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At least 829 records · Page 46

Evaluation of Cloud Physical Properties of ECMWF Analysis and Re-Analysis (ERA-40 and ERA Interim) against CERES Tropical Deep Convective Cloud Object Observations

This study presents an approach that converts the vertical profiles of grid-averaged cloud properties from large-scale models to probability density functions (pdfs) of subgrid-cell cloud physical properties measured at satellite footprints. Cloud physical and radiative properties, rather than just cloud and precipitation occurrences, of assimilated cloud systems by the European Center for Medium-range Weather Forecasts (ECMWF) operational analysis (EOA) and ECMWF Re-Analyses (ERA-40 and ERA Interim) are validated against those obtained from Earth Observing System satellite cloud object data for January-August 1998 and March 2000 periods. These properties include ice water path (IWP), cloud-top height and temperature, cloud optical depth and solar and infrared radiative fluxes. Each cloud object, a contiguous region with similar cloud physical properties, is temporally and spatially matched with EOA and ERA-40 data. Results indicate that most pdfs of EOA and ERA-40 cloud physical and radiative properties agree with those of satellite observations of the tropical deep convective cloud-object type for the January-August 1998 period. There are, however, significant discrepancies in selected ranges of the cloud property pdfs such as the upper range of EOA cloud top height. A major discrepancy is that the dependence of the pdfs on the cloud object size for both EOA and ERA-40 is not as strong as in the observations. Modifications to the cloud parameterization in ECMWF that occurred in October 1999 eliminate the clouds near the tropopause but shift power of the pdf to lower cloud-top heights and greatly reduce the ranges of IWP and cloud optical depth pdfs. These features persist in ERA-40 due to the use of the same cloud parameterizations. The downgrade of data assimilation technique and the lack of snow water content information in ERA-40, not the coarser horizontal grid resolution, are also responsible for the disagreements with observed pdfs of cloud physical properties although the detection rates of cloud object occurrence are improved for small size categories. A possible improvement to the convective parameterization is to introduce a stronger dependence of updraft penetration heights with grid-cell dynamics. These conclusions will be rechecked using the ERA Interim data, due to recent changes in the ECMWF convective parameterization (Bechtold et al. 2004, 2008). Results from the ERA Interim will be presented at the meeting.

Xu, Kuan-Man↗

Overview of Pre-Flight Physical Training, In-Flight Exercise Countermeasures and the Post-Flight Reconditioning Program for International Space Station Astronauts

International Space Station (ISS) astronauts receive supervised physical training pre-flight, utilize exercise countermeasures in-flight, and participate in a structured reconditioning program post-flight. Despite recent advances in exercise hardware and prescribed exercise countermeasures, ISS crewmembers are still found to have variable levels of deconditioning post-flight. This presentation provides an overview of the astronaut medical certification requirements, pre-flight physical training, in-flight exercise countermeasures, and the post-flight reconditioning program. Astronauts must meet medical certification requirements on selection, annually, and prior to ISS missions. In addition, extensive physical fitness testing and standardized medical assessments are performed on long duration crewmembers pre-flight. Limited physical fitness assessments and medical examinations are performed in-flight to develop exercise countermeasure prescriptions, ensure that the crewmembers are physically capable of performing mission tasks, and monitor astronaut health. Upon mission completion, long duration astronauts must re-adapt to the 1 G environment, and be certified as fit to return to space flight training and active duty. A structured, supervised postflight reconditioning program has been developed to prevent injuries, facilitate re-adaptation to the 1 G environment, and subsequently return astronauts to training and space flight. The NASA reconditioning program is implemented by the Astronaut Strength, Conditioning, and Rehabilitation (ASCR) team and supervised by NASA flight surgeons. This program has evolved over the past 10 years of the International Space Station (ISS) program and has been successful in ensuring that long duration astronauts safely re-adapt to the 1 g environment and return to active duty. Lessons learned from this approach to managing deconditioning can be applied to terrestrial medicine and future exploration space flight missions.

Kerstman, Eric↗

Solar and Space Physics: A Science for a Technological Society

From the interior of the Sun, to the upper atmosphere and near-space environment of Earth, and outward to a region far beyond Pluto where the Sun's influence wanes, advances during the past decade in space physics and solar physics the disciplines NASA refers to as heliophysics have yielded spectacular insights into the phenomena that affect our home in space. This report, from the National Research Council's (NRC's) Committee for a Decadal Strategy in Solar and Space Physics, is the second NRC decadal survey in heliophysics. Building on the research accomplishments realized over the past decade, the report presents a program of basic and applied research for the period 2013-2022 that will improve scientific understanding of the mechanisms that drive the Sun's activity and the fundamental physical processes underlying near-Earth plasma dynamics, determine the physical interactions of Earth's atmospheric layers in the context of the connected Sun-Earth system, and enhance greatly the capability to provide realistic and specific forecasts of Earth's space environment that will better serve the needs of society. Although the recommended program is directed primarily to NASA (Science Mission Directorate -- Heliophysics Division) and the National Science Foundation (NSF) (Directorate for Geosciences -- Atmospheric and Geospace Sciences) for action, the report also recommends actions by other federal agencies, especially the National Oceanic and Atmospheric Administration (NOAA) those parts of NOAA charged with the day-to-day (operational) forecast of space weather. In addition to the recommendations included in this summary, related recommendations are presented in the main text of the report.

Source record↗

The Impacts of Microphysics and Planetary Boundary Layer Physics on Model Simulations of U. S. Deep South Summer Convection

Inspection of output from various configurations of high-resolution, explicit convection forecast models such as the Weather Research and Forecasting (WRF) model indicates significant sensitivity to the choices of model physics parameterizations employed. Some of the largest apparent sensitivities are related to the specifications of the cloud microphysics and planetary boundary layer physics packages. In addition, these sensitivities appear to be especially pronounced for the weakly-sheared, multicell modes of deep convection characteristic of the Deep South of the United States during the boreal summer. Possible ocean-land sensitivities also argue for further examination of the impacts of using unique ocean-land surface initialization datasets provided by the NASA Short-term Prediction Research and Transition (SPoRT Center to select NOAA/NWS weather forecast offices. To obtain better quantitative understanding of these sensitivities and also to determine the utility of the ocean-land initialization data, we have executed matrices of regional WRF forecasts for selected convective events near Mobile, AL (MOB), and Houston, TX (HGX). The matrices consist of identically initialized WRF 24-h forecasts using any of eight microphysics choices and any of three planetary boundary layer choices. The resulting 24 simulations performed for each event within either the MOB or HGX regions are then compared to identify the sensitivities of various convective storm metrics to the physics choices. Particular emphasis is placed on sensitivities of precipitation timing, intensity, and coverage, as well as amount and coverage of lightning activity diagnosed from storm kinematics and graupel in the mixed phase layer. The results confirm impressions gleaned from study of the behavior of variously configured WRF runs contained in the ensembles produced each spring at the Center for the Analysis and Prediction of Storms, but with the benefit of more straightforward control of the physics package choices. The design of the experiments thus allows for more direct interpretation of the sensitivities to each possible physics combination. The results should assist forecasters in their efforts to anticipate and correct for possible biases in simulated WRF convection patterns, and help the modeling community refine their model parameterizations.

McCaul, E. W., Jr.↗

The Impact of Microphysics and Planetary Boundary Layer Physics on Model Simulation of U.S. Deep South Summer Convection

Inspection of output from various configurations of high-resolution, explicit convection forecast models such as the Weather Research and Forecasting (WRF) model indicates significant sensitivity to the choices of model physics pararneterizations employed. Some of the largest apparent sensitivities are related to the specifications of the cloud microphysics and planetary boundary layer physics packages. In addition, these sensitivities appear to be especially pronounced for the weakly-sheared, multicell modes of deep convection characteristic of the Deep South of the United States during the boreal summer. Possible ocean-land sensitivities also argue for further examination of the impacts of using unique ocean-land surface initialization datasets provided by the NASA Short-term Prediction Research and Transition (SPoRn Center to select NOAAlNWS weather forecast offices. To obtain better quantitative understanding of these sensitivities and also to determine the utility of the ocean-land initialization data, we have executed matrices of regional WRF forecasts for selected convective events near Mobile, AL (MOB), and Houston, TX (HGX). The matrices consist of identically initialized WRF 24-h forecasts using any of eight microphysics choices and any of three planetary boWldary layer choices. The resulting 24 simulations performed for each event within either the MOB or HGX regions are then compared to identify the sensitivities of various convective storm metrics to the physics choices. Particular emphasis is placed on sensitivities of precipitation timing, intensity, and coverage, as well as amount and coverage oflightuing activity diagnosed from storm kinematics and graupel in the mixed phase layer. The results confirm impressions gleaned from study of the behavior of variously configured WRF runs contained in the ensembles produced each spring at the Center for the Analysis and Prediction of Storms, but with the benefit of more straightforward control of the physics package choices. The design of the experiments thus allows for more direct interpretation of the sensitivities to each possible physics combination. The results should assist forecasters in their efforts to anticipate and correct for possible biases in simulated WRF convection patterns, and help the modeling community refine their model parameterizations.

McCaul, Eugene W., Jr.↗

Inclusion of Linearized Moist Physics in Nasa's Goddard Earth Observing System Data Assimilation Tools

Inclusion of moist physics in the linearized version of a weather forecast model is beneficial in terms of variational data assimilation. Further, it improves the capability of important tools, such as adjoint-based observation impacts and sensitivity studies. A linearized version of the relaxed Arakawa-Schubert (RAS) convection scheme has been developed and tested in NASA's Goddard Earth Observing System data assimilation tools. A previous study of the RAS scheme showed it to exhibit reasonable linearity and stability. This motivates the development of a linearization of a near-exact version of the RAS scheme. Linearized large-scale condensation is included through simple conversion of supersaturation into precipitation. The linearization of moist physics is validated against the full nonlinear model for 6- and 24-h intervals, relevant to variational data assimilation and observation impacts, respectively. For a small number of profiles, sudden large growth in the perturbation trajectory is encountered. Efficient filtering of these profiles is achieved by diagnosis of steep gradients in a reduced version of the operator of the tangent linear model. With filtering turned on, the inclusion of linearized moist physics increases the correlation between the nonlinear perturbation trajectory and the linear approximation of the perturbation trajectory. A month-long observation impact experiment is performed and the effect of including moist physics on the impacts is discussed. Impacts from moist-sensitive instruments and channels are increased. The effect of including moist physics is examined for adjoint sensitivity studies. A case study examining an intensifying Northern Hemisphere Atlantic storm is presented. The results show a significant sensitivity with respect to moisture.

Convection↗

Evaluation Methodologies for Early Conceptual Design Using Virtual Reality and Physical Test Environments

In this study, human factor design engineers wanted to know, by using subject matter experts (SMEs), if there would be any differences in testing low-fidelity conceptual designs in a physical environment compared to a digital/virtual one. Results indicated that when testing a design concept at this early stage, a high correlation between the two environments exists, meaning SMEs found little to no difference when evaluating a design in either a physical or a digital/virtual environment. There are advantages and limitations to both environments. The virtual world gave the experts a better sense of the microgravity space environment and the relationships of space and human presence that are difficult to simulate in a 1-g physical environment. However, the interaction between human and mechanics is better enhanced in the physical world compared to the virtual world. These advantages and limitations of each environment are important; however, cost is also an important consideration when early design concepts are being used. With the cost analysis of materials, hardware, and labor conducting for this study, virtual reality showed a 68% decrease in cost over the physical mock-up build. Thus, taking all aspects of the study into consideration, at this early design life cycle phase, virtual reality shows great promise as an evaluation environment for testing early design concepts that will cost less, give more options, and increase designer’s time to design.

Harry L. Litaker Jr↗

Physics and Chemistry of Te and HgTe-based Ternary Melts

Historically, the theoretical treatment of the liquid phases has always been more difficult and complicated than that for solid and gas phases. A liquid has no lattice structure as crystalline solids and the atoms/molecules in the liquid can migrate through it relatively rapidly. On the other hand, it is also interacting with many other atoms/molecules so that the simplifications of the kinetic theory of gases cannot be employed. For more complicated liquids, such as the liquids of high ionicity and those containing hydrogen bonds and electric dipoles, the understanding is far from complete. At the same time, accurate information on the physics and chemistry of semiconductor melts is needed for the quantitative descriptions of the process of crystal growth from melt. The pre-crystallization phenomena in the liquid phase are critical because the properties of the grown crystals depend on the state and structure of the melt as well as the thermal history of the melt during solidification process. However, the data on the liquid phase, such as thermophysical properties of semiconductor melts are scarce, especially for the HgTe-based II-VI ternary compound semiconductors because of their high vapor pressure and extreme toxicity. Analysis of the thermophysical properties of the melt can provide information about structural transitions of the melt during the solidification process. From a broader point of view, the structure of liquids is much more complicated than the crystalline solids, especially the relaxation behavior through different thermal histories. The theory of hetero-phase fluctuations of liquids is applicable to any many-body systems including condensed-matter physics, field theory, physics of nuclear-matter, cosmology, biology and even sociology. This book summarizes the physics and chemistry from the experimental measurements and theoretical analyses of phase diagram, thermodynamic properties, density, thermal conductivity, viscosity, and electrical conductivity on the binary, pseudo-binary and ternary melts of the most advanced IR-detector material systems of HgCdTe and HgZnTe as well as the analyses of these results. The main objectives of this study are: (1) to provide the phase diagrams and thermodynamic properties of Hg-Cd-Te and Hg-Zn-Te systems through quantitatively fitting the experimental data by assuming an associated solution model for the liquid phase, (2) to experimentally measure the thermophysical properties of the Hg-Cd-Te and Hg-Zn-Te melts, including density, viscosity, electrical conductivity and thermal conductivity as functions of temperature and composition and (3) to enhance the fundamental knowledge of hetero-phase fluctuations and relaxation phenomena in the melts and extend our understanding of the solidification process in order to interpret the experimental results of crystal growth so as to improve the melt growth processes of the compound semiconductor. The physics and chemistry of Te and HgTe-based ternary melts were explored through the studies of the structural transformation during melting, the supercooling during solidification, the relaxation phenomena after rapid cooling of the melts and the metal-semiconductor transition in the melts through the analyses of electrical conductivity and Lorenz number. An in-depth study on the thermophysical properties and their time-dependent structural dynamic processes taking place in the vicinity of the solid-liquid phase transition of the narrow homogeneity range HgTe-based ternary semiconductors as well as the analysis of the homogenization process in the melt will also be presented.

Thermophysical properties↗

Physical Properties of the Solar Atmosphere Derived from Comparison of Spectro-Polarimetric SDO/HMI Observables with 3D Radiative MHD Simulations

In this study, we compare the SDO/HMI line-of-sight observables (magnetic field, velocity, continuum intensity, and line depth) with the related physical properties for several dynamo simulation runs performed using the "StellarBox" 3D Radiative MHD code. The modeling of the Fe I 6173 A Stokes profiles is performed using the SPINOR radiative transfer code in the LTE approximation. The reproduced SDO/HMI line-of-sight pipeline is applied to the modeled spectra, and the observables are synthesized with high (numerical) and SDO/HMI (instrumental) resolutions. Correlations between the observables and the physical properties at various heights in the atmosphere are studied for a set of view angles (0, 30, 45, 60, 70, and 80 degrees away from the solar disk center). It is found that the SDO/HMI magnetic field and velocity measurements are unambiguously correlated with physical parameters at certain heights of the solar atmosphere. These heights increase from about 100 km above the photosphere for the disk center case to 300-600 km above the photosphere for the 80-degree case. The heights are found to be slightly lower in regions where stronger magnetic fields are found. The comparison of the photospheric magnetic flux and integrated continuum intensity derived from the SDO/HMI observables and high-resolution observations and spectra is discussed. The results of our study improve physics-based interpretations of the SDO/HMI observables and provide a better understanding of the physical properties of the solar atmosphere.

SMD↗

Physics-informed Machine Learning Method for Forecasting and Uncertainty Quantification of Partially Observed and Unobserved States in Power Grids

We present a physics-informed Gaussian Process Regression (GPR) model to predict the phase angle, angular speed, and wind mechanical power from a limited number of measurements. In the traditional data-driven GPR method, the form of the Gaussian Process covariance matrix is assumed and its parameters are found from measurements. In the physics-informed GPR, we treat unknown variables (including wind speed and mechanical power) as a random process and compute the covariance matrix from the resulting stochastic power grid equations. We demonstrate that the physics-informed GPR method is significantly more accurate than the standard data-driven one for immediate forecasting of generators' angular velocity and phase angle. We also show that the physics-informed GPR provides accurate predictions of the unobserved wind mechanical power, phase angle, or angular velocity when measurements from only one of these variables are available. The immediate forecast of observed variables and predictions of unobserved variables can be used for effectively managing power grids (electricity market clearing, regulation actions) and early detection of abnormal behavior and faults. The physics-based GPR forecast time horizon depends on the combination of input (wind power, load, etc.) correlation time and characteristic (relaxation) time of the power grid and can be extended to short and medium-range times.

machine learning, power grid, forecasting, Gaussia↗

A Mathematical Framework for Representing Cyber-Physical System Interdependencies and Resilience

U.S. critical infrastructure is increasingly composed of integrated cyber-physical systems (CPS) whose components are operationally interdependent. These interdependencies can create additional vulnerabilities beyond those that are typically evaluated through independent physical and cyber risk assessments. These additional vulnerabilities, previously undetected at the sub-system and/or component level, could cause cascading effects across both the physical and cyber domains that could lead to infrastructure disruption or failure. This paper will review an initial mathematical framework developed to help understand the dynamics of these interfacing physical and cyber components at a holistic system level. The resulting framework also provides a method for modeling and assessing the resilience of CPS in complex and adaptive systems. It frames the system in terms of mission performance and the potential effects to performance caused by attacks that are cyber, physical, or blended in nature. The framework utilizes a systems-based, state-space modeling approach to reason about risk, resilience, and interdependencies in CPS. Probabilities are applied to each CPS component regarding a threat (both man-made and natural) and the likelihood of that particular component being impacted, along with indirect impact to other interdependent components. These component-level impacts from threats then translate into mission-level impact and systemic state change.

Brigantic, Robert T.↗

Transforming U.S. Particle Physics Education: A Snowmass 2021 Study

The pursuit of knowledge in particle physics requires constant learning. As new tools become available, new theories are developed, and physicists search for new answers with ever-evolving methods. However, it is the case that formal educational systems serve as the primary training grounds for particle physicists. Graduate school (and undergraduate school to a lesser extent) is where researchers learn most of the technical skills required for research, develop scientific problem-solving abilities, learn how to establish themselves in their field, and begin developing their career. It is unfortunate, then, that the skills gained by physicists during their formal education are often mismatched with the skills actually required for a successful career in physics. We performed a survey of the U.S. particle physics community to determine the missing elements of graduate and undergraduate education and to gauge how to bridge these gaps. In this contributed paper, part of the 2021-22 Snowmass Community Planning Exercise, we report the results of this survey. We also recommend several specific community actions to improve the quality of particle physics education; the "community" here refers to physics departments, national labs, professional societies, funding agencies, and individual physicists.

Bitter, O.↗

How Community Agreements Can Improve Workplace Culture in Physics

Equity, Diversity, and Inclusion (EDI) committees and Codes of Conduct (CoC) have become common in laboratories and physics departments across the country. However, very often these EDI committees and CoC are not equipped to provide practical consequences for violations, and therefore are mostly performative in nature. A considerable effort has been devoted by various groups within APS units and beyond the APS in developing instead what are now called Community Guidelines. Community Guidelines help implement the core principles in CoC, by setting expectations for participation in in-person events and virtual communication. When further accompanied by accountability and enforcement processes, they develop into Community Agreements. This White Paper discusses the elements necessary to create and implement an effective Community Agreement, reviews examples of Community Agreements in physics, and argues that physics collaborations, physics departments, and ultimately as many physics organizations as possible, however large or small, should have a Community Agreement in place. We advocate that Community Agreements should become part of the bylaws of any entity that has bylaws.

Barzi, Emanuela↗

Bio-Medical and Plant Biology Imaging Tools Derived from Nuclear Physics Detector Development

Basic nuclear physics research requires continuing advances in detector technology. Often, new detection technology can have applications outside basic nuclear physics research. For over 80 years various sciences have been using radioactive isotopes as tracers for increasing our understanding of biological processes in living systems. New nuclear physics detection technologies using scintillators and photo multipliers have been used to develop imaging tools for radioisotope detection and imaging in bio-medical and plant biology applications. Nuclear imaging techniques such as positron emission tomography (PET) and single photon emission computed tomography (SPECT) benefit greatly from advances in nuclear physics detector technology. Bio-medical research utilizing animals as in pre-clinical research and in clinical applications such as cancer detection and treatment have benefited much from nuclear physics detector advances. New imaging tools are being developed for plant biology research to enhance our understanding of metabolic processes necessary for efficient biofuel production in a changing environment and of best bioassays for environmental remediation. The Radiation Detector and Imaging Group at Thomas Jefferson National Accelerator Facility has been applying detector technology to these applications. The examples of detector systems for medical and plant biology applications as well as scientific motivations driving use of radioisotope tracers in these applications will be presented.

Weisenberger, Andrew↗

Physics-constrained fault diagnosis framework for monitoring a multi-component thermal hydraulic system

A method for diagnosing faults includes receiving a system description of a thermal hydraulic system, the system description indicating a plurality of components and sensors. The method also includes constructing, based on physical conservations laws and using the system description, a plurality of physics-based models for the plurality of components, each of the plurality of physics-based models including unknown parameters. The method further includes receiving historical measurements and calibrating the physics-based models by calculating the unknown parameters of each of the physics-based models using the historical measurements to produce calibrated models. The method also includes receiving sensor measurements of the sensors, and calculating residuals corresponding to differences between measurements predicted by the plurality of calibrated models and the sensor measurements. The method also includes determining, based on the calculated residuals, a fault of a component or a sensor, and generating an alert indicating the fault.

Nguyen, Tat Nghia↗

Multi-Physics Surrogate Modeling with Dimensionality Reduction

This summary provides a new algorithm to construct surrogate models for multi-physics, nonlinear, high dimensional models which typically suffer from the curse of dimensionality. To deal with the high computational cost and difficult error estimation, we employ recent advances in reduced order modeling (ROM) techniques to do an error-preserving reduction for the number of influential model parameters, followed by a conventional surrogate construction process. To implement ROM for a multiphysics model, a range finding algorithm (RFA) is used to identify a linear transformation in which the number of influential parameters can be minimized and the errors resulting from the non-influential parameters can be upper-bounded. The proposed algorithm is applied to the MAMMOTH coupled code system developed at the Idaho National Laboratory. In particular, we investigate the reducibility of Rattlesnake and BISON codes and their multi-physics coupling. The most important result of this work is that the reduction obtained with coupled physics is more significant than that with individual physics models. This summary explores the application of ROM techniques on multi-physics coupling codes system. Concise methodology is provided and selected numerical results are provided to show that coupling system provides additional reduction at interfaces. Future work could be invested to determine the optimum surrogate model format. (authors)

97 MATHEMATICS AND COMPUTING↗

Preliminary analysis of effect of Vanadium Self-Powered Neutron Detectors on AP1000 reactor core physical parameters - 360

For the AP1000 reactor, the Vanadium Self-Powered Neutron Detectors are installed in the instrumentation thimbles of the fuel assembly. The (n,? ) reaction of Vanadium SPNDs will impact on the neutron spectrum of the location, and finally impact on the reactor core physical parameters. But, this effect is not considered for the AP1000 reactor Nuclear Design. So, it is necessary to analyze the effect of the presence of Vanadium SPNDs on the AP1000 reactor core physical parameters. CASMO5 is used to calculate physical parameters of four typical assemblies of AP1000 reactor, and SIMULATE5 is used to calculate physical parameters of the initial cycle. The results show that the maximum absolute deviations of K-infinite, pin power, thermal flux for the assemblies are 181 pcm, 6.3% and 20.1%, separately. The maximum absolute deviations of critical boron concentration, heat flux hot channel factor, nuclear enthalpy rise hot channel factor, axial offset, quadrant power tilt ratio and axial power distribution of the initial cycle are 5 ppm, 0.7%, 0.5%, 0.1%,0.09% and 0.19%,separately. So, the presence of Vanadium SPNDs has a significant impact on the power distribution of pin cells around the instrumentation thimble and the thermal flux in the location of instrumentation thimble, but doesn't affect core physical parameters of the initial cycle very much. As is shown, it is very important to accurately consider the effect of presence of Vanadium SPNDs when calculating the Vanadium SPNDs current response. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

MFANS 2024 - Formally Proving Characteristics of Cyber-Physical Systems

Cyber-physical systems (CPS) are engineered systems that rely on the smooth integration of computational algorithms and physical elements. This integration presents new challenges for verifying that systems will behave as expected. The goal of this presentation is to present current challenges and potential solutions for the formal verification of cyber-physical systems. For cyber systems, formal methods refer to systematically rigorous mathematical techniques employed in the specification, development, analysis, and verification of both software and hardware systems. Recent advancements in computer science have yielded sophisticated tools specifically designed to address challenges associated with formal methods in complex systems. These tools leverage various foundational concepts such as logic, formal languages, program semantics, type systems, type theory, and automata theory. A notable achievement in the application of formal methods is the seL4 microkernel, claimed to be the first general-purpose operating-system kernel to be verified. Its proof implies the absence of bugs and guarantees that the kernel meets specifications. For physical systems, dynamic and control theory has a history of using rigorous analytic techniques to prove functional correctness. Lyapunov, optimal, classical, modern, and robust control theories all provide rigorous mathematical methods both to analyze system performance and to design controller that can be guaranteed to meet certain objectives. Recent computational techniques like level set theory and reachability analysis provide assertions that a system's state will avoid unsafe regions. Even though success has been independently achieved for cyber systems and physical systems, the integration of such systems creates new challenges. In particular, there is an obvious discrepancy between finite-state machines and infinite-state systems, resulting in different approaches for modeling and analyzing these system. While it is possible to simulate hybrid systems, this provides only a demonstration of a performance and not proof. For hybrid systems, current formal methods and system analysis approaches typically require a workarounds to work on hybrid systems like CPS. This paper will outline the state of the art and limits of current practice for formally verifying CPS and will identify possible research directions that require attention.

97 MATHEMATICS AND COMPUTING↗