Youyan Liu

Elastic wave band gaps for three-dimensional phononic crystals with two structural units

We investigated the absolute elastic wave band gaps in three-dimensional systems consisting of steel inclusions embedded in plastic matrix. Numerical results show that the configurations formed by inserting an additional steel object (either a sphere of different size or a cube) into each unit cell of a simple cubic structure with spherical steel inclusions, exhibit larger absolute elastic wave band gaps compared with the original simple cubic structure. However, for simple cubic structures originally consisting of steel cubes embedded in plastic matrix, it shows inserting additional cubes results in smaller band gaps.

The bandgap of a photonic crystal with triangular dielectric rods in a honeycomb lattice

The photonic band structures of a two-dimensional photonic crystal consisting of a honeycomb lattice with triangular dielectric rods embedded in air are studied numerically. In a honeycomb lattice, the largest absolute photonic bandgap is achieved by the use of triangular rods which have the same shape as that of the coordination polygon of a lattice point; the reason why triangular dielectric rods in a honeycomb lattice can generate the largest gap is also discussed.

Acoustic band gaps for a two-dimensional periodic array of solid cylinders in viscous liquid

We investigated the absolute acoustic band gaps for two-dimensional periodic arrays of silica cylinders in viscous liquid. Acoustic band structures, which have complex eigenfrequencies for these systems, are calculated with the plane wave expansion method. They show that when the viscous penetration depth is comparable to the structural length scale, the structures possess large absolute acoustic band gaps compared with those without viscosity. We also found that the magnitude of the viscosity plays an important role in these band gaps.

Relationship between Penrose vertices and decagonal covering configurations

Two-dimensional quasicrystals are generally described by the Penrose tiling model. An alternative is the cluster covering approach developed recently. There exists a correspondence between the two schemes. The distributions of rhombus vertices in Penrose tilings and the nearest neighbor configurations in the decagonal covering structures are studied. Their occurrence probabilities are expressed in terms of the powers of the golden mean τ and their relationship is obtained.

Configuration correlations in decagonal covering structures

Quasiperiodic structures can be generated by cluster covering approach. In a decagonal covering pattern there are nine nearest neighbor configurations. These basic configurations exhibit certain correlations in the whole system and will develop to higher order configurations, which reflect the local structures concerning the neighbors beyond the nearest ones.

Bound states of an electron in a dimerized chain with a single nonlinear impurity

Abstract The bound states of an electron moving in a dimerized chain with a single nonlinear impurity of arbitrary strength and nonlinearity are studied. Some novel properties have been found.

Electronic properties of one-dimensional quasilattices

We study the on-site model of a new class of one-dimensional qusiperiodic lattices, for which the substitution rules areB→BA, andA→BAB. By means of the renormalization-group approach, a interesting multifractal specrral behavior has been found, which has been confirmed by numerical simulation. A Cantor-like energy spectra is obtained by using the Kohmoto-Kadanaff-Tang (KKT) renormalization-group method. Three kinds of wave-function behavior (extended, localized, and intemediate states) are definitely found.

Generalized Möbius inverse formulas

Abstract The Mobius inverse formula is extended to an operator form which is much more useful for studying some inverse physical problems. Several new results are given, the contents of which cover many previous works on the Mobius inverse formulas.

GAP-LABELING PROPERTIES OF THE ENERGY SPECTRUM FOR TWO-DIMENSIONAL FIBONACCI QUASILATTICES

We have analytically obtained the occupation probabilities on subbands of the hierarchical energy spectrum and the step heights of the integrated density of states for two-dimensional Fibonacci quasilattices. Based on the above results, the gap-labeling properties of the energy spectrum are found, which claim that the step height is equal to {mτ}, where the braces denote the fractional part, and m is an integer that can be used to label the corresponding energy gap. Numerical results confirm these results very well.