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A New Direction in Mathematics for Materials ScienceInfluence of Mathematics on Materials Science Upto Date

A New Direction in Mathematics for Materials Science: Influence of Mathematics on Materials... [This chapter discusses the historical influence of mathematics on materials science and mathematical techniques and tools widely used in materials science today. There were many occasions in the past when mathematics and materials science met and interacted to inspire advances. From ancient times, humans are believed to have had an empirical knowledge of materials that was related to mathematics, such as awareness of crystal shape. Such knowledge probably played some basic role in the understanding of materials and in creating new materials. In this chapter, we first focus on the ancients’ speculation of atoms. The early concept of atoms was produced by some ancient Greek philosophers. Although it took humans more than two thousand years to establish the concept of crystals from the age of the ancient Greeks, the idea of geometrical packing of small building blocks (atoms, molecules, or unit cells in modern science) is supposed to have been somewhere in the humans’ consideration. After explaining crystals as one of the most fundamental forms of materials, we will show quantum materials and pattern formation as the fields with which mathematics has a strong relationship.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

A New Direction in Mathematics for Materials ScienceInfluence of Mathematics on Materials Science Upto Date

Part of the SpringerBriefs in the Mathematics of Materials Book Series (volume 1)
Ikeda, Susumu; Kotani, Motoko
Springer Journals — Dec 9, 2015
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39 pages

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Publisher
Springer Japan
Copyright
© The Author(s) 2015
ISBN
978-4-431-55862-0
Pages
11 –50
DOI
10.1007/978-4-431-55864-4_2
Publisher site
See Chapter on Publisher Site

Abstract

[This chapter discusses the historical influence of mathematics on materials science and mathematical techniques and tools widely used in materials science today. There were many occasions in the past when mathematics and materials science met and interacted to inspire advances. From ancient times, humans are believed to have had an empirical knowledge of materials that was related to mathematics, such as awareness of crystal shape. Such knowledge probably played some basic role in the understanding of materials and in creating new materials. In this chapter, we first focus on the ancients’ speculation of atoms. The early concept of atoms was produced by some ancient Greek philosophers. Although it took humans more than two thousand years to establish the concept of crystals from the age of the ancient Greeks, the idea of geometrical packing of small building blocks (atoms, molecules, or unit cells in modern science) is supposed to have been somewhere in the humans’ consideration. After explaining crystals as one of the most fundamental forms of materials, we will show quantum materials and pattern formation as the fields with which mathematics has a strong relationship.]

Published: Dec 9, 2015

Keywords: Crystallography; Aperiodic system; Standard realization; Band theory; Quantum Hall effect; Topological insulator; Pattern formation; Crystal growth; Reaction-diffusion equation

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