Diffusion of point-like particles in a two-dimensional channel of varying width is studied. The particles are driven by an arbitrary space dependent force. We construct a general recurrence procedure mapping the corresponding two-dimensional advection-diffusion equation onto the longitudinal coordinate x. Unlike the previous specific cases, the presented procedure enables us to find the one-dimensional description of the confined diffusion even for non-conservative (vortex) forces, e.g. caused by flowing solvent dragging the particles. We show that the result is again the generalized Fick-Jacobs equation. Despite of non existing scalar potential in the case of vortex forces, the effective one-dimensional scalar potential, as well as the corresponding quasi-equilibrium and the effective diffusion coefficient [Formula: see text] can be always found.
Download full-text PDF |
Source |
|---|---|
| http://dx.doi.org/10.1088/1361-648X/aac146 | DOI Listing |
Publication Analysis
Top Keywords
Similar Publications
Reaction-advection-diffusion model of highly pathogenic avian influenza with behavior of migratory wild birds.
J Math Biol
January 2025
School of Mathematics and Statistics, Northeast Normal University, 5268 Renmin Street, Changchun, 130024, Jilin, People's Republic of China.
Wild birds are one of the main natural reservoirs for avian influenza viruses, and their migratory behavior significantly influences the transmission of avian influenza. To better describe the migratory behavior of wild birds, a system of reaction-advection-diffusion equations is developed to characterize the interactions among wild birds, poultry, and humans. By the next-generation operator, the basic reproduction number of the model is formulated.
View Article and Find Full Text PDFWell-posedness of Keller-Segel systems on compact metric graphs.
J Evol Equ
December 2024
Department of Mathematics and Statistics, Auburn University, Auburn, AL 36849 USA.
Chemotaxis phenomena govern the directed movement of microorganisms in response to chemical stimuli. In this paper, we investigate two Keller-Segel systems of reaction-advection-diffusion equations modeling chemotaxis on thin networks. The distinction between two systems is driven by the rate of diffusion of the chemo-attractant.
View Article and Find Full Text PDFEnhanced rotational diffusion and spontaneous rotation of an active Janus disk in a complex fluid.
Soft Matter
January 2025
Aragon Institute of Engineering Research (I3A), University of Zaragoza, Zaragoza, Spain.
Article Synopsis
- Active colloids like Janus disks behave differently in complex fluids compared to simple fluids, showing enhanced diffusion and instabilities.
- This study uses simulations to model the interactions between a self-propelling Janus disk and a complex fluid, revealing how these interactions affect rotational motion and diffusion.
- Findings suggest that increasing the disk's speed could lead to spontaneous rotation and significantly greater diffusion rates, depending on the fluid's composition and particle interactions, making the model applicable to various active systems.
Inference of weak-form partial differential equations describing migration and proliferation mechanisms in wound healing experiments on cancer cells.
ArXiv
October 2024
Department of Mechanical Engineering, University of Michigan, United States.
Targeting signaling pathways that drive cancer cell migration or proliferation is a common therapeutic approach. A popular experimental technique, the scratch assay, measures the migration and proliferation-driven cell closure of a defect in a confluent cell monolayer. These assays do not measure dynamic effects.
View Article and Find Full Text PDFExploring the role of different cell types on cortical folding in the developing human brain through computational modeling.
Sci Rep
October 2024
Institute of Continuum Mechanics and Biomechanics, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058, Erlangen, Germany.
The human brain's distinctive folding pattern has attracted the attention of researchers from different fields. Neuroscientists have provided insights into the role of four fundamental cell types crucial during embryonic development: radial glial cells, intermediate progenitor cells, outer radial glial cells, and neurons. Understanding the mechanisms by which these cell types influence the number of cortical neurons and the emerging cortical folding pattern necessitates accounting for the mechanical forces that drive the cortical folding process.
View Article and Find Full Text PDFWant AI Summaries of new PubMed Abstracts delivered to your In-box?
Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!