×

Generalized dynamics of soft-matter quasicrystals. Mathematical models and solutions. (English) Zbl 1383.82002

Springer Series in Materials Science 260. Singapore: Springer; Beijing: Beijing Institute of Technology Press (ISBN 978-981-10-4949-1/hbk; 978-981-10-4950-7/ebook). xvi, 184 p. (2017).
This treatise introduces the featured properties and the mathematical models and solutions of generalized hydrodynamics of soft-matter quasicrystals (e.g., liquid crystals, colloids, polymers and alike) under the mechanical effects in linear elastic range. Soft-matter quasicrystals, which were found in nature after the discovery of quasicrystals, exhibit the physical properties of both quasicrystals and fluids. The treatise by an author, who made some contributions on soft-matter quasicrystals, comprises a self-explanatory preface, thirteen chapters with references and a subject index.
Chapter 1 introduces briefly various kinds of soft-matter quasicrystals and especially liquid crystals, considers the fluidity or the flow effect, the elasticity of matter and their interaction in the modelling of hydrodynamics of soft-matter quasicrystals. Chapter 2 deals with the important discovery and characters of first and second kinds of two-dimensional soft-matter quasicrystals with 12- and 18-fold symmetries, and discusses some concepts concerning possible hydrodynamics on soft-matter quasicrystals. Chapter 3–6 report some preparing knowledge from the background of applied physics and mathematics so as to study the basic equations of soft-matter quasicrystals, which are complex liquids or structured fluids. Chapter 3 gives an introduction on elasticity and generalized hydrodynamics of solid quasicrystals and states the basic equations in a system of rectangular Cartesian coordinates. Chapter 4 focuses only on some very special cases of the equation of state for a class of soft matter. Chapter 5 introduces the Poisson bracket method in condensed matter physics, and using the method gives an outline of the derivation of the equations of motion of soft-matter quasicrystals. Chapter 6 provides some basic knowledge about liquid dynamics and especially the Oseen and generalized Oseen flows in the two-dimensional case. The Oseen steady state solutions of flow of the incompressible fluid and the generalized Oseen flow of a compressible viscous fluid past a circular cylinder are numerically obtained. Chapter 7 is the only chapter devoted to the mathematical modeling of a soft-matter quasicrystal with 12-fold symmetry, which might be the most important ones of soft-matter quasicrystals. The two- and three-dimensional governing equations of the soft-matter quasicrystal and their simplified versions are given in a system of rectangular Cartesian and polar coordinates. Some solutions of an initial boundary value problem are discussed for a plane field of the two-dimensional softy-matter quasicrystal. A quasi-steady flow of the soft-matter quasicrystal past a circular cylinder is studied and some numerical results are found. An approximate solution of dislocation is reported and the problems of possible crack and propagation are simply introduced in the soft-matter quasicrystal. The solid quasicrystal with 7-, 9-, 14- and 18-fold symmetries have not been observed so far. The discussion on these kinds of quasiperiodic structures and possible mechanical and physical properties are considered to be significant. They might be observed in the near future, and some of a new soft-matter quasicrystals may be included in the future editions. Nevertheless, as in Chapter 7, the two- and three-dimensional basic equations of possible soft-matter quasicrystals with various symmetries are given and some sample applications are reported. A detailed analysis of possible soft-matter quasicrystals with 5- and 10-fold symmetries is presented in Chapter 8 and those with 8-fold symmetry in Chapter 9, with 18-fold symmetry in Chapter 10 and with 7-, 9- and 14-fold symmetry in Chapter 11. Chapter 12 reports the basic equations of smectic A liquid crystals and solutions of screw dislocation and plastic crack. Chapter 13 presents some concluding remarks on future needs of research topics on soft-matter quasicrystals. On the other hand, besides the subject index, a major index for material constants of solid and soft-matter quasicrystals, which is of special importance in numerical applications, and an author index remain for future editions.
In brief, this pioneering treatise presents a clear and lucid account of the generalized dynamics of soft-matter quasicrystals. The treatise may give vision and insight to fascinate a very new and growing area of research field. Certainly, it may appeal to researchers and engineers just interested in or working on soft-matter quasicrystal.

MSC:

82-02 Research exposition (monographs, survey articles) pertaining to statistical mechanics
82D25 Statistical mechanics of crystals
00A79 Physics
76A15 Liquid crystals
76D07 Stokes and related (Oseen, etc.) flows
35Q35 PDEs in connection with fluid mechanics
76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics
PDFBibTeX XMLCite
Full Text: DOI