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At least 1,135 records · Page 63

Topology-Aware Reinforcement Learning for Voltage Control: Centralized and Decentralized Strategies

Volt-VAR control (VVC) methods based on deep reinforcement learning (DRL) can effectively control distribution grid voltage and minimize power loss by implementing corrective and preventive control measures on the reactive power output of inverter-based distributed energy resources (DERs). However, model-free DRL-based VVC approaches usually cannot capture the important topological feature of the power system since they use a fully-connected network (FCN) to deliver the action. Therefore, this paper proposes a graph convolutional network (GCN)-based DRL approach that can employ the topological information of the network to take better control action for regulating the voltage. Our implementation allows for both centralized and decentralized configurations, utilizing a single agent and multiple agents respectively. Although the centralized GCN-based DRL approach has its advantages of minimizing voltage fluctuation and power loss, it is not suitable for large scale power systems due to its challenges in terms of scalability, computation speed and potential single points of failure. Therefore, these problems can be resolved using the decentralized GCN-based DRL approach. Moreover, to ensure the safe operation of the model, our proposed approach incorporates an exponential barrier function while formulating the reward function for each agent. To validate performance of the proposed approaches, the proposed model is tested on modified IEEE test systems and the performances are measured in terms on voltage fluctuation reduction, minimization of power loss and computational speed. Finally, the results show that the proposed topology-aware approach outperforms the FCN-based DRL approach in terms of reducing voltage fluctuation and minimizing power loss of the network. Moreover, it is shown that the decentralized GCN-based DRL has faster computational speed than other approaches.

42 ENGINEERING↗

Testing of a Line Driver With Configurable Pre-Emphasis on Lossy Transmission Lines

Rare-event physics experiments such as the Deep Underground Neutrino Experiment (DUNE) or the next Enriched Xenon Observatory (nEXO) experiment search for rare, low-energy events, detected by sensitive detectors immersed in a cryogenic noble liquid (e.g., liquid argon or xenon). Readout electronics used within such detectors must consume minimal power while operating reliably in cryogenic environments. Furthermore, in the case of nEXO, maximizing the radiopurity of the environment is vital to minimize background noise, thus placing strict limits on the volume of dielectric materials, leading to high-loss data cables spanning distances up to 12 m. Such cables cause high attenuation and intersymbol interference (ISI), resulting in a high bit-error rate (BER). These issues were addressed by developing an integrated line driver with configurable pre-emphasis in a 65-nm CMOS process. The pre-emphasis parameters can be programmed to minimize BER for specific cables and data rates under power constraints. Here, the driver was tested at both room and cryogenic temperatures. In both cases, the output BER was found to be strongly correlated with the pre-emphasis settings. Furthermore, analysis and simulation showed that adapting the pre-emphasis settings based on the incoming bit sequence can further improve performance with minimal changes to the current solution.

47 OTHER INSTRUMENTATION↗

Resiliency-Driven Proactive Distribution System Reconfiguration With Synchrophasor Data

Measuring and enabling resiliency of electric distribution systems with increasing weather and cyber events are important. Some of the extreme events (e.g. Earthquakes, Hurricanes) and associated paths are predicted and monitored closely in advance and allow to take pre-event proactive control actions. The Distribution Phasor Measurement Units (D-PMUs) provide new opportunities and supporting such proactive actions. Here, a synchrophasor based resiliency driven pre-event reconfiguration can ensure minimizing impact of the expected event on the power distribution system and associated performance. However, the D-PMUs will also face challenges in terms of data quality similar to the transmission PMUs. The focus of this paper is to provide data mining approaches for anomaly detection in D-PMUs and proposing resiliency-driven pre-event reconfiguration with islanding as a proactive mechanisms to minimize the impact of adverse events on system using processed synchrophasors data. Results are validated for real industrial feeders and test cases with satisfactory response

controlled islanding↗

Limited Role of Absolute Humidity in Intraurban Heat Variability

Abstract Monitoring and understanding the variability of heat within cities is important for urban planning and public health, and the number of studies measuring intraurban temperature variability is growing. Recognizing that the physiological effects of heat depend on humidity as well as temperature, measurement campaigns have included measurements of relative humidity alongside temperature. However, the role the spatial structure in humidity, independent from temperature, plays in intraurban heat variability is unknown. Here we use summer temperature and humidity from networks of stationary sensors in multiple cities in the United States to show spatial variations in the absolute humidity within these cities are weak. This variability in absolute humidity plays an insignificant role in the spatial variability of the heat index and humidity index (humidex), and the spatial variability of the heat metrics is dominated by temperature variability. Thus, results from previous studies that considered only intraurban variability in temperature will carry over to intraurban heat variability. Also, this suggests increases in humidity from green infrastructure interventions designed to reduce temperature will be minimal. In addition, a network of sensors that only measures temperature is sufficient to quantify the spatial variability of heat across these cities when combined with humidity measured at a single location, allowing for lower-cost heat monitoring networks. Significance Statement Monitoring the variability of heat within cities is important for urban planning and public health. While the physiological effects of heat depend on temperature and humidity, it is shown that there are only weak spatial variations in the absolute humidity within nine U.S. cities, and the spatial variability of heat metrics is dominated by temperature variability. This suggests increases in humidity will be minimal resulting from green infrastructure interventions designed to reduce temperature. It also means a network of sensors that only measure temperature is sufficient to quantify the spatial variability of heat across these cities when combined with humidity measured at a single location.

Meteorology & Atmospheric Sciences↗

ORNL_AISD_NiNb

This dataset describes the nickel-niobium solid solution binary alloy, where the two constituent elements nickel (Ni) and niobium (Nb) are randomly placed on an underlying crystal lattice. This dataset for nickel-niobium (Ni-Nb) alloys available includes the formation energy and bulk modulus for each crystal structure. Each atomic sample has a disordered phase which is obtained starting from an initial regular crystal structure of type body-centered cubic (BCC), face-centered cubic (FCC), or hexagonal compact packed (HCP). The geometry optimization ensures that all the alloy samples reached the equilibrium with negative formation energy. We perform geometry optimizations using the LAMMPS simulation package [1], a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales. We utilized the embedded atom model (EAM) potential for Ni and Nb developed in a previous study [2]. The potential could describe behaviors of the liquid and solid phases of Ni-Nb alloy. The structural factors and angular distributions of three atoms are well-matched with X-ray and ab initio-based molecular dynamics data. We prepared the three different crystals with different initial lattice parameters (3.52 Ã… for FCC, 3.32 Ã… for BCC, and 3.5 Ã… for HCP). We performed energy minimization in two steps. Firstly, we minimized the structures with an isotropic unit cell to minimize the side effects from our arbitrary lattice parameters for all other compositions. Then, we applied geometry optimization with a triclinic (non-orthogonal) unit cell to fully minimize the stress components to calculate the elastic constants. In this procedure, we chose 10,000 as the maximum number of allowable steps aimed at obtaining fully relaxed atomic geometries. The dataset consists of three sets of crystal structures. The first set contains 46,086 irregular crystal structures, each of them with 54 atoms, obtained through optimization starting from a regular BCC crystal structure. The second set contains 24,543 irregular crystal structures, each of them with 32 atoms, obtained through optimization starting from a regular FCC crystal structure. The third set contains 39,303 irregular crystal structures, each of them with 48 atoms, obtained through optimization starting from a regular HCP crystal structure. The atomic configurations within each set span the possible compositional range. The three sets have been unified in a global dataset, which is extremely heterogeneous in terms of crystal structures, lattice volumes, and atomic configurations. Organization of files inside the dataset: the dataset contains three subdirectories called • BCC_opt • FCC_opt • HCP_opt based on the type of initial regular structure used to start the geometry optimization. Inside each of these folders, every atomic structure is identified by a string “A_B_Câ€, where A denotes the number of Nb in the system, B denotes index of structure with a given Nb number, and C denotes the total number of structures generated with a given Nb number. For each optimized crystal structure identified by the unique string of characters “A_B_Câ€, three files are provided: • A_B_C_opt.xyz: The optimized geometries in xyz format • A_B_C_opt.cfg: The optimized geometries in cfg format. It includes cell information and atomic energy, and forces calculated from LAMMPS. • A_B_C.elastic: Raw data of 21 elastic constants from LAMMPS output. • A_B_C.bulk: Calculated upper and lower bounds of bulk modulus and averaged one based on Voigt-Reuss-Hill approach from *.elastic. References: [1] A. P. Thompson, H. M. Aktulga, R. Berger, D. S. Bolintineanu, W. M. Brown, P. S. Crozier, P. J. in 't Veld, A. Kohlmeyer, S. G. Moore, T. D. Nguyen, R. Shan, M. J. Stevens, J. Tranchida, C. Trott, and S. J. Plimpton. LAMMPS - a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales. Comp. Phys. Comm., 271:108171, 2022. [2] Y Zhang, R Ashcraft, MI Mendelev, CZ Wang, and KF Kelton. Experimental and molecular dynamics simulation study of structure of liquid and amorphous ni62nb38 alloy. The Journal of chemical physics, 145(20):204505, 2016.

36 MATERIALS SCIENCE↗

TEAMER: DAISY Flow-noise Testing (Abstract)

Evaluating impacts of marine energy devices is generally difficult given the dynamic environment where these devices need to be placed. The University of Washington’s (UW) DAISY (The Drifting Acoustic Instrumentation SYstem) is designed to measure radiated noise around marine energy converters operating in energetic waves and currents. In currents, a primary limitation for measurement fidelity at low frequencies (< 100 Hz) is the potential for non-propagating “flow-noise” to mask propagating sound and inflate estimates of the radiated noise from marine energy converters at frequencies that overlap with hearing sensitivities of fish and some marine mammals. While free-drifting measurements help to minimize the relative velocity that produces flow-noise, significant levels were still observed during initial DAISY tests. This motivated the development of a fabric “flow shield” around the hydrophone that disrupts both flow-noise generation mechanisms proposed by the initial tests. First, the flow shield is a source of substantial drag which keeps the hydrophone package moving with the approximate velocity of the surrounding water, compensating for differential wind or current forcing on the surface expression. By minimizing relative velocity around the hydrophone, turbulence shed by the hydrophone is also minimized. Second, the flow shield creates a largely quiescent pocket around the hydrophone, minimizing advection of free stream turbulence over the hydrophone element. Field data collected in these experiments will test effectiveness of these flow shields and provide quantitative data use and deployment.

16 TIDAL AND WAVE POWER↗

Optimizing Performance on Trinity Utilizing Machine Learning, Proxy Applications and Scheduling Priorities

The sheer number of nodes continues to increase in today’s supercomputers, the first half of Trinity alone contains more than 9400 compute nodes. Since the speed of today’s clusters are limited by the slowest nodes, it more important than ever to identify slow nodes, improve their performance if it can be done, and assure minimal usage of slower nodes during performance critical runs. This is an ongoing maintenance task that occurs on a regular basis and, therefore, it is important to minimize the impact upon its users by assessing and addressing slow performing nodes and mitigating their consequences while minimizing down time. These issues can be solved, in large part, through a systematic application of fast running hardware assessment tests, the application of Machine Learning, and making use of performance data to increase efficiency of large clusters. Proxy applications utilizing both MPI and OpenMP were developed to produce data as a substitute for long runtime applications to evaluate node performance. Machine learning is applied to identify underperforming nodes, and policies are being discussed to both minimize the impact of underperforming nodes and increase the efficiency of the system. In this paper, I will describe the process used to produce quickly performing proxy tests, consider various methods to isolate the outliers, and produce ordered lists for use in scheduling to accomplish this task.

97 MATHEMATICS AND COMPUTING↗

Slow Strain Rate Testing of A537 Tank Wall Material

At Savannah River Site (SRS), High-Level Waste is stored in below-grade carbon steel tanks. This waste in part consists of sludge, salt cake, and/or supernate. Preparation of this waste for future processing involves dissolution of the salt cake layer. The salt dissolution process can create conditions that leave the carbon steel tanks susceptible to localized corrosion. The salt to be dissolved contains high concentrations of nitrate, that once released, create an environment that may be conducive to pitting corrosion and/or stress corrosion cracking (SCC) of carbon steel. The salt dissolution process also liberates interstitial liquid trapped between the salt crystals. This liquid is initially high in nitrite and hydroxide concentration. High pH and greater ratios of nitrite to nitrate act as inhibitors to minimize corrosion of carbon steel in high nitrate environments. However, as dissolution proceeds, the concentration of nitrate will increase, while the hydroxide and nitrite concentration of the interstitial liquid will deplete and become insufficient to prevent the onset of corrosion attack. Tank blending and the addition of inhibitors are used to ensure adequate concentrations of hydroxide and nitrite. However, this is not desirable during salt dissolution as it can reduce process efficiency and increase the amount of waste that needs processing. This testing program was designed to examine the risk of SCC associated with utilizing the pitting factor (PF) and nitrite/nitrate (NO 2 - /NO 3 - ) ratio limits for handling dissolved salt solutions at an elevated temperature in the carbon steel waste tanks. The previously identified limits are a PF of 1.2 and an NO 2 - /NO 3 - ratio of 0.15. The results indicate that as long as the NO 2 - /NO 3 - ratio exceeds 0.1 and the PF is above approximately 0.8, there is a discernible safety margin between the open circuit potential (OCP) and the critical cracking potential (CCP) observed during applied potential testing. However, this margin, defined by the difference between the OCP and CCP, is relatively narrow, ranging from 0.1 to 0.25 volts. This small margin raises concerns about potential shifts in OCP during waste retrieval operations, which could inadvertently increase the risk of SCC if the OCP approaches or exceeds the CCP. These results confirm that dissolved salt solutions provide a potent chemistry that, under certain conditions, makes carbon steel susceptible to SCC. The next question to consider is the influence these results have on decisions for storage and retrieval of waste from the tanks. For Type III/IIIA waste tanks, the risk of SCC remains very low. First, and most importantly, the post-weld stress relief of the tanks has reduced the residual stress near the welds. Thus, without the stress component, SCC risk is minimized. The material of construction (A537 Carbon steel) for the Type III/IIIA tanks is superior to the steel in its resistance to SCC than the steel that was utilized for the Type I, II, and IV tanks (A285 carbon steel). From a chemistry control standpoint for a Type III/IIIA tank directly involved with handling dissolved salt solutions, the PF and NO 2 - /NO 3 - ratio limits may be utilized wherein chemistry control provides an extra layer of defense against SCC. Chemistry control for a Type III/IIIA tank minimizes the risk for a tank that may receive the dissolved salt solution, particularly if that tank is a Type I, II, or IV waste tank. On the other hand, if the dissolved salt solution is handled by a Type I, II, or IV waste tank the risk of SCC is real. The potent chemistry, absence of stress relief, and inferior material result in a condition that is conducive to cracking. Efforts should be made to either avoid transferring waste that may not meet the PF and NO 2 - /NO 3 - ratio criteria to one of these tanks or if it is unavoidable, take measures to minimize the consequences of a leak. As shown by these tests, even if the PF and NO 2 - /NO 3 - ratio criteria are met, there is a risk that the tank potential may be disturbed in the positive direction and the risk of SCC increase.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

A novel large-scale EV charging scheduling algorithm considering V2G and reactive power management based on ADMM

Electric vehicle aggregators (EVAs) that utilize vehicle-to-grid (V2G) technologies can function as both controllable loads and virtual power plants, providing key energy management services to the distribution system operator (DSO). EVAs can also balance the grid’s reactive power as a virtual static VAR compensator (SVC) and provide voltage stability by utilizing advanced electric vehicle (EV) chargers that are capable of four-quadrant operations to provide reactive power management. Finally, managed charging can benefit EVAs themselves by minimizing power factor penalties in their electricity bills. In this paper, we propose a novel EV charging scheduling algorithm based on a hierarchical distributed optimization framework that minimizes peak load and provides reactive power compensation for the DSO by collaboration with EVAs that manage both the active and the reactive charging and discharging power of participating EVs. Utilizing the alternative direction method of multipliers (ADMM), the proposed distributed optimization approach scales well with increased EV charging infrastructure by balancing active and reactive power while decreasing computational burden. In our proposed hierarchical approach, each EVA schedules the active and reactive EV charging and discharging power for 1) reactive power compensation in order to minimize power factor penalty and electricity cost accrued by the EVA, 2) satisfaction of each EV’s energy demand at minimal charging cost, and 3) peak shaving and load management for the DSO. When compared with an uncoordinated charging model, the efficacy of this proposed model is successfully demonstrated through a 300% decreased peak EV load for the DSO, 28% lower electricity costs for EV users, and 98.55% smaller power factor penalty, along with 17.58% lower overall electricity costs, for EVAs. The performance of our approach is validated in a case study with 50 EVs at multiple EVAs in an IEEE 13-bus test case and compared the results with uncoordinated EV charging.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Protection Against Graph-Based False Data Injection Attacks on Power Systems

Graph signal processing (GSP) has emerged as a powerful tool for practical network applications, including power system monitoring. By representing power system voltages as smooth graph signals, recent research has focused on developing GSP-based methods for state estimation, attack detection, and topology identification. Included, efficient methods have been developed for detecting false data injection (FDI) attacks, which until now were perceived as non-smooth with respect to the graph Laplacian matrix. Consequently, these methods may not be effective against smooth FDI attacks. In this paper, we propose a graph FDI (GFDI) attack that minimizes the Laplacian-based graph total variation (TV) under practical constraints. In addition, we develop a low-complexity algorithm that solves the non-convex GDFI attack optimization problem using ell_1-norm relaxation, the projected gradient descent (PGD) algorithm, and the alternating direction method of multipliers (ADMM). We then propose a protection scheme that identifies the minimal set of measurements necessary to constrain the GFDI output to high graph TV, thereby enabling its detection by existing GSP-based detectors. Our numerical simulations on the IEEE-57 bus test case reveal the potential threat posed by well-designed GSP-based FDI attacks. Moreover, we demonstrate that integrating the proposed protection design with GSP-based detection can lead to significant hardware cost savings compared to previous designs of protection methods against FDI attacks.

Morgenstern, Gal↗

Turbulence flight director analysis and preliminary simulation

A control column and trottle flight director display system is synthesized for use during flight through severe turbulence. The column system is designed to minimize airspeed excursions without overdriving attitude. The throttle system is designed to augment the airspeed regulation and provide an indication of the trim thrust required for any desired flight path angle. Together they form an energy management system to provide harmonious display indications of current aircraft motions and required corrective action, minimize gust upset tendencies, minimize unsafe aircraft excursions, and maintain satisfactory ride qualities. A preliminary fixed-base piloted simulation verified the analysis and provided a shakedown for a more sophisticated moving-base simulation to be accomplished next. This preliminary simulation utilized a flight scenario concept combining piloting tasks, random turbulence, and discrete gusts to create a high but realistic pilot workload conducive to pilot error and potential upset. The turbulence director (energy management) system significantly reduced pilot workload and minimized unsafe aircraft excursions.

Johnson, D. E.↗

Characteristic Elastic Systems of Time-Limited Optimal Maneuvers

Optimizing an elastic system and its active control is discussed. Maneuvers from an initial state to a final state in a finite time interval are considered. An active generalized control force that accomplishes the desired maneuver of a prespecified system is optimal if it minimizes a given quadratic cost function. By also varying a set of design parameters, the elastic system can be determined so as to further minimize the cost function. Here, the elastic system that minimizes the actual control cost is compared with the system that minimizes the ratio of actual cost to the cost of optimally maneuvering a rigid system of the same inertial properties. It is shown that an elastic system corresponding to an extremum of the ratio is actually a characteristic of the time-limited maneuver. Because both the spatial domain and the time interval are fixed, a characteristic elastic system is tuned to the specified temporal boundary conditions. The implication for rest-to-rest, spinup, and spin reversal maneuvers of spacecraft is that the optimal control for a characteristic elastic spacecraft is identical to the optimal control for the same spacecraft as if it were rigid.

Hale, A. L.↗

The effects of type of knowledge upon human problem solving in a process control task

The question of what the operator of a dynamic system needs to know was investigated in an experiment using PLANT, a simulation of a generic dynamic production process. Knowledge of PLANT was manipulated via different types of instruction, so that four different groups were created: (1) minimal instructions only; (2) minimal instructions and guidelines for operation (procedures); (3) minimal instructions and dynamic relationships (principles); and (4) minimal instructions, and procedures, and principles. Subjects controlled PLANT in a variety of situations which required maintaining production while also diagnosing familiar and unfamiliar failures. Despite the fact that these manipulations resulted in differences in subjects' Knowledge, as assessed via a written test at the end of the experiment, instructions had no effect upon achievement of the primary goal of production, or upon subjects' ability to diagnose unfamiliar failures. However, those groups receiving procedures controlled the system in a more stable manner. Possible reasons for the failure to find an effect of principles are presented, and the implications of these results for operator training and aiding are discussed.

Morris, N. M.↗

Optimization of payload mass placement in a dual keel space station

In order to keep a Space Station in a stable low-Earth orbit, angular momentum storage and translational attitude control systems will have to be used. In order to minimize the size of these attitude control systems, the induced gravity gradient torque effects will have to be minimized. This can be done by minimizing the cross-products of inertia of the Station through the management of payload placement with the Station geometry. A derived and automated methodology is presented which utilizes mathematical nonlinear programming techniques. An optimal arrangement of a set of five payloads on a Dual Keel Space Station was found that minimized the cross products of inertia and thus the required controllability resources.

Ferebee, Melvin J., Jr.↗

A physical model for earthquakes. III - Thermodynamical approach and its relation to nonclassical theories

An earthquake theory based on fundamental thermodynamical considerations was developed using two principles. The first principle is that physical systems, including fault systems, tend toward a state of minimal Helmholtz free energy, which corresponds to static equilibrium. The second postulate is that, if the system is not at minimal free energy, thermodynamic forces arise which drive the system back toward a minimum. According to this theory, the propagation of a fracture, or the formation of a slip on a frictional surface, are manifestations of the physics which attempt to return the system to minimal free energy. It is shown that the process of return to minimal free energy by the system corresponds to the production of entropy, thereby rendering the process irreversible.

Rundle, John B.↗

High temperature flexible seal

This device is concerned with sealing the sliding interfaces between structural panels that are roughly perpendicular to each other or whose edges are butted against one another. The gap which the seal element must seal is not uniform along the seal length requiring significant seal flexibility. The seal is mounted in a rectangular groove in a moveable structural panel. The seal comprises a plurality of rectangular shaped wafers stacked next to one another and preloaded in the axial direction to minimize leakage between wafers. The wafers are laterally preloaded to maintain sealing contact along the wafer faces which engage the adjacent wall of a sidewall using one of several approaches, such as the pressurized linear bellows. The seal accommodates distortions in the adjacent panel by relative sliding between adjacent wafers. Leakage between wafers is further minimized with good wafer surface finishes. Leakage between the seal nose and the adjacent structural panel is minimized when sealing against a distorted sidewall with relatively thin wafers and suitable seal preload apparatus. Leakage behind the seal is minimized with good groove tolerances and good sealing contact between the preload system and the back of the peripheral edge of the wafers.

Steinetz, Bruce M.↗

Comparison of joint space versus task force load distribution optimization for a multiarm manipulator system

It is often proposed that the redundancy in choosing a force distribution for multiple arms grasping a single object should be handled by minimizing a quadratic performance index. The performance index may be formulated in terms of joint torques or in terms of the Cartesian space force/torque applied to the body by the grippers. The former seeks to minimize power consumption while the latter minimizes body stresses. Because the cost functions are related to each other by a joint angle dependent transformation on the weight matrix, it might be argued that either method tends to reduce power consumption, but clearly the joint space minimization is optimal. A comparison of these two options is presented with consideration given to computational cost and power consumption. Simulation results using a two arm robot system are presented to show the savings realized by employing the joint space optimization. These savings are offset by additional complexity, computation time and in some cases processor power consumption.

Soloway, Donald I.↗

Optimal trajectories for an aerospace plane. Part 2: Data, tables, and graphs

Data, tables, and graphs relative to the optimal trajectories for an aerospace plane are presented. A single-stage-to-orbit (SSTO) configuration is considered, and the transition from low supersonic speeds to orbital speeds is studied for a single aerodynamic model (GHAME) and three engine models. Four optimization problems are solved using the sequential gradient-restoration algorithm for optimal control problems: (1) minimization of the weight of fuel consumed; (2) minimization of the peak dynamic pressure; (3) minimization of the peak heating rate; and (4) minimization of the peak tangential acceleration. The above optimization studies are carried out for different combinations of constraints, specifically: initial path inclination that is either free or given; dynamic pressure that is either free or bounded; and tangential acceleration that is either free or bounded.

Miele, Angelo↗