{"paper":{"title":"A Spectral-Based Method for Network-Formation PDEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Claudia Wytrzens, Pedro Aceves-Sanchez, Pierre Degond, Sara Merino-Aceituno","submitted_at":"2026-06-04T21:10:54Z","abstract_excerpt":"We propose and study a simple and scalable Fourier-based spectral method for a continuum model of network formation under periodic boundary conditions. The model provides the evolution of the pressure $p$ and the conductivity $m$ over time. The evolution of $p$ is given by an anisotropic Poisson equation, while the equation for $m$ contains three terms corresponding to a diffusion and an activation term of the network -- that depends on the gradient of the pressure -- as well as a relaxation term that acts as a decaying term. This system arises as a formal $L^2$-gradient flow of a non-convex e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.06720","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.06720/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}