Quenched KS light hadron mass at \beta=6.5 on a 64\times 48^3 lattice

We report our quenched staggered light hadron mass calculation at the coupling of \beta = 6.5 on a 48^3 \times 64 lattice, based on an increased statistics of two hundred gauge configurations. Staggered quark wall sources with mass of m_q a = 0.01, 0.005, 0.0025 and 0.00125 are used. Flavor symmetry is restored for pion and \rho meson. The lattice scale is estimated to be a^{-1} = 3.7(2) GeV.Comment: 4 pages, espcrc2.sty, epsf.sty, Poster presented at LATTICE96(poster

Towards the continuum limit with quenched staggered quarks

We extend previous work on finite-size effects with dynamical staggered quarks to the quenched approximation. We again emphasize the large volume limit that is of interest for spectrum calculations which may hope to approach the experimental values. Relying on new calculations at $6/g^2=5.7$ and recent work with weaker couplings, we extrapolate to the continuum limit and find a nucleon to rho mass ratio in close agreement with the experimental value and the value obtained by extrapolations from calculations with Wilson quarks. Additional calculations that should be done to improve the reliability of the extrapolation are discussed.Comment: 3 pages, PostScript, Contribution to Lattice '9

Chiral limit of light hadron mass in quenched staggered QCD

We discuss chiral limit of light hadron mass from our quenched staggered calculations with a high lattice cutoff of (a^{-1})(\sim)3.7 GeV at (\beta)=6.5 and a large lattice volume of (48^3\times 64). We added six heavier quark mass values of (m_qa)=0.0075, 0.015, 0.02, 0.03, 0.04 and 0.05 to the previously existing 0.01, 0.005, 0.0025, and 0.00125. An interesting curvature is observed in the (m_\pi^2/m_q) to (m_q) plot near (m_qa)=0.01.Comment: LATTICE98(spectrum),3 pages and 4 figure

Notes on complexity of packing coloring

A packing $k$-coloring for some integer $k$ of a graph $G=(V,E)$ is a mapping $\varphi:V\to\{1,\ldots,k\}$ such that any two vertices $u, v$ of color $\varphi(u)=\varphi(v)$ are in distance at least $\varphi(u)+1$. This concept is motivated by frequency assignment problems. The \emph{packing chromatic number} of $G$ is the smallest $k$ such that there exists a packing $k$-coloring of $G$. Fiala and Golovach showed that determining the packing chromatic number for chordal graphs is \NP-complete for diameter exactly 5. While the problem is easy to solve for diameter 2, we show \NP-completeness for any diameter at least 3. Our reduction also shows that the packing chromatic number is hard to approximate within $n^{{1/2}-\varepsilon}$ for any $\varepsilon > 0$. In addition, we design an \FPT algorithm for interval graphs of bounded diameter. This leads us to exploring the problem of finding a partial coloring that maximizes the number of colored vertices.Comment: 9 pages, 2 figure

QCD Spectrum --- 1996

Progress on the calculation of the spectrum from lattice calculations is reviewed. Particular emphasis is placed on discussing our ability to control possible systematic errors coming from finite volume, and extrapolations in quark mass and lattice spacing. Recent approaches based on improved actions are compared.Comment: Plenary talk presented at LATTICE96(spectrum), 13 pages, LaTeX, 17 eps figures. Uses espcrc2, epsf. Additional figures may be found at: http://physics.indiana.edu/~sg/lat96_spectrum.htm

Fracture simulation for zirconia toughened alumina microstructure

Purpose - The purpose of this paper is to describe finite element modelling for fracture and fatigue behaviour of zirconia toughened alumina microstructures. Design/methodology/approach - A two-dimensional finite element model is developed with an actual $Al{_2}O{_3}$ - 10 vol% $ZrO{_2}$ microstructure. A bilinear, time-independent cohesive zone law is implemented for describing fracture behaviour of grain boundaries. Simulation conditions are similar to those found at contact between a head and a cup of hip prosthesis. Residual stresses arisen from the mismatch of thermal coefficient between grains are determined. Then, effects of a micro-void and contact stress magnitude are investigated with models containing residual stresses. For the purpose of simulating fatigue behaviour, cyclic loadings are applied to the models. Findings - Results show that crack density is gradually increased with increasing magnitude of contact stress or number of fatigue cycles. It is also identified that a micro-void brings about the increase of crack density rate. Social implications - This paper is the first step for predicting the lifetime of ceramic implants. The social implications would appear in the next few years about health issues. Originality/value - This proposed finite element method allows describing fracture and fatigue behaviours of alumina-zirconia microstructures for hip prosthesis, provided that a microstructure image is available

Quenched staggered light hadron spectroscopy from 483×6448^3\times64 at β=6.5\beta = 6.5

We report our light hadron mass calculation based on an increased statistics of 250 quenched gauge configurations on a (48^3 \times 64) lattice at (\beta = 6.5). Quark propagators are calculated for each of these configurations with staggered wall source and point sink at quark mass values of (m_q = 0.01, 0.005, 0.0025) and (0.00125). We also did additional calculations to improve our understanding of systematic biases arising from autocorrelation, source size, and propagator calculations. Our earlier conclusions that the flavor symmetry breaking is reduced and the ratio (m_N/m_\rho (\sim 1.25(4))) is small remains robust.Comment: 3 pages and 4 figures, poster presented at the lattice 97 conferenc

Edge states for topological insulators in two dimensions and their Luttinger-like liquids

Topological insulators in three spatial dimensions are known to possess a precise bulk/boundary correspondence, in that there is a one-to-one correspondence between the 5 classes characterized by bulk topological invariants and Dirac hamiltonians on the boundary with symmetry protected zero modes. This holographic characterization of topological insulators is studied in two dimensions. Dirac hamiltonians on the one dimensional edge are classified according to the discrete symmetries of time-reversal, particle-hole, and chirality, extending a previous classification in two dimensions. We find 17 inequivalent classes, of which 11 have protected zero modes. Although bulk topological invariants are thus far known for only 5 of these classes, we conjecture that the additional 6 describe edge states of new classes of topological insulators. The effects of interactions in two dimensions are also studied. We show that all interactions that preserve the symmetries are exactly marginal, i.e. preserve the gaplessness. This leads to a description of the distinct variations of Luttinger liquids that can be realized on the edge.Comment: 13 pages with 4 Tables. Version 2: published version. Some clarifying discussions has been added; main results are unchange

Holographic classification of Topological Insulators and its 8-fold periodicity

Using generic properties of Clifford algebras in any spatial dimension, we explicitly classify Dirac hamiltonians with zero modes protected by the discrete symmetries of time-reversal, particle-hole symmetry, and chirality. Assuming the boundary states of topological insulators are Dirac fermions, we thereby holographically reproduce the Periodic Table of topological insulators found by Kitaev and Ryu. et. al, without using topological invariants nor K-theory. In addition we find candidate Z_2 topological insulators in classes AI, AII in dimensions 0,4 mod 8 and in classes C, D in dimensions 2,6 mod 8.Comment: 19 pages, 4 Table