Orbit Size Research Articles

Relativistic hydrodynamical simulations of the effects of the stellar wind and the orbit on high-mass microquasar jets

ABSTRACT High-mass microquasar jets, produced in an accreting compact object in orbit around a massive star, must cross a region filled with stellar wind. The combined effects of the wind and orbital motion can strongly affect the jet properties on binary scales and beyond. The study of such effects can shed light on how high-mass microquasar jets propagate and terminate in the interstellar medium. We study for the first time, using relativistic hydrodynamical simulations, the combined impact of the stellar wind and orbital motion on the properties of high-mass microquasar jets on binary scales and beyond. We have performed 3-dimensional relativistic hydrodynamic simulations, using the PLUTO code, of a microquasar scenario in which a strong weakly relativistic wind from a star interacts with a relativistic jet under the effect of the binary orbital motion. The parameters of the orbit are chosen such that the results can provide insight on the jet-wind interaction in compact systems like for instance Cyg X-1 or Cyg X-3. The wind and jet momentum rates are set to values that may be realistic for these sources and lead to moderate jet bending, which together with the close orbit and jet instabilities could trigger significant jet precession and disruption. For high-mass microquasars with orbit size a ∼ 0.1 AU, and (relativistic) jet power $L_j\sim 10^{37}(\dot{M}_w/10^{-6}\, {\rm M}_\odot \, {\rm yr}^{-1})$ erg s−1, where $\dot{M}_w$ is the stellar wind mass rate, the combined effects of the stellar wind and orbital motion can induce relativistic jet disruption on scales ∼1 AU.

Meeting covered elements in ν-Tamari lattices

For each meet-semilattice M, we define an operator PopM:M→M byPopM(x)=⋀({y∈M:y⋖x}∪{x}). When M is the right weak order on a symmetric group, PopM is the pop-stack-sorting map. We prove some general properties of these operators, including a theorem that describes how they interact with certain lattice congruences. We then specialize our attention to the dynamics of PopTam(ν), where Tam(ν) is the ν-Tamari lattice. We determine the maximum size of a forward orbit of PopTam(ν). When Tam(ν) is the nthm-Tamari lattice, this maximum forward orbit size is m+n−1; in this case, we prove that the number of forward orbits of size m+n−1 is1n−1((m+1)(n−2)+m−1n−2). Motivated by the recent investigation of the pop-stack-sorting map, we define a lattice path μ∈Tam(ν) to be t-Pop-sortable if PopTam(ν)t(μ)=ν. We enumerate 1-Pop-sortable lattice paths in Tam(ν) for arbitrary ν. We also give a recursive method to generate 2-Pop-sortable lattice paths in Tam(ν) for arbitrary ν; this allows us to enumerate 2-Pop-sortable lattice paths in a large variety of ν-Tamari lattices that includes the m-Tamari lattices.

GPS, GLONASS, and Galileo orbit geometry variations caused by general relativity focusing on Galileo in eccentric orbits

Three main effects from general relativity (GR) may change the geometry and orientation of artificial earth satellite orbits, i.e., the Schwarzschild, Lense–Thirring, and De Sitter effects. So far, the verification of GR effects was mainly based on the observations of changes in the orientation of satellite orbital planes. We directly observe changes of the satellite orbit geometry caused by GR represented by the semimajor axis and eccentricity. We measure the variations of orbit size and shape of GPS, GLONASS, and Galileo satellites in circular and eccentric orbits and compare the results to the theoretical effects using three years of real GNSS data. We derive a solution that assumes the GR to be true, and a second solution, in which the post-Newtonian parameters are estimated, thus, allowing satellites to find their best spacetime curvature. For eccentric Galileo, GR changes the orbital shape and size in perigee in such a way that the orbit becomes smaller but more circular. In the apogee, the semimajor axis decreases but eccentricity increases, and thus, the orbit becomes more eccentric. Hence, the orbital size variabilities for eccentric orbits are greatly compensated by the orbital shape changes, and thus the total effect of satellite height change is much smaller than the effects for the size and shape of the orbit, individually. The mean semimajor axis offset based on all GPS, GLONASS, and Galileo satellites is − 17.41 ± 2.90 mm, which gives a relative error of 0.36% with respect to the theoretical value.

Protoplanet collisions: Statistical properties of ejecta

ABSTRACT The last phase of the formation of rocky planets is dominated by collisions among Moon- to Mars-sized planetary embryos. Simulations of this phase need to handle the difficulty of including the post-impact material without saturating the numerical integrator. A common approach is to include the collision-generated material by clustering it into few bodies with the same mass and uniformly scattering them around the collision point. However, this approach oversimplifies the properties of the collision material by neglecting features that can play important roles in the final structure and composition of the system. In this study, we present a statistical analysis of the orbital architecture, mass, and size distributions of the material generated through embryo–embryo collisions and show how they can be used to develop a model that can be directly incorporated into the numerical integrations. For instance, results of our analysis indicate that the masses of the fragments follow an exponential distribution with an exponent of −2.21 ± 0.17 over the range of 10−7 to 2 × 10−2 Earth-masses. The distribution of the post-impact velocities show that a large number of fragments are scattered towards the central star. The latter is a new finding that may be quite relevant to the delivery of material from the outer regions of the asteroid belt to the accretion zones of terrestrial planets. Finally, we present an analytical model for the 2D distribution of fragments that can be directly incorporated into numerical integrations.

Sensitive searches for wormholes

The realm of strong classical gravity and perhaps even quantum gravity are waiting to be explored. In this letter we consider the recently detected triple system composed of two stars and a non-accreting black hole. Using published observations of this system we conduct the most sensitive test to date for whether the black hole is actually a wormhole by looking for orbital perturbations due to an object on the other side of the wormhole. The mass limit obtained on the perturber is $\sim4$ orders of magnitude better than for observations of S2 orbiting the supermassive black hole at Sgr A*. We also consider how observations of a pulsar could test for whether the black hole in a pulsar-black hole binary is a wormhole. A pulsar in a similar orbit to S2 would be $\sim10$ orders of magnitude more sensitive than observations of S2. For a nominal pulsar-black hole binary of stellar masses, with orbital size similar to that of the Hulse-Taylor binary pulsar, one year of observations could set a mass limit on a perturber that is $\sim6$ orders of magnitude better than observations of a pulsar around Sgr~A*. A range of limits between the pulsar-Sgr~A* and Hulse-Taylor cases could be obtained for a possible population of pulsar-black hole binaries that may exist near the galactic center.

On the Experimental Dynamic Force Performance of a Squeeze Film Damper Supplied Through a Check Valve and Sealed With O-Rings

Abstract In rotor-bearing systems, squeeze film dampers (SFDs) assist to reduce vibration amplitudes while traversing a critical speed and also offer a means to suppress rotor instabilities. Along with an elastic support element, SFDs are effective means to isolate a rotor from its casing. O-rings (ORs), piston rings (PRs), and side plates as end seals reduce leakage and air ingestion while amplifying the viscous damping in configurations with limited physical space. ORs also add a centering stiffness and damping to a SFD. The paper presents experiments to quantify the dynamic forced response of an O-rings sealed ends SFD (OR-SFD) lubricated with ISO VG2 oil supplied at a low pressure (0.7 bar(g)). The damper is 127 mm in diameter (D), short in axial length L = 0.2D, and the film clearance c = 0.279 mm. The lubricant flows into the film land through a mechanical check valve and exits through a single port. Upstream of the check valve, a large plenum filled with oil serves to attenuate dynamic pressure disturbances. Multiple sets of single-frequency dynamic loads, 10 Hz to 120 Hz, produce circular centered orbits with amplitudes r =0.1c, 0.15c, and 0.2c. The experimental results identify the test rig structure, ORs, and SFD force coefficients, namely, stiffness (K), mass (M), and viscous damping (C). The ORs' coefficients are frequency independent and show a sizeable direct stiffness, KOR ∼ 50% of the test rig structure stiffness, along with a quadrature stiffness, K0 ∼ 0.26KOR, demonstrative of material damping. The lubricated system damping coefficient equals CL = (CSFD + COR); the ORs contributing 10% to the total. The experimental SFD damping and inertia coefficients are large in physical magnitude; CSFD slightly grows with orbit size, whereas MSFD is relatively constant. The added mass (MSFD) is approximately fourfold the bearing cartridge (BC) mass; hence, the test rig natural frequency drops by ∼50% once lubricated. A computational physics model predicts force coefficients that are just 10% lower than those estimated from experiments. The amplitude of measured dynamic pressures upstream of the plenum increases with excitation frequency. Unsuspectedly, during dynamic load operation, the check valve did allow for lubricant backflow into the plenum. Post-tests verification demonstrates that, under static pressure conditions, the check valve does work since it allows fluid flow in just one direction.

Relationships between symmetry-based graph measures

This paper addresses the problem of comparing different measures of graph symmetry. Two measures, each based on the number and respective sizes of the vertex orbits of the automorphism group or a graph, are compared. A real valued distance measure is used to compare the symmetry measures by establishing the limiting value of the distances for several well known classes of graphs.

Purcell-like Enhancement of Electron-Phonon Interactions in Long-Period Superlattices: Linear-Temperature Resistivity and Cooling Power.

In the Purcell effect, the efficiency of optical emitters is enhanced by reducing the optical mode volume. Here we predict an analogous enhancement for electron-phonon (el-ph) scattering, achieved by compressing the electronic Wannier orbitals. Reshaped Wannier orbitals are a prominent attribute of graphene moiré superlattices, where the orbital size is tunable by the twist angle. A reduction in the orbital size leads to an enhancement in the el-ph interaction strength, yielding the values considerably larger than those in pristine monolayer graphene. The enhanced coupling boosts the el-ph scattering rates, pushing them above the values expected for the flat-band-enhanced density of electronic states. The enhanced phonon emission and scattering rates are manifested through the observables such as the electron-lattice cooling and the linear-temperature (T) resistivity, both of which are directly tunable by the moiré twist angle.

Performance Analysis of Retrial Queueing Model with Working Vacation, Interruption, Waiting Server, Breakdown and Repair

In this present paper, an M/M/1 retrial queueing model with a waiting server subject to breakdown and repair under working vacation, vacation interruption is considered. Customers are served at a slow rate during the working vacation period, and the server may undergo breakdowns from a normal busy state. The customer has to wait in orbit for the service until the server gets repaired. Steady-state solutions are obtained using the probability generating function technique. Probabilities of different server states and some other performance measures of the system are developed. The variation in mean orbit size, availability of the server, and server state probabilities are plotted for different values of breakdown parameter and repair rate with the help of MATLAB software. Finally, cost optimization of the system is also discussed, and the optimal value of the slow service rate for the model is obtained.

Orbital Growth is Associated with Eyeball Size: A Study Using CT-based Three-dimensional Techniques

ABSTRACT Aim of the study This study was aimed to investigate the growth patterns and the relationship of the eyeball and the orbit using computed tomography (CT)-based three-dimensional (3D) techniques. Materials and Methods A total of 175 Chinese patients who had undergone craniofacial or orbital CT scans were enrolled. This study only included data from the unaffected eye and orbit. Images were processed using 3D reconstruction to obtain the eyeball and the orbit parameters. Results In early postnatal years, the sizes of eyeball and orbit increased significantly with age (p < 0.001) and reached a turning point at a critical age (8.967 and 12.800 years for the eyeball and orbit volume, respectively). The orbital index and orbital depth index, showing the shape of the orbital aperture and walls, decreased significantly with age (p < 0.001). In all ages, the orbit size was correlated with eyeball size (p < 0.001). The eye-orbit index, equivalent to the ratio of eye volume to orbital volume, declined steadily with age (p < 0.001). Conclusions The eyeball and orbit developed rapidly in early postnatal years, and then matured at a critical age. The eyeball size significantly contributed to the orbital growth; this contribution may be reduced as the eye-orbit index decreased with age. To the best of our knowledge, this is the first report on the growth and interrelation of the eyeball and the orbit using CT-based 3D techniques.

Evolution of orbit size in toothed whales (Artiodactyla: Odontoceti).

For many marine tetrapods, vision is important for finding food and navigating underwater, and eye size has increased to improve the capture of light in dim ocean depths. Odontocete whales, in contrast, rely instead on echolocation for navigation and prey capture. We tested whether the evolution of echolocation has influenced the orbit size, a proxy for eye size, and examined how orbit size evolved over time. We also assessed variation in orbit size amongst whales and tested how body size, diving ability, sound production, foraging habitat, and prey capture strategy influenced the orbit size using phylogenetic independent contrasts and phylogenetic ANOVAs. Using measurements of orbit length and bizygomatic width, we calculated proportional orbit size for 70 extant and 29 extinct whale taxa, with an emphasis on Odontoceti. We then performed ancestral character state reconstruction on a time-calibrated composite phylogeny. Our analysis revealed that there was no shift in proportional orbit size from archaeocetes through stem odontocetes, indicating that the evolution of echolocation did not influence the orbit size. Proportional orbit size increased in Ziphiidae, Phocoenidae, and Cephalorhynchus. Proportional orbit size decreased in Balaenidae, Physeteridae, Platanistidae, and Lipotidae. Body size, diving ability, foraging environment, and prey capture strategy had a significant influence on orbit size, but only without phylogenetic correction. An increase in orbit size is associated with deep diving behavior in beaked whales, while progenesis and retention of juvenile features into adulthood explain the pattern observed in Phocoenidae and Cephalorhynchus. Decrease in proportional orbit size is associated with adaptation toward murky freshwater environments in odontocetes and skim feeding in balaenids. Our study reveals that the evolution of echolocation had little effect on orbit size, which is variable in whales, and that adaptation for different feeding modes and habitat explains some of this variance.

Distance complexity measures versus the orbit-entropy measure of dendrimers

In this article, we compute several distance-based topological indices dendrimers. Indeed, based on the distances of related graphs, we investigate the distance-based complexity of these graphs. We also, determine an orbit entropy measure of these structures based on the size of orbits. The analysis results obtained by computing the correlations between given numerical data shows that the correlation between Winer complexity with GP-index, Wiener index, and Wiener polarity is quite low. As a result, we have inferred that the Wiener-complexity can be considered as new measures for quantitative structure-activity relationship/quantitative structure-property relationship (QSAR/QSPR) models of dendrimers. Hence, the W-complexity might be interesting for further investigations in predicting the physicochemical properties of molecules.

Resolving the dynamical mass tension of the massive binary 9 Sagittarii

Context. Direct dynamical mass measurements of stars with masses above 30 M⊙ are rare. This is the result of the low yield of the upper initial mass function and the limited number of such systems in eclipsing binaries. Long-period, double-lined spectroscopic binaries that are also resolved astrometrically offer an alternative to eclipsing binaries for obtaining absolute masses of stellar objects. 9 Sgr (HD 164794) is one such long-period, high-mass binary. Unfortunately, a large amount of tension exists between its total dynamical mass inferred spectroscopically from radial velocity measurements and that from astrometric data. Aims. Our goal is to resolve the mass tension of 9 Sgr that exists in literature, to characterize the fundamental parameters and surface abundances of both stars, and to determine the evolutionary status of the binary system, henceforth providing a reference calibration point to confront evolutionary models at high masses. Methods. We obtained the astrometric orbit from existing and new multi-epoch VLTI/PIONIER and VLTI/GRAVITY interferometric measurements. Using archival and new spectroscopy, we performed a grid-based spectral disentangling search to constrain the semi-amplitudes of the radial velocity curves. We computed atmospheric parameters and surface abundances by adjusting FASTWIND atmosphere models and we compared our results with evolutionary tracks computed with the Bonn Evolutionary Code (BEC). Results. Grid spectral disentangling of 9 Sgr supports the presence of a 53 M⊙ primary and a 39 M⊙ secondary, which is in excellent agreement with their observed spectral types. In combination with the size of the apparent orbit, this puts 9 Sgr at a distance of 1.31 ± 0.06 kpc. Our best-fit models reveal a large mass discrepancy between the dynamical and spectroscopic masses, which we attribute to artifacts from repeated spectral normalization before and after the disentangling process. Comparison with BEC evolutionary tracks shows the components of 9 Sgr are most likely coeval with an age of roughly 1 Myr. Conclusions. Our analysis clears up the contradiction between mass and orbital inclination estimates reported in previous studies. We detect the presence of significant CNO-processed material at the surface of the primary, suggesting enhanced internal mixing compared to currently implemented in the BEC models. The present measurements provide a high-quality high-mass anchor to validate stellar evolution models and to test the efficiency of internal mixing processes.

Orbit sizes and odd order composition factors of finite linear groups

In this paper, we study the existence of large orbits of odd-order subgroups of a finite solvable linear group G, and present some applications on bounding the odd-order parts of the chief series of an arbitrary linear group G. We also find applications to Gluck's conjecture as well as a related question of Navarro.

Focal-point approach with pair-specific cusp correction for coupled-cluster theory.

We present a basis set correction scheme for the coupled-cluster singles and doubles (CCSD) method. The scheme is based on employing frozen natural orbitals (FNOs) and diagrammatically decomposed contributions to the electronic correlation energy, which dominate the basis set incompleteness error (BSIE). As recently discussed in the work of Irmler et al. [Phys. Rev. Lett. 123, 156401 (2019)], the BSIE of the CCSD correlation energy is dominated by the second-order Møller-Plesset (MP2) perturbation energy and the particle-particle ladder term. Here, we derive a simple approximation to the BSIE of the particle-particle ladder term that effectively corresponds to a rescaled pair-specific MP2 BSIE, where the scaling factor depends on the spatially averaged correlation hole depth of the coupled-cluster and first-order pair wavefunctions. The evaluation of the derived expressions is simple to implement in any existing code. We demonstrate the effectiveness of the method for the uniform electron gas. Furthermore, we apply the method to coupled-cluster theory calculations of atoms and molecules using FNOs. Employing the proposed correction and an increasing number of FNOs per occupied orbital, we demonstrate for a test set that rapidly convergent closed and open-shell reaction energies, atomization energies, electron affinities, and ionization potentials can be obtained. Moreover, we show that a similarly excellent trade-off between required virtual orbital basis set size and remaining BSIEs can be achieved for the perturbative triples contribution to the CCSD(T) energy employing FNOs and the (T*) approximation.

Orbital floor fractures: epidemiology and outcomes of 1594 reconstructions

ObjectiveThe aim of this study was to retrospectively review the midface and orbital floor fractures treated at our institution with regard to epidemiological aspects, surgical treatment options and postoperative complications and discuss this data with the current literature.Study designOne thousand five hundred and ninety-four patients with midface and orbital fractures treated at the Department of Oral, Cranio-Maxillofacial and Facial Plastic Surgery of the Goethe University Hospital in Frankfurt (Germany) between 2007 and 2017 were retrospectively reviewed. The patients were evaluated by age, gender, etiology, fracture pattern, defect size, surgical treatment and complications.ResultsThe average patient age was 46.2 (± 20.8). Most fractures (37.5%) occurred in the age between 16 and 35. Seventy-two percent of patients were male while 28% were female. The most common cause of injury was physical assault (32.0%) followed by falls (30.8%) and traffic accidents (17.0%). The average orbital wall defect size was 297.9 mm2 (± 190.8 mm2). For orbital floor reconstruction polydioxanone sheets (0.15 mm 38.3%, 0.25 mm 36.2%, 0.5 mm 2.8%) were mainly used, followed by titanium meshes (11.5%). Reconstructions with the 0.15 mm polydioxanone sheets showed the least complications (p < 0.01, r = 0.15). Eighteen percent of patients who showed persistent symptoms and post-operative complications: 12.9% suffered from persistent hypoesthesia, 4.4% suffered from post-operative diplopia and 3.9% showed intra-orbital hematoma.ConclusionResults of the clinical outcome in our patients show that 0.15 mm resorbable polydioxanone sheets leads to significantly less post-operative complications for orbital floor defects even for defects beyond the recommended 200 mm2.

Asymmetric Rydberg blockade of giant excitons in Cuprous Oxide

The ability to generate and control strong long-range interactions via highly excited electronic states has been the foundation for recent breakthroughs in a host of areas, from atomic and molecular physics to quantum optics and technology. Rydberg excitons provide a promising solid-state realization of such highly excited states, for which record-breaking orbital sizes of up to a micrometer have indeed been observed in cuprous oxide semiconductors. Here, we demonstrate the generation and control of strong exciton interactions in this material by optically producing two distinct quantum states of Rydberg excitons. This is made possible by two-color pump-probe experiments that allow for a detailed probing of the interactions. Our experiments reveal the emergence of strong spatial correlations and an inter-state Rydberg blockade that extends over remarkably large distances of several micrometers. The generated many-body states of semiconductor excitons exhibit universal properties that only depend on the shape of the interaction potential and yield clear evidence for its vastly extended-range and power-law character.

Combinatorial invariants for nets of conics in mathrm {PG}(2,q)

The problem of classifying linear systems of conics in projective planes dates back at least to Jordan, who classified pencils (one-dimensional systems) of conics over {mathbb {C}} and mathbb {R} in 1906–1907. The analogous problem for finite fields mathbb {F}_q with q odd was solved by Dickson in 1908. In 1914, Wilson attempted to classify nets (two-dimensional systems) of conics over finite fields of odd characteristic, but his classification was incomplete and contained some inaccuracies. In a recent article, we completed Wilson’s classification (for q odd) of nets of rank one, namely those containing a repeated line. The aim of the present paper is to introduce and calculate certain combinatorial invariants of these nets, which we expect will be of use in various applications. Our approach is geometric in the sense that we view a net of rank one as a plane in mathrm {PG}(5,q), q odd, that meets the quadric Veronesean in at least one point; two such nets are then equivalent if and only if the corresponding planes belong to the same orbit under the induced action of mathrm {PGL}(3,q) viewed as a subgroup of mathrm {PGL}(6,q). Since q is odd, the orbits of lines in mathrm {PG}(5,q) under this action correspond to the aforementioned pencils of conics in mathrm {PG}(2,q). The main contribution of this paper is to determine the line-orbit distribution of a plane pi corresponding to a net of rank one, namely, the number of lines in pi belonging to each line orbit. It turns out that this list of invariants completely determines the orbit of pi , and we will use this fact in forthcoming work to develop an efficient algorithm for calculating the orbit of a given net of rank one. As a more immediate application, we also determine the stabilisers of nets of rank one in mathrm {PGL}(3,q), and hence the orbit sizes.

Find the food first: An omnivorous sensory morphotype predates biomechanical specialization for plant based diets in phyllostomid bats.

The role of mechanical morphologies in the exploitation of novel niche space is well characterized; however, the role of sensory structures in unlocking new niches is less clear. Here, we investigate the relationship between the evolution of sensory structures and diet during the radiation of noctilionoid bats. With a broad range of foraging ecologies and a well-supported phylogeny, noctilionoids constitute an ideal group for studying this relationship. We used diffusible iodine-based contrast enhanced computed tomography scans of 44 noctilionoid species to analyze relationships between the relative volumes of three sensory structures (olfactory bulbs, orbits, and cochleae) and diet. We found a positive relationship between frugivory and both olfactory and orbit size. However, we also found a negative relationship between nectarivory and cochlea size. Ancestral state estimates suggest that larger orbits and olfactory bulbs were present in the common ancestor of family Phyllostomidae, but not in other noctilionoid. This constellation of traits indicates a shift toward omnivory at the base of Phyllostomidae, predating their radiation into an exceptionally broad range of dietary niches. This is consistent with a scenario in which changes in sensory systems associated with foraging and feeding set the stage for subsequent morphological modification and diversification.

On the Roots of the Modified Orbit Polynomial of a Graph

The definition of orbit polynomial is based on the size of orbits of a graph which is OG(x)=∑ix|Oi|, where O1,…,Ok are all orbits of graph G. It is a well-known fact that according to Descartes’ rule of signs, the new polynomial 1−OG(x) has a positive root in (0,1), which is unique and it is a relevant measure of the symmetry of a graph. In the current work, several bounds for the unique and positive zero of modified orbit polynomial 1−OG(x) are investigated. Besides, the relation between the unique positive root of OG in terms of the structure of G is presented.