Habitat use of migrating dwarf minke whales (Balaenoptera acutorostrata subspecies) in Tasmanian waters

The Great Barrier Reef hosts the only known reliable aggregation of dwarf minke whale (Balaenoptera acutorostrata subspecies) in Australian waters. While this short seasonal aggregation is quite predictable, the distribution and movements of the whales during the rest of their annual cycle are poorly understood. In particular, feeding and resting areas on their southward migration which are likely to be important have not been described. Using satellite telemetry data, I modelled the habitat use of seven whales during their southward migration through waters surrounding Tasmania. The whales were tagged with LIMPET satellite tags in the GBR in July 2013 (2 individuals) and 2014 (5 individuals). The study area around Tasmania was divided into 10km² cells and the time spent by each individual in each cell was calculated and averaged based on the number of animals using the cell. Two areas of high residency time were highlighted: south-western Bass Strait and Storm Bay (SE Tasmania). Remotely sensed ocean data were extracted for each cell and averaged temporally during the entire period of residency. Using Generalised Additive Models I explored the influence of key environmental characteristics. Nine predictors (bathymetry, distance from coast, distance from shore, gradient of sea surface temperature, sea surface height (absolute and variance), gradient of current speed, wind speed and chlorophyll-a concentration) were retained in the final model which explained 68% of the total variance. Regions of higher time-spent values were characterised by shallow waters, proximity to the coast (but not to the shelf break), high winds and sea surface height but low gradient of sea surface temperature. Given that the two high residency areas corresponded with regions where other marine predators also forage in Bass Strait and Storm Bay, I suggest the whales were probably feeding, rather than resting in these areas.

Mathematical models for cellular aggregation: the chemotactic instability and clustering formation

In this thesis we present a mathematical formulation of the interaction between microorganisms such as bacteria or amoebae and chemicals, often produced by the organisms themselves. This interaction is called chemotaxis and leads to cellular aggregation. We derive some models to describe chemotaxis. The first is the pioneristic Keller-Segel parabolic-parabolic model and it is derived by two different frameworks: a macroscopic perspective and a microscopic perspective, in which we start with a stochastic differential equation and we perform a mean-field approximation. This parabolic model may be generalized by the introduction of a degenerate diffusion parameter, which depends on the density itself via a power law. Then we derive a model for chemotaxis based on Cattaneo's law of heat propagation with finite speed, which is a hyperbolic model. The last model proposed here is a hydrodynamic model, which takes into account the inertia of the system by a friction force. In the limit of strong friction, the model reduces to the parabolic model, whereas in the limit of weak friction, we recover a hyperbolic model. Finally, we analyze the instability condition, which is the condition that leads to aggregation, and we describe the different kinds of aggregates we may obtain: the parabolic models lead to clusters or peaks whereas the hyperbolic models lead to the formation of network patterns or filaments. Moreover, we discuss the analogy between bacterial colonies and self gravitating systems by comparing the chemotactic collapse and the gravitational collapse (Jeans instability).

Generalized hydrodynamics of a (1+1)-dimensional integrable scattering theory with roaming trajectories

The emergence of hydrodynamic features in off-equilibrium (1 + 1)-dimensional integrable quantum systems has been the object of increasing attention in recent years. In this Master Thesis, we combine Thermodynamic Bethe Ansatz (TBA) techniques for finite-temperature quantum field theories with the Generalized Hydrodynamics (GHD) picture to provide a theoretical and numerical analysis of Zamolodchikov’s staircase model both at thermal equilibrium and in inhomogeneous generalized Gibbs ensembles. The staircase model is a diagonal (1 + 1)-dimensional integrable scattering theory with the remarkable property of roaming between infinitely many critical points when moving along a renormalization group trajectory. Namely, the finite-temperature dimensionless ground-state energy of the system approaches the central charges of all the minimal unitary conformal field theories (CFTs) M_p as the temperature varies. Within the GHD framework we develop a detailed study of the staircase model’s hydrodynamics and compare its quite surprising features to those displayed by a class of non-diagonal massless models flowing between adjacent points in the M_p series. Finally, employing both TBA and GHD techniques, we generalize to higher-spin local and quasi-local conserved charges the results obtained by B. Doyon and D. Bernard [1] for the steady-state energy current in off-equilibrium conformal field theories.