Banca de QUALIFICAÇÃO: PAULO DOUGLAS SANTOS DE LIMA

Uma banca de QUALIFICAÇÃO de DOUTORADO foi cadastrada pelo programa.
STUDENT : PAULO DOUGLAS SANTOS DE LIMA
DATE: 25/10/2024
TIME: 14:00
LOCAL: Plataforma Google Meet
TITLE:

Inverse Problems Across Scales

KEY WORDS:

inverse problems. inverse theory. inverse material design. full waveform inversion. Monte Carlo methods.
quantum disordered systems

 

PAGES: 175
BIG AREA: Ciências Exatas e da Terra
AREA: Física
SUMMARY:

Predicting the shape of the shadow generated by a 3D object is a straightforward task. However, it can be challenging to solve
the inverse problem of finding the object's shape solely from its projected shadow. Analogous situations appear in many areas
of Physics, either to detect gas reservoirs or to design a new quantum material. In this regard, inverse problems typically
involve extracting physical properties from a noisy and limited information scenario. The typical length scale and the
interactions between physical parameters introduce distinct challenges for each inverse problem. Motivated by it, I cross scales
in this thesis by analysing four problems and their inverse counterparts. Guided by a cross-fertilisation scheme and following a
multiscale approach, I started investigating what mass density a hanging cable must possess in order to assume a specific
shape. Then, I solve the Bayesian full waveform inversion problem for single and multiple time-dependent seismic surveys. To
address this inverse problem, I employed the Hamiltonian Monte Carlo method with a proposed mass matrix design. After that,
I migrate to the forward problem of determining the ordered structures and collapse conditions of self-assembled magnetic
particles. Finally, I investigate the quantum inverse problem of finding the spatial position of randomly distributed impurities

in a one-dimensional electronic device. These problems provide valuable insights into solving inverse problems and have
applications in a variety of different fields.

COMMITTEE MEMBERS:
Presidente - 2492756 - JOAO MEDEIROS DE ARAUJO
Externo à Instituição - JOERG DIETRICH WILHELM SCHLEICHER - UNICAMP
Interno - 1294916 - MADRAS VISWANATHAN GANDHI MOHAN
Externo à Instituição - MAURO SANTOS FERREIRA - TRINITY