Espanol M. Research in Mathematics of Materials Science 2022

Textbook in PDF format

This volume highlights contributions of women mathematicians in the study of complex materials and includes both original research papers and reviews. The featured topics and methods draw on the fields of Calculus of Variations, Partial Differential Equations, Functional Analysis, Differential Geometry and Topology, as well as Numerical Analysis and Mathematical Modelling. Areas of applications include foams, fluid-solid interactions, liquid crystals, shape-memory alloys, magnetic suspensions, failure in solids, plasticity, viscoelasticity, homogenization, crystallization, grain growth, and phase-field models.
Interaction Between Oscillations and Singular Perturbations in a One-Dimensional Phase-Field Model
Grain Growth and the Effect of Different Time Scales
Regularity of Minimizers for a General Class of Constrained Energies in Two-Dimensional Domains with Applications to Liquid Crystals
On Some Models in Radiation Hydrodynamics
Poro-Visco-Elasticity in Biomechanics: Optimal Control
Global Gradient Estimate for a Divergence Problem and Its Application to the Homogenization of a Magnetic Suspension
On Static and Evolutionary Homogenization in Crystal Plasticity for Stratified Composites
On the Prescription of Boundary Conditions for Nonlocal Poisson's and Peridynamics Models
Existence of Global Solutions for 2D Fluid–Elastic Interaction with Small Data
Doubly Nonlocal Cahn–Hilliard Equations
3D Image-Based Stochastic Micro-structure Modelling of Foams for Simulating Elasticity
Machine Learning for Failure Analysis: A Mathematical Modelling Perspective
Invertibility of Orlicz–Sobolev Maps
Global Existence of Solutions for the One-Dimensional Response of Viscoelastic Solids Within the Context of Strain-Limiting Theory
GENERIC for Dissipative Solids with Bulk–Interface Interaction
Phase Separation in Heterogeneous Media
Some Recent Results on 2D Crystallization for Sticky Disc Models and Generalizations for Systems of Oriented Particles
Pattern Formation for Nematic Liquid Crystals—Modelling, Analysis, and Applications
On Applications of Herglotz-Nevanlinna Functions in Material Sciences, I: Classical Theory and Applications of Sum Rules
On Applications of Herglotz–Nevanlinna Functions in Material Sciences, II: Extended Applications and Generalized Theory
Rigidity and Flexibility in the Modelling of Shape-Memory Alloys