Advances in Kinetic Theory and Its Application

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Physics".

Deadline for manuscript submissions: 31 October 2026 | Viewed by 1096

Special Issue Editors


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Guest Editor
Institue of Mechanics, Chinese Academy of Sciences, Beijing, China
Interests: high-temperature gas dynamics; rarefied gas dynamics

E-Mail Website
Guest Editor
Institute of Mechanics, Chinese Academy of Sciences, Beijing 101400, China
Interests: computational fluid dynamics; kinetic theory; scientific machine learning
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Kinetic theory underpins the microscopic and mesoscopic understanding of gases, liquids, plasmas, and complex media. Advances in numerical simulation, multiscale modeling, non-equilibrium statistical mechanics, machine learning methods, and high-performance computing have greatly expanded its reach. These tools enable the study of processes beyond classical hydrodynamics, with applications in micro- and nano-fluidics, rarefied gas dynamics, high-speed reacting flows, and energy technologies. As the need for accurate modeling of non-equilibrium phenomena grows, kinetic theory remains essential for bridging fundamental physics and practical applications.

This Special Issue will highlight recent advances, innovative methods, and applications in kinetic theory. The scope directly aligns with that of Axioms, which emphasizes the rigorous exploration of fundamental principles, theoretical frameworks, and interdisciplinary approaches in science and mathematics.

In this Special Issue, original research articles and reviews are welcome. Research areas may include (but not limited to) the following:

  • Classical and generalized Boltzmann equations;
  • BGK-type models, lattice Boltzmann models, and discrete kinetic schemes;
  • Non-equilibrium gas dynamics and rarefied flow phenomena;
  • Kinetic methods for plasma dynamics and electromagnetic coupling;
  • Reaction kinetics and energy transfer mechanisms;
  • Stochastic kinetic models and Monte Carlo simulations;
  • Machine learning-assisted kinetic modeling and data-driven closures;
  • Applications in aerospace engineering, microfluidics, atmospheric science, and astrophysics;
  • Numerical methods, high-performance computing, and algorithmic advancements in solving kinetic equations.

We look forward to receiving your contributions.

Dr. Qizhen Hong
Prof. Dr. Tianbai Xiao
Guest Editors

Manuscript Submission Information

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • kinetic theory
  • non-equilibrium dynamics
  • Boltzmann equation
  • multiscale modeling
  • computational methods

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Published Papers (1 paper)

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Research

31 pages, 1650 KB  
Article
Reconstruction of Hansen’s High-Temperature Air Model
by Alexander Dunn, Jordan Ranstead and Semih Ölçmen
Axioms 2026, 15(4), 283; https://doi.org/10.3390/axioms15040283 - 13 Apr 2026
Viewed by 758
Abstract
C. F. Hansen’s NASA TR R-50 published in 1959 remains one of the most widely used analytic approximations for the thermodynamic and transport properties of high-temperature air. Although modern equilibrium and nonequilibrium models extend the temperature range and species sets, Hansen’s expressions continue [...] Read more.
C. F. Hansen’s NASA TR R-50 published in 1959 remains one of the most widely used analytic approximations for the thermodynamic and transport properties of high-temperature air. Although modern equilibrium and nonequilibrium models extend the temperature range and species sets, Hansen’s expressions continue to provide a transparent, closed-form representation valuable for hypersonic aerothermodynamics, preliminary design, and code verification studies up to 15,000 K. In this work, we reconstruct the full Hansen model from his source equations, implement the formulation in a consistent modern notation, and derive all thermodynamic and transport quantities explicitly. The transport-property model developed by Hansen is discussed in comparison to research by Thompson et al., Gordon and McBride, and D’Angola et al. The resulting implementation provides a clean, analytic 7-species-air model for high-speed/hypersonic applications where rapid evaluations of thermodynamic and transport properties are required. Full article
(This article belongs to the Special Issue Advances in Kinetic Theory and Its Application)
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