Universitat Politècnica de Catalunya
Universitat Politècnica de Catalunya. Departament de Matemàtiques
Estrada Rodríguez, Gissell
2026-01-27
This thesis investigates the application of the Boltzmann equation to opinion consensus and polarization dynamics. Building on classical kinetic gas theory, we examine opinion models that incorporate agent-specific variables, such as external diffusion and compromise propensity, to describe social interactions. To solve the governing equations, we develop and implement Direct Simulation Monte Carlo (DSMC) algorithms for the homogeneous Boltzmann equation. The numerical scheme is extensively studied and subsequently applied to simulate and analyze the proposed opinion dynamics.
Bachelor thesis
Anglès
Àrees temàtiques de la UPC::Matemàtiques i estadística; Monte Carlo method; Numerical analysis; Stochastic processes; Kinetic equations; opinions; Monte Carlo methods.; Montecarlo, Mètode de; Anàlisi numèrica; Processos estocàstics; Classificació AMS::82 Statistical mechanics, structure of matter::82C Time-dependent statistical mechanics (dynamic and nonequilibrium); Classificació AMS::91 Game theory, economics, social and behavioral sciences::91D Mathematical sociology; Classificació AMS::65 Numerical analysis::65C Probabilistic methods, simulation and stochastic differential equations
Universitat Politècnica de Catalunya
http://creativecommons.org/licenses/by/4.0/
Open Access
Attribution 4.0 International
Treballs acadèmics [82075]
