arXiv subjects
Publications and source records attributed to Tian-You Fan.
Based on extended free energy of soft-matter quasicrystals and the variation principle on thermodynamic stability, this study reports the results on stability of the first kind of soft-matter quasicrystals. They are dependent only upon the material constants, and quite simple and intuitive, the material constants can be measured by experiments. The results are significant in studying thermodynamics of the matter.
This article reports the spherical coordinate form of three-dimensional generalized dynamics of soft-matter quasicrystals with 12-fold symmetry which provides a basis for solving initial-boundary value problems of the equations under some important cases. Some relevant solving methods are discussed as well.
This letter presents a three-dimensional form of governing equations of generalized dynamics of 18-fold symmetry soft-matter quasicrystals, according to the dynamics basis there are first and second phason elementary excitations apart from phonons and fluid phonon. In the derivation, the group representation theory is a key point. The complete form of the theory includes an equation of state. The governing equations present some important meaning in the study on thermodynamics of the matter which is also introduced.
The equations of generalized dynamics of the first kind of soft-matter quasicrystals are derived and given in the previous report, we now introduce the equations of the dynamics for the second kind of quasicrystals in soft matter.
The three-dimensional generalized dynamics of soft-matter quasicrystals was investigated, in which the governing equations of the dynamics are derived for observed 12-fold symmetry quasicrystals and possible observed 8- and 10-symmetry ones in near future in soft matter. The solving methods, possible solutions for some initial and boundary value problems of the equations and possible applications are discussed as well.
The equation systems of generalized hydrodynamics, or generalized dynamics for simplicity, for soft-matter quasicrystals were established. Considering the fluidity of the matter with high order we introduced a new elementary excitation---fluid phonon to the quasicrystals, and the equation of state is necessary and introduced too. By considering other two elementary excitations---phonons and phasons, a theory---generalized hydrodynamics for soft-matter quasicrystals is set up, in which the governing equations of the dynamics are reported in this letter.
This article provides a detailed review on the generalized dynamics of soft-matter quasicrystals developed recent years. Comparing to solid quasicrystals consisted mainly with metallic alloys, soft-matter quasicrystals have been observed in liquid crystals, polymers, colloids, nanoparticles, and surfactants, which indicate quite different formation mechanism. Based on Landau-Anderson theory and group representation theory, we have studied the symmetry, symmetry breaking and elementary excitations for the observed and possible soft-matter quasicrystals. We further proposed one more elementary excitation: fluid phonon additional to the phonon and phason for solid quasicrystals, to quantitatively describe the dynamics of soft-matter quasicrystals. The general governing equations and the solutions of the dynamics evolution on the distribution, deformation and motion of the new phase are studied, which reveal quite distinguishing dynamic behavior with those of conventional fluids and solid quasicrystals. Some applications are introduced, which show this is an important field of new materials and materials science.
Following our previous work this article reports a study on the stability of the 18-fold symmetry soft-matter quasicrystals, in which the extended free energy is a basis for the analysis that is similar to the study of the 12-fold symmetry quasicrystals. Due to the differences in structure between these two kinds of quasicrystals, their stabilities present some different characters to each other. Because there were no any results of the stability of 18-fold symmetry soft-matter quasicrystals reported yet, perhaps the present work is the first probe on the topic.
This letter presents a study on the stability of the 12-fold symmetry soft-matter quasicrystals from the angle of thermodynamics combining dynamics of the matter. The results are quantitative, which depend upon only the material constants of the novel phase and very simple and intuitive, these material constants can be measured by experiments.