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Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

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Two-species reaction-diffusion system with equal diffusion constants: anomalous density decay at large times

Konkoli¹, Johannesson

¹NORDITA, Blegdamsvej 17, DK 2100 Kobenhavn, Denmark and Institute of Theoretical Physics, Chalmers University of Technology and Goteborg University, SE 412 96 Goteborg, Sweden.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

|November 23, 2000

Summary

In a two-species reaction-diffusion model, the minority species density decays at the same rate as the majority species in dimensions less than or equal to two, challenging prior expectations.

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Area of Science:

Statistical Physics
Chemical Kinetics
Mathematical Biology

Background:

Reaction-diffusion systems model complex spatio-temporal phenomena.
Annihilation reactions and diffusion govern particle dynamics.
Species with different initial densities interact and diffuse.

Purpose of the Study:

Investigate the long-time behavior of a two-species reaction-diffusion model.
Analyze the decay rates of minority and majority species densities.
Compare theoretical predictions with numerical simulations.

Main Methods:

Field-theoretic renormalization group analysis.
Monte Carlo simulations in one and two dimensions.
Analysis of reaction rates (lambda(0), delta(0)) and diffusion constants.

Main Results:

The minority species density decays at the same rate as the majority species for d <= 2.
This counter-intuitive result emerges from renormalization group analysis.
Monte Carlo data in d=1 support the theoretical prediction.

Conclusions:

The large-time behavior of this reaction-diffusion system is non-trivial.
Theoretical predictions are supported by simulations in lower dimensions.
Numerical verification in d=2 is complicated by slow convergence to asymptotic behavior.