Skip to main content
  • Book
  • © 2022

Generalized Dynamics of Soft-Matter Quasicrystals

Mathematical Models, Solutions and Applications

Authors:

  • Discusses the dynamics of soft-matter quasicrystals with different rotational symmetries
  • Provides the theoretical derivations and mathematical solutions in an easy-to-follow style
  • Covers new findings in experimental research and applications of soft-matter quasicrystals

Part of the book series: Springer Series in Materials Science (SSMATERIALS, volume 260)

Buy it now

Buying options

eBook USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

This is a preview of subscription content, log in via an institution to check for access.

Table of contents (18 chapters)

  1. Front Matter

    Pages i-xviii
  2. Introduction to Soft Matter

    • Tian-You Fan, Wenge Yang, Hui Cheng, Xiao-Hong Sun
    Pages 1-4
  3. Discovery of Soft-Matter Quasicrystals and Their Properties

    • Tian-You Fan, Wenge Yang, Hui Cheng, Xiao-Hong Sun
    Pages 5-19
  4. Introduction on Elasticity and Hydrodynamics of Solid Quasicrystals

    • Tian-You Fan, Wenge Yang, Hui Cheng, Xiao-Hong Sun
    Pages 21-36
  5. Case Study of Equation of State in Several Structured Fluids

    • Tian-You Fan, Wenge Yang, Hui Cheng, Xiao-Hong Sun
    Pages 37-41
  6. Poisson Brackets and Derivation of Equations of Motion in Soft-Matter Quasicrystals

    • Tian-You Fan, Wenge Yang, Hui Cheng, Xiao-Hong Sun
    Pages 43-57
  7. Oseen Theory and Oseen Solution

    • Tian-You Fan, Wenge Yang, Hui Cheng, Xiao-Hong Sun
    Pages 59-68
  8. Dynamics of Soft-Matter Quasicrystals with 12-Fold Symmetry

    • Tian-You Fan, Wenge Yang, Hui Cheng, Xiao-Hong Sun
    Pages 69-94
  9. Dynamics of 10-Fold Symmetrical Soft-Matter Quasicrystals

    • Tian-You Fan, Wenge Yang, Hui Cheng, Xiao-Hong Sun
    Pages 95-117
  10. Dynamics of 8-Fold Symmetric Soft-Matter Quasicrystal Models

    • Tian-You Fan, Wenge Yang, Hui Cheng, Xiao-Hong Sun
    Pages 119-133
  11. Dynamics of 18-Fold Symmetric Soft-Matter Quasicrystals

    • Tian-You Fan, Wenge Yang, Hui Cheng, Xiao-Hong Sun
    Pages 135-157
  12. The Possible 7-, 9-, and 14-fold Symmetry Quasicrystals in Soft Matter

    • Tian-You Fan, Wenge Yang, Hui Cheng, Xiao-Hong Sun
    Pages 159-176
  13. Re-Discussion on Symmetry Breaking and Elementary Excitations

    • Tian-You Fan, Wenge Yang, Hui Cheng, Xiao-Hong Sun
    Pages 177-181
  14. An Application to the Thermodynamic Stability of Soft-Matter Quasicrystals

    • Tian-You Fan, Wenge Yang, Hui Cheng, Xiao-Hong Sun
    Pages 183-202
  15. Applications to Device Physics—Photon Band Gap of Holographic Photonic Quasicrystals

    • Tian-You Fan, Wenge Yang, Hui Cheng, Xiao-Hong Sun
    Pages 203-213
  16. Possible Applications to General Soft Matter

    • Tian-You Fan, Wenge Yang, Hui Cheng, Xiao-Hong Sun
    Pages 215-220
  17. An Application to Smectic A Liquid Crystals, Dislocation, and Crack

    • Tian-You Fan, Wenge Yang, Hui Cheng, Xiao-Hong Sun
    Pages 221-234
  18. Conclusion Remarks

    • Tian-You Fan, Wenge Yang, Hui Cheng, Xiao-Hong Sun
    Pages 235-235
  19. Correction to: Introduction on Elasticity and Hydrodynamics of Solid Quasicrystals

    • Tian-You Fan, Wenge Yang, Hui Cheng, Xiao-Hong Sun
    Pages C1-C1

About this book

This book highlights the mathematical models and solutions of the generalized dynamics of soft-matter quasicrystals (SMQ) and introduces possible applications of the theory and methods. Based on the theory of quasiperiodic symmetry and symmetry breaking, the book treats the dynamics of individual quasicrystal systems by reducing them to nonlinear partial differential equations and then provides methods for solving the initial-boundary value problems in these equations. The solutions obtained demonstrate the distribution, deformation and motion of SMQ and determine the stress, velocity and displacement fields. The interactions between phonons, phasons and fluid phonons are discussed in some fundamental materials samples. The reader benefits from a detailed comparison of the mathematical solutions for both solid and soft-matter quasicrystals, gaining a deeper understanding of the universal properties of SMQ. 
The second edition covers the latest research progress on quasicrystals in topics such as thermodynamic stability, three-dimensional problems and solutions, rupture theory, and the photonic band-gap and its applications. These novel chapters make the book an even more useful and comprehensive reference guide for researchers in condensed matter physics, chemistry and materials sciences.

Authors and Affiliations

  • School of Physics, Beijing Institute of Technology, Beijing, China

    Tian-You Fan

  • Center for High Pressure Science and Technology Advanced Research, Shanghai, China

    Wenge Yang

  • Hebei University of Engineering, Handan, China

    Hui Cheng

  • Zhengzhou University, Zhengzhou, China

    Xiao-Hong Sun

About the authors

Prof. Tian-You Fan



After studying at Peking University, Tianyou Fan began his academic career at the Beijing Institute of Technology, as assistant and lecturer (1963-1979), associate professor (1980-1985) and professor (1986-present). He was an Alexander von Humboldt Research Fellow several times at the Universities of Kaiserslautern and Stuttgart, and held visiting professorships at the Universities of Waterloo, Tokyo and South Carolina.


Fan was nominated as a member of the 9th and 10th National Committee of the People’s Political Consultative Conference (1998-2007), and has worked as a member of the American Mathematical Society, and the Association of Applied Mathematics and Mechanics (Gesellschaft fuer Angewandte Mathematik und Mechanik, GAMM) of Germany. He is the associate editor of Applied Mechanics Reviews of American Society of Mechanical Engineers, and a reviewer of Mathematical Reviews of the American MathematicalSociety. He has published several monographs, and is recipient of numerous awards, including the Science and Technology Prize of the Defense Science, Technology and Industrial Committee of China (1999), the China Book Prize (1991 and 2012), Outstanding Scientific Monograph Prize of Educational Committee of China (1992), and the Nature Science Prize of Educational Ministry of China (2007).

Dr. Wenge Yang

Wenge Yang works in the Shanghai Laboratory of the Center of High Pressure Science & Technology Advanced Research as Staff Scientist and Associate Director.


Prof. Xiao-Hong Sun


Xiao-Hong Sun works in Zhengzhou University as Professor, with research interests in photonic band gap of quasicrystals.


Dr. Hui Cheng



Hui Cheng works in Hebei University of Engineering, with research interests in generalized dynamics of soft matter.



Bibliographic Information

Buy it now

Buying options

eBook USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access