We construct Dirac operators and spectral triples for certain, not necessarily selfsimilar, fractal sets built on curves. Connes’ distance formula of noncommutative geometry provides a natural metric on the fractal. To motivate the construction, we address Kigami’s measurable Riemannian geometry, which is a metric realization of the Sierpinski gasket as a self-affine space with continuously dif...

We investigate an antiferromagnetic s=1/2 quantum spin system with anisotropic spin exchange on a fractal lattice, the Sierpiński gasket. We introduce a novel approximative numerical method, the configuration selective diagonalization (CSD) and apply this method to a the Sierpiński gasket with N=42. Using this and other methods we calculate ground state energies, spin gap, spin–spin correlation...

We investigate bond percolation on the non-p.c.f. Sierpiński gasket and the hexacarpet. With the use of the diamond fractal, we are able to bound the critical probability of percolation on the non-p.c.f. gasket from above by √ 5−1 2 , or approximately 0.618. We then show how the two fractals are related via the barycentric subdivisions of a triangle: the two spaces exhibit duality properties al...

Localization due to space structure, rather than due to randomness, is investigated by studying the usual tight-binding model on the Sierpinski gasket. Some exact results are obtained from the decimation —renormalization-group method. It is surprising that there exist an infinite number of extended states on the Sierpinski gasket. This set of extended states forms a Cantor set. The rest of the ...

The article mainly studies the contracting similarity fixed point and the structure of the general Sierpinski gasket. Firstly, the paper analyzes the importance of contracting similarity fixed point in fractal geometry. Based on a series of definitions, the article studies the contracting similarity fixed point. Then, the paper researches on the structure of the general Sierpinski gasket, and d...

Abstract Type-III secretion systems (T3SSs) of the bacterial flagellum and evolutionarily related injectisome are capable translocating proteins with a remarkable speed several thousand amino acids per second. Here, we investigate how T3SSs able to transport at such high rate while preventing leakage small molecules. Our mutational evolutionary analyses demonstrate that an ensemble conserved me...

Asbestos-free gaskets have been used to seal flanged connections on various applications. This paper discusses the use of a different style of gasket and details the advantages and benefits resulting from such a change. The discussion includes an analysis, supported by laboratory testing and successful field experiences. The paper is sectioned into three case studies, each topic relating to a t...

Combined high pressure phase transformations (PTs) and plastic flow in a sample within a gasket compressed in diamond anvil cell (DAC) are studied for the first time using finite element method. The key point is that phase transformations are modelled as strain-induced, which involves a completely different kinetic description than for traditional pressure-induced PTs. The model takes into acco...