Research in Mathematics of Materials Science

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.

Autorentext

Malena Espanol is an applied mathematician specializing in Numerical Analysis and Numerical Linear Algebra. Her research involves developing, analyzing, and applying mathematical models and numerical methods to problems arising in materials science and image processing. She is a faculty member in the School of Mathematical and Statistical Sciences at Arizona State University, USA. Marta Lewicka is a mathematician specializing in Analysis and PDEs. She has contributed results in the theory of nonlinear elasticity, hyperbolic systems of conservation laws, fluid dynamics, calculus of variations, potential theory and differential games. She is a Fellow of the American Mathematical Society and she holds Professor's scientific title awarded by the President of the Republic of Poland. She works at the University of Pittsburgh, USA. Lucia Scardia is a mathematician working in the calculus of variations and partial differential equations with applications in materials science. In particular, her interests include homogenization (deterministic and stochastic), harmonic analysis, non-local aggregation problems, dislocation theory, plasticity, and fracture and damage. She is an Associate Professor at Heriot-Watt University in Edinburgh, UK. Anja Schlömerkemper is a professor of mathematics specializing in Mathematical Analysis with applications to Materials Science and Physics. She studies elastic and magnetic materials by involving methods from calculus of variations, PDEs and homogenization theory. She is the president of the International Society for the Interaction of Mechanics and Mathematics and she leads the chair of Mathematics in the Sciences at the University of Würzburg, Germany.

Inhalt

Part I: Research Paper - Interaction between oscillation and singular perturbations in a one-dimensional phase-field model (I. Zeppieri).- Grain growth and the effect of different time scales (Epshteyn).- Regularity of minimizers for a general class of constrained energies in two-dimensional domains with applications to liquid crystals (P. Bauman).- On some models in radiation hydrodynamic Poro-visco-elasticity in biomechanics - optimal control (L. Bociu).- Global gradient estimate for a divergence problem and its application to the homogenization of a magnetic suspension (Y. Gorb).- On static and evolutionary homogenization in crystal plasticity for stratified composites (E. Davoli).- On the prescription of boundary conditions for nonlocal Poisson's and peridynamics models (D'Elia).- Existence of global solutions for 2D fluid-elastic interaction with small data (M. Luckas).- Doubly nonlocal Cahn-Hillard equations. Wellposedness and asymptotic behavior (P. Radu).- 3D image based stochastic micro-structure modelling of foams for simulating elasticity (K. Schladitz).- Machine learning for failure analysis: a mathematical modelling perspective (Pérez-Velázquez).- Invertibility of Orlicz-Sobolev maps (B. Stroffolini).- Global existence of solutions for the one-dimensional response of viscoelastic solids within the context of strain limiting theory (Y. Sengül).- Generic for dissipative solids with bulk-interface interaction (M. Thomas).- PART II: Review Papers - Phase separation in heterogeneous media (R. Venkataraman).- Some recent results on 2d crystallization for sticky disc models and generalizations for systems of oriented particles (De Luca).- Pattern formation for nematic liquid crystals-modelling, analysis, and applications (A. Majumdar).- On applications of Herglotz-Nevanlinna functions in material sciences, I: classical theory and applications of sum rules (Yvonne Ou).- On applications of Herglotz-Nevanlinna functions in material sciences, II: extended applications and generalized theory (Yvonne Ou).- Rigidity and flexibility in the modelling of shape-memory alloys (A. Rüland).