Universitat Politècnica de Catalunya
Universitat Politècnica de Catalunya. Departament de Matemàtiques
Estrada Rodríguez, Gissell
2025-06-17
This bachelor’s thesis explores the use of the Boltzmann equation for opinion formation models. It begins with an introduction to kinetic gas theory and the Boltzmann equation, the cornerstone of the model. This is followed by opinion dynamics models in which individuals have, in addition to their opinion, a variable for leadership qualities. Political segregation is then modeled by considering spatial positions instead of assertiveness. Finally, two Monte Carlo algorithms to solve the homogeneous Boltzmann equation are introduced, enabling the simulation of one of the proposed models.
Bachelor thesis
Anglès
Àrees temàtiques de la UPC::Matemàtiques i estadística; Statistical physics; Stochastic processes; Monte Carlo method; Física estadística; Processos estocàstics; Simulació de Monte Carlo; Classificació AMS::82 Statistical mechanics, structure of matter::82C Time-dependent statistical mechanics (dynamic and nonequilibrium); Classificació AMS::35 Partial differential equations::35Q Equations of mathematical physics and other areas of application; Classificació AMS::65 Numerical analysis::65C Probabilistic methods, simulation and stochastic differential equations
Universitat Politècnica de Catalunya
http://creativecommons.org/licenses/by-nc-sa/4.0/
Open Access
Attribution-NonCommercial-ShareAlike 4.0 International
Treballs acadèmics [82541]
