Titlebook: Research in Mathematics of Materials Science; Malena I. Espa?ol,Marta Lewicka,Anja Schl?merkempe Book 2022 The Editor(s) (if applicable) a

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Poro-Visco-Elasticity in Biomechanics: Optimal Controlen permeability .(., .), which translates into a convex control problem, with both distributed and boundary controls. We focus on investigating the problem of maintaining the solid displacement and Darcy pressure close to desired values (motivated by applications related to tissue perfusion in the e

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Global Gradient Estimate for a Divergence Problem and Its Application to the Homogenization of a Mag a non-dilute suspension of magnetic particles in a viscous flow. More specifically, in this paper, a restrictive assumption on the coefficients of the coupled equation, made in Dang et al. (SIAM J. Appl. Math. 81(6):2547–2568, 2021), that significantly narrowed the applicability of the homogenizati

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On Static and Evolutionary Homogenization in Crystal Plasticity for Stratified Compositesed in (Christowiak and Kreisbeck, Calc. Var. PDE, 2017) as a homogenization limit via Γ-convergence. First, we analyze the minimizers of this limit model, addressing the question of uniqueness and deriving necessary conditions. In particular, it turns out that at least one of the defining quantities

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Existence of Global Solutions for 2D Fluid–Elastic Interaction with Small Data incompressible viscous fluid. We consider a fixed-domain system, or ., that corresponds to the assumption of linear elasticity. The key ingredients of the proof are an approximation argument that transfers recent results on regularity-preserving strong solutions to a weaker functional analytic sett

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3D Image-Based Stochastic Micro-structure Modelling of Foams for Simulating Elasticitybles geometric characterization of the micro-structure of materials. Stochastic geometry models can be fit to the observed micro-structures. By alteration of the model parameters, virtual micro-structures with modified geometry can be generated. Numerical simulation of elastic properties in realizat

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Machine Learning for Failure Analysis: A Mathematical Modelling Perspective this context, from the mathematical perspective, failure is a gradual or sudden loss of the ability to operate. Failure analysis leads to many interesting mathematical challenges spanning from model development to mathematical foundations including simulations and machine learning approaches. From

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