Period Orbit Research Articles

Physical and Mutual Orbit Characteristics of Near-Earth Binary Asteroid (163693) Atira

We report physical and mutual orbit characteristics of near-Earth binary asteroid (163693) Atira. Using S-band (2380 MHz, 12.6 cm) radar observations from the Arecibo Observatory and several epochs of lightcurve observations from 2003 to 2019 with SHAPE modeling software, we determine the shape, size, rotational period, and mutual orbit of the primary and secondary components and the density of the primary component. We confirm the primary’s sidereal rotation period to be 3.398521 ± 0.000003 hr, and we find a likely spin axis orientation of ecliptic longitude and latitude (187°, −53°) ± 12°. We find the primary’s volume-equivalent diameter to be 4.92 ± 0.95 km and the secondary’s volume-equivalent diameter to be 0.80 ± 0.30 km. We find the primary component’s density to be 1.43 ± 0.87 g cm−3. We also find that the secondary has a semimajor axis of 7.8 ± 0.5 km and a sidereal orbital period of 15.577 ± 0.003 hr based on orbital calculations using delay and Doppler offsets between the primary and secondary and the timing of mutual events observed in lightcurve data. This work represents the first detailed analysis of the shape of an Atira-class asteroid.

Is WR 104 a face-on, colliding-wind binary?

ABSTRACT Two decades of extensive spectroscopic monitoring of WR 104 is used to confront what we think we understand about this iconic prototype of the dust-producing pinwheel stars. Convincing SB1 orbital solutions are obtained for both the WC9d star and its OB companion. The period ($241.54 \pm 0.14$ d) and circular orbit agree perfectly with results from modelling images of the rotating dust spiral. Contrary to those results though, the orbit is found to be significantly inclined instead of face-on. The two SB1 solutions each indicate $i \sim 45^{\circ }$ but could be as low as $\sim 34^{\circ }$. This result naturally provides an explanation for the long puzzling photometric and emission line strength variations but is difficult to reconcile with the imaging. Confirmation that colliding winds are present is found by the detection of variable excess emission in two of the lines where it would be most expected. The changing shapes of this excess emission are not perfectly phase-locked though, which will complicate future modelling.

Climate change in hell: Long-term variation in transits of the evaporating planet K2-22b

Rocky planets on ultra-short period orbits can have surface magma oceans and rock-vapour atmospheres in which dust can condense. Observations of that dust can inform us about the composition and surface conditions on these objects. We constrained the properties and long-term (decade) behaviour of the transiting dust cloud from the evaporating planet K2-22b. We observed K2-22b around 40 predicted transits with MuSCAT ground-based multi-optical channel imagers, and complemented these data with long-term monitoring by the ground-based ATLAS (2018-2024) and space-based (2021-2023) surveys. We detected signals during 7 transits, none of which showed significant wavelength dependence. The expected number of MuSCAT-detected transits is $ indicating a decline in mean transit depth since the discovery observations in 2014. The lack of a significant wavelength dependence indicates that dust grains are large or the cloud is optically thick. Long-term trends of depth could be due to a magnetic cycle on the host star or to overturn of the planet's dayside surface magma ocean. The possibility that K2-22b is disappearing altogether is ruled out by the stability of the transit ephemeris against non-gravitational forces, which constrains the mass to be at least comparable to Ceres.

A Perfect Tidal Storm: HD 104067 Planetary Architecture Creating an Incandescent World

The discovery of planetary systems beyond the solar system has revealed a diversity of architectures, most of which differ significantly from our system. The initial detection of an exoplanet is often followed by subsequent discoveries within the same system as observations continue, measurement precision is improved, or additional techniques are employed. The HD 104067 system is known to consist of a bright K-dwarf host star and a giant planet in a ∼55 days period eccentric orbit. Here we report the discovery of an additional planet within the HD 104067 system, detected through the combined analysis of radial velocity (RV) data from the High Resolution Echelle Spectrometer and High Accuracy Radial velocity Planet Searcher instruments. The new planet has a mass similar to Uranus and is in an eccentric ∼14 days orbit. Our injection-recovery analysis of the RV data exclude Saturn-mass and Jupiter-mass planets out to 3 au and 8 au, respectively. We further present Transiting Exoplanet Survey Satellite observations that reveal a terrestrial planet candidate (R p = 1.30 ± 0.12 R ⊕) in a ∼2.2 days period orbit. Our dynamical analysis of the three planet model shows that the two outer planets produce significant eccentricity excitation of the inner planet, resulting in tidally induced surface temperatures as high as ∼2600 K for an emissivity of unity. The terrestrial planet candidate may therefore be caught in a tidal storm, potentially resulting in its surface radiating at optical wavelengths.

Chaotic dynamics of a three-species food chain model

An analysis of a discrete-time food chain model is presented in this paper to investigate the effects of strong prey pressure on the chain. A bifurcation and stability theory is used to analyze equilibrium formation in system. It is shown by numerical simulations that chaos occurs as a result of the bifurcation of invariant curves following Neimark-Sacker (NS) bifurcation rules. The OGY method on stable periodic orbits of period 1 further controls chaos. Stability is achieved through iterations for chaotic motion controlled by different regulator poles. Numerical simulations are performed to examine the effects of the control method along with the results of our theoretical analysis.

On stable and quasi-chaotic regimes in a one-dimensional unimodal mapping obtained by modeling the dynamics of a biological population

The paper considers the properties of the difference equation describing the dynamics of the animal population, obtained earlier in the framework of studies of tundra communities. We have considered a special case in which the model is represented by a one-parameter difference equation that defines a one-dimensional unimodal mapping of a segment into itself, similar to the well-known triangular (tent) mapping, supplemented by a region with a constant value. A change in the mapping parameter generates a bifurcation scenario, in which stability zones arise, characterized by orbits of a constant period, interspersed with zones with more complicated, “quasi-chaotic” regimes. Based on the properties of the n-iterated triangular mapping, a necessary and sufficient condition for the localization of cyclic orbits in the considered type of unimodal mappings is formulated, which makes it possible to identify stability regions for any given period n. On the basis of this condition an algorithm for detecting stability zones is proposed. The main subject of the study is the fractal properties of the set, which is the complement of the obtained set of stability regions to the entire domain of mapping definition. The dynamics of the DH (n) value is obtained, the limit of which at n → ∞ is equal to the fractal dimension dH . It is shown that in the studied range of n (2 ≤ n ≤ 22), the DH (n) < 0.9, which suggest that dH < 1. If so, then according to the definition of a fractal set, its topological dimension is dT = 0, which means that the complement of the set of stability regions consists of isolated points.

The Periodic Integer Orbits of Polynomial Recursions With Integer Coefficients

We show that polynomial recursions $x_{n+1}=x_{n}^{m}-k$ where $k,m$ are integers and $m$ is positive have no nontrivial periodic integral orbits for $m\geq3$. If $m=2$ then the recursion has integral two-cycles for infinitely many values of $k$ but no higher period orbits. We also show that these statements are true for all quadratic recursions.

Memory loss can prevent chaos in games dynamics.

Recent studies have raised concerns on the inevitability of chaos in congestion games with large learning rates. We further investigate this phenomenon by exploring the learning dynamics in simple two-resource congestion games, where a continuum of agents learns according to a simplified experience-weighted attraction algorithm. The model is characterized by three key parameters: a population intensity of choice (learning rate), a discount factor (recency bias or exploration parameter), and the cost function asymmetry. The intensity of choice captures agents' economic rationality in their tendency to approximately best respond to the other agent's behavior. The discount factor captures a type of memory loss of agents, where past outcomes matter exponentially less than the recent ones. Our main findings reveal that while increasing the intensity of choice destabilizes the system for any discount factor, whether the resulting dynamics remains predictable or becomes unpredictable and chaotic depends on both the memory loss and the cost asymmetry. As memory loss increases, the chaotic regime gives place to a periodic orbit of period 2 that is globally attracting except for a countable set of points that lead to the equilibrium. Therefore, memory loss can suppress chaotic behaviors. The results highlight the crucial role of memory loss in mitigating chaos and promoting predictable outcomes in congestion games, providing insights into designing control strategies in resource allocation systems susceptible to chaotic behaviors.

Braids and linked periodic orbits of disc homeomorphisms

This paper concerns on linked periodic orbits of orientation-preserving homeomorphisms of the 2-disc in the sense of Gambaudo. We interpret the linking of periodic orbits by using their induced braids. Then based on the forcing relation of braids, we present a method for finding periodic orbits which are linked with a given one. In particular, for 3-periodic orbits of pseudo-Anosov braid types, we provide new examples of linked orbits of periods at most 4.

Order-chaos transition in correlation diagrams and quantization of period orbits.

Eigenlevel correlation diagrams has proven to be a very useful tool to understand eigenstate characteristics of classically chaotic systems. In particular, we showed in a previous publication [Phys. Rev. Lett. 80, 944 (1998)0031-900710.1103/PhysRevLett.80.944] how to unveil the scarring mechanism, a cornerstone in the theory of quantum chaos, using the Planck constant as the correlation parameter. By increasing the Planck constant, we induced a transition from order to chaos, in which scarred wave functions appeared as the interaction of pairs of eigenstates in broad avoided crossings, forming a well-defined frontier in the correlation diagram. In this paper, we demonstrate that this frontier can be obtained by means of the semiclassical quantization of the involved scarring periodic orbits. Additionally, in order to calculate the Maslov index of each scarring periodic orbit, which is necessary for the semiclassical quantization procedure, we introduce a straightforward method based on Lagrangian descriptors. We illustrate the theory using the vibrational eigenstates of the LiCN molecular system.

Periodic orbits in a near Yang-Mills potential

We study numerically the orbits in the Yang-Mills (YM) potential and in the potentials of the general form . We found that the stable period-9 periodic orbit of the YM potential belongs to a family of orbits that bifurcates from a basic period-9 family of the general form of the potential V, when α is slightly above zero. This basic period-9 family and its bifurcations exist only up to a maximum value of . We calculate the Hénon stability index of these orbits. The pattern of the stability diagram is the same for all the symmetric orbits of odd periods 3,5,7,9 and 11, that we have found. We also found the stability diagrams for asymmetric orbits of period 2,3,4,5 which have again the same pattern. All these orbits are unstable for α=0 (YM potential) except for the stable orbits of period-9 and some orbits with multiples of 9 periods.

Meta-Machine-Learning-Based Quantum Scar Detector

A remarkable phenomenon in contemporary physics is quantum scarring in systems whose classical dynamics are chaotic, where certain wave functions tend to concentrate on classical periodic orbits of low periods. Quantum scarring has been studied for more than four decades, but detecting quantum scars still mostly relies on human visualization of the wave-function patterns. The widespread and successful applications of machine learning in many branches of physics suggest the possibility of using artificial neural networks for automated detection of quantum scars. Conventional machine learning often requires substantial training data, but, for quantum scars, this poses a significant challenge: in typical systems the available distinct quantum scarring states are rare. We develop a meta machine-learning approach to accurately detect quantum scars in a fully automated and highly efficient fashion. In particular, taking advantage of some standard large datasets such as Omniglot from the field of image classification, we train a ``preliminary'' version of the neural network that has the ability to distinguish different classes of noisy images. We then perform few-shot classification to further train the neural network but with a small number of quantum scars. We demonstrate that the meta-learning scheme can find the correct quantum scars from thousands of images of wave functions without any human intervention, regardless of the symmetry of the underlying system. From a general applied point of view, our success opens the door to exploiting meta learning for solving challenging image detection and classification problems in other fields of science and engineering. For example, in microlasing systems, identifying scarring states is critical as these states are desired for directional emission. The task is also important for quantum-dot devices where the scarring states can lead to resonances in the conductance.

High-order analytical solutions of bounded relative motions for Coulomb formation flying

Close-proximity Coulomb formation flying offers attractive prospects in multiple astronautical missions. A semi-analytical method of constructing the series solution up to an arbitrary order for the relative motion near the equilibrium of Coulomb formation systems is proposed to facilitate the design of Coulomb formations based on a Lindstedt–Poincaré method. The details of the series expansion and coefficient solution for arbitrary $$m\!:\!n$$ -period orbits are discussed. To verify the effectiveness of the proposed method, the practical convergence domain of the high-order series solution is computed by comparing it with corresponding numerical solutions that satisfy the specified boundary conditions. Simulation results demonstrate the efficacy of the Lindstedt–Poincaré method in constructing series solutions for the relative motion of Coulomb formation systems.

The X-ray activity of F stars with hot Jupiters: KELT-24 versus WASP-18

X-rays emitted by the coronae of solar-type stars are a feature present in up to late-A types during the main sequence phase. F stars, either with or without hot Jupiters, are usually X-ray emitters. The very low level of X-ray emission of the F5 star WASP-18 despite its relatively young age and spectral type is thus quite peculiar. In this paper we compare the X-ray activity of KELT-24 to that of WASP-18. KELT-24 is an F5 star nearly coeval to the Hyades stars that hosts a 5 MJup in a 5.6-day period orbit. The properties of the KELT-24 system are similar to, although less extreme than, those of WASP-18. We observed KELT-24 with XMM-Newton for a total of 43 ks in order to test if the X-ray activity of this star is depressed by the interaction with its massive hot Jupiter, as is the case of WASP-18. KELT-24 is detected in combined EPIC images with a high significance level. Its average coronal spectrum is well described by a cool component at 0.36 keV and a hotter component at 0.98 keV. We detected a flare with a duration of about 2 ks, during which the coronal temperature reached 3.5 keV. The unabsorbed quiescent flux in 0.3–8.0 keV is ∼1.33 × 10−13 erg s−1 cm−2, corresponding to a luminosity of 1.5 × 1029 erg s−1 at the distance of the star. The luminosity is well within the range of the typical X-ray luminosity of F stars in Hyades, which are coeval. We conclude that the activity of KELT-24 appears normal, as expected, and is not affected by any star–planet interaction. From the analysis of TESS light curves, we infer a distribution of optical flares for KELT-24 and WASP-18. Small optical flickering similar to flares is recognized in WASP-18 but at lower levels of energy and amplitude than in KELT-24. We discuss the causes of the low activity of WASP-18. Either WASP-18b could hamper the formation of a corona bright in X-rays in its host star through some form of tidal interaction, or the star has entered a minimum of activity similar to the solar Maunder minimum. This latter hypothesis would make WASP-18 among the few candidates showing such a quench of stellar activity.

Chaotic renormalization group flow and entropy gradients over Haros graphs.

Haros graphs have been recently introduced as a set of graphs bijectively related to real numbers in the unit interval. Here we consider the iterated dynamics of a graph operator R over the set of Haros graphs. This operator was previously defined in the realm of graph-theoretical characterization of low-dimensional nonlinear dynamics and has a renormalization group (RG) structure. We find that the dynamics of R over Haros graphs is complex and includes unstable periodic orbits of arbitrary period and nonmixing aperiodic orbits, overall portraiting a chaotic RG flow. We identify a single RG stable fixed point whose basin of attraction is associated with the set of rational numbers, and find periodic RG orbits that relate to (pure) quadratic irrationals and aperiodic RG orbits, related with (nonmixing) families of nonquadratic algebraic irrationals and transcendental numbers. Finally, we show that the graph entropy of Haros graphs is globally decreasing as the RG flows towards its stable fixed point, albeit in a strictly nonmonotonic way, and that such graph entropy remains constant inside the periodic RG orbit associated to a subset of irrationals, the so-called metallic ratios. We discuss the possible physical interpretation of such chaotic RG flow and put results regarding entropy gradients along RG flow in the context of c-theorems.

Existence and stability of the periodic orbits induced by grazing bifurcation in a cantilever beam system with single rigid impacting constraint

Grazing, which can induce many nonclassical bifurcations, is a special dynamic phenomenon in some non-smooth dynamical systems such as vibro-impact systems with clearance. In this paper, the existence and stability of the periodic orbits induced by the grazing bifurcation in a cantilever beam system with impacts are uncovered. Firstly, the Poincaré mapping of the system is obtained by adopting the discontinuous mapping method. Then, by means of shooting method, the periodic orbits are determined, followed by the acquisition of Jacobian matrix in the case of non-impact is obtained subsequently. In addition, for various impacting patterns, a combination of inhomogeneous equations and inequations is obtained to determine the existence of period orbits after grazing, with the stability criterion of the grazing-induced periodic orbits given. Numerical results verify the effectiveness of theoretical analysis. What is more, we also give a conjecture about the relationship between eigenvalues and the type of periodic orbits when eigenvalues are imaginary numbers.

Fictitious time integration method for seeking periodic orbits of nonlinear dynamical systems

In the paper, we compute the period and periodic orbit of an n-dimensional nonlinear dynamical system by developing two iterative algorithms based on the fictitious time integration method (FTIM). Periodicity condition, also known as the Poincaré map, is a necessary condition for the existence of a periodic motion in the state space, which consists of n implicit nonlinear algebraic equations (NAEs). Instead of solving the NAEs by the Newton–Raphson method, we derive an equivalent nonlinear scalar equation to determine unknown period by using the FTIM. The resulting sequence of the iterated periods monotonically converges to a desired period, wherein the unknown initial point on the periodic orbit is determined simultaneously. We find that the second iterative algorithm using the matrix shape function to convert the periodic problem into a corresponding initial value problem is convergent faster than the first iterative algorithm. A key point is that the periodicity condition is satisfied automatically by the second iterative algorithm when the terminal values of the new variables are convergent. Numerical examples exhibit some major advantages of these two iterative algorithms.

Bifurcation Analysis of a Discrete‐Time Chemostat Model

In this article, a discretized two‐dimensional chemostat model is investigated. By using the algebraic technique, it is proved that the discrete chemostat model has semitrivial equilibrium solution for all involved parametric values, but it has an interior equilibrium solution under certain parametric conditions. We have studied the local dynamics with topological classifications about the semitrivial and interior equilibrium solution on the basis of the theory of the discrete dynamical system. By bifurcation theory, we studied the existence of bifurcations for the understudied discrete chemostat model and proved that at a semitrivial equilibrium solution, it did not undergo flip bifurcation, but it undergoes flip bifurcation at interior equilibrium solution, and no other bifurcation occurs at this point. It has also explored the existence of periodic points and chaos control by the state feedback method. Finally, with the help of MATLAB software, flip bifurcation diagrams and corresponding maximum Lyapunov exponents were also presented. These numerical simulations not only show the correctness of theoretical results but also reveal the complex dynamics such as the orbits of period −7, −8, −13, and −16.

Passive periodic motion of an asymmetric spring loaded inverted pendulum hopping robot

For improving the energy efficiency of hopping robot, an asymmetric spring loaded inverted pendulum hopping model with leg mass is considered. The period orbit problem of two-legged hopping robot is investigated. Firstly, the hybrid dynamic model is constructed. Then the passive hopping gaits are found using quasi-newton optimization method. Secondly, a PD controller is implemented to track the desired pitch trajectory of the body. Through applying control during stance phase, period orbits of the robot with offset body mass is obtained. Finally, the effect of the location of the leg mass and the body mass on hopping performances is investigated.

Radial velocity confirmation of a hot super-Neptune discovered by TESS with a warm Saturn–mass companion

ABSTRACT We report the discovery and confirmation of the planetary system TOI-1288. This late G dwarf harbours two planets: TOI-1288 b and TOI-1288 c. We combine TESS space-borne and ground-based transit photometry with HARPS-N and HIRES high-precision Doppler measurements, which we use to constrain the masses of both planets in the system and the radius of planet b. TOI-1288 b has a period of $2.699835^{+0.000004}_{-0.000003}$ d, a radius of 5.24 ± 0.09 R⊕, and a mass of 42 ± 3 M⊕, making this planet a hot transiting super-Neptune situated right in the Neptunian desert. This desert refers to a paucity of Neptune-sized planets on short period orbits. Our 2.4-yr-long Doppler monitoring of TOI-1288 revealed the presence of a Saturn–mass planet on a moderately eccentric orbit ($0.13^{+0.07}_{-0.09}$) with a minimum mass of 84 ± 7 M⊕ and a period of $443^{+11}_{-13}$ d. The five sectors worth of TESS data do not cover our expected mid-transit time for TOI-1288 c, and we do not detect a transit for this planet in these sectors.