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Materials inspired by mathematics

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Pages 253-259 | Received 17 Mar 2016, Accepted 15 Apr 2016, Published online: 08 Jun 2016

References

  • Heisenberg WK . Der Teil Und Das Ganze [The part and the whole]. München: Piper Verlag; 1971.
  • Pan D , Inoue A , Sakurai T , et al . Experimental characterization of shear transformation zones for plastic flow of bulk metallic glasses. Proc Natl Acad Sci USA. 2008;105:14769–14772. 10.1073/pnas.0806051105
  • Wang D , Fujinami S , Liu H , et al . Investigation of true surface morphology and nanomechanical properties of Poly(styrene- b -ethylene- co -butylene- b -styrene) using nanomechanical mapping: effects of composition. Macromolecules. 2010;43:9049–9055. 10.1021/ma100959v
  • Liu YH , Wang D , Nakajima K , et al . Characterization of nanoscale mechanical heterogeneity in a metallic glass by dynamic force microscopy. Phys Rev Lett. 2011;106:125504. 10.1103/PhysRevLett.106.125504
  • Wang D , Liu Y , Nishi T , et al . Length scale of mechanical heterogeneity in a glassy polymer determined by atomic force microscopy Appl. Phys. Lett. 2012;100:251905.
  • Wigner, EP . The unreasonable effectiveness of mathematics in the natural sciences. Richard Courant lecture in mathematical sciences delivered at New York Univesity, May 11, 1959. Comm. Pure Appl. Math. 190;13:1–14.
  • Cromwell PR . Polyhedra: one of the most charming chapters of geometry. Cambridge: Cambridge University Press; 1997.
  • Kotani M , Sunada T . Spectral geometry of crystal lattices. Contemp. Math. 2003;338:271–306.
  • Kotani M , Sunada T . Standard realization of crystal lattice via harmonic maps. Trans Amer Math Soc. 2000;353:1–20.
  • Shechtman D , Blech I , Gratias D , et al . Metallic phase with long-range orientational order and no translational symmetry. Phys Rev Lett. 1984;53:1951–1953. 10.1103/PhysRevLett.53.1951
  • Connes A . Noncommutative geometry. San Diego, CA : Academic Press Inc; 1994.
  • Baake M , Moody RV , editors. Directions in mathematical quasicrystals: CRM monograph series. vol. 13. Soc: Amer. Math; 2000.
  • Edelsbrunner H , Cohen-Steiner D , Harer J . Topological persistence and simplification. Discrete Comput Geom. 2002;28:511–533. 10.1007/s00454-002-2885-2
  • Hirata A , Kang L. J , Fujita T , et al . Geometric frustration of icosahedron in metallic glasses. Science. 2013;341:376–379. 10.1126/science.1232450
  • Nakamura T , Hiraoka Y , Hirata A , et al . Description of medium-range order in amorphous structures by persistent homology. arxiv:1501.03611.
  • Nakamura T , Hiraoka Y , Hirata A , et al . Persistent homology and many-body atomic structure for medium-range order in the glass. Nanotechnology. 2015;26:304001. 10.1088/0957-4484/26/30/304001
  • Kane CL , Mele EJ . Quantum spin Hall effect in graphene. Phys Rev Lett. 2005;95:226801. 10.1103/PhysRevLett.95.226801
  • Bellissard J , van Elst A , Schulz-Baldes H . The non-commutative geometry of the quantum hall effect. J Math Phys. 1994;35:5373–5451. 10.1063/1.530758
  • Schulz-Baldes H . Persistence of spin edge currents in disordered quantum spin hall systems. Comm Math Phys. 2013;324:589–600. 10.1007/s00220-013-1814-y
  • Kotani M , Schulz-Baldes H . Villegas-Blas, Carlos quantization of interface currents. J Math Phys. 2014;55:121901. 10.1063/1.4902377
  • Graf GM , Porta M . Bulk-Edge correspondence for two-dimensional topological insulators. Comm Math Phys. 2013;324:851–895. 10.1007/s00220-013-1819-6
  • Kubota Y . Controlled topological phases and bulk-edge correspondence. preprint
  • Sunada T . Crystals that nature might miss creating 2008 Not . Amer Math Soc. 2008;55:208–215.
  • Itoh M , Kotani M , Naito H , et al . New metallic carbon crystal. Phys Rev Lett. 2009;102:055703. 10.1103/PhysRevLett.102.055703
  • Tagami M , Liang Y , Naito H , et al . Negatively curved cubic carbon crystals with octahedral symmetry. Carbon. 2014;76:266–274.10.1016/j.carbon.2014.04.077
  • Weng H , Liang Y. Xu Q. et al . Topological node-line semimetal in three dimensional graphene network. Phys Rev B. 2015;92:45108.
  • Kotani M , Naito H , Omori T . A discrete surface theory. arXiv:1601.07272.
  • Packwood DM , Jin T , Fujita T , et al . Mixing time of molecules inside of nanoporous gold. SIAM J Appl Math. 2014;74:1298–1314.
  • Louzguine-Luzgin DV , Packwood D M , Xie G , et al . On deformation behavior of a Ni-based bulk metallic glass produced by flux treatment. J alloys compd. 2013;561:241–246. 10.1016/j.jallcom.2013.01.193
  • Odom W . Report of the senior assessment panel for the international assessment of the U.S. mathematicalsciences. National Science Foundation (NSF); 1998. Available from: http://www.nsf.gov/publications/pub_summ.jsp?ods_key=nsf9895
  • Brown DL , Bell J , Estep D , et al . Applied mathematics at the U.S. department of energy: past, present and view to the future. U.S. Department of Energy (DOE); 2008. Available from: http://science.energy.gov/~/media/ascr/pdf/program-documents/docs/brown_report_may_08.pdf
  • Global Science Forum. Report on mathematics in industry. Organisation for Economic Co-operation and Development (OECD). Available from: http://www.oecd.org/science/sci-tech/41019441.pdf 2008
  • Ikeda S , Kotani M . A new direction in mathematics for materials science. In SpringerBriefs in the mathematics of materials. Tokyo: Springer;2015. vol.1.