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Speed of pulled fronts with a cutoff
1Facultad de Física, Pontificia Universidad Católica de Chile, Casilla 306, Santiago, Chile.
Summary
Investigating a small cutoff (epsilon) in one-dimensional pulled fronts reveals its impact on propagation speed. The study derives a lower bound for this speed, aligning with the Brunet-Derrida expression for leading order terms.
Area of Science:
- Physics
- Applied Mathematics
Background:
- Pulled fronts are crucial in various physical and biological phenomena.
- Understanding front propagation dynamics is essential for modeling complex systems.
- Previous models often simplified or neglected small-scale cutoff effects.
Purpose of the Study:
- To analyze the influence of a small cutoff (epsilon) on the velocity of one-dimensional pulled fronts.
- To derive a precise lower bound for the front speed as a function of the cutoff.
- To adapt existing variational principles for enhanced applicability.
Main Methods:
- Utilized a variational principle to analyze front dynamics.
- Transformed variables within the variational principle for improved suitability.
- Derived analytical expressions for the front speed and its dependence on the cutoff epsilon.
Main Results:
- Established a lower bound for the pulled front velocity.
- Demonstrated that the leading order terms of the derived speed match the established Brunet-Derrida expression.
- Showcased the effectiveness of the modified variational principle.
Conclusions:
- The small cutoff epsilon significantly influences the velocity of one-dimensional pulled fronts.
- The derived lower bound provides a more accurate prediction of front speed.
- The adapted variational principle offers a valuable tool for future research in front propagation.
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