collider project. In this document, we discuss areas where the U.S. can and must play a leading role in the conceptual design and R&D for detectors for $e^+e^-$ colliders.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Characterization of Microwave Loss Using Multimode Superconducting Resonators

Measuring the losses arising from different materials and interfaces is crucial to improving the coherence of superconducting quantum circuits. Although this has been of interest for a long time, current studies can either only provide bounds to those losses, or require several devices for a complete characterization. In this work, we introduce a method to measure the microwave losses of materials and interfaces with a single multi-mode superconducting resonator. We demonstrate a formalism for analyzing the loss sensitivity of multi-mode systems and discuss the design strategies of multi-mode resonators for material loss studies. We present two types of multi-mode superconducting resonators for the study of bulk superconductors: the forky whispering-gallery-mode resonator (FWGMR) and the ellipsoidal cavity. We use these resonators to measure the surface dielectric, conductor, and seam losses of high-purity (5N5) aluminum and aluminum alloy (6061), as well as how they are affected by chemical etching, diamond turning, and thin-film coating. Here, we find that chemical etching and diamond turning reduce both the surface dielectric and conductive losses of high-purity aluminum, but provide no appreciable improvement to the seam. Coating the surfaces of diamond-turned aluminum alloys with e-beam evaporated or sputtered aluminum thinfilms significantly reduces all three losses under study. In addition, we study the effect of chemical etching on the surface of high-purity aluminum using transmission electron microscopy (TEM) and find that the chemical etching process creates a thinner and more uniform oxide layer, consistent with the observed improvement in the surface dielectric loss.

25 ENERGY STORAGE↗

Synthesis of Correct Digital Controller Models from Specifications by Model Transformation (21-0320)

The design of high consequence controllers (in weapons systems, autonomy, etc.) that do what they are supposed to do is a significant challenge. Testing simply does not come close to meeting the requirements for assurance. Today circuit designers at Sandia (and elsewhere) typically capture the core behavior of their components using state models in tools such as STATEFLOW. They then check that their models meet certain requirements (e.g. “The system bus must not deadlock” or “both traffic lights at an intersection must not be green at the same time”) using tools called model checkers. If the model checker returns “yes” then the property is guaranteed to be satisfied by the model. However, there are several drawbacks to this industry practice: (1) there is a lot of detail to get right, this is particularly challenging when there are multiple components requiring complex coordination (2) any errors returned by the model checker have to be traced back through the design and fixed, necessitating rework, (3) there are severe scalability problems with this approach, particularly when dealing with concurrency. All this places high demands on the designers who now face not only an accelerated schedule but also controllers of increasing complexity. This report describes a new and fundamentally different approach to the construction of safety-critical digital controllers. Instead of directly constructing a complete model and then trying to verify it, the designer can start with an initial abstract (think “sketch”) model plus the requirements, from which a correct concrete model is automatically synthesized. There is no need for post-hoc verification of required functional properties. Having tool to carry this out will significantly impact the nation’s ability to ensure the safety of high-consequence digital systems. The approach has been implemented in a prototype tool, along with a suite of examples, including ones that reflect actual problems faced by designers. Our approach operates on a variant of Statecharts developed at Sandia called Qspecs. Statecharts are a widely used formalism for developing concurrent reactive systems, supporting scalability through allowing state models containing composite states, which are the serial or parallel composition of substates which can themselves contain statecharts. Statecharts enable an incremental style of development, in which states are progressively refined to incorporate greater detail in an incremental model of software development. Our approach formulates a set of constraints from the structure of the models and the requirements and propagates these constraints to a fixpoint. The solution to the constraints is an inductive invariant along with guards on the transitions. We also show how our approach extends to implementation refinement, decomposition, composition, and elaboration. We currently handle safety requirements written in LTL (Linear Temporal Logic)

42 ENGINEERING↗

Phase equilibria of advanced technology uranium silicide-based nuclear fuel

The phases in uranium-silicide binary system were evaluated in regards to their stabilities, phase boundaries, crystal structures, and phase transitions. The results from this study were used in combination with a well assessed literature to optimize the U-Si phase diagram using the CALPHAD method. A thermodynamic database was developed, which could be used to guide nuclear fuel fabrication, could be incorporated into other nuclear fuel thermodynamic databases, or could be used to generate data required by fuel performance codes to model fuel behavior in normal or off-normal reactor operations. The U 3 Si 2 and U 3 Si 5 phases were modeled using the Compound Energy Formalism model with 3 sublattices to account for the variation in composition. The crystal structure used for the USi phase was the tetragonal with an I4/mmm space. Above 450°C, the U 3 Si 5 phase was modeled. The composition of the USi 2 phase was adjusted to USi 1.84 . The calculated invariant reactions and the enthalpy of formation for the stoichiometric phases were in agreement with experimental data.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Climate Model Output Rewriter

The Climate Model Output Rewriter (CMOR) software was first developed by LLNL’s PCMDI program in early 2000s and was formally released with v1.0 (July 2006), v2.0 (January 2011), and v3.1(June 2016). CMOR is used to produce Climate and Forecast Convention (http://cfconventions.org/) CF-compliant netCDF files, in the standard format required to satisfy the World Climate Research Program (WCRP) Coupled Model Intercomparison Project (CMIP). The software has been used across multiple phases of the Earth System Modeling (ESM) project CMIP (CMIP3, CMIP5, CMIP6, and planned use in CMIP7) along with numerous parallel projects focused on preparation observations for use in model evaluation (obs4MIPs) and forcing datasets (input4MIPs) to guide ESM simulations to meet strict experimental protocols. More information can be obtained from the CMOR website and code repositories: https://cmor.llnl.gov/; https://github.com/pcmdi/cmor; https://github.com/PCMDI/cmor3_documentation The ESM variable definitions used as input for CMOR can also be viewed in code repositories: https://github.com/PCMDI/cmip3-cmor-tables/; https://github.com/PCMDI/cmip5-cmor-tables/; https://github.com/PCMDI/cmip6-cmor-tables/

Mauzey, ChristopherF↗

Performance Evaluation of Comparative Vacuum Monitoring and Piezoelectric Sensors for Structural Health Monitoring of Rotorcraft Components

The costs associated with the increasing maintenance and surveillance needs of aging structures are rising at an unexpected rate. Multi-site fatigue damage, hidden cracks in hard-to-reach locations, disbonded joints, erosion, impact, and corrosion are among the major flaws encountered in today’s extensive fleet of aging aircraft and space vehicles. Aircraft maintenance and repairs represent about a quarter of a commercial fleet’s operating costs. The application of Structural Health Monitoring (SHM) systems using distributed sensor networks can reduce these costs by facilitating rapid and global assessments of structural integrity. The use of in-situ sensors for real-time health monitoring can overcome inspection impediments stemming from accessibility limitations, complex geometries, and the location and depth of hidden damage. Reliable, structural health monitoring systems can automatically process data, assess structural condition, and signal the need for human intervention. The ease of monitoring an entire on-board network of distributed sensors means that structural health assessments can occur more often, allowing operators to be even more vigilant with respect to flaw onset. SHM systems also allow for condition-based maintenance practices to be substituted for the current time-based or cycle-based maintenance approach thus optimizing maintenance labor. The Federal Aviation Administration has conducted a series of SHM validation and certification programs intended to comprehensively support the evolution and adoption of SHM practices into routine aircraft maintenance practices. This report presents one of those programs involving a Sandia Labs-aviation industry effort to move SHM into routine use for aircraft maintenance. The Airworthiness Assurance NDI Validation Center (AANC) at Sandia Labs, in conjunction with Sikorsky, Structural Monitoring Systems Ltd., Anodyne Electronics Manufacturing Corp., Acellent Technologies Inc., and the Federal Aviation Administration (FAA) carried out a trial validation and certification program to evaluate Comparative Vacuum Monitoring (CVM) and Piezoelectric Transducers (PZT) as a structural health monitoring solution to specific rotorcraft applications. Validation tasks were designed to address the SHM equipment, the health monitoring task, the resolution required, the sensor interrogation procedures, the conditions under which the monitoring will occur, the potential inspector population, adoption of CVM and PZT systems into rotorcraft maintenance programs and the document revisions necessary to allow for their routine use as an alternate means of performing periodic structural inspections. This program addressed formal SHM technology validation and certification issues so that the full spectrum of concerns, including design, deployment, performance and certification were appropriately considered. Sandia Labs designed, implemented, and analyzed the results from a focused and statistically relevant experimental effort to quantify the reliability of a CVM system applied to Sikorsky S-92 fuselage frame application and a PZT system applied to an S-92 main gearbox mount beam application. The applications included both local and global damage detection assessments. All factors that affect SHM sensitivity were included in this program: flaw size, shape, orientation and location relative to the sensors, as well as operational and environmental variables. Statistical methods were applied to performance data to derive Probability of Detection (POD) values for SHM sensors in a manner that agrees with current nondestructive inspection (NDI) validation requirements and is acceptable to both the aviation industry and regulatory bodies. The validation work completed in this program demonstrated the ability of both CVM and PZT SHM systems to detect cracks in rotorcraft components. It proved the ability to use final system response parameters to provide a Green Light/Red Light (“GO” – “NO GO”) decision on the presence of damage. In additional to quantifying the performance of each SHM system for the trial applications on the S-92 platform, this study also identified specific methods that can be used to optimize damage detection, guidance on deployment scenarios that can affect performance and considerations that must be made to properly apply CVM and PZT sensors. These results support the main goal of safely integrating SHM sensors into rotorcraft maintenance programs. Additional benefits from deploying rotorcraft Health and Usage Monitoring Systems (HUMS) may be realized when structural assessment data, collected by an SHM system, is also used to detect structural damage to compliment the operational environment monitoring. The use of in-situ sensors for health monitoring of rotorcraft structures can be a viable option for both flaw detection and maintenance planning activities. This formal SHM validation will allow aircraft manufacturers and airlines to confidently make informed decisions about the proper utilization of CVM and PZT technology. It will also streamline future regulatory actions and formal certification measures needed to assure the safe application of SHM solutions.

42 ENGINEERING↗

Solving gyrokinetic systems with higher-order time dependence

We discuss theoretical and numerical aspects of gyrokinetics as a Lagrangian field theory when the field perturbation is introduced into the symplectic part. A consequence is that the field equations and particle equations of motion in general depend on the time derivatives of the field. The most well-known example is when the parallel vector potential is introduced as a perturbation, where a time derivative of the field arises only in the equations of motion, so an explicit equation for the fields may still be written. We will consider the conceptually more problematic case where the time-dependent fields appear in both the field equations and equations of motion, but where the additional term in the field equations is formally small. The conceptual issues were described by Burby (J. Plasma Phys., vol. 82 (3), 2016, 905820304): these terms lead to apparent additional degrees of freedom to the problem, so that the electric field now requires an initial condition, which is not required in low-frequency (Darwin) Vlasov–Maxwell equations. Also, the small terms in the Euler–Lagrange equations are a singular perturbation, and these two issues are interlinked. For well-behaved problems the apparent additional degrees of freedom are spurious, and the physically relevant solution may be directly identified. Because we needed to assume that the system is well behaved for small perturbations when deriving gyrokinetic theory, we must continue to assume that when solving it, and the physical solutions are thus the regular ones. The spurious nature of the singular degrees of freedom may also be seen by changing coordinate systems so the varying field appears only in the Hamiltonian. We then describe how methods appropriate for singular perturbation theory may be used to solve these asymptotic equations numerically. We then describe a proof-of-principle implementation of these methods for an electrostatic strong-flow gyrokinetic system; two basic test cases are presented to illustrate code functionality.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Towards satellite tests combining general relativity and quantum mechanics through quantum optical interferometry: progress on the deep space quantum link

The Deep Space Quantum Link (DSQL) is a space-mission concept that aims to explore the interplay between general relativity and quantum mechanics using quantum optical interferometry. This mission concept was formally presented to the United States National Academy of Science Decadal Survey as a research campaign for Fundamental Physics in 2022. Since then, advances have been made in the space-based quantum optical technologies required to conduct a DSQL-type mission. In addition, other research efforts have defined alternative measurement concepts to explore the same scientific questions motivating the DSQL mission. This paper serves as an update to the community on the status of the DSQL mission concept and related research and technology development efforts.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Multimerization of Ebola GPΔmucin on protein nanoparticle vaccines has minimal effect on elicitation of neutralizing antibodies

Ebola virus (EBOV), a member of the Filoviridae family of viruses and a causative agent of Ebola Virus Disease (EVD), is a highly pathogenic virus that has caused over twenty outbreaks in Central and West Africa since its formal discovery in 1976. The only FDA-licensed vaccine against Ebola virus, rVSV-ZEBOV-GP (Ervebo®), is efficacious against infection following just one dose. However, since this vaccine contains a replicating virus, it requires ultra-low temperature storage which imparts considerable logistical challenges for distribution and access. Additional vaccine candidates could provide expanded protection to mitigate current and future outbreaks. Here, we designed and characterized two multimeric protein nanoparticle subunit vaccines displaying 8 or 20 copies of GPΔmucin, a truncated form of the EBOV surface protein GP. Single-dose immunization of mice with GPΔmucin nanoparticles revealed that neutralizing antibody levels were roughly equivalent to those observed in mice immunized with non-multimerized GPΔmucin trimers. These results suggest that some protein subunit antigens do not elicit enhanced antibody responses when displayed on multivalent scaffolds and can inform next-generation design of stable Ebola virus vaccine candidates.

60 APPLIED LIFE SCIENCES↗

Theoretical framework for soft X-ray Fourier transform spectroscopy using the Wigner function

This work presents a theoretical framework for the propagation of partially coherent Gaussian radiation in a modified Mach–Zehnder interferometer designed for Fourier transform spectroscopy (FTS) applications. Using the Wigner function formalism, we analytically propagate the radiation through the system and benchmark our approach by comparing the resulting interference pattern and interferogram with previous works in the diffraction limit. Our analysis reveals that the transverse coherence length requirement of the incident light field for detectable modulation is less stringent than previously assumed. Additionally, we provide theoretical demonstrations of FTS performance across various wavelengths using the proposed setup. These findings underscore the potential of this interferometer to achieve high-resolution FTS in the soft X-ray regime.

Fourier transform spectroscopy↗

Prospects for Characterizing the Haziest Sub-Neptune Exoplanets with High-resolution Spectroscopy

Observations to characterize planets larger than Earth but smaller than Neptune have led to largely inconclusive interpretations at low spectral resolution due to hazes or clouds that obscure molecular features in their spectra. However, here we show that high-resolution spectroscopy (R ∼ 25,000–100,000) enables one to probe the regions in these atmospheres above the clouds where the cores of the strongest spectral lines are formed. We present models of transmission spectra for a suite of GJ 1214b–like planets with thick photochemical hazes covering 1–5 μm at a range of resolutions relevant to current and future ground-based spectrographs. Furthermore, we compare the utility of the cross-correlation function that is typically used with a more formal likelihood-based approach, finding that only the likelihood-based method is sensitive to the presence of haze opacity. We calculate the signal-to-noise ratio (S/N) of these spectra, including telluric contamination, Required to robustly detect a host of molecules such as CO, CO{sub 2}, H{sub 2}O, and CH{sub 4} and photochemical products like HCN as a function of wavelength range and spectral resolution. Spectra in the M band require the lowest S/N{sub res} to detect multiple molecules simultaneously. CH{sub 4} is only observable for the coolest models (T {sub eff} = 412 K) and only in the L band. We quantitatively assess how these requirements compare to what is achievable with current and future instruments, demonstrating that characterization of small cool worlds with ground-based high-resolution spectroscopy is well within reach.

79 ASTRONOMY AND ASTROPHYSICS↗

Building Blocks for Secure and Prosperous Defense Critical Supply Chains: A Case Study from Microelectronics

Securing defense-critical supply chains, built on resilient and sustainable microelectronics fabrication and deployment, is a national imperative and one that requires an investment in basic and applied research, development, and deployment into industries in (and out of) the Defense Industrial Base (DIB). Critical next steps include the development of pilots for revolutionary concepts in a new formal verification model and the Cyber-Physical Passport (CPP) concept for chain of custody. Critical infrastructure leadership should take action with a sense of urgency. Working in conjunction with the Under Secretary for Acquisition and Sustainment, the Assistant Secretary of Defense for Research and Engineering should establish pilot programs with the Defense Advanced Research Projects Agency and the service labs to build and test both concepts in legacy and new system development.. Additionally, the Pentagon may be aware that an existing Manufacturing Innovation Institute is piloting, with the semiconductor industry, cyber innovations to provide verifiable security properties and guarantees of physical functions to build a more cyber secure, resilient and efficient micro-electronics supply chain.

99 GENERAL AND MISCELLANEOUS↗