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1. Curved Fronts of Bistable Reaction-Diffusion Equations in Spatially Periodic Media

   https://doi.org/10.1007/s00205-021-01711-x  

   Guo, Hongjun; Li, Wan-Tong; Liu, Rongsong; Wang, Zhi-Cheng (December 2021, Archive for Rational Mechanics and Analysis)
2. Toward a conceptual model relating chemical reaction fronts to water flow paths in hills

   https://doi.org/10.1016/j.geomorph.2016.09.027  

   Brantley, Susan L.; Lebedeva, Marina I.; Balashov, Victor N.; Singha, Kamini; Sullivan, Pamela L.; Stinchcomb, Gary (January 2017, Geomorphology)
3. Using a neural network – Physics-based hybrid model to predict soil reaction fronts

   https://doi.org/10.1016/j.cageo.2022.105200  

   Wen, Tao; Chen, Chacha; Zheng, Guanjie; Bandstra, Joel; Brantley, Susan L. (August 2022, Computers & Geosciences)
4. Stability of fronts in the diffusive Rosenzweig–MacArthur model

   https://doi.org/10.1111/sapm.12755  

   Ghazaryan, Anna; Lafortune, Stéphane; Latushkin, Yuri; Manukian, Vahagn (August 2024, Studies in Applied Mathematics)

   Abstract We consider a diffusive Rosenzweig–MacArthur predator–prey model in the situation when the prey diffuses at a rate much smaller than that of the predator. In a certain parameter regime, the existence of fronts in the system is known: the underlying dynamical system in a singular limit is reduced to a scalar Fisher–KPP (Kolmogorov–Petrovski–Piskunov) equation and the fronts supported by the full system are small perturbations of the Fisher–KPP fronts. The existence proof is based on the application of the Geometric Singular Perturbation Theory with respect to two small parameters. This paper is focused on the stability of the fronts. We show that, for some parameter regime, the fronts are spectrally and asymptotically stable using energy estimates, exponential dichotomies, the Evans function calculation, and a technique that involves constructing unstable augmented bundles. The energy estimates provide bounds on the unstable spectrum which depend on the small parameters of the system; the bounds are inversely proportional to these parameters. We further improve these estimates by showing that the eigenvalue problem is a small perturbation of some limiting (as the modulus of the eigenvalue parameter goes to infinity) system and that the limiting system has exponential dichotomies. Persistence of the exponential dichotomies then leads to bounds uniform in the small parameters. The main novelty of this approach is related to the fact that the limit of the eigenvalue problem is not autonomous. We then use the concept of the unstable augmented bundles and by treating these as multiscale topological structures with respect to the same two small parameters consequently as in the existence proof, we show that the stability of the fronts is also governed by the scalar Fisher–KPP equation. Furthermore, we perform numerical computations of the Evans function to explicitly identify regions in the parameter space where the fronts are spectrally stable. 

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5. Fronts divide diazotroph communities in the Southern Indian Ocean

   https://doi.org/10.1093/femsec/fiae095  

   Chowdhury, Subhadeep; Berthelot, Hugo; Baudet, Corentin; González-Santana, David; Reeder, Christian_Furbo; L'Helguen, Stéphane; Maguer, Jean-François; Löscher, Carolin_R; Singh, Arvind; Blain, Stéphane; et al (July 2024, FEMS Microbiology Ecology)

   Abstract Dinitrogen (N2) fixation represents a key source of reactive nitrogen in marine ecosystems. While the process has been rather well-explored in low latitudes of the Atlantic and Pacific Oceans, other higher latitude regions and particularly the Indian Ocean have been chronically overlooked. Here, we characterize N2 fixation and diazotroph community composition across nutrient and trace metals gradients spanning the multifrontal system separating the oligotrophic waters of the Indian Ocean subtropical gyre from the high nutrient low chlorophyll waters of the Southern Ocean. We found a sharp contrasting distribution of diazotroph groups across the frontal system. Notably, cyanobacterial diazotrophs dominated north of fronts, driving high N2 fixation rates (up to 13.96 nmol N l−1 d−1) with notable peaks near the South African coast. South of the fronts non-cyanobacterial diazotrophs prevailed without significant N2 fixation activity being detected. Our results provide new crucial insights into high latitude diazotrophy in the Indian Ocean, which should contribute to improved climate model parameterization and enhanced constraints on global net primary productivity projections. 

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