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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… (More)

We study stochastic evolution of optional games on simple graphs. There are two strategies, A and B, whose interaction is described by a general payoff matrix. In addition, there are one or several possibilities to opt out from the game by adopting loner strategies. Optional games lead to relaxed social dilemmas. Here we explore the interaction between… (More)

A photonic quasicrystal consists of two or more dielectric materials arranged in a quasiperiodic pattern with noncrystallographic symmetry that has a photonic band gap. We use a novel method to find the pattern with the widest TM-polarized gap for two-component materials. Patterns are obtained by computing a finite sum of density waves, assigning regions… (More)

Direct reciprocity is a mechanism for the evolution of cooperation based on repeated interactions. When individuals meet repeatedly, they can use conditional strategies to enforce cooperative outcomes that would not be feasible in one-shot social dilemmas. Direct reciprocity requires that individuals keep track of their past interactions and find the right… (More)

We present two sets of rules for constructing quasiperiodic tilings that suggest a simpler structural model of quasicrystals and a more plausible explanation of why quasicrystals form. First, we show that quasiperiodic tilings can be constructed from a single prototile with matching rules which constrain the way that neighbors can overlap. Second, we show… (More)

Cooperation and self-organized criticality are two main keywords in current studies of evolution. We propose a generalized Bak-Sneppen model and provide a natural mechanism which accounts for both phenomena simultaneously. We use the prisoner's dilemma games to mimic the interactions among the members in the population. Each member is identified by its… (More)

- Franz Gg Ahler, Hyeong-Chai Jeong
- 1995

A simple, local cluster interaction is presented, which has as (only) ground states perfectly quasicrystalline tilings from a single local iso-morphism class. Since these tilings do not allow for any perfect matching rules, it is thereby shown that the class of structures which are the ground state of some nite range interaction is considerably larger than… (More)

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… (More)

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