Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

Asymptotic expansion for reversible A+B<-->C reaction-diffusion process.

Zbigniew Koza1

  • 1Institute of Theoretical Physics, University of Wrocław, plac Maxa Borna 9, PL-50204 Wrocław, Poland. zkova@ift.wroc.pl

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 21, 2002
PubMed
Summary
This summary is machine-generated.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Percolation and jamming in random sequential adsorption of straight k-mers on square, triangular, and cubic lattices.

Physical review. E·2025
Same author

Critical p=1/2 in percolation on semi-infinite strips.

Physical review. E·2019
Same author

Jammed systems of oriented needles always percolate on square lattices.

Physical review. E·2017
Same author

Power-exponential velocity distributions in disordered porous media.

Physical review. E·2016
Same author

Anisotropy of flow in stochastically generated porous media.

Physical review. E, Statistical, nonlinear, and soft matter physics·2013
Same author

Hydraulic tortuosity in arbitrary porous media flow.

Physical review. E, Statistical, nonlinear, and soft matter physics·2011

This study analyzes long-time behaviors of reversible reaction-diffusion systems. Researchers developed perturbation expansions to find exact formulas for reactant concentrations and discovered methods to obtain singular solutions from reversible reactions.

Area of Science:

  • Chemical kinetics
  • Mathematical modeling
  • Physical chemistry

Background:

  • Reaction-diffusion systems are fundamental to chemical and biological processes.
  • Understanding the long-time behavior of these systems is crucial for predicting macroscopic properties.
  • Reversible reactions (A+B<-->C) present unique challenges in asymptotic analysis.

Purpose of the Study:

  • To investigate the long-time properties of reversible reaction-diffusion systems.
  • To develop analytical methods for determining asymptotic forms of reactant concentrations.
  • To explore the relationship between reversible and irreversible reaction dynamics.

Main Methods:

  • Utilizing perturbation expansion in powers of 1/t (inverse time).
  • Deriving exact formulas for asymptotic reactant concentrations.

Related Experiment Videos

  • Applying recursive expressions for expansion terms.

    • Main Results:

    • Exact formulas for asymptotic reactant concentrations were derived for systems with equal diffusion coefficients.
    • A complete recursive expression for arbitrary terms in the perturbation expansion was established.
    • It was demonstrated that singular solutions, characteristic of irreversible reactions, can be obtained from reversible reaction systems.

    Conclusions:

    • The perturbation expansion method provides a powerful tool for analyzing long-time behaviors of reversible reaction-diffusion systems.
    • The study reveals a deeper connection between the asymptotic dynamics of reversible and irreversible reaction-diffusion processes.
    • The findings offer new insights into the mathematical modeling of chemical kinetics.