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

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

Priorities for sustainable turfgrass management: a research and industry perspective

This paper provides a brief review and assessment of the key environmental, regulatory and technical issues facing the turfgrass sector with specific reference to the European context. It considers the range of externalities or ‘drivers for change' facing the industry, and the challenges and opportunities available for promoting and achieving more sustainable turfgrass management within the sports, landscape and amenity sectors. The analysis confirms that there are a number of key areas where a concerted research and industrial effort is required. These include responding to the pressures from government demands for greater environmental regulation, the increasing pressure on natural resources (notably water, energy and land), the emerging role of turf management in supporting ecosystem services and enhancing biodiversity, the continued need to promote integrated pest management, and the looming challenges posed by a changing climate, and urgent need to adapt. Whilst many of these externalities appear to be risks to the sports turf industry, there will also be significant opportunities, for those where the labour, energy and agronomic costs are minimized and where the drive to adopt a multifunctional approach to sportsturf management is embraced

Low-density series expansions for directed percolation IV. Temporal disorder

We introduce a model for temporally disordered directed percolation in which the probability of spreading from a vertex $(t,x)$, where $t$ is the time and $x$ is the spatial coordinate, is independent of $x$ but depends on $t$. Using a very efficient algorithm we calculate low-density series for bond percolation on the directed square lattice. Analysis of the series yields estimates for the critical point $p_c$ and various critical exponents which are consistent with a continuous change of the critical parameters as the strength of the disorder is increased.Comment: 11 pages, 3 figure

Quantum noise limited and entanglement-assisted magnetometry

We study experimentally the fundamental limits of sensitivity of an atomic radio-frequency magnetometer. First we apply an optimal sequence of state preparation, evolution, and the back-action evading measurement to achieve a nearly projection noise limited sensitivity. We furthermore experimentally demonstrate that Einstein-Podolsky-Rosen (EPR) entanglement of atoms generated by a measurement enhances the sensitivity to pulsed magnetic fields. We demonstrate this quantum limited sensing in a magnetometer utilizing a truly macroscopic ensemble of 1.5*10^12 atoms which allows us to achieve sub-femtoTesla/sqrt(Hz) sensitivity.Comment: To appear in Physical Review Letters, April 9 issue (provisionally

Molecular Realization of a Quantum NAND Tree

The negative-AND (NAND) gate is universal for classical computation making it an important target for development. A seminal quantum computing algorithm by Farhi, Goldstone and Gutmann has demonstrated its realization by means of quantum scattering yielding a quantum algorithm that evaluates the output faster than any classical algorithm. Here, we derive the NAND outputs analytically from scattering theory using a tight-binding (TB) model and show the restrictions on the TB parameters in order to still maintain the NAND gate function. We map the quantum NAND tree onto a conjugated molecular system, and compare the NAND output with non-equilibrium Green's function (NEGF) transport calculations using density functional theory (DFT) and TB Hamiltonians for the electronic structure. Further, we extend our molecular platform to show other classical gates that can be realized for quantum computing by scattering on graphs.Comment: 17 pages, 6 figures, 1 tabl

Arrays of Josephson junctions in an environment with vanishing impedance

The Hamiltonian operator for an unbiased array of Josephson junctions with gate voltages is constructed when only Cooper pair tunnelling and charging effects are taken into account. The supercurrent through the system and the pumped current induced by changing the gate voltages periodically are discussed with an emphasis on the inaccuracies in the Cooper pair pumping. Renormalisation of the Hamiltonian operator is used in order to reliably parametrise the effects due to inhomogeneity in the array and non-ideal gating sequences. The relatively simple model yields an explicit, testable prediction based on three experimentally motivated and determinable parameters.Comment: 13 pages, 9 figures, uses RevTeX and epsfig, Revised version, Better readability and some new result

Numerical Study of a Field Theory for Directed Percolation

A numerical method is devised for study of stochastic partial differential equations describing directed percolation, the contact process, and other models with a continuous transition to an absorbing state. Owing to the heightened sensitivity to fluctuationsattending multiplicative noise in the vicinity of an absorbing state, a useful method requires discretization of the field variable as well as of space and time. When applied to the field theory for directed percolation in 1+1 dimensions, the method yields critical exponents which compare well against accepted values.Comment: 18 pages, LaTeX, 6 figures available upon request LC-CM-94-00

Bilinear forms on Grothendieck groups of triangulated categories

We extend the theory of bilinear forms on the Green ring of a finite group developed by Benson and Parker to the context of the Grothendieck group of a triangulated category with Auslander-Reiten triangles, taking only relations given by direct sum decompositions. We examine the non-degeneracy of the bilinear form given by dimensions of homomorphisms, and show that the form may be modified to give a Hermitian form for which the standard basis given by indecomposable objects has a dual basis given by Auslander-Reiten triangles. An application is given to the homotopy category of perfect complexes over a symmetric algebra, with a consequence analogous to a result of Erdmann and Kerner.Comment: arXiv admin note: substantial text overlap with arXiv:1301.470