arXiv subjects

Hyeong-Chai Jeong

Publications and source records attributed to Hyeong-Chai Jeong.

23 records · Page 2Linked to original sources

arXiv2003

Inflation rule for Gummelt coverings with decorated decagons and its implication to quasi-unit-cell models

The equivalence between quasi-unit-cell models and Penrose-tile models on the level of decorations is proved using inflation rules for Gummelt coverings with decorated decagons. Due to overlaps, Gummelt arrangement of decorated decagons gives rise to nine different (context-dependent) decagon decorations in the covering. The inflation rules for decagons for each of nine types are presented and shown that inflations from differently typed decagons always produce different decorations of inflated decagons. However, if the original decagon region is divided into ``equivalent'' rhombus Penrose tiles, typed-decagon arrangements in the tiles (of the same shape) become identical for the fourfold inflated decagons. This implies that a decagonal quasi-unit-cell model can be reinterpreted as a Penrose-tile model with fourfold deflated super-tiles.

cond-mat.stat-mech↗

arXiv2002

Rules for Computing Symmetry, Density and Stoichiometry in a Quasi-Unit-Cell Model of Quasicrystals

The quasi-unit cell picture describes the atomic structure of quasicrystals in terms of a single, repeating cluster which overlaps neighbors according to specific overlap rules. In this paper, we discuss the precise relationship between a general atomic decoration in the quasi-unit cell picture atomic decorations in the Penrose tiling and in related tiling pictures. Using these relations, we obtain a simple, practical method for determining the density, stoichiometry and symmetry of a quasicrystal based on the atomic decoration of the quasi-unit cell taking proper account of the sharing of atoms between clusters.

cond-mat.mtrl-sci↗

arXiv2000

Noncommutative Torus from Fibonacci Chains via Foliation

We classify the Fibonacci chains (F-chains) by their index sequences and construct an approximately finite dimensional (AF) $C^*$-algebra on the space of F-chains as Connes did on the space of Penrose tiling. The K-theory on this AF-algebra suggests a connection between the noncommutative torus and the space of F-chains. A noncommutative torus, which can be regarded as the $C^*$-algebra of a foliation on the torus, is explicitly embedded into the AF-algebra on the space of F-chains. As a counterpart of that, we obtain a relation between the space of F-chains and the leaf space of Kronecker foliation on the torus using the cut-procedure of constructing F-chains.

math-ph↗

arXiv1999

Dynamics and Scaling of One Dimensional Surface Structures

We study several one dimensional step flow models. Numerical simulations show that the slope of the profile exhibits scaling in all cases. We apply a scaling ansatz to the various step flow models and investigate their long time evolution. This evolution is described in terms of a continuous step density function, which scales in time according to D(x,t)=F(xt^{-1/γ}). The value of the scaling exponent γdepends on the mass transport mechanism. When steps exchange atoms with a global reservoir the value of γis 2. On the other hand, when the steps can only exchange atoms with neighboring terraces, γ=4. We compute the step density scaling function for three different profiles for both global and local exchange mechanisms. The computed density functions coincide with simulations of the discrete systems. These results are compared to those given by the continuum approach of Mullins.

cond-mat.mtrl-sci↗

arXiv1993

Finite-Temperature Elasticity Phase Transition in Decaconal Quasicrystals

We present evidence for a novel finite-temperature phase transition in the phason elasticity of quasicrystals. A tiling model for energetically stabilized decagonal quasicrystals has been studied in an extensive series of Monte Carlo simulation. Hamiltonian (energetics) of the model is given by nearest-neighbor Penrose-like matching rules between three dimensional unit cells. A new order parameter and diagnostics have been introduced. We show that a transition from locked phason to unlocked phason dynamics occurs at finite temperature. In the unlocked phase, phasons can be thermodynamically excited even though the quasicrystal is energetically stabilized at low temperatures.

cond-mat↗