Co-rich decagonal Al-Co-Ni: predicting structure, orientational order, and puckering

We apply systematic methods previously used by Mihalkovic et al. to predict the structure of the `basic' Co-rich modification of the decagonal Al70 Co20 Ni10 layered quasicrystal, based on known lattice constants and previously calculated pair potentials. The modelling is based on Penrose tile decoration and uses Monte Carlo annealing to discover the dominant motifs, which are converted into rules for another level of description. The result is a network of edge-sharing large decagons on a binary tiling of edge 10.5 A. A detailed analysis is given of the instability of a four-layer structure towards $c$-doubling and puckering of the atoms out of the layers, which is applied to explain the (pentagonal) orientational order.Comment: IOP LaTex; 7 pp, 2 figures. In press, Phil. Mag. A (Proc. Intl. Conf. on Quasicrystals 9, Ames Iowa, May 2005

Peculiar Behavior of Si Cluster Ions in Solid Al

A peculiar ion behavior is found in a Si cluster, moving with a speed of ~0.22c (c: speed of light) in a solid Al plasma: the Si ion, moving behind the forward moving Si ion closely in a several angstrom distance in the cluster, feels the wake field generated by the forward Si. The interaction potential on the rear Si may balance the deceleration backward force by itself with the acceleration forward force by the forward Si in the longitudinal moving direction. The forward Si would be decelerated normally. However, the deceleration of the rear Si, moving behind closely, would be reduced significantly, and the rear Si may catch up and overtake the forward moving Si in the cluster during the Si cluster interaction with the high-density Al plasma

Finite Form of the Quintuple Product Identity

The celebrated quintuple product identity follows surprisingly from an almost-trivial algebraic identity, which is the limiting case of the terminating q-Dixon formula.Comment: 1 pag

A new class of (2+1)(2+1)-d topological superconductor with Z8\mathbb{Z}_8 topological classification

The classification of topological states of matter depends on spatial dimension and symmetry class. For non-interacting topological insulators and superconductors the topological classification is obtained systematically and nontrivial topological insulators are classified by either integer or $Z_2$. The classification of interacting topological states of matter is much more complicated and only special cases are understood. In this paper we study a new class of topological superconductors in $(2+1)$ dimensions which has time-reversal symmetry and a $\mathbb{Z}_2$ spin conservation symmetry. We demonstrate that the superconductors in this class is classified by $\mathbb{Z}_8$ when electron interaction is considered, while the classification is $\mathbb{Z}$ without interaction.Comment: 5 pages main text and 3 pages appendix. 1 figur

Cosmological and Solar-System Tests of f(R) Modified Gravity

We investigate the cosmological and the local tests of the f(R) theory of modified gravity via the observations of (1) the cosmic expansion and (2) the cosmic structures and via (3) the solar-system experiments. To fit the possible cosmic expansion histories under consideration, for each of them we reconstruct f(R), known as "designer f(R)". We then test the designer f(R) via the cosmic-structure constraints on the metric perturbation ratio Psi/Phi and the effective gravitational coupling G_eff and via the solar-system constraints on the Brans-Dicke theory with the chameleon mechanism. We find that among the designer f(R) models specified by the CPL effective equation of state w_eff, only the model closely mimicking general relativity with a cosmological constant (LambdaCDM) can survive all the tests. Accordingly, these tests rule out the frequently studied "w_eff = -1" designer f(R) models which are distinct in cosmic structures from LambdaCDM. When considering only the cosmological tests, we find that the surviving designer f(R) models, although exist for a variety of w_eff, entail fine-tuning.Comment: 22 pages, 9 figures, LaTe

Optimal CUR Matrix Decompositions

The CUR decomposition of an $m \times n$ matrix $A$ finds an $m \times c$ matrix $C$ with a subset of $c < n$ columns of $A,$ together with an $r \times n$ matrix $R$ with a subset of $r < m$ rows of $A,$ as well as a $c \times r$ low-rank matrix $U$ such that the matrix $C U R$ approximates the matrix $A,$ that is, $|| A - CUR ||_F^2 \le (1+\epsilon) || A - A_k||_F^2$, where $||.||_F$ denotes the Frobenius norm and $A_k$ is the best $m \times n$ matrix of rank $k$ constructed via the SVD. We present input-sparsity-time and deterministic algorithms for constructing such a CUR decomposition where $c=O(k/\epsilon)$ and $r=O(k/\epsilon)$ and rank$(U) = k$. Up to constant factors, our algorithms are simultaneously optimal in $c, r,$ and rank$(U)$.Comment: small revision in lemma 4.

Analysis of the X-Factor and X-Factor stretch during the completion of a golf practice session in low-handicap golfers

The X-Factor and X-Factor stretch have been positively correlated with golf long game performance. The aim of this study was to compare the X-Factor, X-Factor stretch and long game performance variables pre and following a golf practice session. A group of male golfers (n = 15, handicap = 3.3 ± 1.7) participated in the laboratory-based-study. Movement and performance variables were collected from five golf swings performed pre and following a golf practice session using a motion capture system and launch monitor respectively. Following the practice session, significant increases were observed in the X-Factor (p = 0.00, d = 0.22) and the X-Factor stretch (p = 0.02, d = 0.25). Specifically, the X-Factor increased from 52.82 ± 5.64 ° to 54.06 ± 5.61 ° following the practice session. The X-Factor stretch increased from 1.54 ± 1.05 ° to 1.90 ± 1.41 ° following the practice session. Significant differences were displayed in club head velocity (p = 0.00, d = 0.35), ball velocity (p = 0.01, d = 0.21) and actual carry distance (p = 0.00, d = 0.29) following the practice session. These findings suggest that performing multiple golf shots is not detrimental in terms of muscular fatigue in the long game performance. In actual fact, the findings demonstrate that performing 100 golf shots increases the X-Factor, X-Factor stretch patterns and performance variables which, in turn, increases long game performance. These findings can help PGA golf Professionals improve teaching practices and formulation of golf programmes and warm-up sessions

Charge order, metallic behavior and superconductivity in La_{2-x}Ba_xCuO_4 with x=1/8

The ab-plane optical properties of a cleaved single crystal of La_{2-x}Ba_xCuO_4 for x=1/8 (T_c ~ 2.4 K) have been measured over a wide frequency and temperature range. The low-frequency conductivity is Drude-like and shows a metallic response with decreasing temperature. However, below ~ 60 K, corresponding to the onset of charge-stripe order, there is a rapid loss of spectral weight below about 40 meV. The gapping of single-particle excitations looks surprisingly similar to that observed in superconducting La_{2-x}Sr_{x}CuO_4, including the presence of a residual Drude peak with reduced weight; the main difference is that the lost spectral weight moves to high, rather than zero, frequency, reflecting the absence of a bulk superconducting condensate.Comment: 4 pages, with 1 table and 3 figure