Seasonal and Vertical Distributions of Planthoppers (Homoptera: Fulgoroidea) Within a Black Walnut Plantation

Information on the seasonal and vertical distributions of 34 species (eight families) of planthoppers was obtained from window trap collections in a North Carolina black walnut plantation in 15 and 1978. The most commonly collected species were Acanalonia conica (Acanaloniidael. Liburniella ornata (Delphacidae), Oliarus ecologus (Cixiidae), and O. quinquelineatus

Spanning trees of graphs on surfaces and the intensity of loop-erased random walk on planar graphs

We show how to compute the probabilities of various connection topologies for uniformly random spanning trees on graphs embedded in surfaces. As an application, we show how to compute the "intensity" of the loop-erased random walk in ${\mathbb Z}^2$, that is, the probability that the walk from (0,0) to infinity passes through a given vertex or edge. For example, the probability that it passes through (1,0) is 5/16; this confirms a conjecture from 1994 about the stationary sandpile density on ${\mathbb Z}^2$. We do the analogous computation for the triangular lattice, honeycomb lattice and ${\mathbb Z} \times {\mathbb R}$, for which the probabilities are 5/18, 13/36, and $1/4-1/\pi^2$ respectively.Comment: 45 pages, many figures. v2 has an expanded introduction, a revised section on the LERW intensity, and an expanded appendix on the annular matri

Boundary Partitions in Trees and Dimers

Given a finite planar graph, a grove is a spanning forest in which every component tree contains one or more of a specified set of vertices (called nodes) on the outer face. For the uniform measure on groves, we compute the probabilities of the different possible node connections in a grove. These probabilities only depend on boundary measurements of the graph and not on the actual graph structure, i.e., the probabilities can be expressed as functions of the pairwise electrical resistances between the nodes, or equivalently, as functions of the Dirichlet-to-Neumann operator (or response matrix) on the nodes. These formulae can be likened to generalizations (for spanning forests) of Cardy's percolation crossing probabilities, and generalize Kirchhoff's formula for the electrical resistance. Remarkably, when appropriately normalized, the connection probabilities are in fact integer-coefficient polynomials in the matrix entries, where the coefficients have a natural algebraic interpretation and can be computed combinatorially. A similar phenomenon holds in the so-called double-dimer model: connection probabilities of boundary nodes are polynomial functions of certain boundary measurements, and as formal polynomials, they are specializations of the grove polynomials. Upon taking scaling limits, we show that the double-dimer connection probabilities coincide with those of the contour lines in the Gaussian free field with certain natural boundary conditions. These results have direct application to connection probabilities for multiple-strand SLE_2, SLE_8, and SLE_4.Comment: 46 pages, 12 figures. v4 has additional diagrams and other minor change

Descriptions of Nymphs of \u3ci\u3eItzalana Submaculata\u3c/i\u3e Schmidt (Homoptera: Fulgoridae), a Species New to the United States

The 3rd, 4th, and 5th instar nymphs of ltzalana submaculata Schmidt are described from southern Texas. Previously recorded only from Surinam, this is the first record of this fulgorid from the United States and Mexico

On the asymptotics of dimers on tori

We study asymptotics of the dimer model on large toric graphs. Let $\mathbb L$ be a weighted $\mathbb{Z}^2$-periodic planar graph, and let $\mathbb{Z}^2 E$ be a large-index sublattice of $\mathbb{Z}^2$. For $\mathbb L$ bipartite we show that the dimer partition function on the quotient $\mathbb{L}/(\mathbb{Z}^2 E)$ has the asymptotic expansion $\exp[A f_0 + \text{fsc} + o(1)]$, where $A$ is the area of $\mathbb{L}/(\mathbb{Z}^2 E)$, $f_0$ is the free energy density in the bulk, and $\text{fsc}$ is a finite-size correction term depending only on the conformal shape of the domain together with some parity-type information. Assuming a conjectural condition on the zero locus of the dimer characteristic polynomial, we show that an analogous expansion holds for $\mathbb{L}$ non-bipartite. The functional form of the finite-size correction differs between the two classes, but is universal within each class. Our calculations yield new information concerning the distribution of the number of loops winding around the torus in the associated double-dimer models.Comment: 48 pages, 18 figure

Behavior of composite bolted joints at elevated temperature

Experimental results from an investigation which examines the combined effects of temperature, joint geometry and out-of-plane constraint upon the response of mechanically fastened composite joints are presented. Data are presented for simulated mechanically fastened joint conditions in two laminate configurations fabricated from Hercules AS/3501-6 graphite-epoxy. Strength and failure mode results are presented for the test temperatures of 21 C, 121 C and 177 C and for a range of the geometric parameters W/D and e/D from 3.71 to 7.43 and 1.85 to 3.69, respectively. A hole diameter, D of 5.16 mm was utilized for all tests. Pin bearing tests with out-of-plane constraint were conducted at room temperature only. All elevated temperature data were generated for pin bearing conditions. Ultrasonic C scan inspection of the failed specimens was employed to assess the damage region and to determine failure mode. Comparative data are presented for pin bearing and out-of-plane constraint conditions for the above mentioned joint configurations. The joint under pin loading was modeled by two dimensional finite element methods. Predicted net section strain concentrations were compared with experimental results

An aid to the development of Botswana's resources: Section on hydrology

The author has identified the following significant results. It is proved that FCC's can be used for a simple estimate of the total evaportranspiring area of the Okavango Delta, sufficiently accurate for preliminary inputs for the development of mathematical model of the surface hydrology of the delta. The color coded matrix has shown as interesting inverse correlation with an array on the same grid prepared by ecologists from air photography study, for percent liable to flood