dc.contributor
Universitat Politècnica de Catalunya. Departament de Matemàtiques
dc.contributor
Estrada Rodríguez, Gissell
dc.contributor.author
Fernández Carballo, Bruno
dc.date.accessioned
2026-02-20T12:13:37Z
dc.date.available
2026-02-20T12:13:37Z
dc.date.issued
2026-01-27
dc.identifier
https://hdl.handle.net/2117/455596
dc.identifier
PRISMA-200624
dc.identifier.uri
https://hdl.handle.net/2117/455596
dc.description.abstract
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.
dc.format
application/pdf
dc.publisher
Universitat Politècnica de Catalunya
dc.rights
http://creativecommons.org/licenses/by/4.0/
dc.rights
Attribution 4.0 International
dc.subject
Àrees temàtiques de la UPC::Matemàtiques i estadística
dc.subject
Monte Carlo method
dc.subject
Numerical analysis
dc.subject
Stochastic processes
dc.subject
Kinetic equations
dc.subject
Monte Carlo methods.
dc.subject
Montecarlo, Mètode de
dc.subject
Anàlisi numèrica
dc.subject
Processos estocàstics
dc.subject
Classificació AMS::82 Statistical mechanics, structure of matter::82C Time-dependent statistical mechanics (dynamic and nonequilibrium)
dc.subject
Classificació AMS::91 Game theory, economics, social and behavioral sciences::91D Mathematical sociology
dc.subject
Classificació AMS::65 Numerical analysis::65C Probabilistic methods, simulation and stochastic differential equations
dc.title
Mathematical modelling and numerics of opinion consensus and polarisation dynamics
