The time course of corticosterone responses in kororā (little penguin, Eudyptula minor) : a thesis presented in partial fulfilment of the requirements of the degree of Master of Science in Zoology at Massey University

When birds and other vertebrates perceive a situation to be threatening the hypothalamopituitary- adrenal (HPA) axis is activated and glucocorticoid hormones are secreted from the adrenal gland. Activation of the HPA axis in response to a stimulus perceived to be threatening is called a stress response. The main glucocorticoid hormone in birds is corticosterone. Corticosterone responses of birds are typically measured by the collection of an initial blood sample when a bird is captured or picked up, then the collection of further blood samples until 30 to 60 minutes has elapsed, at which time the bird is released. Whilst this standard sampling protocol provides information on the size of the corticosterone response, it does not provide any indication of how long it takes for corticosterone concentrations to return to initial values. The main objective of this thesis was to characterise the total duration of the corticosterone response of free-living kororā (little penguins, Eudyptula minor). Little penguins at Oamaru were picked up from their nestboxes and initial blood samples collected. Birds were handled and then restrained by being placed in a box. Further blood samples were collected 15, 30 and 60 min after the birds were first picked up. Birds were then returned to their nest boxes and an additional blood sample collected 15, 30, 60, 120, 240, or 360 min later. Mean corticosterone concentrations declined to initial values two hours after birds were returned to nest boxes. The rates at which corticosterone concentrations increased when a stressor was present and then decreased when the stressor was no longer present were positively correlated. Seasonal changes in corticosterone responses in little penguins were also investigated in this study. Mean corticosterone responses were similar in winter and in the pre-laying period, whereas mean responses were lower in birds during early chick rearing. Corticosterone responses during the pre-laying period were greater in male than female little penguins. The current study is the first to document the complete corticosterone responses of free-living penguins and provides information about changes of corticosterone concentrations after a stressor is removed from the free-living individuals. It is also the first to reveal that free-living penguins with relatively high corticosterone responses to a stressor had relatively high rates of corticosterone decline

Control of a lane-drop bottleneck through variable speed limits

In this study, we formulate the VSL control problem for the traffic system in a zone upstream to a lane-drop bottleneck based on two traffic flow models: the Lighthill-Whitham-Richards (LWR) model, which is an infinite-dimensional partial differential equation, and the link queue model, which is a finite-dimensional ordinary differential equation. In both models, the discharging flow-rate is determined by a recently developed model of capacity drop, and the upstream in-flux is regulated by the speed limit in the VSL zone. Since the link queue model approximates the LWR model and is much simpler, we first analyze the control problem and develop effective VSL strategies based on the former. First for an open-loop control system with a constant speed limit, we prove that a constant speed limit can introduce an uncongested equilibrium state, in addition to a congested one with capacity drop, but the congested equilibrium state is always exponentially stable. Then we apply a feedback proportional-integral (PI) controller to form a closed-loop control system, in which the congested equilibrium state and, therefore, capacity drop can be removed by the I-controller. Both analytical and numerical results show that, with appropriately chosen controller parameters, the closed-loop control system is stable, effect, and robust. Finally, we show that the VSL strategies based on I- and PI-controllers are also stable, effective, and robust for the LWR model. Since the properties of the control system are transferable between the two models, we establish a dual approach for studying the control problems of nonlinear traffic flow systems. We also confirm that the VSL strategy is effective only if capacity drop occurs. The obtained method and insights can be useful for future studies on other traffic control methods and implementations of VSL strategies.Comment: 31 pages, 14 figure

Resonance Identities for Closed Characteristics on Compact Star-shaped Hypersurfaces in R2n{\bf R}^{2n}

Resonance relations among periodic orbits on given energy hypersurfaces are very important for getting deeper understanding of the dynamics of the corresponding Hamiltonian systems. In this paper, we establish two new resonance identities for closed characteristics on every compact star-shaped hypersurface $\Sigma$ in ${\bf R}^{2n}$ when the number of geometrically distinct closed characteristics on $\Sigma$ is finite, which extend those identities established by C. Viterbo in 1989 for star-shaped hypersurfaces assuming in addition that all the closed characteristics and their iterates are non-degenerate, and that by W. Wang, X. Hu and Y. Long in 2007 for strictly convex hypersurfaces in ${\bf R}^{2n}$.Comment: arXiv admin note: substantial text overlap with arXiv:math/0701608. To appear in Journal of Functional Analysis, this is the final versio

The existence of two non-contractible closed geodesics on every bumpy Finsler compact space form

Let $M=S^n/ \Gamma$ and $h$ be a nontrivial element of finite order $p$ in $\pi_1(M)$, where the integer $n\geq2$, $\Gamma$ is a finite group which acts freely and isometrically on the $n$-sphere and therefore $M$ is diffeomorphic to a compact space form. In this paper, we establish first the resonance identity for non-contractible homologically visible minimal closed geodesics of the class $[h]$ on every Finsler compact space form $(M, F)$ when there exist only finitely many distinct non-contractible closed geodesics of the class $[h]$ on $(M, F)$. Then as an application of this resonance identity, we prove the existence of at least two distinct non-contractible closed geodesics of the class $[h]$ on $(M, F)$ with a bumpy Finsler metric, which improves a result of Taimanov in [Taimanov 2016] by removing some additional conditions. Also our results extend the resonance identity and multiplicity results on $\mathcal{R}P^n$ in [arXiv:1607.02746] to general compact space forms.Comment: 33 pages, All comments are welcome. arXiv admin note: substantial text overlap with arXiv:1607.0274

Collective modes of a harmonically trapped one-dimensional Bose gas: the effects of finite particle number and nonzero temperature

Following the idea of the density functional approach, we develop a generalized Bogoliubov theory of an interacting Bose gas confined in a one-dimensional harmonic trap, by using a local chemical potential - calculated with the Lieb-Liniger exact solution - as the exchange energy. At zero temperature, we use the theory to describe collective modes of a finite-particle system in all interaction regimes from the ideal gas limit, to the mean-field Thomas-Fermi regime, and to the strongly interacting Tonks-Girardeau regime. At finite temperature, we investigate the temperature dependence of collective modes in the weak-coupling regime by means of a Hartree-Fock-Bogoliubov theory with Popov approximation. By emphasizing the effects of finite particle number and nonzero temperature on collective mode frequencies, we make comparisons of our results with the recent experimental measurement [E. Haller et al., Science 325, 1224 (2009)] and some previous theoretical predictions. We show that the experimental data are still not fully explained within current theoretical framework.Comment: 10 pages, 8 figure