Departamento de Ingeniería Matemática

Monday, May 13th at 4:20 p.m. DIM seminar room, Beauchef 851, 5th floor.

Speaker: Sebastián Tapia, Universidad de Chile.

Title: «Study and simulation of traffic waves: Jamiton collisions»

Abstract: A jamiton corresponds to a traveling wave type solution that appears from the phantom congestion phenomenon and theoretically in macroscopic traffic equations. The objective was to study numerically the exit velocities and other emergent properties in jamiton collisions on a circular route, motivated by kink-antikink collisions in the phi^4 equation. For this, a numerical method based on finite volumes is established to simulate the jamiton collision with good accuracy. From the simulations, it is conjectured that the collision of two jamitons originates a new jamiton. Then, 274 jamitons of different sizes were collided and it was observed that the exit velocity presents a different behavior than phi^4. Also, the following were studied: The amplitude, length and driver reaction time dependencies.

Monday, May 6th at 4:20 p.m. DIM seminar room, Beauchef 851, 5th floor.

Speaker: Vicente Salinas (Universidad de Chile)

Abstract: The study of the Riemann Zeta function is of utmost importance, particularly for the connection with the distribution of prime numbers and the Riemann Hypothesis. This work presents a different approach by addressing this problem in Number Theory using techniques from partial differential equations (PDEs). To establish this connection, we examine a heat equation with the Riemann Zeta function as the source term.