The Axisymmetric Central Configurations of the Four-Body Problem with Three Equal Masses

In the studied axisymmetric case of the central four-body problem, the axis of symmetry is defined by two unequal-mass bodies, while the other two bodies are situated symmetrically with respect to this axis and have equal masses. Here, we consider a special case of the problem and assume that three of the masses are equal. Using a recently found analytical solution of the general case, we formulate the equations of condition for three equal masses analytically and solve them numerically. A complete description of the problem is given by providing both the coordinates and masses of the bodies. We show furthermore how the three-equal-mass solutions are related to the general case in the coordinate space. The physical aspects of the configurations are also studied and discussed.Comment: 16 pages, 8 figures, appeared in the open-access journal Symmetry (special issue: Astronomy and Symmetry

Application of the Shannon entropy in the planar (non-restricted) four-body problem: the long-term stability of the Kepler-60 exoplanetary system

In this paper, we present an application of the Shannon entropy in the case of the planar (non-restricted) four-body problem. Specifically, the Kepler-60 extrasolar system is being investigated with a primary interest in the resonant configuration of the planets that exhibit a chain of mean-motion commensurabilities with the ratios 5:4:3. In the dynamical maps provided, the Shannon entropy is utilized to explore the general structure of the phase space, while, based on the time evolution of the entropy, we determine also the extent and rate of the chaotic diffusion as well as the characteristic times of stability for the planets. Two cases are considered: (i) the pure Laplace resonance when the critical angles of the 2-body resonances circulate and that of the 3-body resonance librates; and (ii) the chain of two 2-body resonances when all the critical angles librate. Our results suggest that case (ii) is the more favourable configuration but we state too that, in either case, the relevant resonance plays an important role to stabilize the system. The derived stability times are no shorter than $10^8$ yrs in the central parts of the resonances.Comment: 10 pages, 8 figures, accepted for publication in the open-access journal MNRA

Multi-Agent Reinforcement Learning for Railway Rescheduling

Malfunctions, congestions, and accidents occur in every railway system from time to time, which influences the railway traffic on a given section of the system. The disturbance may cause inconvenience for several passengers and disruption in rail freight. Both the schedule and route of the affected trains must be modified to avoid further congestion and minimalize delays. The rigidity of the railway system (e.g., single tracks, vast distances without a service station, no viable alternative in case of malfunction) poses restrictions, unlike other transportation systems. Replanning schedules and train routes (called the railway rescheduling problem) is complex and demanding, even for human operators, as one must consider numerous factors. Thus, finding a satisfying solution poses a significant challenge. This paper presents a MARL-base (Multi-Agent Reinforcement Learning) solution that shows great potential for tackling this problem, even in the case of multiple connected stations

Multi-Agent Reinforcement Learning for Traffic Signal Control: A Cooperative Approach

The rapid growth of urbanization and the constant demand for mobility have put a great strain on transportation systems in cities. One of the major challenges in these areas is traffic congestion, particularly at signalized intersections. This problem not only leads to longer travel times for commuters, but also results in a significant increase in local and global emissions. The fixed cycle of traffic lights at these intersections is one of the primary reasons for this issue. To address these challenges, applying reinforcement learning to coordinating traffic light controllers has become a highly researched topic in the field of transportation engineering. This paper focuses on the traffic signal control problem, proposing a solution using a multi-agent deep Q-learning algorithm. This study introduces a novel rewarding concept in the multi-agent environment, as the reward schemes have yet to evolve in the following years with the advancement of techniques. The goal of this study is to manage traffic networks in a more efficient manner, taking into account both sustainability and classic measures. The results of this study indicate that the proposed approach can bring about significant improvements in transportation systems. For instance, the proposed approach can reduce fuel consumption by 11% and average travel time by 13%. The results of this study demonstrate the potential of reinforcement learning in improving the coordination of traffic light controllers and reducing the negative impacts of traffic congestion in urban areas. The implementation of this proposed solution could contribute to a more sustainable and efficient transportation system in the future

Environment Representations of Railway Infrastructure for Reinforcement Learning-Based Traffic Control

The real-time railway rescheduling problem is a crucial challenge for human operators since many factors have to be considered during decision making, from the positions and velocities of the vehicles to the different regulations of the individual railway companies. Thanks to that, human operators cannot be expected to provide optimal decisions in a particular situation. Based on the recent successes of multi-agent deep reinforcement learning in challenging control problems, it seems like a suitable choice for such a domain. Consequently, this paper proposes a multi-agent deep reinforcement learning-based approach with different state representational choices to solve the real-time railway rescheduling problem. Furthermore, comparing different methods, the proposed learning-based approaches outperform their competitions, such as the Monte Carlo tree search algorithm, which is utilized as a model-based planner, and also other learning-based methods that utilize different abstractions. The results show that the proposed representation has more significant generalization potential and provides superior performance

Multi-Agent Deep Reinforcement Learning (MADRL) for Solving Real-Time Railway Rescheduling Problem

The real-time railway rescheduling problem is a challenging task since several factors have to be considered when a train deviates from the initial timetable. Nowadays, the problem is solved by human operators, which is safe but not optimal. This paper proposes a novel state representation for the introduced control problem that enables the efficient utilization of Multi-Agent Deep Reinforcement Learning. To support our claim, a proof of concept network is implemented, and the performance of the trained agent is evaluated. The results show that our approach enables fast convergence and excellent performance, while the representation has the potential for solving much more complex networks

Surface activity of the G dwarf primary in the quaternary star system V815 Her

We investigate the magnetic activity of the G dwarf primary star in the multiple system V815 Herculis. Recently, TESS Sector 26 data have revealed that V815 Her is in fact a four-star system consisting of two close binaries in a long-period orbit. We give preliminary orbital solution for the long-known but unseen "third body" V815 Her `B', which is itself a close eclipsing binary of two M dwarfs. Long-term spot activity of the G dwarf is presented along with the very first Doppler image reconstructions of its spotted surface.Comment: 3 pages, poster paper presented at the 21th Cambridge Workshop on Cool Stars, Stellar Systems, and the Sun (Toulouse, France) in 202

Superflares on the late-type giant KIC 2852961. Scaling effect behind flaring at different energy levels

Context. The most powerful superflares reaching 1039 erg bolometric energy are from giant stars. The mechanism behind flaring is thought to be the magnetic reconnection, which is closely related to magnetic activity (including starspots). However, it is poorly understood how the underlying magnetic dynamo works and how the flare activity is related to the stellar properties that eventually control the dynamo action. Aims: We analyze the flaring activity of KIC 2852961, a late-type giant star, in order to understand how its flare statistics are related to those of other stars with flares and superflares, and to understand the role of the observed stellar properties in generating flares. Methods: We searched for flares in the full Kepler dataset of KIC 2852961 using an automated technique together with visual inspection. We cross-matched the flare-like events detected by the two different approaches and set a final list of 59 verified flares during the observing term. We calculated flare energies for the sample and performed a statistical analysis. Results: The stellar properties of KIC 2852961 are revised and a more consistent set of parameters are proposed. The cumulative flare energy distribution can be characterized by a broken power law; that is to say, on the log-log representation the distribution function is fitted by two linear functions with different slopes, depending on the energy range fitted. We find that the total flare energy integrated over a few rotation periods correlates with the average amplitude of the rotational modulation due to starspots. Conclusions: Flares and superflares seem to be the result of the same physical mechanism at different energy levels, also implying that late-type stars in the main sequence and flaring giant stars have the same underlying physical process for emitting flares. There might be a scaling effect behind the generation of flares and superflares in the sense that the higher the magnetic activity, the higher the overall magnetic energy released by flares and/or superflares