Mathematical Challenges in a New Phase of Materials Science

Name: Mathematical Challenges in a New Phase of Materials Science | Kyoto, Japan, August 2014
Brand: Springer
Price: 96.29 EUR
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Kyoto, Japan, August 2014

Yasumasa Nishiura Motoko Kotani(Herausgeber*in)

Springer (Verlag)

Erschienen am 11. Juli 2016

VII, 157 Seiten

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978-4-431-56104-0 (ISBN)

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Inhalt

Intro
Preface
Contents
Generation of Defects and Disorder from Deeply Quenching a Liquid to Form a Solid
1 Introduction
2 Length Scales in Liquids and Solids
3 Dispersion Relation
4 Speed of Solidification Fronts: Marginal Stability Hypothesis
5 Marginal Stability Calculation for a Simple Model
6 Model Fluid
7 Structures Formed After a Quench
8 A Binary Mixture
9 System with Competing Crystal Structures
10 Concluding Remarks
References
Topological Analysis of the Diblock Copolymer Equation
1 Introduction
2 Homological Microstructure Analysis
3 Long-Term Dynamics and Partial Attractor Structure
4 Future Work and Open Questions
References
An Energy-Consistent Model of Dislocation Dynamics in an Elastic Body
1 Introduction
2 An Energy-Based Approach to Modeling of Dislocation Dynamics
Elastic Energy with Dislocation
Weak Formulations for Jump Problems
Regularization of Energy
3 A Simplified 2D-1D Model
4 Numerical Results
5 Summary and Conclusions
References
Persistence of Common Topological Structures by Commutative Triple Ladder Quiver
1 Introduction
2 Commutative Triple Ladder Persistence
Persistence and Representation Theories
Auslander-Reiten Quiver of Commutative Triple Ladder
3 Algorithm for Computing Persistence Diagram
4 Numerical Example
References
Construction of Negatively Curved Cubic Carbon Crystals via Standard Realizations
1 Introduction
2 Minimal Surfaces and Schwarzites
3 Topological Crystals and Their Standard Realizations
4 Construction of Negatively Curved Carbon Crystals
Construction of Topological Crystals
Construction of Standard Realizations
Construction of Stable Configurations
5 Further Problems
Appendix: Indexes of Single Wall Nanotubes
References
A Note on a Local Ergodic Theorem for an Infinite Towerof Coverings
1 Introduction
2 Notation and Results
Groups and Associated Infinite Towers of Coverings
Particle Systems
3 Proof of Theorem 2.1
References
Unboundedness of Some Solutions to Isentropic Model Equations for the One Dimensional Periodic Motions of a Compressible Self-Gravitating Viscous Fluid
1 Introduction
2 Notation and Main Results
3 Large Time Behavior of Bounded Solutions
4 Structure and Stability of Stationary Solutions
5 Existence of Unbounded Solutions
References
Computer Assisted Verification of the Eigenvalue Problem for One-Dimensional Schrödinger Operator
1 Introduction
2 Setting
3 Eigenvalues and Connecting Orbits
4 Sample Result
5 Discussions
References

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