Log-periodic modulation in one-dimensional random walks

We have studied the diffusion of a single particle on a one-dimensional lattice. It is shown that, for a self-similar distribution of hopping rates, the time dependence of the mean-square displacement follows an anomalous power law modulated by logarithmic periodic oscillations. The origin of this modulation is traced to the dependence on the length of the diffusion coefficient. Both the random walk exponent and the period of the modulation are analytically calculated and confirmed by Monte Carlo simulations.Comment: 6 pages, 7 figure

Division of labour and risk taking in the dinosaur ant, Dinoponera quadriceps

The success of social insects can be largely attributed to division of labour. In contrast to most social insects, many species with simple societies contain workers which are capable of sexual reproduction. Headed by one or a few reproductive individuals, subordinate workers form a dominance hierarchy, queuing to attain the reproductive role. In these species task allocation may be influenced by individual choice based on future reproductive prospects. Individuals with a better chance of inheriting the colony may be less likely to take risks and high-ranking workers that spend a greater amount of time in proximity to the brood may be able to increase the ability to police egg-laying by cheating subordinates. We investigated division of labour and risk taking in relation to dominance rank in the queenless ponerine ant, Dinoponera quadriceps, a species with relatively simple societies. Using behavioural observations, we show that high-ranking workers spend more time performing egg care, less time foraging and are less likely to defend the nest against attack. High-rankers also spent a greater amount of time guarding and inspecting eggs, behaviours which are likely to improve detection of egg laying by cheating subordinates. We also show that high-ranking workers spend a greater amount of time idle, which may help increase lifespan by reducing energy expenditure. Our results suggest that both risk-taking and egg-care behaviours are related to future reproductive prospects in D. quadriceps. This highlights a mechanism by which effective division of labour could have been achieved during the early stages of eusocial evolution

Verification of a Three Dimensional Advection Dispersion Model Using Dye Release Experiment

The study aims to investigate transport processes within the entrance of a coastal lagoon through estimating the advectiondispersion coefficients of the estuary. To this end, an extensive observational data set including water level variation and current has been used for the hydrodynamic calibration of the model. Simulation of water quality variation with time requires mathematical modelling based on the advection and dispersion phenomenon. The advection-dispersion model is setup using a MIKE3 software platform. The model is calibrated using data obtained through monitoring the dilution and movement of a tracer (Rhodamine WT), which is introduced into the water column during a number of experiments at various locations within the study area