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A Convergent Reaction-Drift-Diffusion Master Equation with Interaction Potentials — arXiv:2609.09546

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.09546
License (as archived): CC0-1.0
Archived: 2026-10-16T10:13:17.418Z
SHA-256 of the archived text: c41002649d1ea19940494d13bfbbfa4f81afdb3ec3ab729b2637bdea036572fd
Stable URL of this page: https://metraipolis.com/documento/dc_0948d4fa76ee

How to cite

A Convergent Reaction-Drift-Diffusion Master Equation with Interaction Potentials — arXiv:2609.09546 — arXiv (en), https://arxiv.org/abs/2609.09546 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_0948d4fa76ee (Metraipolis archive dc_0948d4fa76ee, sha256 c41002649d1ea19940494d13bfbbfa4f81afdb3ec3ab729b2637bdea036572fd)

BibTeX

@misc{dc0948d4fa76ee,
  title = {A Convergent Reaction-Drift-Diffusion Master Equation with Interaction Potentials — arXiv:2609.09546},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.09546},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_0948d4fa76ee; sha256 c41002649d1ea19940494d13bfbbfa4f81afdb3ec3ab729b2637bdea036572fd},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.09546. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We extend the convergent reaction-diffusion master equation (CRDME) framework on unstructured grids to include two-body interaction potentials between particles. Such interactions are essential for modeling systems in which particles experience electrostatic repulsion, volume exclusion, or van der Waals attraction. Our approach discretizes the weak form of the forward equation for a particle-based stochastic reaction- drift-diffusion model to obtain a new CRDME by combining two complementary techniques: an edge- averaged finite element method with mass-lumping quadrature for spatial transport terms that include potential interactions, and a mix of finite volume and mass-lumping quadrature approximations for reaction terms. This yields transition rates for a spatial jump process of particles hopping between dual mesh voxels and undergoing reactions. The resulting spatially discrete CRDME retains key physical properties of the continuum system in closed domains. It preserves the Gibbs-Boltzmann equilibrium distribution in the absence of reactions, and satisfies detailed balance of both drift-diffusion and reactive fluxes for systems with reversible reactions. Numerical comparisons with Brownian dynamics simulations validate our method, and we demonstrate empirical second-order convergence as the mesh is refined.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-10 in math.NA).
Categorie arXiv: Numerical Analysis (math.NA).
Pagina del lavoro: https://arxiv.org/abs/2609.09546 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-16T08:46:35.695Z dalla pagina https://arxiv.org/catchup/math.NA/2026-09-10?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).