Applied Mathematics Commons^™

Lecture Note On Delay Differential Equation, Wenfeng Liu

Undergraduate Student Research Internships Conference

Delay differential equation is an important field in applied mathematics since it concerns more situations than the ordinary differential equation. Moreover, it makes the equations more applicable to the object's movement in real life.

My project is the lecture note on the delay differential equation provides a basic introduction to the delay differential equation, its application in real life, improving the ordinary differential equation, the primary method and definition for solving the delay differential equation and the use of the way in the ordinary differential equation to estimate the periodic solution to the delay differential equation.

A Contagion Model Of Emergency Airplane Evacuations, Junyuan Lin

Seaver College Research And Scholarly Achievement Symposium

Motivated by the Asiana Flight 214 crash in San Francisco this summer, this project focuses on modeling an emergency airplane evacuation. Our models are based on the Particle Swarm Optimization (PSO) algorithm, where each agent's position is compared to a fitness function that describes the current environment. Each agent moves according to its knowledge of its own previous best position and the group's current best position. The static environment is modeled by a potential function that describes the layout of the airplane that includes the exits and physical barriers such as the seats. We model the interactions within the swarm …