Research in mathematics of materials science / / edited by Malena I. Español [and three others]

• Record Nr.: UNISA996490345503316
• Pubbl/distr/stampa: Cham, Switzerland : , : Springer, , [2022]; ©2022
• ISBN: 3-031-04496-7
• Descrizione fisica: 1 online resource (514 pages)
• Collana: Association for Women in Mathematics ; ; v.31
• Disciplina: 620.11
• Soggetti: Materials science; Women in mathematics; Ciència dels materials; Investigació matemàtica; Dones matemàtiques; Llibres electrònics
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Intro -- Preface -- Acknowledgements -- Contents -- About the Editors -- Part I Research Papers -- Interaction Between Oscillations and Singular Perturbations in a One-Dimensional Phase-Field Model -- 1 Introduction -- 2 Setting of the Problem and Statement of the Main Result -- 3 Preliminary Results -- 3.1 The Optimal-Profile Problem -- 4 Oscillations on a Larger Scale than the Singular Perturbation -- 5 Oscillations on the Same Scale as the Singular Perturbation -- 6 Oscillations on a Smaller Scale than the Singular Perturbation -- 7 Limit Analysis of m -- References -- Grain Growth and the Effect of Different Time Scales -- 1 Introduction -- 2 Review of the Models with Single Triple Junction -- 3 Extension to Grain Boundary Network -- 4 Experiments and Numerical Simulations -- 4.1 Experimental Results: Grain Boundary Character Distribution -- 4.2 Numerical Experiments -- 5 Conclusion -- References -- Regularity of Minimizers for a General Class of Constrained Energies in Two-Dimensional Domains with Applications to Liquid Crystals -- 1 Introduction. -- 2 Continuity and H2loc Estimates for Minimizers in Two-Dimensional Domains -- 3 ; Proof of Theorem 1 -- 4 Applications to Liquid Crystals -- References -- On Some Models in Radiation Hydrodynamics -- 1 Introduction -- 2 Compressible Viscous Radiation Fluid -- 2.1 Hypotheses and Main Results -- 2.2 Constitutive Equations -- 2.3 Weak Formulation -- 2.4 Existence Result -- 2.5 Semi-Relativistic Models -- 3 Inviscid Case -- 3.1 Euler System with Damping Term -- 3.1.1 Hypotheses -- 3.2 Non-isentropic Euler-Maxwell's System Coupled with Transport of Radiation -- References -- Poro-Visco-Elasticity in Biomechanics: Optimal Control -- 1 Introduction -- 2 Poro-Visco-Elasticity: Well-posedness Analysis -- 3 Optimal Control Problems: Well-Posedness -- 4 Necessary Optimality Condition -- 4.1 Adjoint System.; 4.2 First Order Necessary Optimality Conditions -- References -- Global Gradient Estimate for a Divergence Problem and Its Application to the Homogenization of a Magnetic Suspension -- 1 Introduction -- 2 Formulation -- 2.1 Notation -- 2.2 Setup of the Problem -- 3 Statement and Discussion of the Main Result -- 4 Interior Estimates -- 5 Boundary Estimates, Green Functions, Dirichlet Correctors, and Proof of Main Theorem -- 6 Application to Magnetic Suspensions -- 7 Conclusions -- Appendix -- References -- On Static and Evolutionary Homogenization in Crystal Plasticity for Stratified Composites -- 1 Introduction -- 1.1 Notation -- 2 Minimizers of the Static Homogenized Limit Problem -- 3 Homogenization via Evolutionary -Convergence -- 3.1 The Case s=e2 -- 3.2 The Case s=e1 -- References -- On the Prescription of Boundary Conditions for Nonlocal Poisson's and Peridynamics Models -- 1 Introduction and Motivation -- 2 Preliminaries -- 2.1 The Nonlocal Poisson's Problem -- 2.2 The Linear Peridynamic Solid Model -- 3 Proposed Strategies -- 3.1 Dirichlet-to-Dirichlet Strategy -- 3.2 Dirichlet-to-Neumann Strategy -- 4 Convergence to the Local Limit -- 5 Numerical Tests -- 5.1 Consistency Tests for the Nonlocal Poisson's Equation -- 5.2 Convergence Tests for the Nonlocal Poisson's Equation -- 5.3 Numerical Tests for the LPS Model -- 6 Conclusion -- References -- Existence of Global Solutions for 2D Fluid-Elastic Interaction with Small Data -- List of Definitions -- 1 Introduction -- 2 Local Existence of Solutions -- 3 Existence of Global Solutions for Small Data -- Appendix -- Definition of Spaces and Auxiliary Estimates -- Estimates on (u·) u -- Approximation of Data -- References -- Doubly Nonlocal Cahn-Hilliard Equations -- 1 Introduction -- 2 Nonlocal Vector Calculus -- 3 Asymptotic Behavior of Solutions to Doubly Nonlocal Cahn-Hilliard Systems.; 3.1 Decay Estimates for the Linearized System with Time-Dependent Coefficients -- 4 Steady-State Solutions -- 4.1 Well-posedness of Solutions -- 4.2 Regularity of Steady-State Solutions in the Nonlinear Settings -- 4.3 Higher Integrability of Steady-State Solutions -- 5 Conclusions and Future Directions -- References -- 3D Image-Based Stochastic Micro-structure Modelling of Foams for Simulating Elasticity -- 1 Introduction -- 2 3D Image Analysis for Foams -- 2.1 Random Closed Sets and Their Characteristics -- 2.2 Image Analysis -- 3 Random Laguerre Tessellations and Fitting Them -- 3.1 Laguerre Tessellations Generated by Random Sphere Packings -- 3.2 Fitting a Tessellation Model -- 4 Numerical Simulation of Elastic Properties -- 4.1 Effective Properties of Micro-Structured Materials -- 4.2 Lippmann-Schwinger Fast Fourier Transform-Based Solver -- 5 Application Example -- 5.1 Material -- 5.2 Image Analysis and Model Fit -- 5.3 Prediction of Mechanical Properties -- 6 Conclusion -- References -- Machine Learning for Failure Analysis: A Mathematical Modelling Perspective -- 1 Introduction -- 2 Survival Analysis -- 3 Machine Learning -- 3.1 Discriminative Machine Learning -- 3.1.1 The ; Algorithms of Machine Learning -- 3.1.2 Evaluating a Machine Learning Model -- 3.1.3 Under-fitting and Over-fitting -- 3.2 Generative Machine Learning -- 4 Use Cases -- 4.1 Regression Models -- 4.1.1 Random Forest Regression -- 4.1.2 Survival Analysis -- 4.1.3 Random Survival Forests -- 4.1.4 Neural Networks -- 4.2 Classification Models -- 4.2.1 Support Vector Machines -- 4.2.2 Neural Networks -- 4.3 Anomaly Detection -- 4.4 Generative Models -- 4.4.1 Naïve Bayes -- 4.4.2 Bayesian Networks -- 5 Conclusions -- References -- Invertibility of Orlicz-Sobolev Maps -- 1 Introduction -- 2 Notation -- 3 Orlicz-Sobolev Spaces -- 3.1 Traces.; 4 Some Definitions and Preliminary Results -- 4.1 Degree for Orlicz-Sobolev Maps, Topological Image of a Set, and Geometric Image of a Set -- 5 The Class of Admissible Functions -- 5.1 Extension Properties -- 5.2 Regular Functions in A(Ω) -- 5.3 Some Properties of Orientation-Preserving Functions in A(Ω): Boundedness and Global Invertibility -- 6 Existence of Minimizers -- References -- Global Existence of Solutions for the One-Dimensional Response of Viscoelastic Solids Within the Context of Strain-Limiting Theory -- 1 Introduction -- 2 Preliminaries -- 2.1 Local Existence for the Displacement -- 3 Some Conventions -- 4 Global Existence -- 4.1 Energy Decay -- 5 Revisiting the Smallness Assumptions -- References -- GENERIC for Dissipative Solids with Bulk-Interface Interaction -- 1 Introduction -- 2 The GENERIC Formalism for Closed Systems -- 2.1 Hamiltonian Systems (Q,E,J) -- 2.2 Onsager Systems (Q,S,K) (Gradient Systems) -- 2.3 GENERIC Systems (Q,E,S,J,K) -- 3 GENERIC Formalism for Bulk-Interface Systems -- 3.1 Functional Calculus for Bulk-Interface Systems: Notation, Differentials, and *-Multiplication in the Setup of Definition1 -- 3.2 Direct Implications for Geometric Structures -- 3.3 Weak Form of GENERIC as a Formalism for Bulk-Interface Systems -- 3.4 Tools for Dissipative Solids with Bulk-Interface Interaction -- 4 Delamination Processes in Thermo-viscoelastic Materials -- 4.1 Typical Choices for Interfacial Mechanical Energies for Delamination -- 4.2 Typical Choices of Dissipation Potentials for Delamination -- References -- Part II Review Papers -- Phase Separation in Heterogeneous Media -- 1 Introduction -- 2 Phase Field Model -- 2.1 Sharp Interface Limit -- 2.2 Bounds on the Anisotropic Surface Tension σ -- 2.2.1 A Geometric Framework -- 2.2.2 Structure of Minimizers of the Cell Formula -- 2.2.3 The Planar Metric Problem.; 2.2.4 Bounds on the Anisotropic Surface Tension -- 2.3 Open Problems -- 2.3.1 Different Scales -- 2.3.2 Sharpness of Bounds and Inverse Homogenization -- References -- Some Recent Results on 2D Crystallization for Sticky Disc Models and Generalizations for Systems of Oriented Particles -- 1 Introduction -- 2 Preliminaries on Planar Graphs -- 3 The Sticky Disc Model: Minimizers and Quasi-minimizers -- 3.1 Minimizers of the Heitmann-Radin Sticky Disc Model: Single Crystals -- 3.2 Quasi-minimizers of the Heitmann-Radin Model: Polycrystalline Structures -- 4 Vectorial Crystallization and Collective Behavior -- References -- Pattern Formation for Nematic Liquid Crystals-Modelling, Analysis, and Applications -- 1 Introduction -- 2 The Landau-de Gennes Theory -- 3 Benchmark Example -- 4 Nematic Equilibria on 2D Polygons -- 5 Effects of Geometrical Anisotropy -- 6 Effects of Elastic Anisotropy -- 7 NLC Solution Landscapes on a Hexagon -- 8 Conclusions and Discussions -- 9 Supplement: Numerical Methods -- References -- On Applications of Herglotz-Nevanlinna Functions in Material Sciences, I: Classical Theory and Applications of Sum Rules -- 1 Introduction -- 2 Mathematical Background -- 2.1 Definition and First Examples -- 2.2 Integral Representation -- 2.3 Boundary Behavior -- 2.4 Subclasses -- 2.5 ; Other Representations -- 2.5.1 Operator Representations -- 2.5.2 Exponential Representation -- 2.6 Passive Systems -- 2.7 Asymptotic Behavior -- 2.8 Matrix- and Operator-Valued Herglotz-Nevanlinna Functions -- 3 Applications -- 3.1 Sum Rules and Physical Bounds in Electromagnetics -- 3.2 Physical Bounds via Convex Optimization -- References -- On Applications of Herglotz-Nevanlinna Functions in Material Sciences, II: Extended Applications and Generalized Theory -- 1 Introduction -- 2 Applications -- 2.1 Effective Properties of Two-Phase Composite Materials.; 2.1.1 Effective Properties of Composite Materials and Bounds by Using Theory of the Stieltjes Function.