Deadline for manuscript submissions: 31 March 2026

 

Special Issue Editors

Dr. Shuxia Zhao  Website  E-Mail: zhaonie@dlut.edu.cn
Guest Editor
Dalian University of Technology, China                
Interests: fluid dynamics; plasma sources; self-coagulation theory; particle simulation; gaseous discharge structure

      

Special Issue Information

Dear colleagues,

The engineering and physical issues are related to the differential and integral equation. The differential equation includes the ordinary differential equation, the partial differential equation, and the differential equation set. The complex and nonlinear differential equation set, such as the fluid model of plasma source, is hardly solved by analytics, but relies on the numerics, such as the finite difference, finite element, and finite volume etc. The numerics, e.g., explicit or implicit algorithm and flux-corrected transport algorithm, depend on the stiffness of differential equation and its math types, such as the parabola, ellipse and hyperbola, and on the positive property of specific quantities, e.g., density and temperature. The simple differential equation at reasonable approximations can be solved analytically, hence possibly used to establish new scientific theory, such as the self-coagulation based on a quasi- Helmholtz equation that consists of free diffusion and chemical source term of species depletion (not generation). It is noted that the numerics and analytics of differential equation need to collaborate together to reveal the dynamics of complex system that we are presently confronted with, i.e., they are complementary to advance the scientific researches.

The Boltzmann equation that is the base of transport phenomena is a typical differential and integral equation. Its applications are diverse, including the linear approximation solutions that give the kinetics of plasma source and the transport coefficients for fluid model simulation of plasma source. Besides, the fluid model equation set can be deduced by the different orders of matrix equation of Boltzmann equation. Both the Boltzmann equation and the fluid model simulation of plasma source help people understand the mechanism of plasma source and hence optimize their applications in industry, such as the etching and deposition. Besides for the plasma transport and chemical process, there are still wave dynamics and instabilities in the plasmas and they can be described by the linear wave theory and dispersion relation of wave, which also belong to the analytics, as we believed.

Regarding the above points suggested, this issue hence welcomes any submission that relates to the differential and integral equation, differential equation and their interdisciplinary meanings with the applied physics, such as the fluid simulation of plasma source, the analytics of Boltzmann equation, the possible numerics of it, the benchmark and the numerical stability and precise analysis of computational fluid dynamics, the deduction of fluid model from the Boltzmann equation, the wave and instability existing within plasma or other media, the self-coagulation possible correlations with other disciplines, such as the biology, and the gaseous discharge structure, etc.

Guest Editor

Dr. Shuxia Zhao

 

Keywords

-self-coagulation theory
-fluid simulation
-the differential and integral boltzmann equation
-complementary role of numerics and analytics
-gaseous discharge

 

 

Published Papers