The Symmetrical One-dimensional Newtonian Four-body Problem: A Numerical Investigation

Numerical simulations of the one-dimensional Newtonian four-body problem have been conducted for the special case in which the bodies are distributed symmetrically about the centre of mass. Simulations show a great similarity between this problem and the one-dimensional Newtonian three-body problem. As in that problem the orbits can be divided into three different categories which form well-defined regions on a Poincaré section: there is a region of quasiperiodic orbits about a Schubart-like periodic orbit, there is a region of fast-scattering encounters and in between these two regions there is a chaotic scattering region. The Schubart-like periodic orbit's stability to perturbation is studied. It is apparently stable in one-dimension but is unstable in three-dimensions.This revised version was published online in October 2005 with corrections to the Cover Date.     

A sediment record of trophic state change in an Arkansas (USA) reservoir

Reservoir sediments are used cautiously in paleolimnological studies because of dating uncertainties, possible sediment disturbances and even concerns that indicators of trophic status may behave differently in reservoirs as opposed to natural lakes. We measured loss on ignition (LOI), carbon to nitrogen ratio (C:N), diatom abundance, total nitrogen (TN), total phosphorus (TP), TN:TP ratio, and carbon and nitrogen isotopes (δ¹³C and δ¹⁵N) in an 83-cm sediment core to track recent trophic status changes in Beaver Reservoir, Northwest Arkansas, USA. Measurements showed that LOI, TN, TP and diatom abundance increased significantly from the bottom to the top of the core (p < 0.001). The C:N ratio and δ¹³C indicated a predominantly algal source for organic matter in the sediments. Increases in TN and TP were positively correlated with human population growth (p < 0.01) and the TN:TP ratio recorded a shift from phosphorus to nitrogen limitation around 1990. This shift may have encouraged cyanobacterial growth that caused episodes of taste and odor problems in the reservoir. This study suggests that despite concerns about sediment dating and disturbance, reservoir sediments can provide valuable information on past water quality changes.