Speaker: Josselin Garnier, Ecole Polytechnique
Title: Wave propagation in random media in the branched flow regime
Abstract: Waves propagating through weakly disordered smooth media undergo a universal phenomenon called branched flow when the correlation length of the medium is larger than the wavelength. In this process, the waves split, creating channels (or branches) of enhanced intensity that further divide as they propagate, creating tree-like branching patterns. By considering the random paraxial wave equation as a representative model, we elaborate a multiscale, stochastic theory of branched flow. We consider coherent and partially coherent initial wave fields. We derive closed-form equations that give the evolutions of the field and intensity correlation functions, and we determine the magnitude and the propagation distance of the maximum of the scintillation index (the relative variance of the intensity). These results describe the branched flow dynamics and clarify the role of the coherence properties of the initial field.
Biosketch: Josselin Garnier has been a professor in applied mathematics since 2001, first in Toulouse, France then in Paris at the University Paris Diderot and at the Ecole Normale Superieure, and at the Ecole Polytechnique since 2016. His research interests concern various aspects of applied probability and stochastic modeling, including wave propagation in random media, imaging for waves in complex media, and uncertainty quantification. Among Garnier's awards are the Felix Klein Prize and Blaise Pascal Prize. Garnier is a Member of the Institut Universitaire de France and the French Academy of Sciences.
Hosts: Professors Liliana Borcea & Michael Weinstein
In person attendance at this seminar is only open to Columbia Univesity affiliates. External guests are welcome to attend remotely. Please contact [email protected] if you need the Zoom link for this seminar.
