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PhD Project.

Mathematical modeling of biogeochemical and economic flows: a chemical network-based approach for sustainable French agriculture

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            This PhD project contributes to foresight studies by developing rigorous and innovative mathematical tools to explore the long-term trajectories of agro-environnemental systems. It focuses on the biogeochemical metabolism of agriculture, especially nitrogen cycling through framework inspired by chemical reaction networks and non-equilibrium statistical physics. By reformulating agricultural processes as chemical networks like reactions, the project offers a new way to anticipate systemic dynamics, feedbacks, and tipping points

            Traditional foresight models, especially in economics, often use input-output approaches to assess how resources must be allocated to reach policy targets (e.g. food production, emissions reduction). However, these models typically overlook the internal biophysical constraints that govern real ecosystems. This project instead adopts a metabolic perspective: agricultural systems are modeled as open, non-equilibrium systems where nitrogen stock and flows circulate between compartments (e.g. crops, livestock, soils, waste), governed by physical constraints (such as conservation laws and entropy production) and simple kinetic rules. This allows for a physically grounded analysis of transition scenarios, including increased recycling, reduced inputs, or dietary shifts.

            This project builds on GRAFS-E model (Generative Representation of Agro-Food Systems-Extended), developed in Python by Adrien Fauste-Gay (https://grafs-e.streamlit.app/)., which represents agricultural systems through interconnected compartments (e.g. crops, livestock, population) and processes (e.g. fertilization, food intake) using chemical kinetics formalism (zero/first order). Stocks and fluxes are analyzed as concentrations and reaction rates, allowing analytical treatment using tools from graph theory and stochastic thermodynamics.

            The first phase will focus on the mathematical formalization of GRAFS-E to identify all stationary states, assess system stability, and characterize operating regimes. It will also explore different transition scenarios: increased recycling, dietary shifts, organic agriculture, etc., evaluating their environmental impacts and systemic robustness.

            In the second phase, the methodology will be extended to other biogeochemical cycles (carbon, phosphorus, water) and energy flows. A user-friendly interface will be developed (e.g. with Streamlit) for scenario exploration, enabling use by researchers, decision makers, and stakeholders. Ultimately, the project seeks to provide a systemic, transparent decision-support tool rooted in physical realities, to guide sustainable agricultural transitions.

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Cours électif aux Mines de Nancy (2A, niveau M1). 

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