Lattice Green Function (at 0) for the 4d Hypercubic Lattice

The generating function for recurrent Polya walks on the four dimensional hypercubic lattice is expressed as a Kampe-de-Feriet function. Various properties of the associated walks are enumerated.Comment: latex, 5 pages, Res. Report 1

Characterizing Wood Components as Network Polymers by Dynamic Mechanical Analysis

The characterization of structure-property relationships in wood components, such as lignin, is a critical aspect of utilization. This point has been emphasized recently with concerns directed toward the application of natural products as wood bonding agents. Dynamic mechanical analysis is a valuable technique for the study of these relations because of its sensitivity to variations in polymer structure

Longitudinal surface structures (flowstripes) on Antarctic glaciers

Longitudinal surface structures (“flowstripes”) are common on many glaciers but their origin and significance are poorly understood. In this paper we present observations of the development of these longitudinal structures from four different Antarctic glacier systems; the Lambert Glacier/Amery Ice Shelf area, the Taylor and Ferrar Glaciers in the Ross Sea sector, Crane and Jorum Glaciers (ice-shelf tributary glaciers) on the Antarctic Peninsula, and the onset zone of a tributary to the Recovery Glacier Ice Stream in the Filchner Ice Shelf area. Mapping from optical satellite images demonstrates that longitudinal surface structures develop in two main situations: (1) as relatively wide flow stripes within glacier flow units and (2) as relatively narrow flow stripes where there is convergent flow around nunataks or at glacier confluence zones. Our observations indicate that the confluence features are narrower, sharper, and more clearly defined features. They are characterised by linear troughs or depressions on the ice surface and are much more common than the former type. Longitudinal surface structures within glacier flow units have previously been explained as the surface expression of localised bed perturbations but a universal explanation for those forming at glacier confluences is lacking. Here we propose that these features are formed at zones of ice acceleration and extensional flow at glacier confluences. We provide a schematic model for the development of longitudinal surface structures based on extensional flow that can explain their ridge and trough morphology as well as their down-ice persistence

Luminescence dating of glacial advances at Lago Buenos Aires (∼46 °S), Patagonia

Understanding the timing of past glacial advances in Patagonia is of global climatic importance because of the insight this can provide into the influence on glacier behaviour of changes in temperature and precipitation related to the Southern Westerlies. In this paper we present new luminescence ages determined using single grains of K-feldspar from proglacial outwash sediments that were deposited by the Patagonian Ice Sheet around Lago Buenos Aires (∼46 °S), east of the contemporary Northern Patagonian Icefield. The new luminescence ages indicate that major outwash accumulations formed around ∼110 ± 20 ka to 140 ± 20 ka and that these correspond to the Moreno I and II moraine ridges, which were previously dated using cosmogenic isotope dating to 150 ± 30 ka. Luminescence dating at Lago Buenos Aires has also identified outwash sediments that were deposited during glacial advances ∼30.8 ± 5.7 ka and ∼34.0 ± 6.1 ka (MIS 3) that are not recorded in the moraine record. Younger outwash accumulations were then deposited between ∼14.7 ± 2.1 and 26.2 ± 1.6 ka which correspond to the Fenix I – V moraine ridges. The combined chronology suggests that glacial advances occurred ∼110 ± 20 ka to 150 ± 30 ka (MIS 6), ∼30.8 ± 5.7 ka to ∼34.0 ± 6.1 ka (MIS 3), and ∼14.7 ± 2.1 to 26.2 ± 1.6 ka (MIS 2) at Lago Buenos Aires. Overall luminescence dating using single grains of K-feldspar has excellent potential to contribute towards the ever-increasing geochronological dataset constraining the timings of glacial advances in Patagonia

Exact parent Hamiltonians of bosonic and fermionic Moore-Read states on lattices and local models

We introduce a family of strongly-correlated spin wave functions on arbitrary spin-1/2 and spin-1 lattices in one and two dimensions. These states are lattice analogues of Moore-Read states of particles at filling fraction 1/q, which are non-Abelian Fractional Quantum Hall states in 2D. One parameter enables us to perform an interpolation between the continuum limit, where the states become continuum Moore-Read states of bosons (odd q) and fermions (even q), and the lattice limit. We show numerical evidence that the topological entanglement entropy stays the same along the interpolation for some of the states we introduce in 2D, which suggests that the topological properties of the lattice states are the same as in the continuum, while the 1D states are critical states. We then derive exact parent Hamiltonians for these states on lattices of arbitrary size. By deforming these parent Hamiltonians, we construct local Hamiltonians that stabilize some of the states we introduce in 1D and in 2D.Comment: 15 pages, 7 figure

Lattice Green functions in all dimensions

We give a systematic treatment of lattice Green functions (LGF) on the $d$-dimensional diamond, simple cubic, body-centred cubic and face-centred cubic lattices for arbitrary dimensionality $d \ge 2$ for the first three lattices, and for $2 \le d \le 5$ for the hyper-fcc lattice. We show that there is a close connection between the LGF of the $d$-dimensional hypercubic lattice and that of the $(d-1)$-dimensional diamond lattice. We give constant-term formulations of LGFs for all lattices and dimensions. Through a still under-developed connection with Mahler measures, we point out an unexpected connection between the coefficients of the s.c., b.c.c. and diamond LGFs and some Ramanujan-type formulae for $1/\pi.$Comment: 30 page

Green's function of a finite chain and the discrete Fourier transform

A new expression for the Green's function of a finite one-dimensional lattice with nearest neighbor interaction is derived via discrete Fourier transform. Solution of the Heisenberg spin chain with periodic and open boundary conditions is considered as an example. Comparison to Bethe ansatz clarifies the relation between the two approaches.Comment: preprint of the paper published in Int. J. Modern Physics B Vol. 20, No. 5 (2006) 593-60

New results on the limit for the width of the exotic Theta^+ resonance

We investigate the impact of the \Theta^+(1540) resonance on differential and integrated cross sections for the reaction K^+d{\to}K^0pp, where experimental information is available at kaon momenta below 640 MeV/c. The calculation utilizes the J\"ulich KN model and extensions of it that include contributions from a \Theta^+(1540) state with different widths. The evaluation of the reaction K^+d{\to}K^0pp takes into account effects due to the Fermi motion of the nucleons within the deuteron and the final three-body kinematics. We conclude that the available data constrain the width of the \Theta^+(1540) to be less than 1 MeV.Comment: 5 pages, 5 figures, updated version, accepted for publication in Phys. Lett.