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.
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-Velįzquez).- 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. engül).- 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).< p="">
Malena I. Espańol 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 Professors 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.
