arXiv subjects

Nicolas Martinez

Publications and source records attributed to Nicolas Martinez.

3 recordsLinked to original sources

arXiv2024

Symplectic Geometry, Poisson Geometry, and Beyond

Symplectic and Poisson geometry emerged as a tool to understand the mathematical structure behind classical mechanics. However, due to its huge development over the past century, it has become an independent field of research in differential geometry. In this lecture notes, we will introduce the essential objects and techniques in symplectic geometry (e.g Darboux coordinates, Lagrangian submanifolds, cotangent bundles) and Poisson geometry (e.g symplectic foliations, some examples of Poisson structures). This geometric approach will be motivated by examples from classical physics, and at the end we will explore applications of symplectic and Poisson geometry to Lie theory and other fields of mathematical physics.

math.SG↗

arXiv2020

Holistic Multi-scale Imaging of Oxygen Reduction Reaction Catalyst Degradation in Operational Fuel Cells

Wide proliferation of low temperature hydrogen fuel cell systems, a key part of the hydrogen economy, is hindered by degradation of the platinum cathode catalyst. Here, we provide a device level assessment of the molecular scale catalyst degradation phenomena, using advanced operando X-ray scattering tomography tailored for device-scale imaging. Each cell component, including the catalyst, carbon support, polymer electrolyte, and liquid water can be simultaneously mapped, allowing for deep correlative analysis. Chemical and thermal gradients formed inside the operating fuel cell produce highly heterogeneous degradation of the catalyst nanostructure, which can be linked to the macroscale design of the flow field and water distribution in the cell materials. Striking differences in catalyst degradation are observed between operating fuel cell devices and the liquid cell routinely used for catalyst stability studies, highlighting the rarely studied but crucial impact of the complex operating environment on the catalyst degradation phenomena. This degradation knowledge gap highlights the necessity of multimodal in situ characterization of real devices when assessing the performance and durability of electrocatalysts.

physics.app-ph↗

arXiv2018

Exploiting Capacity of Sewer System Using Unsupervised Learning Algorithms Combined with Dimensionality Reduction

Exploiting capacity of sewer system using decentralized control is a cost effective mean of minimizing the overflow. Given the size of the real sewer system, exploiting all the installed control structures in the sewer pipes can be challenging. This paper presents a divide and conquer solution to implement decentralized control measures based on unsupervised learning algorithms. A sewer system is first divided into a number of subcatchments. A series of natural and built factors that have the impact on sewer system performance is then collected. Clustering algorithms are then applied to grouping subcatchments with similar hydraulic hydrologic characteristics. Following which, principal component analysis is performed to interpret the main features of sub-catchment groups and identify priority control locations. Overflows under different control scenarios are compared based on the hydraulic model. Simulation results indicate that priority control applied to the most suitable cluster could bring the most profitable result.

cs.LG↗