Applications of calculus in wave propagation modeling: a study on Wildfire Propagation

• Grant number: 24/03889-3
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: July 01, 2024
• End date: June 30, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Hengameh Raeisidehkordi
• Grantee: Beatriz Ikuno Malaman dos Santos
• Host Institution: Centro de Matemática, Computação e Cognição (CMCC). Universidade Federal do ABC (UFABC). Ministério da Educação (Brasil). Santo André , SP, Brazil

Abstract

The present research project aims to explore the applications of differential calculus and differential equations in wave modeling, with a specific focus on their use in studying wildfire propagation. The student will employ techniques of derivatives and partial derivatives of functions, as well as techniques of analytic geometry and systems of equations to find propagation models and simulate the behavior of waves in wildfire scenarios, seeking to identify patterns and relevant trends for wildfire prevention and control. The project will investigate wildfire propagation problems in flat spaces and variable conditions. Building upon fundamental notions in Mathematics, such as vectors, scalar products, derivatives, partial derivatives, and systems of equations, this scientific initiation project proposes a detailed and mathematically rigorous study of fire wave behavior. The objective of the project is to familiarize the student with research and the application of concepts learned in mathematics to analyze and study a real-world problem