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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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All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

Friction of ice

Frictional sliding experiments were performed on saw-cut samples of laboratory-made polycrystalline water ice, prepared in the same way as the material used by Kirby et al. (1987) in ice deformation experiments. The data show that the maximum frictional stress is a function of the normal stress but is not measurably dependent on temperature or sliding rate over the ranges covered in these experiments (77-115 K and 0.0003-0.03 mm/s, respectively). The sliding behavior was invariably stick slip, with the sliding surfaces exhibiting only minor gouge development. In samples with anomalously low strength, a curious arrangement of densely packed short vertical fractures was observed. The results of these experiments were applied to a model of near-surface tectonic activity on Ganymede, one of Jupiter's icy moons. The results indicate that a global expansion on Ganymede of 3 linear percent will cause extensional movement on preexisting faults at depths to 7 + or - 3 km.

Beeman, M.↗
NASA NTRS1992

Crustal deformation along the San Andreas, California

The goal is to achieve a better understanding of the regional and local deformation and crustal straining processes in western North America, particularly the effects of the San Andreas and nearby faults on the spatial and temporal crustal deformation behavior. Construction of theoretical models based on the mechanics of coupled elastic plate, viscoelastic foundation and large scale crack mechanics provide a rational basis for the interpretation of seismic and aseismic anomalies and expedite efforts in forecasting the stability of plate boundary deformation. Special focus is placed on the three dimensional time dependent surface deformation due to localized slippage in a elastic layer coupled to a visco-elastic substrate. The numerical analysis is based on a 3-D boundary element technique. Extension to visco-elastic coupling demands the derivation of 3-D time dependent Green's function. This method was applied to analyze the viscoelastic surface displacements due to a dislocated embedded patch. Surface uplift as a function of time and position are obtained. Comparisons between surface uplift for long and short dislocated patches are made.

Li, Victor C.↗
DOE OSTI2025

Temperature-Dependent Mechanical Properties of Ni-Based Concentrated Alloys: Insights from First-Principles Calculations

The present work focuses on predicting temperature-dependent mechanical properties of Ni-based concentrated alloys Ni 18 Cr 10 Co 10 Fe 6 M 4 (abbreviated by X 44 M 4 , with M = Al, V, Mn, Fe, Nb, Mo, and W) using density functional theory (DFT). These predictions are based on shear (plastic) and elastic deformations, utilizing the special quasirandom structure (SQS), the phonon-based quasiharmonic approach (QHA), and the quasistatic approach. The resulting properties include coefficient of thermal expansion via QHA, ideal shear strength (τ IS ), and stable and unstable stacking fault energies (γ SF and γ US ) through pure alias shear deformation, and elastic constants (c ij ), bulk modulus (B 0 ), and shear modules (G 0 ) via elastic deformation. Notably, predicting accurate γ SF is challenging due to uncertainties that can exceed the γ SF values. τ IS and γ US exhibit a strong linear relationship, enabling the accurate prediction of γ US based on the precisely determined τ IS . All mechanical properties of X 44 M 4 decrease with increasing temperature, except for some γ SF cases such as X 44 M 4 with M = V, Mn, Fe, Mo, and W. Among the X 44 M 4 alloys, X 44 Nb 4 exhibits the lowest τ IS , γ US , and G 0 values, and the highest B 0 /G 0 ratio, while X 44 Mn 4 has the lowest B 0 and B 0 /G 0 ratio. We found that volume is a crucial descriptor for understanding and modeling mechanical properties (except B0 and maybe also γ SF ) affected by alloying elements and temperature. Ni-based dilute alloys (e.g., Ni 11 M 1 and Ni 31 M 1 ) and concentrated alloys (e.g., X 44 M 4 ) show similar trends in mechanical properties influenced by alloying elements and temperature, simplifying the analysis and design of Ni-based alloys.

Elastic properties↗
NASA NTRS1988

The Clouds distributed operating system - Functional description, implementation details and related work

Clouds is an operating system in a novel class of distributed operating systems providing the integration, reliability, and structure that makes a distributed system usable. Clouds is designed to run on a set of general purpose computers that are connected via a medium-of-high speed local area network. The system structuring paradigm chosen for the Clouds operating system, after substantial research, is an object/thread model. All instances of services, programs and data in Clouds are encapsulated in objects. The concept of persistent objects does away with the need for file systems, and replaces it with a more powerful concept, namely the object system. The facilities in Clouds include integration of resources through location transparency; support for various types of atomic operations, including conventional transactions; advanced support for achieving fault tolerance; and provisions for dynamic reconfiguration.

Dasgupta, Partha↗
DOE OSTI2023

Digital Twin Technology (“Morpheus”) for Optimized Building Operations [SWR-22-74]

The electrification of buildings is an important step to reducing greenhouse gas emissions across all industries. The management of increasingly electrified buildings is a complex pursuit, and there remains a need for cost-effective software capable of handling the computational burden required of such complexity. Through a partnership with Dallas Fort Worth (DFW) Airport, researchers at NREL have developed a digital twin modeling framework to optimize building operations, called Morpheus. Pairing predictive control with automatic fault detection and diagnostics, Morpheus decreases energy expenditures, costs, and faults for large facilities. Additionally, Morpheus employs artificial intelligence to continuously improve its performance using information provided by sensor systems, human experts with deep industry domain knowledge, and even from other similar machines or fleets of machines. Coupling this novel energy-management software with other digital twins, such as NREL’s Athena software for mobility operations, enables robust decision-making for asset and space management. The implementation of Morpheus at DFW has resulted in significantly improved HVAC system operations and reduced both peak power and overall energy consumption. This enhanced functionality comes at a more affordable price than previously developed digital twins and can be customized for other facilities’ geometries to provide optimal, individualized control of a facility’s energy consumption.

Chinde, Venkatesh↗
DOE OSTI2024

New Safety Feedback Control Design to Guarantee Adequate Frequency Performance in Microgrids

Safety analysis of power systems is concerned with the system's ability to maintain critical variables within specified limits following a disturbance. Frequency control adequacy has become increasingly important as the system inertia decreases due to the increase in renewable energy penetration. Various controllers for inverters have been proposed to improve the system frequency response and few are capable to ensure the safety of the response. In this article, a diesel-wind energy system is considered and modeled as a switching system between normal, faulted, and post-fault modes. Further, a safety feedback controller is designed as a supplementary signal for a wind turbine generator such that the speed of the diesel generator stays within a permissible range in the presence of a finite energy disturbance. Numerical results on the modified 33-bus microgrid system obtained of the proposed novel approach indicate that the suggested control configuration can guarantee adequate frequency response without excessive conservativeness.

barrier function↗
NASA NTRS1990

An integrated approach to system design, reliability, and diagnosis

The requirement for ultradependability of computer systems in future avionics and space applications necessitates a top-down, integrated systems engineering approach for design, implementation, testing, and operation. The functional analyses of hardware and software systems must be combined by models that are flexible enough to represent their interactions and behavior. The information contained in these models must be accessible throughout all phases of the system life cycle in order to maintain consistency and accuracy in design and operational decisions. One approach being taken by researchers at Ames Research Center is the creation of an object-oriented environment that integrates information about system components required in the reliability evaluation with behavioral information useful for diagnostic algorithms. Procedures have been developed at Ames that perform reliability evaluations during design and failure diagnoses during system operation. These procedures utilize information from a central source, structured as object-oriented fault trees. Fault trees were selected because they are a flexible model widely used in aerospace applications and because they give a concise, structured representation of system behavior. The utility of this integrated environment for aerospace applications in light of our experiences during its development and use is described. The techniques for reliability evaluation and failure diagnosis are discussed, and current extensions of the environment and areas requiring further development are summarized.

Patterson-Hine, F. A.↗
NASA NTRS2012

NASA Tech Briefs, September 2012

Topics covered include: Beat-to-Beat Blood Pressure Monitor; Measurement Techniques for Clock Jitter; Lightweight, Miniature Inertial Measurement System; Optical Density Analysis of X-Rays Utilizing Calibration Tooling to Estimate Thickness of Parts; Fuel Cell/Electrochemical Cell Voltage Monitor; Anomaly Detection Techniques with Real Test Data from a Spinning Turbine Engine-Like Rotor; Measuring Air Leaks into the Vacuum Space of Large Liquid Hydrogen Tanks; Antenna Calibration and Measurement Equipment; Glass Solder Approach for Robust, Low-Loss, Fiber-to-Waveguide Coupling; Lightweight Metal Matrix Composite Segmented for Manufacturing High-Precision Mirrors; Plasma Treatment to Remove Carbon from Indium UV Filters; Telerobotics Workstation (TRWS) for Deep Space Habitats; Single-Pole Double-Throw MMIC Switches for a Microwave Radiometer; On Shaft Data Acquisition System (OSDAS); ASIC Readout Circuit Architecture for Large Geiger Photodiode Arrays; Flexible Architecture for FPGAs in Embedded Systems; Polyurea-Based Aerogel Monoliths and Composites; Resin-Impregnated Carbon Ablator: A New Ablative Material for Hyperbolic Entry Speeds; Self-Cleaning Particulate Prefilter Media; Modular, Rapid Propellant Loading System/Cryogenic Testbed; Compact, Low-Force, Low-Noise Linear Actuator; Loop Heat Pipe with Thermal Control Valve as a Variable Thermal Link; Process for Measuring Over-Center Distances; Hands-Free Transcranial Color Doppler Probe; Improving Balance Function Using Low Levels of Electrical Stimulation of the Balance Organs; Developing Physiologic Models for Emergency Medical Procedures Under Microgravity; PMA-Linked Fluorescence for Rapid Detection of Viable Bacterial Endospores; Portable Intravenous Fluid Production Device for Ground Use; Adaptation of a Filter Assembly to Assess Microbial Bioburden of Pressurant Within a Propulsion System; Multiplexed Force and Deflection Sensing Shell Membranes for Robotic Manipulators; Whispering Gallery Mode Optomechanical Resonator; Vision-Aided Autonomous Landing and Ingress of Micro Aerial Vehicles; Self-Sealing Wet Chemistry Cell for Field Analysis; General MACOS Interface for Modeling and Analysis for Controlled Optical Systems; Mars Technology Rover with Arm-Mounted Percussive Coring Tool, Microimager, and Sample-Handling Encapsulation Containerization Subsystem; Fault-Tolerant, Real-Time, Multi-Core Computer System; Water Detection Based on Object Reflections; SATPLOT for Analysis of SECCHI Heliospheric Imager Data; Plug-in Plan Tool v3.0.3.1; Frequency Correction for MIRO Chirp Transformation Spectroscopy Spectrum; Nonlinear Estimation Approach to Real-Time Georegistration from Aerial Images; Optimal Force Control of Vibro-Impact Systems for Autonomous Drilling Applications; Low-Cost Telemetry System for Small/Micro Satellites; Operator Interface and Control Software for the Reconfigurable Surface System Tri-ATHLETE; and Algorithms for Determining Physical Responses of Structures Under Load.

Source record↗
NASA NTRS2016

Human Exploration Spacecraft Testbed for Integration and Advancement (HESTIA)

The proposed paper will cover ongoing effort named HESTIA (Human Exploration Spacecraft Testbed for Integration and Advancement), led at the National Aeronautics and Space Administration (NASA) Johnson Space Center (JSC) to promote a cross-subsystem approach to developing Mars-enabling technologies with the ultimate goal of integrated system optimization. HESTIA also aims to develop the infrastructure required to rapidly test these highly integrated systems at a low cost. The initial focus is on the common fluids architecture required to enable human exploration of mars, specifically between life support and in-situ resource utilization (ISRU) subsystems. An overview of the advancements in both integrated technologies, in infrastructure, in simulation, and in modeling capabilities will be presented, as well as the results and findings of integrated testing,. Due to the enormous mass gear-ratio required for human exploration beyond low-earth orbit, (for every 1 kg of payload landed on Mars, 226 kg will be required on Earth), minimization of surface hardware and commodities is paramount. Hardware requirements can be minimized by reduction of equipment performing similar functions though for different subsystems. If hardware could be developed which meets the requirements of both life support and ISRU it could result in the reduction of primary hardware and/or reduction in spares. Minimization of commodities to the surface of mars can be achieved through the creation of higher efficiency systems producing little to no undesired waste, such as a closed-loop life support subsystem. Where complete efficiency is impossible or impractical, makeup commodities could be manufactured via ISRU. Although, utilization of ISRU products (oxygen and water) for crew consumption holds great promise of reducing demands on life support hardware, there exist concerns as to the purity and transportation of commodities. To date, ISRU has been focused on production rates and purities for propulsion needs. The meshing of requirements between all potential users, producers, and cleaners of oxygen and water is crucial to guiding the development of technologies which will be used to perform these functions. Various new capabilities are being developed as part of HESTIA, which will enable the integrated testing of these technologies. This includes the upgrading of a 20' diameter habitat chamber to eventually support long duration (90+ day) human-in-the-loop testing of advanced life support systems. Additionally, a 20' diameter vacuum chamber is being modified to create Mars atmospheric pressures and compositions. This chamber, designated the Mars Environment Chamber (MEC), will eventually be upgraded to include a dusty environment and thermal shroud to simulate conditions on the surface of Mars. In view that individual technologies will be in geographically diverse locations across NASA facilities and elsewhere in the world, schedule and funding constraints will likely limit the frequency of physical integration. When this is the case, absent subsystems can be either digitally or physically simulated. Using the Integrated Power Avionics and Software (iPAS) environment, HESTIA is able to bring together data from various subsystems in simulated surroundings, insert faults, errors, time delays, etc., and feed data into computer models or physical systems capable of reproducing the output of the absent subsystems for the consumption of a local subsystems. Although imperfect, this capability provides opportunities to test subsystem integration and interactions at a fraction of the cost. When a subsystem technology is too immature for integrated testing, models can be produced using the General-Use Nodal Network Solver (GUNNS) capability to simulate the overall system performance. In doing so, even technologies not yet on the drawing board can be integrated and overall system performance estimated. Through the integrated development of technologies, as well as of the infrastructure to rapidly and at a low cost, model, simulate, and test subsystem technologies early in their development, HESTIA is pioneering a new way of developing the future of human space exploration.

Banker, Brian F.↗
DOE OSTI2025

Induced seismicity and geothermal energy production in the Salton Sea Geothermal Field, California

We analyze the relationship between geothermal energy production and seismic hazards in the Salton Sea Geothermal Field (SSGF) between 1972 and 2022. A clear increase in seismic activity accompanies geothermal energy production and is greatest to the east of the Brawley fault, where the amount of injection exceeds the amount of production. We estimate that, whereas there was a 2% chance of a M6.07 earthquake nucleating inside the SSGF within a fifty-year period prior to energy production (pre-production), there is an equal probability that a M6.70 earthquake nucleates there in a fifty-year period during which historically average energy production conditions persist (syn-production). Similarly, we estimate a 2% chance of a M7.15 and M6.92 occurring in the broader Brawley Seismic Zone (excluding the SSGF) within a fifty-year period during the pre- and syn-production eras, respectively. We find that linear regression models fail to reliably forecast the background seismicity rate as a function of fluid production and injection.

15 GEOTHERMAL ENERGY↗
DOE OSTI2023

Toward Global Regional Seismic Moment Tensor Inversion with Three-Dimensional Earth Models for Nuclear Explosion Monitoring with Sparse Networks: Demonstration of Reciprocity for Strain Greens Tensor Database Simulation with Salvus

Seismic source characterization is an essential function of global nuclear explosion monitoring (NEM). While large events (roughly with moment magnitude, M w , greater than 5.0) can often be easily detected, located and identified with high signal-to-noise ratios at teleseismic distances (> 20°), trends in NEM research require confident source characterization at much lower magnitudes (say down to 3.0) and exploitation of sparse observations (from only a few stations) at regional distance (< 20°). Regional distance waveform inversion to characterize sources is now widely used and effective (e.g. Ford et al., 2009; Alvizuri and Tape, 2018; Alvizuri et al., 2018; Chiang et al., 2018; Ford et al., 2022). These methods obtain the magnitude, depth and seismic moment tensor, which represents the forces that excited the observed seismic waves (slip on an earthquake fault, explosion, collapse or a combination of various forces). Common to many problems in seismology, the isolation of the source 2 properties requires removal of path propagation effects that waves experience while traveling through the three-dimensional (3D) Earth (the structure exists due to different rock types, material properties, temperature and tectonic processes).

58 GEOSCIENCES↗
NASA NTRS1992

Real-time diagnostics for a reusable rocket engine

A hierarchical, decentralized diagnostic system is proposed for the Real-Time Diagnostic System component of the Intelligent Control System (ICS) for reusable rocket engines. The proposed diagnostic system has three layers of information processing: condition monitoring, fault mode detection, and expert system diagnostics. The condition monitoring layer is the first level of signal processing. Here, important features of the sensor data are extracted. These processed data are then used by the higher level fault mode detection layer to do preliminary diagnosis on potential faults at the component level. Because of the closely coupled nature of the rocket engine propulsion system components, it is expected that a given engine condition may trigger more than one fault mode detector. Expert knowledge is needed to resolve the conflicting reports from the various failure mode detectors. This is the function of the diagnostic expert layer. Here, the heuristic nature of this decision process makes it desirable to use an expert system approach. Implementation of the real-time diagnostic system described above requires a wide spectrum of information processing capability. Generally, in the condition monitoring layer, fast data processing is often needed for feature extraction and signal conditioning. This is usually followed by some detection logic to determine the selected faults on the component level. Three different techniques are used to attack different fault detection problems in the NASA LeRC ICS testbed simulation. The first technique employed is the neural network application for real-time sensor validation which includes failure detection, isolation, and accommodation. The second approach demonstrated is the model-based fault diagnosis system using on-line parameter identification. Besides these model based diagnostic schemes, there are still many failure modes which need to be diagnosed by the heuristic expert knowledge. The heuristic expert knowledge is implemented using a real-time expert system tool called G2 by Gensym Corp. Finally, the distributed diagnostic system requires another level of intelligence to oversee the fault mode reports generated by component fault detectors. The decision making at this level can best be done using a rule-based expert system. This level of expert knowledge is also implemented using G2.

Guo, T. H.↗
DOE OSTI2025

The impact of nickel concentration and stacking fault energy on deformation mechanisms in high-purity austenitic Fe-Cr-Ni alloys

Understanding how composition affects deformation mechanisms in austenitic stainless steels is essential for developing accurate predictive models of stress-induced failures and stress corrosion cracking. Nickel (Ni), an element classified as a critical element, plays a crucial role in these processes. It is important to examine how Ni concentration influences stacking fault energy (SFE) and, consequently, the deformation mechanisms of austenitic stainless steels. However, in commercial stainless steels, the effects of other alloying elements and impurities can obscure Ni's role, complicating efforts to isolate its impact. Here, in this study, we use two high-purity Fe-Cr-Ni alloys to investigate how Ni concentration and SFE interact to alter deformation mechanisms and induce martensitic transformation. By combining in situ synchrotron X-ray diffraction (XRD) tensile testing and post-mortem electron microscopy with density functional theory simulations, we gain precise insights into these phenomena. We find that the Fe18Cr10Ni (wt%) alloy, with its low SFE, exhibits higher stacking fault probability, deformation-induced martensitic transformation, and a lesser increase in dislocation density with plastic strain. In contrast, the Fe18Cr14Ni (wt%) alloy, with its higher SFE, shows enhanced deformation twinning and greater dislocation density with increasing strain. These findings from high-purity ternary alloys provide valuable insights that can guide the search for alternative elements to replace Ni while achieving similar effects on phase stability and deformation behavior.

36 MATERIALS SCIENCE↗
NASA NTRS2002

Alternative Metrics for Evaluating the Resilence of Advanced Life Support Systems

Ensuring the safety of the crew is a key performance requirement of a life support system. However, a number of conceptual and practical difficulties arise when devising metrics to concretely measure the ability of a life support system to maintain critical functions in the presence of anticipated and unanticipated faults. Resilience is a dynamic property of a life support system that depends on the complex interactions between faults, controls and system hardware. We review some of the approaches to understanding the robustness or resilience of complex systems being developed in diverse fields such as ecology, software engineering and cell biology and discuss their applicability to regenerative life support systems. We also consider how approaches to measuring resilience vary depending on system design choices such as the definition and choice of the nominal operating regime. Finally, we explore data collection and implementation issues such as the key differences between the instantaneous or conditional and average or overall measures of resilience. Extensive simulation of a hybrid computational model of a water revitalization subsystem (WRS) with probabilistic, component-level faults provides data about off-nominal behavior of the system. The data are used to consider alternative measures of resilience as predictors of the system's ability to recover from component-level faults.

Bell, Ann Maria↗
NASA NTRS1990

Closed-form solution of decomposable stochastic models

Markov and semi-Markov processes are increasingly being used in the modeling of complex reconfigurable systems (fault tolerant computers). The estimation of the reliability (or some measure of performance) of the system reduces to solving the process for its state probabilities. Such a model may exhibit numerous states and complicated transition distributions, contributing to an expensive and numerically delicate solution procedure. Thus, when a system exhibits a decomposition property, either structurally (autonomous subsystems), or behaviorally (component failure versus reconfiguration), it is desirable to exploit this decomposition in the reliability calculation. In interesting cases there can be failure states which arise from non-failure states of the subsystems. Equations are presented which allow the computation of failure probabilities of the total (combined) model without requiring a complete solution of the combined model. This material is presented within the context of closed-form functional representation of probabilities as utilized in the Symbolic Hierarchical Automated Reliability and Performance Evaluator (SHARPE) tool. The techniques adopted enable one to compute such probability functions for a much wider class of systems at a reduced computational cost. Several examples show how the method is used, especially in enhancing the versatility of the SHARPE tool.

Sjogren, Jon A.↗
DOE OSTI2022

A mixed, unified forward/inverse framework for earthquake problems: fault implementation and coseismic slip estimate

SUMMARY We introduce a new finite-element (FE) based computational framework to solve forward and inverse elastic deformation problems for earthquake faulting via the adjoint method. Based on two advanced computational libraries, FEniCS and hIPPYlib for the forward and inverse problems, respectively, this framework is flexible, transparent and easily extensible. We represent a fault discontinuity through a mixed FE elasticity formulation, which approximates the stress with higher order accuracy and exposes the prescribed slip explicitly in the variational form without using conventional split node and decomposition discrete approaches. This also allows the first order optimality condition, that is the vanishing of the gradient, to be expressed in continuous form, which leads to consistent discretizations of all field variables, including the slip. We show comparisons with the standard, pure displacement formulation and a model containing an in-plane mode II crack, whose slip is prescribed via the split node technique. We demonstrate the potential of this new computational framework by performing a linear coseismic slip inversion through adjoint-based optimization methods, without requiring computation of elastic Green’s functions. Specifically, we consider a penalized least squares formulation, which in a Bayesian setting—under the assumption of Gaussian noise and prior—reflects the negative log of the posterior distribution. The comparison of the inversion results with a standard, linear inverse theory approach based on Okada’s solutions shows analogous results. Preliminary uncertainties are estimated via eigenvalue analysis of the Hessian of the penalized least squares objective function. Our implementation is fully open-source and Jupyter notebooks to reproduce our results are provided. The extension to a fully Bayesian framework for detailed uncertainty quantification and non-linear inversions, including for heterogeneous media earthquake problems, will be analysed in a forthcoming paper.

58 GEOSCIENCES↗
NASA NTRS1976

Information and display requirements for independent landing monitors

The ways an Independent Landing Monitor (ILM) may be used to complement the automatic landing function were studied. In particular, a systematic procedure was devised to establish the information and display requirements of an ILM during the landing phase of the flight. Functionally, the ILM system is designed to aid the crew in assessing whether the total system (e.g., avionics, aircraft, ground navigation aids, external disturbances) performance is acceptable, and, in case of anomaly, to provide adequate information to the crew to select the least unsafe of the available alternatives. Economically, this concept raises the possibility of reducing the primary autoland system redundancy and associated equipment and maintenance costs. The required level of safety for the overall system would in these cases be maintained by upgrading the backup manual system capability via the ILM. A safety budget analysis was used to establish the reliability requirements for the ILM. These requirements were used as constraints in devising the fault detection scheme. Covariance propagation methods were used with a linearized system model to establish the time required to correct manually perturbed states due to the fault. Time-to-detect and time-to-correct requirements were combined to devise appropriate altitudes and strategies for fault recovery.

Karmarker, J. S.↗
NASA NTRS2011

Model Checking a Self-Stabilizing Distributed Clock Synchronization Protocol for Arbitrary Digraphs

This report presents the mechanical verification of a self-stabilizing distributed clock synchronization protocol for arbitrary digraphs in the absence of faults. This protocol does not rely on assumptions about the initial state of the system, other than the presence of at least one node, and no central clock or a centrally generated signal, pulse, or message is used. The system under study is an arbitrary, non-partitioned digraph ranging from fully connected to 1-connected networks of nodes while allowing for differences in the network elements. Nodes are anonymous, i.e., they do not have unique identities. There is no theoretical limit on the maximum number of participating nodes. The only constraint on the behavior of the node is that the interactions with other nodes are restricted to defined links and interfaces. This protocol deterministically converges within a time bound that is a linear function of the self-stabilization period.

Malekpour, Mahyar R.↗