FKPP fronts in quenched random media
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918501718949888 |
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| author | Marquis, Ulysse Berestycki, Henri Barthelemy, Marc |
| author_facet | Marquis, Ulysse Berestycki, Henri Barthelemy, Marc |
| contents | We study numerically the evolution of one-dimensional FKPP fronts initiated from steep initial conditions in the presence of a quenched random growth rate. Compared to both the homogeneous case (with velocity $v_0$) and deterministic disorder, quenched randomness increases the average propagation speed. We show that the velocity shift relative to the homogeneous case scales linearly with the disorder variance $σ^2$, with a universal prefactor -- independent of the specific distribution of the disorder -- such that $v = v_0 + a σ^2$, with $a \approx 0.02432 \pm 0.00002$. Moreover, the front position exhibits diffusive fluctuations across disorder realizations. The corresponding effective diffusion coefficient scales quadratically with $σ$, $D = \frac{b^2 σ^2}{2}$, with $b \approx 0.223 \pm 0.002$. These results suggest a universal statistical response of FKPP fronts to quenched heterogeneity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_14914 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | FKPP fronts in quenched random media Marquis, Ulysse Berestycki, Henri Barthelemy, Marc Disordered Systems and Neural Networks Statistical Mechanics Analysis of PDEs We study numerically the evolution of one-dimensional FKPP fronts initiated from steep initial conditions in the presence of a quenched random growth rate. Compared to both the homogeneous case (with velocity $v_0$) and deterministic disorder, quenched randomness increases the average propagation speed. We show that the velocity shift relative to the homogeneous case scales linearly with the disorder variance $σ^2$, with a universal prefactor -- independent of the specific distribution of the disorder -- such that $v = v_0 + a σ^2$, with $a \approx 0.02432 \pm 0.00002$. Moreover, the front position exhibits diffusive fluctuations across disorder realizations. The corresponding effective diffusion coefficient scales quadratically with $σ$, $D = \frac{b^2 σ^2}{2}$, with $b \approx 0.223 \pm 0.002$. These results suggest a universal statistical response of FKPP fronts to quenched heterogeneity. |
| title | FKPP fronts in quenched random media |
| topic | Disordered Systems and Neural Networks Statistical Mechanics Analysis of PDEs |
| url | https://arxiv.org/abs/2605.14914 |