Related Experiment Video
Updated: Apr 6, 2026
10:12
Analyzing Mixing Inhomogeneity in a Microfluidic Device by Microscale Schlieren Technique
Published on: June 12, 2015
8.9K
Multiscale derivation of deterministic and stochastic cross-diffusion models in a fluid: A review
M Bendahmane1, F Karami2, M Zagour3
1Institut de Mathématiques de Bordeaux, Université de Bordeaux, 33076 Bordeaux Cedex, France.
Chaos (Woodbury, N.Y.)
|December 11, 2024
Summary
This review surveys mathematical models for dynamic populations in fluids. It covers multiscale derivations of cross-diffusion systems and new models for pursuit-evasion, cancer, and virus dynamics.
Area of Science:
- Mathematical Biology
- Fluid Dynamics
- Multiscale Modeling
Background:
- Modeling dynamic populations in fluid environments is complex.
- Existing literature lacks a unified multiscale approach.
Purpose of the Study:
- To review and critically analyze mathematical models for dynamic populations in fluid media.
- To present derivations from microscopic kinetic theory to macroscopic systems.
- To introduce novel models for specific applications.
Main Methods:
- Multiscale derivation of deterministic and stochastic cross-diffusion systems.
- Application of the micro-macro decomposition method.
- Review of existing and novel mathematical models.
Main Results:
- Successful derivation of cross-diffusion systems from kinetic theory.
- Presentation of new mathematical models for pursuit-evasion, cancer invasion, and virus dynamics.
- Identification of research gaps and future directions.
Conclusions:
- The study provides a comprehensive overview of mathematical modeling for populations in fluids.
- It bridges microscopic and macroscopic descriptions.
- It highlights the versatility of these models in diverse biological applications.
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