A New Direction in Mathematics for Materials Science by Susumu Ikeda, Motoko Kotani

By Susumu Ikeda, Motoko Kotani

This e-book is the 1st quantity of the SpringerBriefs within the arithmetic of fabrics and gives a entire advisor to the interplay of arithmetic with fabrics technological know-how. The anterior a part of the booklet describes a specific historical past of fabrics technological know-how in addition to the interplay among arithmetic and fabrics in heritage. The emergence of fabrics technology used to be itself as a result an interdisciplinary move within the Fifties and Nineteen Sixties. fabrics technological know-how used to be shaped by means of the combination of metallurgy, polymer technological know-how, ceramics, reliable country physics, and comparable disciplines. We think that such historic historical past is helping readers to appreciate the significance of interdisciplinary interplay resembling mathematics–materials technology collaboration. 

The heart a part of the booklet describes mathematical rules and strategies that may be utilized to fabrics difficulties and introduces a few examples of particular studies―for instance, computational homology utilized to structural research of glassy fabrics, stochastic types for the formation means of fabrics, new geometric measures for finite carbon nanotube molecules, mathematical strategy predicting a molecular magnet, and community research of nanoporous fabrics. the main points of those works can be proven within the next volumes of this SpringerBriefs within the arithmetic of fabrics sequence via the person authors. 
The posterior component to the publication provides how breakthroughs in response to mathematics–materials technology collaborations can emerge. The authors' argument is supported by way of the studies on the complicated Institute for fabrics study (AIMR), the place many researchers from a variety of fields accumulated and tackled interdisciplinary research.

Show description

Read or Download A New Direction in Mathematics for Materials Science PDF

Best topology books

The cube: a window to convex and discrete geometry

8 subject matters concerning the unit cubes are brought inside of this textbook: go sections, projections, inscribed simplices, triangulations, 0/1 polytopes, Minkowski's conjecture, Furtwangler's conjecture, and Keller's conjecture. particularly Chuanming Zong demonstrates how deep research like log concave degree and the Brascamp-Lieb inequality can care for the move part challenge, how Hyperbolic Geometry is helping with the triangulation challenge, how staff jewelry can take care of Minkowski's conjecture and Furtwangler's conjecture, and the way Graph idea handles Keller's conjecture.

Riemannian geometry in an orthogonal frame

Foreword via S S Chern In 1926-27, Cartan gave a sequence of lectures within which he brought external types on the very starting and used largely orthogonal frames all through to enquire the geometry of Riemannian manifolds. during this direction he solved a sequence of difficulties in Euclidean and non-Euclidean areas, in addition to a chain of variational difficulties on geodesics.

Lusternik-Schnirelmann Category

"Lusternik-Schnirelmann type is sort of a Picasso portray. class from assorted views produces different impressions of category's attractiveness and applicability. "

Lusternik-Schnirelmann type is a topic with ties to either algebraic topology and dynamical structures. The authors take LS-category because the important subject matter, after which improve subject matters in topology and dynamics round it. incorporated are routines and lots of examples. The ebook offers the cloth in a wealthy, expository style.

The e-book offers a unified method of LS-category, together with foundational fabric on homotopy theoretic features, the Lusternik-Schnirelmann theorem on serious issues, and extra complicated themes similar to Hopf invariants, the development of services with few serious issues, connections with symplectic geometry, the complexity of algorithms, and classification of 3-manifolds.

This is the 1st booklet to synthesize those subject matters. It takes readers from the very fundamentals of the topic to the cutting-edge. necessities are few: semesters of algebraic topology and, possibly, differential topology. it truly is appropriate for graduate scholars and researchers drawn to algebraic topology and dynamical systems.

Readership: Graduate scholars and learn mathematicians attracted to algebraic topology and dynamical platforms.

Additional info for A New Direction in Mathematics for Materials Science

Sample text

Descr. Syst. Br. J. Radiol. T. Hyde, S. Ramsden, Polycontinuous morphologies and interwoven helical networks. Europhys. Lett. 50, 135–141 (2000) [Hsi] D. , A topological Dirac insulator in a quantum spin Hall phase. Nature 452, 970–974 (2008) [HYZ] Y. Han, D. L. Chng, J. Sun, L. Zhao, X. Y. Ying, A tri-continuous mesoporous material with a silica pore wall following a hexagonal minimal surface. Nat. Chem. 166, 123–127 (2009) [Iij] S. Iijima, Helical microtubules of graphitic carbon. Nature 354, 56–58 (1991) [IIK94] M.

11b). Under larger supersaturation/supercooling conditions, crystals tend to take up more impurities from their environments changing their physical and chemical characteristics considerably. We shall discuss topics related to crystal growth in several parts of this book because crystal growth is a key issue, which combines microscopic processes of materials and their macroscopic properties and features. 30 2 Influence of Mathematics on Materials Science Upto Date (a) Perpendiculars through the tips of vectors whose magnitude correspond to γ (b) Equilibrium shape of a crystal Center of mass Surface energy γ of each orientation Fig.

Indeed, some big projects promoting the application of mathematics such as Mathematics of Planet Earth 2013 and the Deutsche Forschungsgemeinschaft (DFG) Research Center Matheon, are progressing. Some books reporting on the present status of the mathematics–industry cooperation have been published [LER, GK]. In recent years, the importance of the use of “Big Data” is increasing year by year. Also, in materials science, it has been pointed out that it is crucial to rationalize the design and development of materials and tighten the development cycle by constructing databases of research results related to materials, and analyzing Big Data from Informatics Theory and Mathematics.

Download PDF sample

Rated 4.22 of 5 – based on 37 votes