Orbit Size Research Articles

Periapsis precession in general stationary and axisymmetric spacetimes

This work studies the periapsis shift in the equatorial plane of arbitrary stationary and axisymmetric spacetimes. Two perturbative methods are systematically developed. The first works for small eccentricity but very general orbit size and the second, which is post-Newtonian and includes two variants, is more accurate for orbits of large size but allows general eccentricity. Results from these methods are shown to be equivalent under small eccentricity and large size limits. The periapsis shift of Kerr–Newman, Kerr–Sen and Kerr–Taub-NUT spacetimes is computed to high orders. The electric charge and NUT charge are shown to contribute to the leading order but with opposite signs. The frame-dragging term and high-order effect of spacetime spin are given. The electric and NUT charges of the Earth, Sun and Sgr A* are constrained using the Mercury, satellite and S2 precession data. Periapsis shifts of other spacetimes are obtained too.

Height functions on Hecke orbits and the generalised André–Pink–Zannier conjecture

We introduce and study the notion of a generalised Hecke orbit in a Shimura variety. We define a height function on such an orbit and study its properties. We obtain lower bounds for the sizes of Galois orbits of points in a generalised Hecke orbit in terms of this height function, assuming the ‘weakly adelic Mumford–Tate hypothesis’ and prove the generalised André–Pink–Zannier conjecture under this assumption, using Pila–Zannier strategy.

Experimental and numerical investigation of the Doppler-shifted resonance condition for high frequency Alfvén eigenmodes on ASDEX Upgrade

Abstract The Doppler-shifted resonance condition for high frequency Alfvénic eigenmodes has been extensively studied on ASDEX Upgrade in the presence of one or a combination of two neutral beam injected (NBI) fast ion populations. In general, only centrally deposited NBI sources drive these modes, while off-axis sources globally stabilize the mode activity. For the case of a single central NBI source, the observed trend is: the highest frequency modes are driven by the lowest energy and lowest pitch angle NBI sources, in line with the expectation from the Doppler-shifted resonance condition. The expected mode frequencies are determined analytically from the two-fluid cold plasma dispersion relation and the most unstable frequency relation, while the mode growth rates are estimated using the fast ion slowing down distribution functions from the ASCOT code. The overall mode frequency trend in a source-to-source variation is tracked, although a systematic overestimate of ∼1 MHz is observed. Possible causes of this overestimate include the finite size of the resonant fast ion drift orbit and non-linear effects such as mode sideband formation. Alternatively, the expected mode frequencies are determined by tracking the growth rate maxima trajectories, this method improves the agreement with the experimentally measured values. A combination of two central mode-driving NBI sources results in the suppression of the mode driven by the lowest energy and the lowest pitch angle NBI source. Computing the analytically expected mode frequency following the method outlined above, again, generally tracks the experimentally observed trend. The mode’s Alfvénic nature allows for a practical application to track the core hydrogen fraction by following the mode frequency changes in response to a varying ion mass density. Such application is demonstrated in a discharge where the average ion mass is varied from ∼2m p to ∼1.5m p (where m p is the proton mass) via a hydrogen puff in a deuterium plasma, in the presence of a strong mode activity. The expected mode frequency changes are computed from the existence of the resonance condition, and the values track the measured results with an offset of ∼0.5 MHz. Overall, the results suggest an intriguing possibility to monitor and control the D-T ion fraction in the core of a fusion reactor in real time using a non-invasive diagnostic.

Grit size effect on HydroFlex polishing dynamics and performance

Controllable, adaptable internal polishing is critical to metal additive manufactured (MAM) complex channels. Conventional fluid-based internal polishing methods are challenging to control the material removal, resulting in varied surface roughness (Sa) depending on channel length, aspect ratio (AR), and complexity. HydroFlex is an internal polishing method which drives a fixed-abrasive grinding wheel via a flexible spindle to navigate complex, high AR channels controllably and predictably removing material. Key to HydroFlex performance is the orbital motion of the grinding wheel governed by the hydrodynamic and cutting forces to achieve uniform polishing. Effect of grit size on orbital motion, and corresponding performance was experimentally evaluated. 46 µm, 76 µm, and 91 µm grit sizes were tested at a rotational speed of 50,000 rpm and a channel to wheel (C/W) ratio of 0.54 and orbital frequency and consistency, grinding force, Sa, material removal rate (MRR), and wheel wear were compared. Orbital frequency was found to directly correlate with increasing grit size and consistency of orbit shown to be highest at moderate grinding forces. Sa and MRR were inversely proportional with sub-micron roughness achieved at 0.15 g/min and 0.34 g/min corresponding to 2.2 µm Sa. Wheel wear was effected by grain pullout, attrition, and capping with all grit sizes experiencing similar wear. These findings suggest that orbital motion can be controlled through manipulation of wheel kinetics enabling precise control of grinding dynamics essential to adaptable performance in complex, non-uniform MAM channels.

Bundled matrix product states represent low-energy excitations faithfully

Abstract We consider a set of density matrices. All of which are written in the same orbital basis, but the orbital basis size is less than the total Hilbert space size. We ask how each density matrix is related to each of the others by establishing a norm between density matrices based on the truncation error in a partial trace for a small set of orbitals. We find that states with large energy differences must have large differences in their density matrices. Small energy differences are divided into two groups, one where two density matrices have small differences and another where they are very different, as is the case of symmetry. We extend these ideas to a bundle of matrix product states and show that bond dimension of the wavefunction ansatz for two states with large energy differences are larger. Meanwhile, low energy differences can have nearly the same bond dimensions for similar states.

Cranial anatomy of Acynodon adriaticus and extreme durophagous adaptations in Eusuchia (Reptilia: Crocodylomorpha).

Acynodon adriaticus, a small eusuchian from the Late Cretaceous of Italy, is known for its well-preserved cranial and postcranial material. Despite its excellent preservation, many details remain hidden due to the physical overlap between the elements and matrix obliteration. We used Micro-CT scans to reveal previously overlooked anatomical features and describe in detail the cranial and dental anatomy of this taxon, shedding new light on its palaeoecology. The holotypic specimen, SC 57248, represents a mature individual exhibiting signs of hyperossification, developed ornamentation, and various pathologies, including jaw arthritis and a possible dental anomaly. Acynodon adriaticus exhibits significant durophagous adaptations, including a robust, brevirostrine skull optimized for powerful biting and stress-load capacity. Its specialized dentition, lacking caniniform teeth, features anterior chisel-like teeth and hypertrophic posterior molariforms with thick enamel, indicative of a diet specializing in hard-shelled prey. The dentition pattern, accelerated molariform replacement rate, and reduced orbit size suggest adaptations for durophagous foraging in turbid, densely vegetated aquatic environments. The paleoecological context during the Late Cretaceous, characterized by increased freshwater habitats and high invertebrate diversity, likely facilitated the evolution of such specialized traits in A. adriaticus. This small crocodylomorph likely foraged slowly in shallow, benthic environments, using its powerful bite to process mollusks and large arthropods. The study of A. adriaticus, along with comparisons with other crocodylomorphs and ecomorphologically similar taxa like Iharkutosuchus makadii and Gnatusuchus pebasensis, provides a valuable morphofunctional model for understanding the evolutionary pathways of extinct crocodylians to durophagy.

Initial Frontal Sinus and Orbit Tumor Signaling Late Distant Metastasis in Kidney Cancer.

Although metastases to the paranasal sinuses are exceedingly rare, when they do occur, renal clear cell carcinoma is the most frequent primary tumor involved. The aim of this work was to present a case of metastatic clear cell renal carcinoma in the frontal sinus and orbit region, 7 years after the initial diagnosis and treatment. The patient was referred to our clinic due to drooping of the left eyelid and displacement of the left eyeball. Computed tomography revealed an expansive lesion in the left frontal sinus and orbit, causing destruction of its anterior, lateral, and roof walls. Profuse bleeding from the tumor and left orbit hindered a comprehensive assessment of tumor extension into the orbit and residual tumor size. Therefore, complete tumor removal was not possible; instead, reduction was achieved. Subsequent histopathologic and immunohistochemical analysis confirmed the lesion as a metastasis of renal cell carcinoma in the sinonasal tract. Unfortunately, 10 weeks later, the patient passed away. Treatment of metastatic clear cell renal carcinoma depends on the localization of the disease as well as the overall condition of the patient. If there is a solitary metastatic lesion, as in the case of the sinonasal region, surgical treatment is recommended. Metastasis of clear cell renal carcinoma to the sinonasal region is a rare occurrence; however, it is essential to consider it in cases of rapidly growing tumor masses, typically presenting with symptoms such as epistaxis and nasal obstruction.

Unreliable M[X]/G(P1,P2)/1 feedback retrial queues with combined working vacation

The study examines M[X]/G(P1,P2)/1 feedback retrial queues coupled with starting failure, repair, delay to repair, working vacation, and general retrial times. Also, it explores how different batch sizes affect performance and how bulk arrival affects system behavior. When the server is not in use, a single customer initiates the system while the remaining customers transition to a state of orbit. A new customer must turn on the server to provide two phases of mandatory service at any time. The server could have starting issues. If the service is successfully started (with likelihood α), the customer receives service immediately. In the absence of that, the likelihood of starting failure happens (with likelihood 1−α=α¯). The server was taken for repair with some delay and that customer was transported to an orbital location. When the server was busy or unavailable, the arriving customers queued by FCFS in the orbit. We also discuss the idea of reworking with probability p, and restarting unsuccessful service attempts to improve customer happiness and service efficiency. We also introduce the concept of working vacation, which permits servers to temporarily stop providing services, affecting system performance and availability at both peak and off-peak times. A supplementary variable technique was adopted for the system's and orbit size's probability-generating function. Various performance measurements were provided with appropriate numerical examples.

Two-types of service facilities in interconnected stochastic queueing and queueing-inventory system with marked Markovian arrival process

This article explores the performance of interconnected queueing systems and queueing-inventory systems (IQSQIS) in stochastic modeling. IQSQIS features two types of service facilities with dual service stations: one providing non-commodity service with a multi-server, and another handling commodity sales with a single server. As directed, a customer type i,i=1,2 can approach the station i,i=1,2 whose arrival pattern follows the marked Markovian arrival process (MMAP) since we assume that both service stations have an equal arrival phase. The IQSQIS gives an offer to the type-2 customer to choose type-1 service at the end of their service completion. Numerical results suggest that this option reduces customer wait times, orbit size, and overall system costs. The comparative analysis of heterogeneous and homogeneous servers in station-1 and queue-dependent and non-queue-dependent service facilities in station-2 is presented and investigated using the numerical outputs.

Equivariant embedding of finite-dimensional dynamical systems

We prove an equivariant version of the classical Menger-Nöbeling theorem regarding topological embeddings: Whenever a group G acts on a finite-dimensional compact metric space X, a generic continuous equivariant function from X into ([0,1]r)G is a topological embedding, provided that for every positive integer N the space of points in X with orbit size at most N has topological dimension strictly less than rN2. We emphasize that the result imposes no restrictions whatsoever on the acting group G (beyond the existence of an action on a finite-dimensional space). Moreover if G is finitely generated then there exists a finite subset F⊂G so that for a generic continuous map h:X→[0,1]r, the map hF:X→([0,1]r)F given by x↦(f(gx))g∈F is an embedding. This constitutes a generalization of the Takens delay embedding theorem into the topological category.

Analysis of Cephalometric Differences of the Midface and Upper Face in Males and Females: A Radiographic Study.

Gender affirmation facial surgery (GAFS) is an important component in treating gender dysphoria among transgender individuals by addressing gender incongruence of the face. There is a paucity of literature describing objective characterizations of the anatomic differences between male and female faces. In this study, cephalometric measurements were taken on routine CT imaging performed on cisgender patients between 2017 and 2020. Specifically defined cephalometric landmarks of the upper and midface were measured and compared between male and female cohorts. Thirty-eight patients, 19 male and 19 female, were identified for this study. Significant differences were identified in the frontal prominence, orbital size, malar height, bizygomatic width, nose, and upper lip, with moderate rates of specificity for each gender. Some important ratios are also presented. Differences in the malar region and the orbit highlight the importance of these areas as a point of focus for GAFS. These cephalometric findings provide objective evidence and parameters for perceived anatomic differences in male and female faces. In addition, they help both corroborate current surgical techniques as well as guide future approaches to GAFS.

Characteristics of Multiplanetary Systems with One Host Star

The characteristics of 100 multiplanetary systems with single central stars of different spectral classes were examined. The data for these systems were taken from the NASA Exoplanet Archive. Among the systems, those were selected for which the exoplanet mass and radius were simultaneously known. For 293 planets from these systems masses, radii, orbital radii, orbital periods, and types of exoplanets were analyzed. It occurred that the rarest type in such systems were terrestrial planets and after them the gas giants. Most of the exoplanets belonged to the type of super-earths. The distribution of the number of planets in a system showed that systems with many exoplanets are less common than those with a smaller number. The system with the largest number of exoplanets in this sample is TRAPPIST-1 (7 planets systems). The properties of exoplanets in multiplanetary systems with one host star in terms of characteristics, orbital sizes, and number of planets, are investigated and compared with the Solar system. It turned out that the Solar system is rather an exception to the considered extrasolar multiplanetary systems.

Gas, not dust: Migration of TESS/Gaia hot Jupiters possibly halted by the magnetospheres of protoplanetary disks

Context. The presence of short-period (< 10 days) planets around main sequence (MS) stars has been associated either with the dust-destruction region or with the magnetospheric gas-truncation radius in the protoplanetary disks that surround them during the pre-MS phase. However, previous analyses have only considered low-mass FGK stars, making it difficult to disentangle the two scenarios. Aims. This exploratory study is aimed at testing whether it is the inner dust or gas disk driving the location of short-period, giant planets. Methods. By combining TESS and Gaia DR3 data, we identified a sample of 47 intermediate-mass (1.5−3 M⊙) MS stars hosting confirmed and firm candidate hot Jupiters. We compared their orbits with the rough position of the inner dust and gas disks, which are well separated around their Herbig stars precursors. We also made a comparison with the orbits of confirmed hot Jupiters around a similarly extracted TESS/Gaia sample of low-mass sources (0.5−1.5 M⊙). Results. The orbits of hot Jupiters around intermediate-mass stars tend to be closer to the central sources than the inner dust disk, most generally consistent with the small magnetospheric truncation radii typical of Herbig stars (≲5 R*). A similar study considering the low-mass stars alone has been less conclusive due to the similar spatial scales of their inner dust and gas disks (≳5 R*). However, considering the whole sample, we do not find the correlation between orbit sizes and stellar luminosities that is otherwise expected if the dust-destruction radius limits the hot Jupiters’ orbits. On the contrary, the comparative analysis reveals that such orbits tend to be closer to the stellar surface for intermediate-mass stars than for low-mass stars, with both being mostly consistent with the rough sizes of the corresponding magnetospheres. Conclusion. Our results suggest that the inner gas (ad not the dust) disk limits the innermost orbits of hot Jupiters around intermediate-mass stars. These findings also provide tentative support to previous works that have claimed this is indeed the case for low-mass sources. We propose that hot Jupiters could be explained via a combination of the core-accretion paradigm and migration up to the gas-truncation radius, which may be responsible for halting inward migration regardless of the stellar mass regime. Larger samples of intermediate-mass stars with hot Jupiters are necessary to confirm our hypothesis, which implies that massive Herbig stars without magnetospheres (> 3−4 M⊙) may be the most efficient in swallowing their newborn planets.

The largest orbit sizes of linear group actions and abelian quotients

Let G be a finite group and let V be a finite and faithful G-module such that V is completely reducible, possibly of mixed characteristic, or V is a G-module over a field of characteristic p with Op(G)=1. Suppose that M is the largest orbit size in the action of G on V. It is known that the index of the commutator subgroup G′ in G is bounded by M, that is, |G:G′|≤M. In this paper, we classify all linear group actions in which |G:G′|=M. It turns out that our classification is a vast generalization of a classic 1967 result by D. Passman. We also include an application of the main results to Brauer's k(B)-problem.

Non-Markovian Feedback Retrial Queue with Two Types of Customers and Delayed Repair Under Bernoulli Working Vacation

This paper deals with an M/G/1 feedback retrial G-queue and delayed repair incorporating Bernoulli working vacation. Arrivals of both favorable and unfavorable consumers are two independent Poisson processes. The server is subjected to breakdown during the regular busy period due to the arrival of unfavorable customers and then the server will be down for a short period of time. Further, the concept of delay time is also discussed. After the fulfillment of regular service, the dissatisfied consumer may re-join the orbit to receive another service as a feedback consumer. During the working vacation period, the server provides the service to consumers at a reduced rate. By applying the supplementary variable technique (SVT), we have analyzed the steady-state probability generating function (PGF) for the system size and orbit size. In addition, we have presented the system performance, reliability indicators, and stochastic decomposition property. Finally, we provided numerical examples to illustrate our model’s mathematical results.

Performance analysis of a collision channel with abandonments

We consider a Markovian retrial queueing system with customer collisions and abandonment in the context of carrier-sense multiple access systems. Using z-transform techniques, we find a set of first-order differential equations for the probability generating functions of the orbit size when the server is empty, busy, or in the collision phase. We then rely on series expansion techniques to extract approximations for relevant performance measures from this set of differential equations. More precisely, we construct a numerical algorithm to calculate the terms in the series expansions of various factorial moments of the orbit size. To improve the accuracy of our series expansion approach, we apply Wynn’s epsilon algorithm which not only speeds up convergence, but also extends the region of convergence. We illustrate the accuracy of our approach by means of some numerical examples, and find that the method is both fast and accurate for a wide range of the parameter values.

Maximum Entropy Solution for M^X/G/1 Priority Reiterate G-queue Under Working Breakdown and Working Vacation

The maximum entropy principle has grown progressively more pertinent to queueing systems. The principle of maximum entropy (PME) presents an impartial framework as a promising method to examine complex queuing processes. This principle can be employed to assess the most appropriate probability distributions for queueing scenarios in a variety of widespread industrial issues. The aspects of general service bulk arrival retrial G-queue including working vacation, state-dependent arrival, priority users, and working breakdown are all explored in this article. Real-world applications for this kind of waiting line include computer systems, industrial companies, packet-switching networks, and communication facilities, etc. The adverse users (or negative arrivals) can make an appearance when the server (operator) is preoccupied with a positive user. Consumer’s arrival patterns follow the Poisson distribution. Priority consumers and regular (ordinary) consumers are the two groups of consumers that are considered in this investigation. Priority consumers do not have to wait in line and are granted a special right of prevention that allows them to receive services before ordinary consumers. Initially, we have estimated performance metrics including orbit size and long-run probabilities in this research work. The maximum entropy approach is then used to give a comparative perusal between the system’s exact and estimated waiting times. Apart from that a bi-objective optimization model is developed to diminish both consumers waiting times and estimated costs simultaneously. It is manageable to establish an effective balance between the standard of service and operating expenses using the analytical strategy that has been provided.

A Mathematical Approach to Ullmann Reaction: ANFIS Computing of a Chemical Retrial Queue Model under Hybrid Vacation

Herein, we developed the first report on the chemical retrial queue and hybrid vacation process for the significant Ullmann coupling for enhanced high-throughput reaction discovery. The problem of controlling the waiting time for chemical retrials is addressed here. We incorporated the supplementary variables method (SVT) and generated the steady-state probability generating function (PGF) for system size and orbit size. Important cases are outlined, and a few key metrics are utilized to evaluate system performance. Additionally, the impact of changing certain system parameters has also been analyzed via numerical examples. One particularly interesting aspect of this research is the comparison of neuro-fuzzy technique results with validation results utilizing the "adaptive neuro-fuzzy inference system" (ANFIS).

Sensitivity analysis of a non-Markovian feedback retrial queue, reneging, delayed repair with working vacation subject to server breakdown

This study investigated the steady-state characteristics of a non-Markovian feedback retrial queue with reneging, delayed repair, and working vacation. In this scenario, we assumed that consumers arrive through Poisson processes and the server provides service to consumers during both regular and working vacation periods. However, it is subject to breakdowns at any moment, resulting in a service interruption for a random duration. Additionally, the concept of delay time was also presented. The consumer that is dissatisfied with the service may re-enter the orbit to receive another service; this individual is considered a feedback consumer. The server will go on a working vacation if the orbit is empty after successfully serving a satisfied consumer. By utilizing the supplementary variable technique (SVT), we examined the steady-state probability generating function of the system and orbit sizes. Finally, numerical outcomes and a sensitivity analysis were given to verify the analytical findings of important performance indicators.

Finding the Fixing Number of Johnson Graphs J(n, k) for k Є {2; 3}

The graph invariant, aptly named the fixing number, is the smallest number of vertices that, when fixed, eliminate all non-trivial automorphisms (or symmetries) of a graph. Although many graphs have established fixing numbers, Johnson graphs, a family of graphs related to the graph isomorphism problem, have only partially classified fixing numbers. By examining specific orbit sizes of the automorphism group of Johnson graphs and classifying the subsequent remaining subgroups of the automorphism group after iteratively fixing vertices, we provide exact minimal sequences of fixed vertices, in turn establishing the fixing number of infinitely many Johnson graphs. KEYWORDS: Graph Automorphism Groups; Symmetry Breaking; Fixing Number; Determining Number; Johnson Graphs; Kneser Graphs; Graph Invariants; Permutation Groups; Minimal Sized Bases.