It is proposed that the Gaussian type distribution constant b<sub>q<sub>i</sub></sub> in the Gaussian model depends on the coordination number q<sub>i</sub> of site i, and that the ...It is proposed that the Gaussian type distribution constant b<sub>q<sub>i</sub></sub> in the Gaussian model depends on the coordination number q<sub>i</sub> of site i, and that the relation b<sub>q<sub>i</sub></sub>/b<sub>q<sub>j</sub></sub> = q<sub>i</sub>/q<sub>j</sub> holds among b<sub>q<sub>i</sub></sub>’s. The Gaussian model is then studied on a family of the diamond-type hierarchical （or DH） lattices, by the decimation real-space renormalization group following spin-resealing method. It is found that the magnetic property of the Gaussian model belongs to the same universal class, and that the critical point K<sup>*</sup> and the critical exponent v are given by K<sup>*</sup>= b<sub>q<sub>i</sub></sub>/q<sub>i</sub> and v=1/2, respectively.展开更多
Commercially available lattices contain various kinds of morphological imperfections which result in great degradation in lattices＇ mechanical properties, therefore, to obtain imperfection insensitive lattice structu...Commercially available lattices contain various kinds of morphological imperfections which result in great degradation in lattices＇ mechanical properties, therefore, to obtain imperfection insensitive lattice structure is obviously a practical research subject. Hierarchical structure materials were found to be a class of promising anti-defect materials, This paper builds hierarchical lattice by adding soft adhesion to lattice＇s cell edges and numerical results show that its imperfection sensitivity to missing bars is minor compared with the classic lattice. Soft adhesion with appropriate properties reinforce cell edge＇s bending stiffness and thus reduce the bending deformation in lattice caused by missing bars defect, which is confirmed by statistical analysis of normalized node displacements of imperfect lattices under hydrostatic compression and shear loads.展开更多
The Gaussian spin model with periodic interactions on the diamond-type hierarchical lattices is constructed by generalizing that with uniform interactions on translationally invariant lattices according to a class of ...The Gaussian spin model with periodic interactions on the diamond-type hierarchical lattices is constructed by generalizing that with uniform interactions on translationally invariant lattices according to a class of substitution sequences. The Gaussian distribution constants and imposed external magnetic fields are also periodic depending on the periodic characteristic of the interaction bonds. The critical behaviors of this generalized Gaussian model in external magnetic fields are studied by the exact renormalization-group approach and spin rescaling method. The critical points and all the critical exponents are obtained. The critical behaviors are found to be determined by the Gaussian distribution constants and the fractal dimensions of the lattices. When all the Gaussian distribution constants are the same, the dependence of the critical exponents on the dimensions of the lattices is the same as that of the Gaussian model with uniform interactions on translationally invariant lattices.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No. 19775008)the National Basic Research Project "Nonlinear Science"+1 种基金the National Education Committee Foundation for Training PhD students the Natural Science Found
文摘It is proposed that the Gaussian type distribution constant b<sub>q<sub>i</sub></sub> in the Gaussian model depends on the coordination number q<sub>i</sub> of site i, and that the relation b<sub>q<sub>i</sub></sub>/b<sub>q<sub>j</sub></sub> = q<sub>i</sub>/q<sub>j</sub> holds among b<sub>q<sub>i</sub></sub>’s. The Gaussian model is then studied on a family of the diamond-type hierarchical （or DH） lattices, by the decimation real-space renormalization group following spin-resealing method. It is found that the magnetic property of the Gaussian model belongs to the same universal class, and that the critical point K<sup>*</sup> and the critical exponent v are given by K<sup>*</sup>= b<sub>q<sub>i</sub></sub>/q<sub>i</sub> and v=1/2, respectively.
基金supported by the 973 Program(No.2014CB049000,2011CB610304)National Natural Science Foundation of China(11372062,91216201)+2 种基金LNET Program(LJQ2013005)China Postdoctoral Science Foundation(2014M551070)111Project(B14013)
文摘Commercially available lattices contain various kinds of morphological imperfections which result in great degradation in lattices＇ mechanical properties, therefore, to obtain imperfection insensitive lattice structure is obviously a practical research subject. Hierarchical structure materials were found to be a class of promising anti-defect materials, This paper builds hierarchical lattice by adding soft adhesion to lattice＇s cell edges and numerical results show that its imperfection sensitivity to missing bars is minor compared with the classic lattice. Soft adhesion with appropriate properties reinforce cell edge＇s bending stiffness and thus reduce the bending deformation in lattice caused by missing bars defect, which is confirmed by statistical analysis of normalized node displacements of imperfect lattices under hydrostatic compression and shear loads.
文摘The Gaussian spin model with periodic interactions on the diamond-type hierarchical lattices is constructed by generalizing that with uniform interactions on translationally invariant lattices according to a class of substitution sequences. The Gaussian distribution constants and imposed external magnetic fields are also periodic depending on the periodic characteristic of the interaction bonds. The critical behaviors of this generalized Gaussian model in external magnetic fields are studied by the exact renormalization-group approach and spin rescaling method. The critical points and all the critical exponents are obtained. The critical behaviors are found to be determined by the Gaussian distribution constants and the fractal dimensions of the lattices. When all the Gaussian distribution constants are the same, the dependence of the critical exponents on the dimensions of the lattices is the same as that of the Gaussian model with uniform interactions on translationally invariant lattices.
基金Project supported by the National Natural Science Foundation of China（Nos.61303198,61471409,61472470,and 61402112） the Natural Science Foundation of Shandong Province,China（No.ZR2013FQ031）
