## Mathematical Challenges in a New Phase of Materials Science: Kyoto, Japan, August 2014This volume comprises eight papers delivered at the RIMS International Conference "Mathematical Challenges in a New Phase of Materials Science", Kyoto, August 4–8, 2014. The contributions address subjects in defect dynamics, negatively curved carbon crystal, topological analysis of di-block copolymers, persistence modules, and fracture dynamics. These papers highlight the strong interaction between mathematics and materials science and also reflect the activity of WPI-AIMR at Tohoku University, in which collaborations between mathematicians and experimentalists are actively ongoing. |

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### Contents

1 | |

Topological Analysis of the Diblock Copolymer Equation | 27 |

An EnergyConsistent Model of Dislocation Dynamics in an Elastic Body | 53 |

Persistence of Common Topological Structures by Commutative Triple Ladder Quiver | 69 |

Construction of Negatively Curved Cubic Carbon Crystals via Standard Realizations | 83 |

A Note on a Local Ergodic Theorem for an Infinite Towerof Coverings | 101 |

Unboundedness of Some Solutions to Isentropic Model Equations for the One Dimensional Periodic Motions of a Compressible SelfGravitating Visc... | 117 |

Computer Assisted Verification of the Eigenvalue Problem for OneDimensional Schrödinger Operator | 145 |

### Other editions - View all

Mathematical Challenges in a New Phase of Materials Science: Kyoto, Japan ... Yasumasa Nishiura,Motoko Kotani No preview available - 2016 |

Mathematical Challenges in a New Phase of Materials Science: Kyoto, Japan ... Yasumasa Nishiura,Motoko Kotani No preview available - 2018 |

### Common terms and phrases

algorithm Auslander-Reiten quiver Betti numbers bifurcation diagrams bifurcation point boundary Cahn-Hilliard equation carbon computational computer-assisted proofs connecting orbit consider corresponding crystal lattice decomposition define denote density modulations density profile diblock copolymer model discrete surfaces dislocation curve dynamics energy form equation equilibrium solutions Euler characteristic evolution example exclusion processes exists finite function bundle global graph hexagonal lattice homogeneous indecomposable indecomposable modules initial interval Kotani Lemma linear Mackay-Terrones marginal stability Math Mathematics microstructure minimal minimal surfaces morphism negatively curved networks Nishiura nodal domains obtain parameter particles peak persistence diagrams persistence modules persistent homology perturbation phase field Phys quench residually finite screw dislocation secondary bifurcation slip plane solidification front space spectral gap spinodal spinodal decomposition Springer stable standard realization stationary solutions stochastic subspaces SWNT temperature Theorem tn–H topological crystal trivial solution vector Wanner wavenumber