Interaction between static holes in a quantum dimer model on the kagome lattice

A quantum dimer model (QDM) on the kagome lattice with an extensive ground-state entropy was recently introduced [Phys. Rev. B 67, 214413 (2003)]. The ground-state energy of this QDM in presence of one and two static holes is investigated by means of exact diagonalizations on lattices containing up to 144 kagome sites. The interaction energy between the holes (at distances up to 7 lattice spacings) is evaluated and the results show no indication of confinement at large hole separations.Comment: 6 pages, 3 figures. IOP style files included. To appear in J. Phys.: Condens. Matter, Proceedings of the HFM2003 conference, Grenobl

Stability of the hard-sphere icosahedral quasilattice

The stability of the hard-sphere icosahedral quasilattice is analyzed using the differential formulation of the generalized effective liquid approximation. We find that the icosahedral quasilattice is metastable with respect to the hard-sphere crystal structures. Our results agree with recent findings by McCarley and Ashcroft [Phys. Rev. B {\bf 49}, 15600 (1994)] carried out using the modified weighted density approximation.Comment: 15 pages, 2 figures available from authors upon request, (revtex), submitted to Phys. Rev.

Magnetic Properties of Undoped C60C_{60}

The Heisenberg antiferromagnet, which arises from the large $U$ Hubbard model, is investigated on the $C_{60}$ molecule and other fullerenes. The connectivity of $C_{60}$ leads to an exotic classical ground state with nontrivial topology. We argue that there is no phase transition in the Hubbard model as a function of $U/t$, and thus the large $U$ solution is relevant for the physical case of intermediate coupling. The system undergoes a first order metamagnetic phase transition. We also consider the S=1/2 case using perturbation theory. Experimental tests are suggested.Comment: 12 pages, 3 figures (included

Recursion and Path-Integral Approaches to the Analytic Study of the Electronic Properties of C60C_{60}

The recursion and path-integral methods are applied to analytically study the electronic structure of a neutral $C_{60}$ molecule. We employ a tight-binding Hamiltonian which considers both the $s$ and $p$ valence electrons of carbon. From the recursion method, we obtain closed-form {\it analytic} expressions for the $\pi$ and $\sigma$ eigenvalues and eigenfunctions, including the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) states, and the Green's functions. We also present the local densities of states around several ring clusters, which can be probed experimentally by using, for instance, a scanning tunneling microscope. {}From a path-integral method, identical results for the energy spectrum are also derived. In addition, the local density of states on one carbon atom is obtained; from this we can derive the degree of degeneracy of the energy levels.Comment: 19 pages, RevTex, 6 figures upon reques

A Menu of Activities in Different Intelligence Areas to Differentiate Instruction for Upper Elementary Students Related to the Book Because of Winn-Dixie

Today’s elementary classrooms are becoming more diverse, requiring teachers to provide effective instruction to children with a wide range of academic performance, ability, background, and interest. This work focuses on the development of a menu of differentiated instructional activities for teaching literacy to upper elementary students. The author, a former elementary teacher, worked with a faculty member and her literacy methods class of undergraduate preservice elementary teachers to develop this teaching unit based on a popular, award-winning children’s novel (DiCamillo, 2000). The menu of various activities organized in ten different intelligence areas (logical-mathematical, linguistic, bodilykinesthetic, spatial, musical, interpersonal, intrapersonal, naturalist, moral, and spiritual) and arranged at different levels of Bloom’s taxonomy (knowledge, comprehension, application, analysis, synthesis and evaluation) allows a teacher to easily select assignments designed to deepen comprehension or appreciation of this literary work to meet the individual needs of students. Each activity is accompanied by an example correct response so that teachers may gauge its demands. The reactions of preservice teachers to this project from beginning to end were examined. Before participation in the project, preservice teachers emphasized fame and recognition as being motivators and effects of publication. After participation in the project, they focused on the effects of the work on their employment opportunities, emphasizing a sense of accomplishment and downplaying fame/recognition. [5 tables, 11 references, 2 appendices

Rules for Computing Symmetry, Density and Stoichiometry in a Quasi-Unit-Cell Model of Quasicrystals

The quasi-unit cell picture describes the atomic structure of quasicrystals in terms of a single, repeating cluster which overlaps neighbors according to specific overlap rules. In this paper, we discuss the precise relationship between a general atomic decoration in the quasi-unit cell picture atomic decorations in the Penrose tiling and in related tiling pictures. Using these relations, we obtain a simple, practical method for determining the density, stoichiometry and symmetry of a quasicrystal based on the atomic decoration of the quasi-unit cell taking proper account of the sharing of atoms between clusters.Comment: 14 pages, 8 figure

The "Square Kagome" Quantum Antiferromagnet and the Eight Vertex Model

We introduce a two dimensional network of corner-sharing triangles with square lattice symmetry. Properties of magnetic systems here should be similar to those on the kagome lattice. Focusing on the spin half Heisenberg quantum antiferromagnet, we generalise the spin symmetry group from SU(2) to SU(N). In the large N limit, we map the model exactly to the eight vertex model, solved by Baxter. We predict an exponential number of low-lying singlet states, a triplet gap, and a two-peak specific heat. In addition, the large N limit suggests a finite temperature phase transition into a phase with ordered ``resonance loops'' and broken translational symmetry.Comment: 5 pages, revtex, 5 eps figures include

Nonequilibrium dynamics of fully frustrated Ising models at T=0

We consider two fully frustrated Ising models: the antiferromagnetic triangular model in a field of strength, $h=H T k_B$, as well as the Villain model on the square lattice. After a quench from a disordered initial state to T=0 we study the nonequilibrium dynamics of both models by Monte Carlo simulations. In a finite system of linear size, $L$, we define and measure sample dependent "first passage time", $t_r$, which is the number of Monte Carlo steps until the energy is relaxed to the ground-state value. The distribution of $t_r$, in particular its mean value, $$, is shown to obey the scaling relation, $\sim L^2 \ln(L/L_0)$, for both models. Scaling of the autocorrelation function of the antiferromagnetic triangular model is shown to involve logarithmic corrections, both at H=0 and at the field-induced Kosterlitz-Thouless transition, however the autocorrelation exponent is found to be $H$ dependent.Comment: 7 pages, 8 figure

Chemical composition and radiative properties of nascent particulate matter emitted by an aircraft turbofan burning conventional and alternative fuels

Aircraft engines are a unique source of carbonaceous aerosols in the upper troposphere. There, these particles can more efficiently interact with solar radiation than at ground. Due to the lack of measurement data, the radiative forcing from aircraft exhaust aerosol remains uncertain. To better estimate the global radiative effects of aircraft exhaust aerosol, its optical properties need to be comprehensively characterized. In this work we present the link between the chemical composition and the optical properties of the particulate matter (PM) measured at the engine exit plane of a CFM56-7B turbofan. The measurements covered a wide range of power settings (thrust), ranging from ground idle to take-off, using four different fuel blends of conventional Jet A-1 and hydro-processed ester and fatty acids (HEFA) biofuel. At the two measurement wavelengths (532 and 870&thinsp;nm) and for all tested fuels, the absorption and scattering coefficients increased with thrust, as did the PM mass. The analysis of elemental carbon (EC) and organic carbon (OC) revealed a significant mass fraction of OC (up to 90&thinsp;%) at low thrust levels, while EC mass dominated at medium and high thrust. The use of HEFA blends induced a significant decrease in the PM mass and the optical coefficients at all thrust levels. The HEFA effect was highest at low thrust levels, where the EC mass was reduced by up to 50&thinsp;%–60&thinsp;%. The variability in the chemical composition of the particles was the main reason for the strong thrust dependency of the single scattering albedo (SSA), which followed the same trend as the fraction of OC to total carbon (TC). Mass absorption coefficients (MACs) were determined from the correlations between aerosol light absorption and EC mass concentration. The obtained MAC values (MAC532=7.5±0.3&thinsp;m2&thinsp;g−1 and MAC870=5.2±0.9&thinsp;m2&thinsp;g−1) are in excellent agreement with previous literature values of absorption cross section for freshly generated soot. While the MAC values were found to be independent of the thrust level and fuel type, the mass scattering coefficients (MSCs) significantly varied with thrust. For cruise conditions we obtained MSC532=4.5±0.4&thinsp;m2&thinsp;g−1 and MSC870=0.54±0.04&thinsp;m2&thinsp;g−1, which fall within the higher end of MSCs measured for fresh biomass smoke. However, the latter comparison is limited by the strong dependency of MSC on the particles' size, morphology and chemical composition. The use of the HEFA fuel blends significantly decreased PM emissions, but no changes were observed in terms of EC∕OC composition and radiative properties.</p