The importance of interaction strength for food web dynamics and ecosystem functioning

Global biodiversity is eroding at an alarming rate, through a combination of anthropogenic disturbance and environmental change. Ecological communities are bewildering in their complexity. Experimental ecologists strive to understand the mechanisms that drive the stability and structure of these complex communities in a bid to inform nature conservation and management. Two fields of research have had high profile success at developing theories related to these stabilising structures and testing them through controlled experimentation. Biodiversity-ecosystem functioning (BEF) research has explored the likely consequences of biodiversity loss on the functioning of natural systems and the provision of important ecosystem services. Empirical tests of BEF theory often consist of simplified laboratory and field experiments, carried out on subsets of ecological communities. Such experiments often overlook key information relating to patterns of interactions, important relationships, and fundamental ecosystem properties. The study of multi-species predator-prey interactions has also contributed much to our understanding of how complex systems are structured, particularly through the importance of indirect effects and predator suppression of prey populations. A growing number of studies describe these complex interactions in detailed food webs, which encompass all the interactions in a community. This has led to recent calls for an integration of BEF research with the comprehensive study of food web properties and patterns, to help elucidate the mechanisms that allow complex communities to persist in nature. This thesis adopts such an approach, through experimentation at Lough Hyne marine reserve, in southwest Ireland. Complex communities were allowed to develop naturally in exclusion cages, with only the diversity of top trophic levels controlled. Species removals were carried out and the resulting changes to predator-prey interactions, ecosystem functioning, food web properties, and stability were studied in detail. The findings of these experiments contribute greatly to our understanding of the stability and structure of complex natural communities.

Differential and numerical models of hysteretic systems with stochastic and deterministic inputs

Many deterministic models with hysteresis have been developed in the areas of economics, finance, terrestrial hydrology and biology. These models lack any stochastic element which can often have a strong effect in these areas. In this work stochastically driven closed loop systems with hysteresis type memory are studied. This type of system is presented as a possible stochastic counterpart to deterministic models in the areas of economics, finance, terrestrial hydrology and biology. Some price dynamics models are presented as a motivation for the development of this type of model. Numerical schemes for solving this class of stochastic differential equation are developed in order to examine the prototype models presented. As a means of further testing the developed numerical schemes, numerical examination is made of the behaviour near equilibrium of coupled ordinary differential equations where the time derivative of the Preisach operator is included in one of the equations. A model of two phenotype bacteria is also presented. This model is examined to explore memory effects and related hysteresis effects in the area of biology. The memory effects found in this model are similar to that found in the non-ideal relay. This non-ideal relay type behaviour is used to model a colony of bacteria with multiple switching thresholds. This model contains a Preisach type memory with a variable Preisach weight function. Shown numerically for this multi-threshold model is a pattern formation for the distribution of the phenotypes among the available thresholds.

Correlations in low dimensional quantum systems

In this thesis I present the work done during my PhD in the area of low dimensional quantum gases. The chapters of this thesis are self contained and represent individual projects which have been peer reviewed and accepted for publication in respected international journals. Various systems are considered, the first of which is a two particle model which possesses an exact analytical solution. I investigate the non-classical correlations that exist between the particles as a function of the tunable properties of the system. In the second work I consider the coherences and out of equilibrium dynamics of a one-dimensional Tonks-Girardeau gas. I show how the coherence of the gas can be inferred from various properties of the reduced state and how this may be observed in experiments. I then present a model which can be used to probe a one-dimensional Fermi gas by performing a measurement on an impurity which interacts with the gas. I show how this system can be used to observe the so-called orthogonality catastrophe using modern interferometry techniques. In the next chapter I present a simple scheme to create superposition states of particles with special emphasis on the NOON state. I explore the effect of inter-particle interactions in the process and then characterise the usefulness of these states for interferometry. Finally I present my contribution to a project on long distance entanglement generation in ion chains. I show how carefully tuning the environment can create decoherence-free subspaces which allows one to create and preserve entanglement.

Interaction of additive and quantization noises in digital PLLs

Phase-locked loops (PLLs) are a crucial component in modern communications systems. Comprising of a phase-detector, linear filter, and controllable oscillator, they are widely used in radio receivers to retrieve the information content from remote signals. As such, they are capable of signal demodulation, phase and carrier recovery, frequency synthesis, and clock synchronization. Continuous-time PLLs are a mature area of study, and have been covered in the literature since the early classical work by Viterbi [1] in the 1950s. With the rise of computing in recent decades, discrete-time digital PLLs (DPLLs) are a more recent discipline; most of the literature published dates from the 1990s onwards. Gardner [2] is a pioneer in this area. It is our aim in this work to address the difficulties encountered by Gardner [3] in his investigation of the DPLL output phase-jitter where additive noise to the input signal is combined with frequency quantization in the local oscillator. The model we use in our novel analysis of the system is also applicable to another of the cases looked at by Gardner, that is the DPLL with a delay element integrated in the loop. This gives us the opportunity to look at this system in more detail, our analysis providing some unique insights into the variance `dip' seen by Gardner in [3]. We initially provide background on the probability theory and stochastic processes. These branches of mathematics are the basis for the study of noisy analogue and digital PLLs. We give an overview of the classical analogue PLL theory as well as the background on both the digital PLL and circle map, referencing the model proposed by Teplinsky et al. [4, 5]. For our novel work, the case of the combined frequency quantization and noisy input from [3] is investigated first numerically, and then analytically as a Markov chain via its Chapman-Kolmogorov equation. The resulting delay equation for the steady-state jitter distribution is treated using two separate asymptotic analyses to obtain approximate solutions. It is shown how the variance obtained in each case matches well to the numerical results. Other properties of the output jitter, such as the mean, are also investigated. In this way, we arrive at a more complete understanding of the interaction between quantization and input noise in the first order DPLL than is possible using simulation alone. We also do an asymptotic analysis of a particular case of the noisy first-order DPLL with delay, previously investigated by Gardner [3]. We show a unique feature of the simulation results, namely the variance `dip' seen for certain levels of input noise, is explained by this analysis. Finally, we look at the second-order DPLL with additive noise, using numerical simulations to see the effects of low levels of noise on the limit cycles. We show how these effects are similar to those seen in the noise-free loop with non-zero initial conditions.

Optical micro- and nanofibres: Higher mode generation and particle manipulation studies

This thesis is centred on two experimental fields of optical micro- and nanofibre research; higher mode generation/excitation and evanescent field optical manipulation. Standard, commercial, single-mode silica fibre is used throughout most of the experiments; this generally produces high-quality, single-mode, micro- or nanofibres when tapered in a flame-heated, pulling rig in the laboratory. Single mode fibre can also support higher transverse modes, when transmitting wavelengths below that of their defined single-mode regime cut-off. To investigate this, a first-order Laguerre-Gaussian beam, LG01 of 1064 nm wavelength and doughnut-shaped intensity profile is generated free space via spatial light modulation. This technique facilitates coupling to the LP11 fibre mode in two-mode fibre, and convenient, fast switching to the fundamental mode via computer-generated hologram modulation. Following LP11 mode loss when exponentially tapering 125μm diameter fibre, two mode fibre with a cladding diameter of 80μm is selected fir testing since it is more suitable for satisfying the adiabatic criteria for fibre tapering. Proving a fruitful endeavour, experiments show a transmission of 55% of the original LP11 mode set (comprising TE01, TM01, HE21e,o true modes) in submicron fibres. Furthermore, by observing pulling dynamics and progressive mode-lass behaviour, it is possible to produce a nanofibre which supports only the TE01 and TM01 modes, while suppressing the HE21e,o elements of the LP11 group. This result provides a basis for experimental studies of atom trapping via mode-interference, and offers a new set of evanescent field geometries for sensing and particle manipulation applications. The thesis highlights the experimental results of the research unit’s Cold Atom subgroup, who successfully integrated one such higher-mode nanofibre into a cloud of cold Rubidium atoms. This led to the detection of stronger signals of resonance fluorescence coupling into the nanofibre and for light absorption by the atoms due to the presence of higher guided modes within the fibre. Theoretical work on the impact of the curved nanofibre surface on the atomic-surface van der Waals interaction is also presented, showing a clear deviation of the potential from the commonly-used flat-surface approximation. Optical micro- and nanofibres are also useful tools for evanescent-field mediated optical manipulation – this includes propulsion, defect-induced trapping, mass migration and size-sorting of micron-scale particles in dispersion. Similar early trapping experiments are described in this thesis, and resulting motivations for developing a targeted, site-specific particle induction method are given. The integration of optical nanofibres into an optical tweezers is presented, facilitating individual and group isolation of selected particles, and their controlled positioning and conveyance in the evanescent field. The effects of particle size and nanofibre diameter on pronounced scattering is experimentally investigated in this systems, as are optical binding effects between adjacent particles in the evanescent field. Such inter-particle interactions lead to regulated self-positioning and particle-chain speed enhancements.

Corporeal prisons: dynamics of body and mise-en-scène in three films by Paul Schrader

This thesis focuses on the complex relationship between representations of the human body and the formal processes of mise-en-scène in three consecutive films by the writer-director Paul Schrader: American Gigolo (1980), Cat People (1982) and Mishima: A Life in Four Chapters (1985). While Schrader’s work has typically been critiqued under the broad category of masculinity in crisis (and often as a subset of the films of his more famous long-time collaborator, Martin Scorsese), I focus on a fiveyear early period of his filmography when he sought to explore his key themes of bodily crisis, fragmentation and alienation through an unusually intense focus upon the expressive potential of film form, specifically via the combined elements of colour, lighting, camerawork and production design. By approaching these three films as corporeal character studies of troubled figures whose emotional and psychosexual neurosis is experienced in and through the body, I will locate Schrader’s filmmaking process and style within the thematic and aesthetic contexts of both his own early film criticism and the European and Japanese art cinemas that he claims as his primary influence. In doing so, I will establish Schrader’s position as a director whose literary and theological background differentiated him from his peers of the postclassical Hollywood generation, and who thus continually sought to develop his own visual literacy through his relationship with the camera and his collaborations with more overtly style-oriented film artists. But instead of merely focusing on mise-en-scène to gain a formalist appreciation of these films, I mobilise stylistic analysis as a new critical approach towards the problematic discourses of identity and embodiment that have haunted Schrader’s career from the beginning. In particular, I argue that paying closer attention to Schrader’s formal choices sheds new light on how these films – which he approached as exercises in style – repeatedly deal with the volatile and unavoidably body-oriented categories of race, gender and sexuality. In the process, I argue that a formalist attentiveness to mise-en-scène can also provide valuable cultural insights into Schrader’s oeuvre.