Low-density series expansions for directed percolation III. Some two-dimensional lattices

We use very efficient algorithms to calculate low-density series for bond and site percolation on the directed triangular, honeycomb, kagom\'e, and $(4.8^2)$ lattices. Analysis of the series yields accurate estimates of the critical point $p_c$ and various critical exponents. The exponent estimates differ only in the $5^{th}$ digit, thus providing strong numerical evidence for the expected universality of the critical exponents for directed percolation problems. In addition we also study the non-physical singularities of the series.Comment: 20 pages, 8 figure

Absence of orbital-selective Mott transition in Ca_2-xSr_xRuO4

Quasi-particle spectra of the layer perovskite Sr$_2$RuO$_4$ are calculated within Dynamical Mean Field Theory for increasing values of the on-site Coulomb energy $U$. At small $U$ the planar geometry splits the $t_{2g}$ bands near $E_F$ into a wide, two-dimensional $d_{xy}$ band and two narrow, nearly one-dimensional $d_{xz,yz}$ bands. At larger $U$, however, the spectral distribution of these states exhibit similar correlation features, suggesting a common metal-insulator transition for all $t_{2g}$ bands at the same critical $U$.Comment: 4 pages, 4 figure

Enumeration of self-avoiding walks on the square lattice

We describe a new algorithm for the enumeration of self-avoiding walks on the square lattice. Using up to 128 processors on a HP Alpha server cluster we have enumerated the number of self-avoiding walks on the square lattice to length 71. Series for the metric properties of mean-square end-to-end distance, mean-square radius of gyration and mean-square distance of monomers from the end points have been derived to length 59. Analysis of the resulting series yields accurate estimates of the critical exponents $\gamma$ and $\nu$ confirming predictions of their exact values. Likewise we obtain accurate amplitude estimates yielding precise values for certain universal amplitude combinations. Finally we report on an analysis giving compelling evidence that the leading non-analytic correction-to-scaling exponent $\Delta_1=3/2$.Comment: 24 pages, 6 figure

Shear induced breaking of large internal solitary waves

The stability properties of 24 experimentally generated internal solitary waves (ISWs) of extremely large amplitude, all with minimum Richardson number less than 1/4, are investigated. The study is supplemented by fully nonlinear calculations in a three-layer fluid. The waves move along a linearly stratified pycnocline (depth h2) sandwiched between a thin upper layer (depth h1) and a deep lower layer (depth h3), both homogeneous. In particular, the wave-induced velocity profile through the pycnocline is measured by particle image velocimetry (PIV) and obtained in computation. Breaking ISWs were found to have amplitudes (a1) in the range a1>2.24 √h1h2(1+h2/h1), while stable waves were on or below this limit. Breaking ISWs were investigated for 0.27 0.86 and stable waves for Lx/λ < 0.86. The results show a sort of threshold-like behaviour in terms of Lx/λ. The results demonstrate that the breaking threshold of Lx/λ = 0.86 was sharper than one based on a minimum Richardson number and reveal that the Richardson number was found to become almost antisymmetric across relatively thick pycnoclines, with the minimum occurring towards the top part of the pycnoclinePostprintPeer reviewe

A new transfer-matrix algorithm for exact enumerations: Self-avoiding polygons on the square lattice

We present a new and more efficient implementation of transfer-matrix methods for exact enumerations of lattice objects. The new method is illustrated by an application to the enumeration of self-avoiding polygons on the square lattice. A detailed comparison with the previous best algorithm shows significant improvement in the running time of the algorithm. The new algorithm is used to extend the enumeration of polygons to length 130 from the previous record of 110.Comment: 17 pages, 8 figures, IoP style file

Self-avoiding walks and polygons on the triangular lattice

We use new algorithms, based on the finite lattice method of series expansion, to extend the enumeration of self-avoiding walks and polygons on the triangular lattice to length 40 and 60, respectively. For self-avoiding walks to length 40 we also calculate series for the metric properties of mean-square end-to-end distance, mean-square radius of gyration and the mean-square distance of a monomer from the end points. For self-avoiding polygons to length 58 we calculate series for the mean-square radius of gyration and the first 10 moments of the area. Analysis of the series yields accurate estimates for the connective constant of triangular self-avoiding walks, $\mu=4.150797226(26)$, and confirms to a high degree of accuracy several theoretical predictions for universal critical exponents and amplitude combinations.Comment: 24 pages, 6 figure

Low-density series expansions for directed percolation II: The square lattice with a wall

A new algorithm for the derivation of low-density expansions has been used to greatly extend the series for moments of the pair-connectedness on the directed square lattice near an impenetrable wall. Analysis of the series yields very accurate estimates for the critical point and exponents. In particular, the estimate for the exponent characterizing the average cluster length near the wall, $\tau_1=1.00014(2)$, appears to exclude the conjecture $\tau_1=1$. The critical point and the exponents $\nu_{\parallel}$ and $\nu_{\perp}$ have the same values as for the bulk problem.Comment: 8 pages, 1 figur