Oscillatory processes in the theory of particulate formation in supersaturated chemical solutions

We study a nonlinear problem which occurs in the theory of particulate formation in supersaturated chemical solutions. Mathematically, the problem involves the bifurcation of time-periodic solutions in an initial-boundary value problem involving a nonlinear integro-differential equation. The mechanism controlling the oscillatory states is revealed by combining the theory of characteristics for first order partial differential equations with the multi-time scale perturbation analysis of a certain third order system of nonlinear ordinary differential equations

Effects of direct application of selected pesticides upon honey bee colonies

The purpose of this investigation was to determine the effects of seven selected pesticides upon colonies of honey bees. Tests were conducted in a specially constructed building on The University of Tennessee Agriculture Campus. Healthy frames from strong hives were placed in glass observation hives. These frames were then treated by direct application with one of the seven pesticides to be tested: carbaryl, malathion, diazinon, carbofuran, Kelthane, alkanolamine salts of 2,4-D, and low-volatile ester formulation of 2,4-D. The results indicated that carbofuran, diazinon, £ind malathion are highly toxic to bees when the hive is contaminated by direct application. Carbaryl caused only light mortality. Kelthane is nontoxic, as were both formulations of the herbicide 2,4-D. An attempt was made to construct a dead bee trap which would be functional on an observation hive of the type used in this experiment. All attempts were unsuccessful. A laboratory experiments, with the greater wax moth Galleria mellonella (L.), was conducted during the winter months. Different media were tested and the number of larval instars studied

Pulse propagation in discrete systems of coupled excitable cells

Propagation of pulses in myelinated fibers may be described by appropriate solutions of spatially discrete FitzHugh-Nagumo systems. In these systems, propagation failure may occur if either the coupling between nodes is not strong enough or the recovery is too fast. We give an asymptotic construction of pulses for spatially discrete FitzHugh-Nagumo systems which agrees well with numerical simulations and discuss evolution of initial data into pulses and pulse generation at a boundary. Formulas for the speed and length of pulses are also obtained.Comment: 16 pages, 10 figures, to appear in SIAM J. Appl. Mat