Foreword
Preface
ICIAM Congresses
ICIAM Prize Winners
Organization of ICIAM 2019-Valencia
Opening Ceremony
Maria J. Esteban, President of ICIAM
ICIAM 2019 in Numbers
Contents
Editors and Contributors
Invited Lectures
Asteroid-Generated Tsunamis: A Review
1 Introduction
2 Simulations of Airburst-Generated Tsunamis
2.1 Background
2.2 Analytical and Computational Results for Shallow Water Equations
3 The Linearized Euler Equations
3.1 Analytical and Computational Results for Linearized Euler
4 Conclusions
References
Some Case Studies in Environmental and Industrial Mathematics
1 Introduction
2 Environmental Flows. The Shallow Water Equations
3 Gas Network Simulation
3.1 Mathematical Modelling: Homogeneous Gas Flow in a Pipe
3.2 Numerical Solution: One Single Pipe with Homogeneous Gas
3.3 Network with Heterogeneous Gas
3.4 Experimental Validation in a Real Small Network
4 Non-destructive Testing: Magnetic Particle Inspection (MPI)
4.1 Circular Magnetization. Axisymmetric Model
4.2 Hysteresis Modelling
5 Accelerated Simulation of Electric Machines
5.1 Description of the New Methodology
5.2 Numerical Experiments with Real Electric Machines
References
Modelling Our Sense of Smell
1 Introduction
1.1 Transduction of Olfactory Signals
1.2 Kleene's Experimental Procedure
1.3 An Integral Equation Model
1.4 Non-diffusive Kernels
2 A General Convolution Equation
2.1 A Priori Estimates
3 Observability of CNG Channels
4 Unstable Identifiability, Non Existence of Observability Inequalities
References
State Estimation—The Role of Reduced Models
1 Introduction
2 Models and Data
2.1 The Model
2.2 The Data
2.3 Optimality Criteria and Numerical Recovery
3 The One-Space Method
3.1 Subspace Regularization
3.2 Optimal Affine Recovery
3.3 Rate-Optimal Reduced Bases
4 Nonlinear Models
4.1 Piecewise Affine Reduced Models
4.2 Approximate Metric Projection and Parameter Estimation
4.3 Concluding Remarks
References
Pattern Formation Inside Living Cells
1 Introduction: Motile Cells and Their Inner Workings
1.1 Actin Powers Cell Motility
1.2 GTPases Are Master Regulators
2 Mathematical Models
2.1 How Wave-Pinning Works
3 Recent Work: Analysis, Simulation, and Contact with Experiments
3.1 Analysis of Slow-Fast Reaction Diffusion Systems: LPA
3.2 Simulating the PDEs in Dynamic Cell-Shaped Domains
3.3 Contact with Biological Experiments
4 Extending the Minimal Model
5 Discussion
References
Private AI: Machine Learning on Encrypted Data
1 Motivation: Privacy in Artificial Intelligence
1.1 Real-World Applications
2 What Is Homomorphic Encryption?
2.1 History
2.2 Lattice-Based Solutions
2.3 Encoding Data
2.4 Brakerski/Fan-Vercauteren Scheme (BFV)
2.5 Other Homomorphic Encryption Schemes
2.6 Microsoft SEAL
2.7 Standardization of Homomorphic Encryption ch6HES
3 What Kind of Computation Can We Do?
3.1 Statistical Computations
3.2 Heart Attack Risk
3.3 Cancer Patient Statistics
3.4 Genomic Privacy
3.5 Machine Learning: Training and Prediction
4 How Do We Assess Security?
5 Conclusion
References
Mathematical Approaches for Contemporary Materials Science: Addressing Defects in the Microstructure
1 Introduction
1.1 Contemporary Materials Science
1.2 Basics of Homogenization Theory
2 A Mathematical Toolbox for ``Weakly'' Random Problems
2.1 Random Deformations of the Periodic Setting
2.2 Small Random Perturbations of the Periodic Setting
2.3 Rare but Possibly Large Random Perturbations
3 Deterministic Defects Within an Otherwise Periodic Structure
4 Multi-scale Finite Element Approaches and Nonperiodicity
5 Homogenization Under Partial Information
References
Hyperbolic Model Reduction for Kinetic Equations
1 Historical Overview
2 Theoretical Framework
2.1 Review of Globally Hyperbolic Moment System
2.2 Hyperbolic Regularization Framework
2.3 Further Progress
3 Numerical Validation
3.1 Shock Structure
3.2 Fourier Flow
3.3 A Summary of Numerical Experiments
4 Conclusion
References
Cryptography and Digital Transformation
1 Digital Transformation
2 Cryptographic Foundations
2.1 Encryption Schemes
2.2 Digital Signature Schemes
2.3 Interactive Proofs
3 Digitalizing Voting
3.1 Requirements for Voting
3.2 Designing Voting Protocol
3.3 Shuffling Encrypted Data Using Probabilistic Encryption
4 Bitcoin Blockchain
4.1 Modeling Blockchain
4.2 Crypto Puzzle for Synchronization
4.3 Incentives for Data Managers
5 Concluding Remarks
References
Efficient Algorithms for Tracking Moving Interfaces in Industrial Applications: Inkjet Plotters, Electrojetting, Industrial Foams, and Rotary Bell Painting
1 Modeling Interface Evolution Using Level Set Methods
1.1 Equations of Motion
1.2 Computational Advances
2 Industrial Printing
2.1 Physical Problem and Modeling Goals
2.2 Equations of Motion and Computational Challenges
3 Droplet Formation and Electro-jetting
3.1 Physical Problem and Modeling Goals
3.2 Equations of Motion
3.3 Computational Challenges
3.4 Example Results
3.5 Charged Droplet Separation
3.6 Equations of Motion and Computational Challenges
3.7 Example Results
4 Industrial Foams
4.1 Physical Problem and Modeling Goals
4.2 Computational Challenges
4.3 Voronoi Implicit Interface Methods
4.4 Application of VIIM to Foam Dynamics
4.5 Example Results
5 Rotary Bell Painting in the Automotive Industry
5.1 Computational Challenges
5.2 Level Set Methods and High-Order Multiphase Flow
6 Conclusions and Summary
References
Numerical Study for Blood Flows in Thoracic Aorta
1 Introduction
2 Numerical Methods and Results
2.1 Governing Equations
2.2 Finite Difference Approximation
2.3 Finite Element Approximation
3 Conclusions
References
An Iterative Thresholding Method for Topology Optimization for the Navier–Stokes Flow
1 Introduction
2 Derivation of the Method
2.1 The Mathematical Model
2.2 The Relaxation and Approximation of the Problem
2.3 Derivation of the Method
3 Numerical Implementation
4 Numerical Experiments
4.1 Two Dimensional Results
4.2 Three Dimensional Results
5 Conclusion
References
Dynamics of Complex Singularities of Nonlinear PDEs
1 Introduction
2 The Inviscid Burgers Equation
3 The Viscous Burgers Equation
4 The Benjamin-Ono Equation
5 The Korteweg-De Vries Equation
6 Recurrence
7 Numerical Tools
References
Author Index