Mathematical and Computational Modelling Across the Scales

Many physical and engineering systems deal withmicro-, meso-, macro-, and multi-scale phenomena. The accurate description and the reliable simulation of such phenomena entail major challenges from the point of view of both mathematical modelling and computational engineering.This book covers a selection ofchallenges related to "Mathematical and Computational Modelling Across the Scales", stemming fromthe lecture notes of theXX edition of the Jacques-Louis Lions Spanish-French School in Numerical Simulations in Physics & Engineering.The thematic focus is broad, encompassing mathematical models of complex physical problems, theoretical results on their derivation, and development of numerical methods for their efficient simulation. The contributions of the book include: uncertainty quantification for phenomena at different scales such as epidemic dynamics, medical imaging, and geophysical exploration; structural health monitoring integrating small-scale sensor data in large-scale computational models; frontier numerical methods for the simulation ofgeophysical and heliophysical dynamics accounting formulti-scale, heterogeneous media; multi-physics, multi-scale models for the mechanobiology of atheroma plaques formation; locomotion models for swimming at the micro-scale; mathematical foundations of quantum mechanics phenomena at the micro-scale. The book is addressed to scientists and engineers, from both academia and industry,interested in the mathematical modelling and numerical simulation ofa variety of complex systems in physics and engineeringcharacterised by multiple scales.