About

Zhihong Jeff Xia is a faculty member involved in the RTG Dynamics: Classical, Modern, and Quantum at Northwestern University. His work is part of a research group that supports activities to expose young researchers to dynamical systems in the broad sense. The group aims to increase the strength of research in the field of dynamics, which describes the time-evolution of mechanical systems and abstract models of such systems. The research and training activities supported by this group include summer thematic schools, research workshops, and undergraduate research experiences, all designed to enhance training across the US. The research in this group, including the work of Professor Xia, covers a vibrant area of mathematics originating with Poincare in celestial mechanics. The focus is on understanding the dynamics of mechanical systems and their abstract models. The group emphasizes bringing more researchers into the field of dynamical systems to create a strong and educated workforce, with vertically integrated mentoring in all programs. The goal is to improve training in dynamics to boost US competitiveness in this internationally visible field, with broader dissemination through public lectures. The faculty involved, including Professor Xia, have specialties that span a wide range of dynamical fields and interact with numerous other areas of mathematics.

Research topics

• Astrophysics
• Physics
• Astronomy
• Mathematics
• Artificial Intelligence
• Computer Science
• Algorithm
• Quantum mechanics
• Paleontology
• Statistical physics
• Geology
• Geometry
• Optics
• Particle physics
• Mathematical physics
• Aerospace engineering
• Classical mechanics

Selected publications

• Asymmetry in the number of L4 and L5 Jupiter Trojans driven by jumping Jupiter

  Astronomy and Astrophysics · 2022 · 25 citations

  • Physics
  • Astrophysics
  • Astronomy

  Context. More than 10 000 Jupiter Trojans have been detected so far. They are moving around the L4 and L5 triangular Lagrangian points of the Sun-Jupiter system and their distributions can provide important clues about the early evolution of the Solar System. Aims. The number asymmetry of the L4 and L5 Jupiter Trojans is a longstanding problem. We aim to test a new mechanism in order to explain this anomalous feature by invoking the jumping-Jupiter scenario. Methods. First, we introduce the orbital evolution of Jupiter caused by the giant planet instability in the early Solar System. In this scenario, Jupiter could undergo an outward migration at a very high speed. We then investigate how such a jump changes the numbers of the L4 ( N 4 ) and L5 ( N 5 ) Trojans. Results. The outward migration of Jupiter can distort the co-orbital orbits near the Lagrangian points, resulting in L4 Trojans being more stable than the L5 ones. We find that this mechanism could potentially explain the unbiased number asymmetry of N 4 / N 5 ~ 1.6 for the known Jupiter Trojans. The uncertainties of the system parameters, such as Jupiter’s eccentricity and inclination as well as the inclination distribution of Jupiter Trojans, are also taken into account and our results about the L4/L5 asymmetry have been further validated. However, the resonant amplitudes of the simulated Trojans are excited to higher values compared to the current population. A possible solution is that collisions among the Trojans may reduce their resonant amplitudes.

  DOI

• Machine-learning prediction for mean motion resonance behaviour – The planar case

  Monthly Notices of the Royal Astronomical Society · 2022 · 9 citations

  • Artificial Intelligence
  • Computer Science
  • Physics

  ABSTRACT Most recently, machine learning has been used to study the dynamics of integrable Hamiltonian systems and the chaotic 3-body problem. In this work, we consider an intermediate case of regular motion in a non-integrable system: the behaviour of objects in the 2:3 mean motion resonance with Neptune. We show that, given initial data from a short 6250 yr numerical integration, the best-trained artificial neural network (ANN) can predict the trajectories of the 2:3 resonators over the subsequent 18 750 yr evolution, covering a full libration cycle over the combined time period. By comparing our ANN’s prediction of the resonant angle to the outcome of numerical integrations, the former can predict the resonant angle with an accuracy as small as of a few degrees only, while it has the advantage of considerably saving computational time. More specifically, the trained ANN can effectively measure the resonant amplitudes of the 2:3 resonators, and thus provides a fast approach that can identify the resonant candidates. This may be helpful in classifying a huge population of KBOs to be discovered in future surveys.

  DOI

• Mean plane of the Kuiper belt beyond 50 AU in the presence of Planet 9

  Astronomy and Astrophysics · 2020 · 6 citations

  Senior authorCorresponding
  • Physics
  • Astrophysics
  • Astronomy

  Context. A recent observational census of Kuiper belt objects (KBOs) has unveiled anomalous orbital structures. This has led to the hypothesis that an additional ∼5 − 10 m ⊕ planet exists. This planet, known as Planet 9, occupies an eccentric and inclined orbit at hundreds of astronomical units. However, the KBOs under consideration have the largest known semimajor axes at a > 250 AU; thus they are very difficult to detect. Aims. In the context of the proposed Planet 9, we aim to measure the mean plane of the Kuiper belt at a > 50 AU. In a comparison of the expected and observed mean planes, some constraints would be put on the mass and orbit of this undiscovered planet. Methods. We adopted and developed the theoretical approach of Volk & Malhotra (2017, AJ, 154, 62) to the relative angle δ between the expected mean plane of the Kuiper belt and the invariable plane determined by the eight known planets. Numerical simulations were constructed to validate our theoretical approach. Then similar to Volk & Malhotra (2017, AJ, 154, 62), we derived the angle δ for the real observed KBOs with 100 < a < 200 AU, and the measurement uncertainties were also estimated. Finally, for comparison, maps of the theoretically expected δ were created for different combinations of possible Planet 9 parameters. Results. The expected mean plane of the Kuiper belt nearly coincides with the said invariable plane interior to a = 90 AU. But these two planes deviate noticeably from each other at a > 100 AU owing to the presence of Planet 9 because the relative angle δ could be as large as ∼10°. Using the 1 σ upper limit of δ < 5° deduced from real KBO samples as a constraint, we present the most probable parameters of Planet 9: for mass m 9 = 10 m ⊕ , orbits with inclinations i 9 = 30°, 20°, and 15° should have semimajor axes a 9 > 530 AU, 450 AU, and 400 AU, respectively; for m 9 = 5 m ⊕ , the orbit is i 9 = 30° and a 9 > 440 AU, or i 9 < 20° and a 9 > 400 AU. In this work, the minimum a 9 increases with the eccentricity e 9 (∈[0.2, 0.6]) but not significantly.

  DOI

Frequent coauthors

• Jian Li

  Collaborative Innovation Center of Advanced Microstructures

  11 shared

• Fumi Yoshida

  University of Occupational and Environmental Health Japan

  8 shared

• Nikolaos Georgakarakos

  8 shared

• Xin Li

  3 shared

• Hanlun Lei

  Beijing Academy of Agricultural and Forestry Sciences

  3 shared

• Xin Li

  2 shared

• Jian Li

  Institute of Information Engineering

  1 shared

• Li-Yong Zhou

  Nanjing University

  1 shared

Labs

• RTG Dynamics: Classical, Modern and QuantumPI

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