Mathematical Mechanics and Inverse Problems

Researchers

Coordinators of Mathematical Mechanics area:  Carlos Conca and  Jorge San Martín

Coordinators of Inverse Problems area:   Jaime Ortega and Axel Osses

UTFSM: Eduardo Cerpa, Alberto Mercado

Associate member: Álvaro Valencia

About the research group

The group is organized into two complementary areas: Mathematical Mechanics and Inverse Problems. Our goal is to conduct frontier research in applied mathematics in science and engineering that has strong interactions with direct and inverse problems governed by partial differential equations (PDE). The main theoretical research topics are: modeling of PDE, fluid dynamics, homogenization, controllability theory and more recently inverse problems, and calculus of variations and image processing. The applications of these topics cover a wide range of applied areas in science and engineering including mining, medicine, biomechanics, electronic devices, earth and environmental sciences, astronomical interferometry, medical imaging, cellular dynamics, texture analysis, and remote sensing.

The research directions of the group are: Fluid-structure interaction and biomechanics, biomathematics and biological models,  optimal shape design through homogenization,  inverse geometrical problems, inverse problems in earth sciences, inverse problems related with astronomy, inverse problems in medical sciences, controllability theory, image processing, and calculus of variations.

 

The group has given rise to outstanding contributions to areas in applied mathematics and modeling which has facilitated strong interactions with diverse areas in mechanics and mathematical physics. The breadth, depth and quality of this achievement places the group in a prime position in the international scientific community, acknowledging our seminal work in numerical and mathematical analysis in fluid mechanics and fluid-structure type interactions, besides having established the foundations of and developed the theory on which Bloch analysis in homogenization is based.

The impact of our research is reflected by the number of references to our publications made by influential mathematicians in their books, as well as citations in publications derived from our works which appear in the specialist literature. Our works registered more than 450 citations of articles and books. As a further indication of the importance of our work to the international mathematical community, members of the group have been invited to deliver plenary talks and inaugural presentations at renowned international mathematics meetings.

Over the years, we have established an international network of collaboration that includes researchers from different institutions and universities in France, Spain, India and USA. In Latin America we highlight our collaboration with IMPA and University of Campinas. The group of researchers in mathematical mechanics has a long history of interaction as much with industry in Chile as with industry overseas.

An initiative which illustrates this is our FONDEF project on the fluid-dynamics of fusion, conversion and refining of copper which was carried out over three and a half years in cooperation with CODELCO and IM2. Contributions by the IM2 engineers were critical in suggesting modifications to the design of the Teniente-converter. More recently, members of the group have been awarded the following applied contracts which are currently in progress: The Mathematical Modeling of In Situ Leaching Technology (with CODELCO) and the Numerical Simulation of Ventilation Conditions in Trains with METRO. Also we have opened the Mathematical Modeling in Mining and Metallurgy Laboratory (LM4) to consolidate a multidisciplinary technology development team which focuses on providing decision making support in important investment plans elaborated by CODELCO.