James Hurley

A biophysical model for buzz pollination in angiosperms

Abstract The stamens of most of the worlds flowering plants are longitudinally dehiscent, releasing their pollen passively, whereupon floral visitors may collect it. In nearly 400 genera in 65 plant families, the anthers dehisce by means of short apical slits or true pores. In these forms, the small light pollen can only be efficiently released by native bees capable of vibrating these stamens. This intrafloral behavior propels pollen out of the pores striking the bees on their venters. It is then collected for use in larval cell provisions. Aspects of the historical development of this novel pollination syndrome, known as “buzz” or vibratile (equals vibrational) pollination, are presented including a discussion and figures of a poricidal anther, a buzzing bee and the model system. A biophysical model for the pollen/locule wall interactions resulting in pollen expulsion upon bee or artificial vibration is developed. The model was created with the morphology of anthers of Solanum (Solanaceae) in mind, but the results obtained are generally applicable to any apically dehiscent flower which is vibrated by bees to release pollen. The anthers were modeled as a tall rectangular box with an apical pore and containing numerous small particles. As the box vibrates, particles striking the walls rebound elastically. If a pollen grain strikes a receding wall, it loses energy. If a grain strikes an advancing wall, it gains energy in the collision. In each oscillation, there is a net gain in the energy of the particles. As the anther (box) is shaken, vibrational energy is transmitted from the pterothorax of the bees to the flower, the pollen grains gaining significant energy. As the energy increases and the particles begin to move about more and more vigorously, they will begin to escape through the hole in the box (or stamina] pore). The rate at which particles leave the box and time required to empty the box are calculated as functions of the geometry of the model system and the frequency of vibration. In order to test the influence of air currents, Bernolli effects and viscous drag, the flowers were mecahnically vibrated in vacuum. The pollen cloud thus produced was virtually unchanged ans so it seems unlikely that air plays any significant role in the phenomenon of vibrational pollen release. Finally, variables such as: inelastic interactions, electrostatic forces, slightly sticky pollen due to presence of “pollenkitt”, duration and types of bee buzzes are discussed in relation to the mathematical model presented.

One-dimensional three-body problem.

The three‐body problem in one dimension is examined to determine for what class of interactions the Schrodinger equation may be solved by separation of variables.

Symmetry properties of nonlinear barrier coefficients

This paper concerns the properties of a symmetric barrier between two reservoirs. The barrier can passK conserved quantities. The current of theith quantity is assumed to satisfy the nonlinear relationJi=AijΔβj+BijklΔβjΔβkΔβl where the Δβis are the affinity differences across the barrier andAij andBijkl are functions of the average affinities of the reserviors. It is shown thatBijkl is symmetric in all indices.

Upper Bound on Plasma Containment. II

Since a plasma cannot be self‐contained, it may be supposed that a given external magnetic field is capable of confining only a finite amount of plasma. Two general classes of confined plasmas are considered, and upper bounds are obtained for the total particle energy as simple functionals of the given confining field. As a particular example, the upper bound is evaluated for the Van Allen belts.