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Variational and PDE Methods in Nonlinear Science
This book presents three short courses on topics at the intersection of Calculus of Variations, PDEs and Material Science, based on lectures given at the CIME summer school “Variational and PDE Methods in Nonlinear Science”, held in Cetraro (Italy), July 10–14, 2023. Fabrice Bethuel discusses aympototics for Allen–Cahn systems, providing an overview of classical methods and tools for the scalar case and further results for the two-dimensional vectorial case. An alternate monotonicity formula is described, and the still open parabolic vectorial case is considered. Angkana Rüland considers the modelling and analysis of microstructures in shape-memory alloys, including material on quas...
Variational and PDE Methods in Nonlinear Science
This book presents three short courses on topics at the intersection of Calculus of Variations, PDEs and Material Science, based on lectures given at the CIME summer school "Variational and PDE Methods in Nonlinear Science", held in Cetraro (Italy), July 10-14, 2023. Fabrice Bethuel discusses aympototics for Allen-Cahn systems, providing an overview of classical methods and tools for the scalar case and further results for the two-dimensional vectorial case. An alternate monotonicity formula is described, and the still open parabolic vectorial case is considered. Angkana Rüland considers the modelling and analysis of microstructures in shape-memory alloys, including material on quasiconvexi...
Mathematical Methods in Liquid Crystal Optics and Lens Design
Freeform lens design has numerous applications in imaging, aerospace, and biomedicine. Due to recent advancements in precision cutting and grinding, the manufacturing of freeform optical lenses with very high precision is now possible. However, there is still a significant lack of mathematical literature on the subject, and essentially none related to liquid crystals. Liquid crystals are appealing for use in imaging due to their flexibility and unique electro-optical properties. This book fills a gap in mathematical literature and attracts focus to liquid crystals for freeform lens design. It provides a rigorous mathematical perspective on liquid crystal optics, focusing on ray tracing in th...
Ecología de Comunidades
En esta segunda edición de Ecología de comunidades se explica la teoría que sirve de base a la praxis ecológica-comunitaria, y se presentan análisis y ejemplos que caracterizan la ecología de comunidades, con énfasis en estudios de nuestra región, principalmente de Chile y Argentina. En relación a la primera edición se han eliminado secciones que en la última década han quedado obsoletas y se han agregado temas álgidos tales como redes tróficas e invasiones biológicas. El libro está organizado en 14 capítulos autocontenidos, que no requieren leerse en ningún orden particular y se complementa con dos apéndices: uno con perspectiva histórica y otro con énfasis epistemológico. Las más de mil referencias citadas cubren desde trabajos clásicos hasta contemporáneos. La citación es ecléctica, con una mezcla de autores principalmente estadounidenses, europeos y australianos, pero también con numerosas referencias a trabajos que han hecho contribuciones importantes desde Sudamérica, en particular por ecólogos comunitarios chilenos, argentinos y uruguayos.
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