Dr. Miguel Bustamante

Dr. Miguel Bustamante collaborates with the ERC project

Dr Bustamante holds a permanent Lectureship at University College Dublin since January 2009. He earned his PhD in Physics in 2003 in Universidad de Chile, where he became an expert in non-canonical Hamiltonian structures for nonlinear evolution equations. After that he took postdoctoral positions at ENS Paris and The University of Warwick, receiving first-hand training on numerical methods and high-resolution numerical simulations of turbulence and inviscid fluids.

Dr Bustamante combines his expertise in differential-geometrical, numerical and analytical methods to the study of fundamental problems in the area of nonlinear and numerical applied mathematics. His current focus is on two strands:

(I) Testing the validity of the hypothesis of finite-time singularity in 3D Euler and other fluid equations, by using a combination of numerical methods and mathematical analysis.

(II) Studying the energy-transfer mechanisms that dominate the nonlinear wave interactions in several scenarios (such as planetary waves, ocean waves, and nonlinear optics), using tools from discrete wave turbulence, number theory and statistics of resonant-cluster dynamics.
Web page: http://mathsci.ucd.ie/~miguel/

Full publication list: http://mathsci.ucd.ie/~miguel/Publications_Miguel_Bustamante.html

Selected Publications:

For Strand (I):

M. D. Bustamante, R. M. Kerr, 3D Euler about a 2D Symmetry Plane, Physica D 237 (2008) 1912–1920

J. D. Gibbon, M. D. Bustamante, R. M. Kerr, The three-dimensional Euler equations: singular or non-singular? Nonlinearity 21 (2008) T123–T129

M. D. Bustamante, 3D Euler equations and ideal MHD mapped to regular systems: Probing the finite-time blowup hypothesis, Physica D 240 (2011) 1092–1099

M. D. Bustamante, M. Brachet, On the interplay between the BKM theorem and the analyticity-strip method to investigate numerically the incompressible Euler singularity problem, Phys. Rev. E 86 (2012), 066302

For Strand (II):
M. D. Bustamante, E. Kartashova, Dynamics of nonlinear resonances in Hamiltonian systems, EPL 85 (2009) 14004

M. D. Bustamante, E. Kartashova, Effect of the dynamical phases on the nonlinear amplitudes' evolution, EPL 85 (2009) 34002

E. Kartashova, M. D. Bustamante, Resonance clustering in wave turbulent regimes: Integrable dynamics, Commun. Comput. Phys. 10 (2011) 1211–1240

J. Harris, M. D. Bustamante, C. Connaughton, Externally forced triads of resonantly interacting waves: Boundedness and integrability properties, Commun. Nonlinear Sci. Numer. Simulat. 17 (2012) 4988–5006

Email: miguel.bustamante@ucd.ie