Proyectos

Esta propuesta está dedicada al estudio de problemas locales y no locales, elípticos y parabólicos, en Ecuaciones en Derivadas Parciales (EDP). Se espera obtener resultados de existencia para los problemas planteados, son 3 los problemas que se quieren estudiar: El primer modelo involucra al Laplaciano Fraccionario con singularidades no lineales (Ecuación Fraccionaria de Burger ver (3)). En este problema queremos probar la existencia y la no unicidad de soluciones débiles de (3), teniendo en cuenta que las soluciones de entropía son soluciones débiles, el primer paso será probar existencia de soluciones de entropía, para esto usaremos el método de sub y supersoluciones, donde probaremos los resultados de los principios de Comparación y L1-Contracción. Una vez teniendo la existencia de solución de entropía, pasaremos a construir una solución débil que no sea solución de entropía, donde esta solución débil se obtendrá como límite de soluciones a problemas regularizados estacionarios, en donde usaremos métodos variacionales para resolver el problema regularizado. El segundo problema, es una extensión al caso no local del problema estudiado en [L. Jeanjean and V. Radulescu, Nonhomogeneous quasilinear elliptic problems: linear and sublinear cases, Journal d'Analyse Mathématique (2021)]. Para probar existencia de soluciones aplicaremos estudios de mínimos locales y el teorema del paso de montaña para el funcional de energía asociado. Para finalizar nuestra propuesta, queremos encontrar soluciones periódicas para sistemas de EDP de cuarto orden (tipo Fisher-Kolmogorov generalizado, ver (9). Siguiendo las técnicas en [P. Smyrnelis, Connecting orbits in Hilbert Spaces and application to PDEs, Comm. Pure Appl Anal 19 (5): 2897--2818 (2020)], usaremos métodos variacionales para probar la existencia de órbitas conectadas en espacios de Hilbert. Construiremos órbitas periódicas usando la construcción desarrollada por Alessio, Montecchiari y Zúñiga en [F. Alessio and P. Montecchiari and A. Zuniga, Prescribed energy connecting orbits for gradient systems, Discr. Cont. Dyn. Systems 39 (8): 4895--4928 (2019].

KhipuX support grant for organizing the Third Latin American Summer School on Cognitive Robotics (LACORO) https://www.lacoro.org/

KhipuX support grant for organizing the Third Latin American Summer School on Cognitive Robotics (LACORO) https://www.lacoro.org/

The world's transition to using cleaner energy sources to address climate change has led to a sharp rise in the demand for base and precious metals. Consequently, discovering new ore deposits to meet this growing demand and prevent supply shortages has emerged as one of the greatest challenges of the 21st century. Discovery of new magmatic-hydrothermal ore deposits can be improved based on a fundamental understanding of the geological processes that control the flux and focusing of ore-constituting elements in the Earth’s crust, and by identifying the differences between the bulk-rock and mineral chemistry of ore-forming and ordinary—barren—granitoids. Large metal anomalies in the Earth’s upper crust, such as porphyry copper-(molybdenum) deposits (PCDs), occur in intimate association with oxidized and water-rich arc magmatism in subduction zones. However, these deposits occur in restricted crustal domains and form in response to specific tectono-magmatic events, indicating that not all arc magmas have the same ore-forming potential. Understanding why only some magmas produced large PCDs while most other arc magmas remain barren is a fundamental scientific question and key to developing efficient exploration strategies. The volatile element composition of arc magmas, including water, sulfur, and halogens such as chlorine and fluorine, as well as their oxygen fugacity, exert a critical control on their ore-forming potential (i.e., ore fertility). These components are not only key to the complexation and transport of ore metals during hydrothermal activity, but also influence the amount of ore metals transported by magmas and the efficiency to which they are transferred from magmas to exsolved fluids. Magmatic differentiation in lower crustal hot zones beneath thick crustal regions is expected to enhance the volatile element budget and oxygen fugacity of evolving magmas that are discharged to the upper crust. This occurs due to the accumulation of incompatible volatile elements during successive cycles of recharge by mafic magmas and crystallization, facilitated by the deeper and hotter conditions beneath thicker arc crusts. As such, an increasingly recognized hypothesis holds that ore-forming magmas display a particularly increased budget of volatile elements and higher oxygen fugacities when compared to barren arc magmas, and that this is largely influenced by the arc crust thickness. The proposed work will test this hypothesis by focusing on the Miocene to Mio-Pliocene magmatism and associated world-class PCD mineralization in the Andes of central Chile. From the Early Miocene to the Mio-Pliocene, the arc segment located between latitudes ~33–34.5° S in the Andes of central Chile has seen a continued increase in crustal thickness and has evolved from being barren in the Early Miocene to producing some of the largest PCDs of the world in the Mio-Pliocene, such as El Teniente and Rio Blanco-Los Bronces. This geological scenario and the spatial and age distribution of the associated outcropping intrusive rocks offer a unique opportunity to investigate the temporal evolution of the volatile composition of magmas and its consequences for ore fertility. The goal of this proposal is to examine, adopting a regional scale perspective, the evolution in the volatile composition and oxygen fugacity of magmas produced in this arc segment and its relationship to magmatic ore fertility, as well as how this may have been influenced by changes in crustal thickness. To achieve this, I will sample an extensive suite of granitoids that represent a continuum from Early Miocene to Mio-Pliocene magmas, including porphyry-forming intrusions. By combining zircon petrochronology, apatite, biotite, and amphibole mineral chemistry, in conjunction with the bulk-rock composition of intermediate to felsic intrusive rocks, I will be able to constrain relative changes in the hydration state, sulfur contents, halogen and oxygen fugacities, as well as in their associated crustal thickness during the evolution of the selected arc segment. This will be done by implementing a combination of cutting-edge analytical techniques, including synchrotron-based sulfur X-ray absorption near edge structure spectroscopy, electron probe microanalysis, (laser ablation) inductively coupled plasma mass spectrometry, and X-ray fluorescence spectrometry. I aim at (1) testing the differences in the volatile composition of barren and ore-forming intrusive rocks; (2) determining whether there is a gradual change in the volatile systematics of magmas during the evolution of the studied arc segment; and (3) analyzing the relationship between variations in crustal thickness and the volatile composition of associated magmas. The results of this proposal will lead to a better understanding of the magmatic controls underpinning the formation of giant PCDs and will provide valuable insights into identifying the differences between the bulk-rock and mineral chemistry of ore-forming and barren granitoids as tools for vectoring mineralized regions.

Estudio e implementación de métodos híbridos para la resolución computacional de EDP aplicadas a Ciencia de Datos.

Escuela de Verano Latino Americana de Robotica (LACORO)

Escuela de Verano Latino Americana de Robotica (LACORO)

The research project "Matrices, Optimization, and Randomness with Applications in Data Science (MORA-DataS)" is composed of research teams from Bolivia, Chile, France, and Peru. This project is funded by the regional program MATH-Amsud in cooperation with UMSA (Bolivia), ANID, CMM (Chile), MEAE (France), and CONCYTEC (Peru). The aim of this project is to study diverse optimization models, deterministic and stochastic, and to investigate various problems in matrix analysis with potential applications in data science. Some of the research topics are computing angles between convex cones, inverse eigenvalue problems, proximal algorithms for symmetric cone optimization, nonlinear second-order cone programming problems, nonsmooth joint chance constrained optimization problems, and Euclidean Jordan algebras for optimization.

Interpretar el paleoclima del Pleistoceno de Chile central