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Instituto de Ingeniería Matemática y Computacional

Facultad de Matemáticas - Escuela de Ingeniería

Actividades

David M. Hernandez, Institute for Theory and Computation, Harvard-Smithsonian Center for Astrophysics.

Miércoles 18 de mayo de 2022, 13 hrs. (Presencial en Auditorio San Agustín)

ABSTRACT

I describe new mathematical tools I've built to solve different problems in gravitational dynamics. I first describe maps that solve the gravitational system of ordinary differential equations describing asteroids in the Solar System.  Enforcing that these maps be time-reversible and symplectic can significantly improve the reliability of the long-term dynamics of these bodies.

I then tackle the problem of the stability of the Solar System.  Although great progress has been made in the last decades towards an understanding of chaos and stability of the Solar System due to the development of modern computers, I show that important studies are affected by numerical chaos, which causes artificial Solar System chaos and instability.  This numerical instability arises from resonances between the time step and physical Solar System frequencies, and is an inherent property of symplectic maps.  I discuss our current work to calculate Solar System stability, and in particular Mercury's future trajectory, without the effects of numerical chaos.

I next describe a suite of tools, including powerful new Kepler solvers and new symplectic integrators and their tangent equations that are designed to solve for the orbits of planets in exoplanetary systems.  Unlike other popular methods, we can solve planetary systems with arbitrary geometries and orbits including moons.  We have implemented these tools to solve the transit timing variation problem, and derive the properties and possible compositions of TRAPPIST-1 planets.  Some of this work has been incorporated in the popular Rebound code.

El miércoles 13 de noviembre, a las 13 hrs se presenta el seminario "Modeling poisson equations with strong localized source terms using the virtual element method with extrinsic enrichment", con Edgardo Olate-Sanzana, Departamento de Ingeniería, Mecánica, University of Chile.

El seminario se llevará a cabo el miércoles 13 de noviembre, a las 13:00 horas, en el Auditorio San Agustín, Campus San Joaquín UC. +info

El lunes 11 de noviembre, a las 13 hrs se presenta el seminario "Some Results on Differentially Private Hypothesis Testing", con Marco Gaboardi, assistant professor, Boston University

El seminario se llevará a cabo el lunes 11 de noviembre, a las 13:00 horas, en el Auditorio San Agustín, Campus San Joaquín UC. +info

El miércoles 16 de octubre, a las 13 hrs se presenta el seminario "Cadenas dipolares y sus ramas de equilibrio ocultas", con Jaime Cisternas, Profesor Titular, Facultad de Ingeniería y Ciencias Aplicadas; Director, Departamento de Ciencias, Centro de Estudios Generales, Universidad de los Andes.

El seminario se llevará a cabo el miércoles 16 de octubre, a las 13:00 horas, en el Auditorio San Agustín, Campus San Joaquín UC. +info

El martes 12 de noviembre, a las 13 hrs se presenta el seminario "Therapeutic Ultrasound: reviewing the physics and discussing the mathematical challenges", con Reza Haqshenas, Research Fellow, Ultrasonics Group, Department of Mechanical Engineering, University College London. He specialises in physical acoustics, with applications to pharmaceutical and biomedical problems. He has been involved in developing a theoretical understanding of phase transition in fluids and tissues mediated by acoustic waves, such as formation of crystals or bubbles in an acoustic field, and modelling the wave propagation in tissues for the therapeutic applications of ultrasound.

El seminario se llevará a cabo el martes 19 de noviembre, a las 13:00 horas, en el Auditorio San Agustin, Campus San Joaquín UC. +info