Central Body Research Articles

Quantitative Measurements in the Exhaust Flow of a Rotating Detonation Combustor Using Rainbow Schlieren Deflectometry

Abstract This study employs Rainbow Schlieren Deflectometry (RSD) to characterize the unsteady, supersonic/subsonic exhaust plume of a Rotating Detonation Combustor (RDC). Firstly, RSD images are analyzed to quantify the frequency and strength of flow oscillations and their relationship to the detonation wave. Secondly, a 3D tomographic algorithm is used to obtain the local 3D density field across the whole region of interest (ROI). The tomographic analysis relies upon wave rotation to infer projection data of the 3D exhaust plume at multiple view angles using a single RSD/camera system and was previously validated using phantom data from computational fluid dynamics analysis of an RDC. The annular RDC operated on methane and 2/3 O2 - 1/3 N2 oxidizer mixture is equipped with a converging nozzle to pressurize the combustion chamber. The product flow exiting the nozzle throat expands across an unoptimized conical aerospike attached to the center body of the RDC. RSD images provide a temporal resolution of 369 ns and spatial resolution of 100 ?m in a 6.4 high and 25.6 mm wide ROI of the exhaust plume. A rainbow filter is calibrated to convert hue in color schlieren images into deflection angle data. This data is used to characterize the unsteady flow oscillations that show excellent agreement with PCB pressure probe measurements acquired inside the combustion chamber. Tomographic analysis yields a 3D local density field that shows distinct features, consistent with published numerical simulations of the RDC exhaust plume.

Some new minimax inequalities for centered convex bodies

AbstractThe purpose of this manuscript is to derive some new minimax inequalities for centered convex bodies in $${\mathbb {R}}^{d}$$ R d . As consequences, new characterizations of ellipsoids will be established as well. Some open problems related to the Busemann-Petty list of problems will also be discussed.

Swirling flow and heat transfer in a pipe: Decay and transition to axial flow

This paper describes an experimental study of heat transfer, local and total swirl flow parameters in the pipe 80 mm in a diameter and 150 diameters long. The pipe consists of 12 separate pipes of different length, connected to each other using 20 mm ring spacers. These spacers were also used to provide the flow and heat transfer measurements. Overall, eight blade-type swirl generators with central body and profiled according to the power low, are installed at the pipe inlet. The actual swirl intensity S of swirl generators is ranged from 0.38 to 1.29. The profiles of mean axial and tangential velocity, surface heat flux, swirl flow angle, static and total pressure, flow and surface temperature are measured. A few novel scientific results and equations are obtained, including the axial and tangential speed maximum, axial and tangential momentum flux, swirl number decay and energy loss transformation. The common link between the local and total swirl parameters, one-valued correlation between tangential and axial velocity were obtained. The results, presented in the paper led to the conclusion that transition from swirling to axial flow occurs at S ≈ 0.19 in terms of the heat transfer decrease, but at S ≈ 0.10 – in terms of the energy loss reduction.

Nonlinear dynamic modeling and vibration analysis for flexible tethered satellite systems under large deformations

The escalating threat posed by space debris necessitates innovative approaches for its removal. This article presents a comprehensive mathematical modeling and dynamic analysis of a flexible tethered satellite system (FTSS) in the post-capture phase, taking into account nonlinear strain effects for the flexible appendages. The FTSS consists of a rigid central body satellite, two identical flexible panels, and a towing mass that manipulates the satellite through a tether. We develop a detailed dynamic model that accurately represents the system’s three-dimensional motion, incorporating the rigid body’s 6 degrees of freedom (DOF), the tether’s 3 DOF motion, and two modal generalized coordinates for each panel. The extended Hamilton method is employed to derive this model, enabling us to investigate the conditions under which nonlinear strain considerations become critical. The findings of this article reveal that nonlinear strain effects can profoundly impact the system’s dynamics under certain geometric and forcing conditions, often overlooked in previous studies. In these scenarios, the panel strains exceed the linear regime, necessitating the use of nonlinear models for accurate representation. This work emphasizes the importance of incorporating nonlinear strain terms in the dynamic analysis of FTSSs, particularly when dealing with large deformations and high-amplitude vibrations encountered in debris removal applications.

ESTABLISHMENT OF THE CONCEPT OF PUBLIC DIPLOMACY IN MODERN SCIENTIFIC DISCOURSE: THE ROLE OF PARADIPLOMACY

The article reveals the essence of the concept of public diplomacy and a retrospective of its formation in the current scientific discourse. It is noted that the field of US public diplomacy is quite actively researched by modern scientists. It is shown that the term “public diplomacy” should be understood as the activity of various actors, both governmental and non-governmental, which is intended to explain to the foreign public the foreign policy pursued by the country and to encourage this or that state to make its foreign policy decisions in the direction that is beneficial to the given actor . It has been established that the concept of “cultural diplomacy” is narrower than the concept of “public diplomacy”, which should be understood as a set of activities carried out by both central and foreign bodies of external relations of the state with the aim of researching the attitude and informing the foreign public. as well as establishing contacts abroad, with the aim of improving the state’s image and achieving national interests. So, in the United States of America, there is no separation of “cultural diplomacy” from “public diplomacy”. The concept of paradiplomacy is also considered as a tool of activity of subnational actors in the international arena and components of diplomatic communication processes taking place in the modern world. It has been proven that paradiplomacy is an integral part of modern international relations along with public diplomacy and cultural diplomacy.

An overactuated aerial robot based on cooperative quadrotors attached through passive universal joints: Modeling, control and 6-DoF trajectory tracking

This article discusses a novel aerial robot architecture that overcomes the underactuation of conventional multirotor systems without adding dedicated rotor tilting actuators. The proposed system is based on four quadrotors cooperatively carrying a central body to which they are attached through passive universal joints. While conventional parallel axis multirotors are underactuated, the proposed mechanism makes the system overactuated, enabling independent position and orientation control of the main body. This implies that the payload can be carried in the minimum drag orientation, it enables take-off and landing on inclined surfaces and it provides thrust-vectoring capabilities to the system, leading to high control authority. A detailed dynamic model is derived making use of Lagrangian formalism and a hierarchical control law based on such model is proposed to stabilize the system. This control law is designed to ensure good tracking while minimizing power consumption. The proposed control law and the capabilities of the architecture are evaluated in simulation and in outdoor experimental flights, where the aerial robot shows autonomous tracking of the six degrees of freedom (DoF) of the main body, an inherently unfeasible maneuver for conventional underactuated multirotors.

Smartphone Usage and Postural Stability in Individuals With Forward Head Posture: A Nintendo Wii Balance Board Analysis.

To assess postural stability, specifically center of body sway during single-leg standing balance, among individuals with and without forward head posture (FHP) during smartphone use. The research recruited 53 healthy smartphone users, aged 18-25, and categorized them into FHP group comprising 26 subjects and the normal (control) group with 27 subjects. Participants were assigned the task of maintaining balance while engaged in smartphone typing during single-leg standing. The experiment involved four specific conditions according to neck posture and stable of surface. The study meticulously quantified body center of pressure (COP) sway amplitudes using the Nintendo Wii Balance Board. The research revealed that individuals with FHP exhibited significantly greater body sway compared to the control group when using smartphones. Notably, distinct variations were observed in path length sway, anteroposterior (AP), and mediolateral (ML) sway amplitude, particularly evident when maintaining flexed neck positions on a soft surface while engaged with smartphones. These findings strongly suggest that individuals with FHP encounter deteriorated postural stability during smartphone use, particularly in challenging head positions.

Solid‐State Bonding of Iron or Steel with Stainless Steels by Spark Plasma Sintering Bonding

In this study, pure iron, S45C carbon steel (Fe–0.45mass%C), carburized iron, and nitrided iron are bonded with two types of stainless steels, i.e., SUS304 austenitic stainless steel (Fe–18mass%Cr–8mass%Ni) with face center cubic structure or SUS430 ferritic stainless steel (Fe–18mass%Cr) with body center cubic structure by a spark plasma sintering (SPS) machine. Bonding experiments are carried out by SPS bonding. It is found that the bonding temperature of the S45C/SUS samples is lower than that of Fe/SUS samples, and carbon atoms in the S45C play important role on the bonding performance. The bonding temperature for SUS304/SUS430 sample is more than 30 °C higher than those for the Fe/SUS and S45C/SUS samples. The presence of thin chromium oxides on both stainless steels reduces the bonding performance of SUS304/SUS430 sample. Better bonding performance is found for the carburized and nitrided iron for bonding with stainless steels. However, continuous single‐phase layer on the surface leads to reduce the bonding performance. It is concluded that not only the concentration of carbon and nitrogen but also the phase configuration in the iron at interface strongly influences the bonding performance between iron alloys and stainless steels by SPS bonding.

Influence of tactile and verbal guidance on lateral weight-shifting in double-leg standing after total hip arthroplasty

IntroductionAnomalous gait after total hip arthroplasty (THA), marked by increased trunk lateral flexion during weight-bearing, is a noteworthy aspect to consider for enhancing ambulatory capacity. One potential training modality that is feasible in the early post-THA period is lateral weight shifting during double-leg standing. However, the influence of physical therapists’ instructional guidance on trunk lateral flexion and hip abductor muscle activity in this context remains unclear. PurposeTo investigate the influence of physical therapist's guidance directed towards reducing the trunk lateral flexion angle during lateral weight-shifting in double-leg standing post-THA. MethodsTwenty THA patients, assessed at 2 weeks postoperatively, performed lateral weight-shifting under two conditions: the normal condition and the instructed condition, for comparison. The latter involved tactile and verbal guidance guidance to minimize trunk lateral flexion. Patients were categorized based on trunk flexion direction for comparison, exploring the correlations between hip abductor muscle activity and kinematic parameters. ResultsIn the instructed condition, a significant reduction in trunk lateral flexion and increased hip lever arm length were observed compared to those in the normal condition. Patients with trunk flexion towards the operated side exhibited a notable reduction, while those on the non-operated side showed no significant changes. Gluteus medius muscle activity correlated with trunk lateral flexion, and tensor fasciae latae muscle activity correlated with body's center of mass lateral displacement and hip adduction angle. ConclusionsPhysical therapist's guidance influenced lateral weight-shifting in double-leg standing post-THA. Differences in the trunk lateral flexion direction may lead to different effects from the guidance.

Features of the types of control on the performance of electronic procedures in the activities of public administration entities

The scientific article highlights the essence of the types of control over the implementation of electronic procedures in the activities of public administration bodies, namely: parliamentary control; from the representative of the Verkhovna Rada of Ukraine on human rights; from the central bodies of executive power. The author substantiates the expediency of improving the legal regulation of the procedure for holding a preliminary meeting before the trial of the case. In particular, it is considered expedient to establish the terms of holding a preparatory meeting from the moment of receipt of an administrative claim, as well as to determine the cases when reconciliation of the parties is not allowed. It was established that the control carried out by local executive bodies has a much smaller scope, but is the closest to the controlled objects. The control powers of the said bodies within the scope of control over the provision of electronic services are enshrined in the Law of Ukraine «On Local State Administrations» (Clause 9 of Article 16). Part 1 of Article 28 of this law stipulates that in order to exercise the powers granted, local state administrations have the right, in particular, to conduct inspections of the state of compliance with the Constitution of Ukraine and the laws of Ukraine, other legislative acts by local self­government bodies. It was concluded that regional state administrations, within the limits of their powers, direct the activities of district state administrations and exercise control over their activities. Local state administrations control the implementation of the powers granted by law to the executive bodies of village, settlement and city councils by their executive bodies and village, settlement and city heads. It has been established that control over the exercise of delegated powers of executive bodies by local self-government bodies is entrusted to the relevant local state administrations, and in cases provided for by law, to ministries and other central bodies of executive power, their territorial bodies. Control is carried out by analyzing acts of local self-government bodies, providing local self-government bodies with information on the implementation of delegated powers of executive bodies, conducting inspections of the activities of executive bodies of village, settlement, and city councils. In addition, local executive bodies can create structural subdivisions to perform control functions.

Relationship between central hemodynamic parameters and body composition and the functional state of neuro-autonomic regulation in young men

The aim of the study is to examine the relationship between central hemodynamic parameters and body composition by considering baseline functional state of neuro-autonomic regulation according to the index of regulatory system activity (IRSA) in young men. Material and methods. A total of 44 male participants were divided into three groups based on the IRSA level. The first group included 26 men with an optimal IRSA level. The second and third groups, each of 9 men, with moderate and high IRSA levels, respectively. The functional state of cardiovascular system was assessed using a device “REOKOM” (Kharkiv). The measurement of body composition was performed by weight-scale “TANITA BC-601” (Japan). The functional state of autonomic nervous system was assessed using a device “CARDIOLAB” (Kharkiv). Results. Our results have demonstrated higher hemodynamic parameters in men with moderate and high level of IRSA. Men with elevated level of sympathetic activity had the highest indices of the pumping function of the heart, and those with the balance between parasympathetic and sympathetic branches had the lowest indices of the pumping heart function. As for the indicators of total peripheral resistance and specific peripheral resistance, another trend was seen, namely, individuals with a balanced state of autonomic nervous regulation had the highest parameters, and those with a predominance of sympathetic tone had the lowest ones. Close correlations have been found between increased levels of regulatory mechanism tension and cardiohemodynamic parameters. An indicator analysis of the body component composition has revealed a significant increase in body mass index, total and visceral fat content in the examined groups with moderate and severe regulatory system tension. In addition, correlations have been found between IRSA and constituting components of body composition. Conclusions. The group assignment of the examined individuals according to IRSA has shown that a high tension of the regulatory mechanisms increased the load on the cardiovascular system, as indicated by higher indicators of central hemodynamics. In individuals with an optimal level of regulatory system functioning, the cardiovascular system activity is optimal and less energy consuming.

Nuskoisporites dulhuntyi from the Cisuralian and Lopingian of the Southern Alps: A morphological comparison between dispersed and in situ prepollen

Nuskoisporites dulhuntyi is considered one of the biostratigraphic marker species for the Lopingian of Europe. A morphological comparison between Kungurian (Cisuralian) and Wuchiapingian (Lopingian) Nuskoisporites dulhuntyi prepollen (dispersed from five outcrops and in situ from one cone) from the Southern Alps has been carried out. Dispersed Nuskoisporites dulhuntyi prepollen grains from the Kungurian (Cisuralian) of the Athesian Volcanic District (AVD) and the Wuchiapingian (Lopingian) of Bletterbach have been compared with the in situ prepollen grains isolated from an Ortiseia cone of the Bletterbach outcrop. Using light microscopy, we measured overall size, central body size, and laesurae length of the prepollen grains revealing significant overlaps in morphological characteristics between the different assemblages. The main difference is the bigger size of the in situ pollen grains in comparison with the dispersed ones, but a significant overlap is still observed. This implies that the prepollen grains from the Kungurian sedimentary successions of the Athesian Volcanic District can be assigned confidentially to the dispersed prepollen species Nuskoisporites dulhuntyi and hence, represent the so far oldest record of this taxon, extending the species range from the Guadalupian back to the late Cisuralian.

Comparative results of computational and theoretical study of the annular nozzle with a flat central body

One of the ways to improve specific characteristics of the power plant of a launch vehicle for ladeploying payload to the near-Earth space is to provide the possibility of operation of a fixed nozzle in the design mode over the whole active leg of the flight trajectory. The nozzle should be compact, lightweight, well-cooled. For detailed testing of the possibility of introducing a nozzle into the rocket engine chamber it is necessary to be able to quickly assess the true value of the thrust and the specific impulse the chamber with such a nozzle can achieve. This article presents the results of comparison of the thrust and specific impulse, obtained during calculations using engineering methods, numerical modeling for the atmospheric section and high-altitude sections of the trajectory. The results of the calculation are compared with the experimental values of the specific impulse obtained on the rocket engine test-bed under atmospheric operating conditions. These results can be effectively applied both to evaluate new and to improve existing nozzle designs of wide-range rocket engines.

Intervertebral Disc Degeneration Induced by Vertebral Body Fracture Associated with Microcirculation Disruption of the Subendplate

Among the causes of the progression of intervertebral disc (IVD) degeneration (IDD) is the loss of nutrient intake to the IVD through the microcirculation disruption of the subendplate. Also, the vertebral body fracture intervenes in the degeneration the adjacent IVD. This research aimed to create an animal model of IDD using these 2 strategies. Thirty male Sprague-Dawley rats were split into 3 groups: a control group, a middle vertebral body injury (MI) associated with ethanol injection (MI+EtOH) group, and an MI associated with phosphate-buffered saline injection group. A vertebral body fracture with or without endplate injection of ethanol was generated by either drilling a hole in the center of a caudal rat vertebral body to form a fracture with an unabated endplate or drilling a hole in the center of a rat coccygeal vertebral body with endplate injection of ethanol to establish a vertebral body fracture with endplate damage. X-ray, macroscopic, histologic, and biochemical evaluations were utilized to assess IDD at weeks 3 and6. According to X-ray findings, the MI+EtOH group demonstrated a significant decrease in intervertebral space height over time in comparison to the 2 other groups. The water content also was significantly decreased. Macroscopic and histological analysis demonstrated progressive degenerative changes in the IVD of the MI+EtOH group. The caudal vertebra fracture with ethanol injection is more likely to induce degeneration of adjacent IVD. This model effectively reproduced IDD, which may serve as a theoretical basis for future clinical intervention for IDD.

Residual deformation analysis of laser powder bed fusion-fabricated lattice structures

ABSTRACT Lattice structures are crucial for weight reduction, and laser powder bed fusion (LPBF) is an efficient fabrication method. However, there's a notable research gap in understanding the residual deformation of LPBF-fabricated lattice structures. This study investigates the residual deformation of three basic lattice structures, body centre cell (BCC), face centre cell (FCC), and diamond cell (DC), fabricated via LPBF to reveal their deformation mechanisms. Analysis covers horizontal direction, building direction, and total deformations, unveiling complex structural responses. Lower relative densities exhibit a prevalent structural deformation mode (SDM) causing significant deformations, while higher densities shift to an intrinsic deformation mode (IDM) dominated by contraction during fabrication. The FCC structure shows optimal stability with minimal residual deformation across most densities. This study offers insightful findings and a detailed mechanistic analysis of residual deformation in LPBF-fabricated lattice structures, applicable across various configurations, ensuring design process uniformity and reliability.

When the Anomalistic, Draconitic and Sidereal Orbital Periods Do Not Coincide: The Impact of Post-Keplerian Perturbing Accelerations

In a purely Keplerian picture, the anomalistic, draconitic and sidereal orbital periods of a test particle orbiting a massive body coincide with each other. Such degeneracy is removed when post-Keplerian perturbing acceleration enters the equations of motion, yielding generally different corrections to the Keplerian period for the three aforementioned characteristic orbital timescales. They are analytically worked out in the case of the accelerations induced by the general relativistic post-Newtonian gravitoelectromagnetic fields and, to the Newtonian level, by the oblateness of the central body. The resulting expressions hold for completely general orbital configurations and spatial orientations of the spin axis of the primary. Astronomical systems characterized by extremely accurate measurements of orbital periods like transiting exoplanets and binary pulsars may offer potentially viable scenarios for measuring such post-Keplerian features of motion, at least in principle. As an example, the sidereal period of the brown dwarf WD1032 + 011 b is currently known with an uncertainty as small as ≃10−5s, while its predicted post-Newtonian gravitoelectric correction amounts to 0.07s; however, the accuracy with which the Keplerian period can be calculated is just 572 s. For double pulsar PSR J0737–3039, the largest relativistic correction to the anomalistic period amounts to a few tenths of a second, given a measurement error of such a characteristic orbital timescale as small as ≃10−6s. On the other hand, the Keplerian term can be currently calculated just to a ≃9 s accuracy. In principle, measuring at least two of the three characteristic orbital periods for the same system independently would cancel out their common Keplerian component, provided that their difference is taken into account.

Velocity dependence of sensory reweighting in human balance control.

The relative contributions of proprioceptive, vestibular, and visual sensory cues to balance control change depending on their availability and reliability. This sensory reweighting is classically supported by nonlinear sway responses to increasing visual surround and/or surface tilt amplitudes. However, recent evidence indicates that visual cues are reweighted based on visual tilt velocity rather than tilt amplitude. Therefore, we designed a study to specifically test the hypothesized velocity dependence of reweighting while expanding on earlier findings for visual reweighting by testing proprioceptive reweighting for standing balance on a tilting surface. Twenty healthy young adults stood with their eyes closed on a toes-up/-down tilting platform. We designed four pseudorandom tilt sequences with either a slow (S) or a fast (F) tilt velocity and different peak-to-peak amplitudes. We used model-based interpretations of measured sway characteristics to estimate the proprioceptive sensory weight (Wprop) within each trial. In addition, root-mean-square values of measured body center of mass sway amplitude (RMS) and velocity (RMSv) were calculated for each tilt sequence. Wprop, RMS, and RMSv values varied depending on the stimulus velocity, exhibiting large effects (all Cohen's d >1.10). In contrast, we observed no significant differences across stimulus amplitudes for Wprop (Cohen's d: 0.02-0.16) and, compared with the differences in velocity, there were much smaller changes in RMS and RMSv values (Cohen's d: 0.05-0.91). These results confirmed the hypothesized velocity, rather than amplitude, dependence of sensory reweighting.NEW & NOTEWORTHY This novel study examined the velocity dependence of sensory reweighting for human balance control using support surface tilt stimuli with independently varied amplitude and velocity. Estimates of the proprioceptive contribution to standing balance, derived from model-based interpretations of sway characteristics, showed greater sensitivity to changes in surface tilt velocity than surface tilt amplitude. These results support a velocity-based mechanism underlying sensory reweighting for human balance control.

The Effect of a Pelvic Clock Tool Exercise on Central Muscle Endurance, Trunk Range of Motion, and Pain Intensity in Middle-aged Women With Nonspecific Chronic Low Back Pain

Background and Aims Despite the advancement of medicine in managing spinal diseases and the increasing development of treatment methods, back pain has remained one of the significant public health problems in industrial and non-industrial countries. Therefore, the present study aimed to investigate the effect of a course of exercise with a pelvic clock device on the endurance of central body muscles, torso range of motion, and pain intensity in middle-aged women with nonspecific chronic low back pain. Methods The present study was quasi-experimental with a pre-test-post-test design and a control group. The statistical population of the present study consisted of middle-aged women with nonspecific chronic low back pain in the age range of 35-50. The statistical sample of the study included 30 middle-aged women who were purposefully and accessibly selected from the study›s statistical population based on the inclusion and exclusion criteria. The exercise protocol was performed with a pelvic clock device for 8 weeks (3 sessions of 45 minutes per week) by a researcher in a sports club. Central body muscle endurance indices were measured using the McGill test (trunk flexural endurance test for abdominal muscle endurance) and modified Bearing Sorenson test. Also, the trunk range of motion and pain intensity were assessed using Schubert's modified test and visual analog scale. The measurement was made while the control group participated only in the pre-test and post-test stages. The paired t-test and independent t-test were used for intra-group and inter-group comparisons, respectively, at a significance level of 0.05. Results The results showed that 8 weeks of exercises with a pelvic clock device could affect the endurance of the muscles of the central body, the range of motion of the trunk, and the severity of pain in middle-aged women with nonspecific chronic low back pain. However, it did not affect the control group (P≤0.05). Conclusion According to the present study findings, it is suggested that exercises with pelvic clock device are used as a cheap and practical modality to increase endurance of central body muscles and torso range of motion but reduce pain in middle-aged women with nonspecific chronic low back pain. It could also be used as a method of prevention.

Boundaries identification of geological structure in lunar Oceanus Procellarum region using full gravity gradient tensor methodology

Boundary recognition visually delineates the horizontal extent of subsurface anomalies, providing a foundational basis for interpreting gravity data. Compared to gravity observations, gravity gradient data offers the benefits of multiple components and the enhancement of shortwave information in graphical representations. In our study, we investigated the delineation of geological structure boundaries in the lunar Oceanus Procellarum region using gravity gradient techniques. First, based on the observations from the Gravity Recovery and Interior Laboratory (GRAIL) mission, we obtained high-precision synthetic full tensor values of the gravity gradient as our primary research data. Moreover, to reduce curvature errors during large-scale terrain forward modeling, we applied the spherical prism of tesseroid to eliminate the effects of near-surface topography. Grounded on the Bouguer anomalies of gravity gradient, four distinct boundary recognition methods have been employed to explore the geological structure of the lunar Oceanus Procellarum region. It includes the Theta map method, the directional Theta map method, the combination of total horizontal derivative and the modulus of full tensor gravity gradient, and the improved edge detection method based on the Theta map method.The common feature of these methods is the utilization of the multi-component data combination from gravity gradient tensors, which can enhance the accuracy of edge detection. From the investigation results presented in the paper, we have found the following: 1) The improved edge detection method, based on the Theta map principle, enables better identification of the center of subsurface anomaly bodies during boundary recognition, utilizing a consistent single color in graphic displays. 2) According to the results of boundary recognition, numerous strip anomalies exist in the Oceanus Procellarum area that show less correlation with topographic relief. One possible explanation for these graphical anomalies of gravity gradient is that they serve as channels for the upwelling of mantle material during lunar evolution.

Quantitative Criteria for Defining Planets

The current International Astronomical Union (IAU) definition of “planet” is problematic because it is vague and excludes exoplanets. Here, we describe aspects of quantitative planetary taxonomy and examine the results of unsupervised clustering of solar system bodies to guide the development of possible classification frameworks. Two unsurprising conclusions emerged from the clustering analysis: (1) satellites are distinct from planets and (2) dynamical dominance is a natural organizing principle for planetary taxonomy. To generalize an existing dynamical dominance criterion, we adopt a universal clearing timescale applicable to all central bodies (brown dwarfs, stars, and stellar remnants). Then, we propose two quantitative, unified frameworks to define both planets and exoplanets. The first framework is aligned with both the IAU definition of planet in the solar system and the IAU working definition of an exoplanet. The second framework is a simpler mass-based framework that avoids some of the difficulties ingrained in current IAU recommendations.