A nonlocal equation arising in the theory of wet combustion

A steady-state equation describing the self-heating of a materialdue to oxidation, hydrolysis, and the evaporation and condensationof water was introduced recently by Sisson et al. (1993, IMAJ. Appl. Math. 50, 285), and some preliminary existence anduniqueness results were derived. In this paper a numerical studyof the equation is undertaken. Critical behaviour and the disappearanceof criticality is observed.     

A Variational Approach to Upper and Lower Solutions

Traditional proofs of the upper and lower solution existenceresults for nonlinear elliptic equations use monotone iterationschemes based on the maximum principle. In this paper, a directvariational method is employed which characterizes the solutionas the global minimum of a functional on a closed convex set.     

DEVELOPMENT OF AN OPTIMAL WATER ALLOCATION DECISION TOOL FOR THE MAJOR CROPS DURING THE WATER DEFICIT PERIOD IN THE SOUTHEAST UNITED STATES

ABSTRACT. We developed a dynamic economic model to optimize irrigation water allocations during water deficit periods for three major crops grown in the humid southeastern United States. Analysis involved the use of crop simulation models to capture (a) the yield water relationship and (b) soil moisture dynamics from one week to another week. A hy‐drological model was used to find the water supply; combinations of hydrological and simulation models were used to find the optimal water allocation during each week in corn, cotton and peanuts. Results indicated that farmers should irrigate the most valuable crop first (peanuts) before applying water to other crops (corn and cotton). Results also showed that, because of restriction on total water supply, an increase in crop acreage did not increase the net revenue of the farm in a proportionate amount. Results should provide guidelines to water managers, engineers, policy makers, and farmers regarding an optimal amount of water allocation that will maximize net returns when water shortage is a serious concern.     

Shear stress correlations in hard and soft sphere fluids

The shear stress autocorrelation function has been studied by molecular dynamics simulation using the q^?n potential for very large n. The results are analysed and interpreted here by comparing them with the shear stress response function for hard spheres. It is shown that the hard sphere response function has a singular contribution, and that this is reproduced accurately by the simulations for large n. A simple model for the stress autocorrelation function at finite n is proposed, based on the required hard sphere limiting form.     

MODELING THE MOVEMENTS OF COWBIRDS: APPLICATION TOWARDS MANAGEMENT AT THE LANDSCAPE SCALE

ABSTRACT. Brood parasitism by brown‐headed cowbirds (Molothrus ater) reduces the reproductive success of two endangered bird species at Fort Hood, Texas. A successful management program has focused on trapping cowbirds at feeding locations, grassland areas almost always associated with the presence of cattle. To enhance the efficacy of this effort, we developed an individual‐based model that predicted visitation rates by cowbirds to all potential feeding locations at Fort Hood and the surrounding landscape. Utilizing GRASS‐GIS and SWARM, the model incorporated the spatial arrangement of habitats, daily movements of cattle, and daily movements of cowbirds from their breeding sites to feeding locations. We simulated four types of movements by cow‐birds as they searched for cattle: 1) random walk, 2) direct return to previous locations (i.e., memory), 3) return to previous locations with en route assessment (i.e., memory with limited perception of the current state of the system), and 4) omniscience. Straight‐line distances between breeding and feeding locations for cowbirds that used the memory‐with‐perception rule were similar to independent telemetry results, and total search distances for this movement type approached those of omniscience. Both movement distance measures were inversely related to perception distance. Maps of cowbird visits to feeding areas differed among movement rules but were not strongly affected by the density of breeding cow‐birds. Maps also identified locations where trapping efforts could reduce parasitism within specific areas known to support endangered species. While it seems plausible that cowbirds are able to remember foraging locations and to perceive their surroundings as they travel, additional studies are needed to document their cognitive abilities. By simulating movements of individual cowbirds across a dynamic landscape, model results may help to strengthen ongoing cowbird control efforts.