Uso de la química de elementos altamente siderófilos y calcófilos para discriminar rocas asociadas a yacimientos minerales productivos
Determination of magma fertility and sulfide saturation for giant porphyry copper deposits in central Chile: A platinum-group element perspective
Fondecyt de Postdoctorado 2025 Proyecto Nº 3250704, Universidad de Chile y Universidad de O’Higgins – Implementación de la investigación ‘Exploración de las bases neuroanatómicas de la alteración del insight en la enfermedad de Alzheimer’ como Investigador Postdoctoral
Implementación de la investigación ‘Uso de inteligencia artificial para la exploración de las bases neuroanatómicas del deterioro del insight en la enfermedad de Alzheimer’ desde el cargo de Investigador Postdoctoral del Instituto de Ciencias de la Ingeniería de la Universidad de O’Higgins.
Fondo de investigación para estudiantes de pregrado, III convocatoria verano 2025. Marco Pérez
PINNs
MagTecSkin: Novel Tactile Sensitive Electronic Skin based on Magnetic Technology
Tactile sensing capabilities are crucial for manual dexterity, yet remain beyond the reach of todays robots. While recently developed robotic skins can measure contact forces accurately, they cannot bend or stretch, and therefore they cannot cover complex robot parts, such as finger joints or deformable links. Lorenzo and team will develop an innovative skin based on magnetic technology that can measure 3D contact forces on multiple contact points, as well as bend and stretch. This will unlock full-cover articulated and soft robots, which will ultimately lead to vastly advanced robot dexterity in manufacturing, logistics, agriculture, healthcare, and beyond.
Fondo de investigación para estudiantes de pregrado, III convocatoria verano 2025. Nilda Molina
A
Qualitative behaviour of nonlinear PDE from Physics and Biology
This research proposal aims to study the long-term behavior of solutions to partial differential equations arising from dispersive dynamics, kinetic models, and integro-differential dynamics in ecology; and to study extremals of functional inequalities in connection to the ground states of partial differential equations arising from quantum mechanics and diffusion phenomena. Five major topics are proposed: Relativistic quantum mechanics, Dirac operators and functional inequalities; Symmetry breaking in weighted functional inequalities and weighted diffusions; long time dynamics in dispersive PDEs in one space dimension; long-term dynamics in nonlocal models from ecology; and hypocoercivity and decay to equilibrium in kinetic models with heavy tails.
The first topic focuses on establishing connections between spectral problems and functional inequalities for Dirac operators. The aim is to analyse the symmetry of optimal spinors in inequalities of Keller-Lieb-Thirring type, and to obtain the solitary waves of Soler-type nonlinear Dirac equations as optimizers of a nonlinear inequality. The second topic aims to characterize a symmetry range in which optimal functions are radially symmetric for weighted logarithmic Sobolev inequalities and a new family of Caffarelli-Kohn-Nirenberg inequalities. A nonlinear carré-du-champ method will be adapted to prove entropy-type estimates. Rigidity, perturbation, and stability issues will be addressed. The third topic seeks to study the asymptotic stability of topological and non-topological solitions for a class of dispersive PDEs in dimension one. A new method is proposed, based on perturbations in weighted spaces with exponential weights, on the so-called virial identities, and on the study of existence of breathers. The fourth topic concerns the description of evolutionary stable strategies of long-term dynamics of integro-differential models that arise in the modeling of structured populations, and to obtain qualitative and quantitative insights on the concentration dynamics. In the fifth topic, the aim is to extend the Dolbeault-Mouhot-Schmeiser method to study the large-time behavior of solutions for a broad family of kinetic equations in which the confinement potential exhibits heavy tails.
The goals of this project are multiple: to strengthen and to create new collaborative research networks between France and Chile in the field of nonlinear partial differential equations and applications, to publish co-authored articles in top-tier journals and disseminate the results in international meetings, and to promote the formation of advanced human capital. In order to achieve these goals, yearly workshops will be organized in France and Chile to account for the progress of the investigations as well as to encourage the participation of students and young researchers. International training of doctoral and postdoctoral researchers will be ensured by allocating resources from this project for exchanges. Considering the history of successful collaboration amongst the members of this project, and their expertise in their research fields, we are confident about the successful termination of the project. In particular, we expect to pave the way for new research avenues.
The main scientific contribution of this proposal involves adapting state-of-the-art techniques from PDEs and nonlinear analysis to obtain qualitative and quantitative results for variational problems and partial differential equations, in which the setting plays a crucial role: complex-valued matrices (first topic), nonlinear and weighted (second topic), strongly nonlinear and dispersive (third topic), nonlocal (fourth topic), general assumption on the tail of the confining potential (fifth topic). This proposed research will provide insights into spectral theory, stability theory of equilibria of differential equations, optimal rates of convergence to equilibria, and their relation to optimal constants in functional inequalities. The expected results will help improving the understanding of various real-life phenomena, including population-dynamics, relativistic quantum mechanics, and diffussion processes. The viability of the project is sustained on the expertise of the members of the Chilean and French research teams, including experts in partial differential equations, nonlinear analysis, calculus of variations, and mathematical physics. Their successful collaboration record and significant contributions to these fields only strengthen the potential of this proposal.
In conclusion, the present research project will not only foster the scientific cooperation between Chile and France but it will also provide meaningful advancements in the aforementioned fields and their application to various physical phenomena.
Determination of magma fertility and sulfide saturation for giant porphyry copper deposits in central Chile: A platinum-group element perspective
Uso de la química de elementos altamente siderófilos y calcófilos para discriminar rocas asociadas a yacimientos minerales productivos
Este proyecto fue adjudicado, pero renunciado por el investigador principal
Overview: Mechanical wave propagation physics is related to traumatic brain injury mechanisms. For instance, nonlinear shear waves can form in the brain progressively with propagation, amplifying the acceleration locally. This phenomenon is compatible with axonal brain injury in which the lesions are localized far from the impact region. Within the brain, not only shear waves propagate. Especially when considering the brain is full of folds and surfaces, including the gray-white matter interface, which can be seen in Fig. 1. The abundance of interfaces or surfaces makes us hypothesize that surface waves might be crucial for describing the biomechanics of traumatic brain injury. The surface waves are named after the nature of the interface. A wave propagating in a solid-vacuum interface is known as a Rayleigh wave, a wave propagating in a solid-fluid interface is known as a Scholte wave, and a wave propagating in a solid-solid interface is known as a Stoneley wave. This last might propagate within an interface formed by two types of soft tissue. An example of this is the interfaces formed by the white and gray matter in the brain (see Fig. 1). Surface waves, although confined to a surface, can penetrate up to a wavelength. In the context of soft tissues, the typical frequencies of elastic waves that propagate are in the range of 10 to 300 Hz. At these frequencies, the wavelengths are on the order Figure 1: Section of a temporal
of centimeters, creating the necessity of studying these waves at brain lobe. Image obtained from depth. Surface waves are not explored sufficiently in incompressible soft the visible human project [1]. solids yet. We recently measured Scholte waves at depth in these materials. However, we are not aware of measurements of Stoneley waves at depth in incompressible soft solids like brain matter or gelatin. The lack
of this experimental evidence is due to the challenges of measuring deformation in opaque materials without disrupting the medium. Thus, the general objective of this proposal is to detect, describe and characterize the propagation of Stoneley waves in interfaces formed by two incompressible tissue-mimicking materials using Ultrafast Ultrasound elastography-related techniques.
Methodology: Advanced ultrasound imaging techniques implemented on a highly customized ultrasound imaging platform designed for high frame-rate imaging will be used to characterize fundamental Stoneley wave physics propagating at the interfaces between two soft solids. We first will perform experiments in flats and simple interfaces to obtain the parameter space (shear modulus, density, and prestress) in which planar Stoneley waves exist. Then, we will explore the effects of the bonding condition between the two mediums on the dispersion relation. Third, we will investigate the interaction of the shape of the interface on the wave propagation, and lastly, we will intend to propagate Stonely waves into 3D inclusions. These observations will be achieved with a number of steps that integrate advancements in ultrasound imaging, algorithms that measure the deformation, and modeling. Custom two-dimensional and three-dimensional imaging sequences, designed for displacement tracking, will be implemented for a dedicated Linear and Matrix array transducer that has 128 or 1024 elements and can reach a spatial resolution of 200microns at a very high framerate in the order of 10000 frames per second (2D or 3D frames respectively).
Expected results: The results of this proposal will elucidate the conditions that the two soft solids need to propagate Stoneley waves. These conditions refer to the combination of mechanical properties of the materials, such as shear modulus and density, and the prestress field needed. We expect to establish the effect that the bonding condition between the two soft solids has on the nature of the Stoneley wave. In particular, we will monitor how the Stoneley wave speed and dispersion change with different bonding conditions. We believe this phenomenology has implications in imaging technology, tumor diagnosis, and brain injury biomechanics.