Active liquid crystals, in which the rod-like constituents endow the fluid they are immersed in with active stresses, have proven successful as a paradigm for biologically inspired complex fluids with orientational alignment. These include suspensions of swimming bacteria or cell extracts comprising cytoskeletal filaments and molecular motors, whose natural environment is characterised by spatial confinement.
In this thesis we study active liquid crystals in three confined geometries – a planar thin film, a droplet on a flat surface, and a spherical shell. For alignment fields with topological defects, which are known to be energy minima for passive liquid crystals in these geometries, we investigate with analytical and numerical methods the effect of activity. Novel results include defect-driven motility of active drops and shells as well as the formation of stable flow vortices in spherical confinement.
In the first part we calculate analytically the active flows in a thin film, which are driven by a generic defective alignment field, and identify the type of flow singularity that a defect with arbitrary topological strength generates. The sliding velocity of an active drop, which moves due to an asymmetrically placed defect within, is calculated analytically. In general, asymmetry in the alignment generates motion of the drop due to directed flows in the bulk, although slip at the substrate and active flows resulting from gradients in the drop shape counteract this motion. Steady state shapes of a drop with a central defect reveal the formation of a hole or a cusp in its free surface.
The thin film model is adapted to a spherical shell in the second part, where locally the defect-driven flows are analogous to a flat film. Globally, the active flow is restrained by the Poincaré -Hopf theorem, which prescribes a total winding of +2. We find that the flow typically forms two counterrotating vortices, which is shown to have crucial implications for the defect motion and for the swimming behaviour of the shell. The dynamics of different defect configurations are simulated numerically with a particle-based model, where the defects move due to elastic forces and active advection, which is extracted from an exact expression for the active flow in the shell. We recover the oscillatory motion of four half-integer defects known from experiments and interpret it in view of the two counterrotating vortices, which advect the defects. The onset of oscillations is captured analytically in a linear stability analysis. Further, new predictions are provided for the scaling of measurable quantities, like oscillation frequency and defect speed, for the dynamics of additional defect-pairs and for polar shells, in which unit strength defects are found to attract or repel due to active flows. Finally, the swimming speeds of active nematic shells through a passive medium are calculated analytically, or numerically if half-integer defects are present. Remarkably, shells with triangular defect arrangements are found to be swimming and rotating.
In summary, this work furthers the understanding of geometrically confined active liquid crystals, highlighting the role of topological defects and the active flows they produce. The results presented here could also find application in microfluidics, for instance aiding in the design of artificial crawlers and swimmers.
Microbial communities present the next research frontier. We argue here that understanding and engineering microbial communities requires a holistic view that considers not only species-species, but also species-environment interactions and feedbacks between ecological and evolutionary dynamics (eco-evo feedbacks). Due this multi-level nature of interactions, we predict that approaches aimed soley at altering specific species populations in a community (through strain enrichment or inhibition), would only have a transient impact, and species-environment and eco-evo feedbacks would eventually drive the microbial community to its original state. We propose a higher-level engineering approach that is based on thermodynamics of microbial growth, and that considers specifically microbial redox biochemistry. Within this approach the emphasis is on enforcing specific environmental conditions onto the community, that generates higher-level thermodynamic bounds onto the system, which the community structure and function can then adapt to. We believe that the resulting end-state can be ecologically and evolutionarily stable, mimicking the natural states of complex communities. Towards designing the exact nature of the environmental enforcement, thermodynamics and redox biochemistry can act as coarse-grained principles, while the use of electrodes - as electron providing or accepting redox agents - can provide implementation with spatiotemporal control.
The ensemble Kalman filter (EnKF) is a widely used methodology for state estimation in partially, noisily observed dynamical systems and for parameter estimation in inverse problems. Despite its widespread use in the geophysical sciences, and its gradual adoption in many other areas of application, analysis of the method is in its infancy. Furthermore, much of the existing analysis deals with the large ensemble limit, far from the regime in which the method is typically used. The goal of this paper is to analyze the method when applied to inverse problems with fixed ensemble size. A continuous time limit is derived and the long-time behavior of the resulting dynamical system is studied. Most of the rigorous analysis is confined to the linear forward problem, where we demonstrate that the continuous time limit of the EnKF corresponds to a set of gradient flows for the data misfit in each ensemble member, coupled through a common preconditioner which is the empirical covariance matrix of the ensemble. Numerical results demonstrate that the conclusions of the analysis extend beyond the linear inverse problem setting. Numerical experiments are also given which demonstrate the benefits of various extensions of the basic methodology.
Ill-posed inverse problems are ubiquitous in applications. Understanding of algorithms for their solution has been greatly enhanced by a deep understanding of the linear inverse problem. In the applied communities ensemble-based filtering methods have recently been used to solve inverse problems by introducing an artificial dynamical system. This opens up the possibility of using a range of other filtering methods, such as 3DVAR and Kalman based methods, to solve inverse problems, again by introducing an artificial dynamical system. The aim of this paper is to analyze such methods in the context of the linear inverse problem.
Bayesian inverse problems often involve sampling posterior distributions on infinite-dimensional function spaces. Traditional Markov chain Monte Carlo (MCMC) algorithms are characterized by deteriorating mixing times upon mesh-refinement, when the finite-dimensional approximations become more accurate. Such methods are typically forced to reduce step-sizes as the discretization gets finer, and thus are expensive as a function of dimension. Recently, a new class of MCMC methods with mesh-independent convergence times has emerged. However, few of them take into account the geometry of the posterior informed by the data. At the same time, recently developed geometric MCMC algorithms have been found to be powerful in exploring complicated distributions that deviate significantly from elliptic Gaussian laws, but are in general computationally intractable for models defined in infinite dimensions. In this work, we combine geometric methods on a finite-dimensional subspace with mesh-independent infinite-dimensional approaches. Our objective is to speed up MCMC mixing times, without significantly increasing the computational cost per step (for instance, in comparison with the vanilla preconditioned Crank–Nicolson (pCN) method). This is achieved by using ideas from geometric MCMC to probe the complex structure of an intrinsic finite-dimensional subspace where most data information concentrates, while retaining robust mixing times as the dimension grows by using pCN-like methods in the complementary subspace. The resulting algorithms are demonstrated in the context of three challenging inverse problems arising in subsurface flow, heat conduction and incompressible flow control. The algorithms exhibit up to two orders of magnitude improvement in sampling efficiency when compared with the pCN method.
This thesis contributes to the understanding of the psychosocial factors associated with skin conditions and the lived experience of visible difference. Chapter one is a systematic literature review that identifies the psychosocial factors associated with the onset and living with alopecia for children and young people. A systematic review of the literature indicated relational factors and frequency of negative life events were associated with the onset of alopecia for young people. Although the findings into the psychosocial factors associated with living with alopecia are mixed, anxiety was the most frequently reported factor for children and young people. The quality of the papers included in the review are mixed, with varying population samples, measures and methodological limitations. Clinical and research implications are discussed.
Chapter two is a qualitative research study that explored the lived experience of six women with rosacea using interpretative phenomenological analysis (IPA). Participants' experiences of rosacea were characterised by an internal struggle to feel in control of their skin condition whilst externally, learning to navigate complex social interactions. Clinical and research implications are discussed.
Chapter three is a reflective account of the researcher's experiences during the research process. The researcher's reflections have been structured around the Acceptance and Commitment Therapy (ACT) Hexaflex model. Particular attention has been paid to the experiences that reflect the researcher's values, cognitive defusion, acceptance, contact with the present moment, self as context and committed action.
Television for Women brings together emerging and established scholars to reconsider the question of 'television for women'. In the context of the 2000s, when the potential meanings of both terms have expanded and changed so significantly, in what ways might the concept of programming, addressed explicitly to a group identified by gender still matter?
The basic idea of importance sampling is to use independent samples from a proposal measure in order to approximate expectations with respect to a target measure. It is key to understand how many samples are required in order to guarantee accurate approximations. Intuitively, some notion of distance between the target and the proposal should determine the computational cost of the method. A major challenge is to quantify this distance in terms of parameters or statistics that are pertinent for the practitioner. The subject has attracted substantial interest from within a variety of communities. The objective of this paper is to overview and unify the resulting literature by creating an overarching framework. A general theory is presented, with a focus on the use of importance sampling in Bayesian inverse problems and filtering.
Today, it is tempting to see the rise of HD television as ushering in a new era of spectacular television. Yet since its earliest days, the medium has been epitomised by spectacle and offered its viewers diverse forms of visual pleasure. Looking at the early promotion of television and the launch of colour broadcasting, Spectacular Television traces a history of television as spectacular attraction, from its launch to the contemporary age of surround sound, digital effects and HD screens. In focusing on the spectacle of nature, landscape, and even our own bodies on television via explorations of popular television dramas, documentary series and factual entertainment, and ambitious natural history television, Helen Wheatley answers the questions: what is televisual pleasure, and how has television defined its own brand of spectacular aesthetics?
Proposing a radical vision of cinema's queer globalism, Karl Schoonover and Rosalind Galt explore how queer filmmaking intersects with international sexual cultures, geopolitics, and aesthetics to disrupt dominant modes of world making. Whether in its exploration of queer cinematic temporality, the paradox of the queer popular, or the deviant ecologies of the queer pastoral, Schoonover and Galt reimagine the scope of queer film studies. The authors move beyond the gay art cinema canon to consider a broad range of films from Chinese lesbian drama and Swedish genderqueer documentary to Bangladeshi melodrama and Bolivian activist video. Schoonover and Galt make a case for the centrality of queerness in cinema and trace how queer cinema circulates around the globe–institutionally via film festivals, online consumption, and human rights campaigns, but also affectively in the production of a queer sensorium. In this account, cinema creates a uniquely potent mode of queer worldliness, one that disrupts normative ways of being in the world and forges revised modes of belonging.
We are interested in computing the expectation of a functional of a PDE solution under a Bayesian posterior distribution. Using Bayes's rule, we reduce the problem to estimating the ratio of two related prior expectations. For a model elliptic problem, we provide a full convergence and complexity analysis of the ratio estimator in the case where Monte Carlo, quasi-Monte Carlo, or multilevel Monte Carlo methods are used as estimators for the two prior expectations. We show that the computational complexity of the ratio estimator to achieve a given accuracy is the same as the corresponding complexity of the individual estimators for the numerator and the denominator. We also include numerical simulations, in the context of the model elliptic problem, which demonstrate the effectiveness of the approach.
We compute the homology of the multiple point spaces of stable
perturbations of two germs (Cn, 0) → (Cn+1, 0) of corank 2, using a variety of techniques based on the image computing spectral sequence ICSS. We provide a reasonably detailed introduction to the ICSS, including some low-dimensional examples of its use. The paper is partly expository.
The recent increase in migration to the European Union raised many concerns for the EU, for Member States and for the individual. Much of the discussion hitherto has been focused on the EU from a state perspective and has been concerned with the policies proposed and adopted to address and limit inward movement of peoples. One issue that has not received requisite attention is that of the meaning of 'protection' from the individual claimant's point of view. This article reflects on the Syrian migration of 2015 and 2016 and the implications of a triumph of realpolitik—that is, state sovereignty—over a generous, meaningful and humane approach to asylum.
Rare b → sℓ+ℓ− flavour-changing-neutral-current processes provide important tests of the Standard Model of particle physics. Angular observables in exclusive b → sℓ+ℓ− processes can be particularly powerful as they allow hadronic uncertainties to be controlled. Amongst the exclusive processes that have been studied by experiments, the decay Λb → Λℓ+ℓ− is unique in that the Λb baryon can be produced polarised. In this paper, we derive an expression for the angular distribution of the Λb → Λℓ+ℓ− decay for the case where the Λb baryon is produced polarised. This extends the number of angular observables in this decay from 10 to 34. Standard Model expectations for the new observables are provided and the sensitivity of the observables is explored under a variety of new physics models. At low-hadronic recoil, four of the new observables have a new short distance dependence that is absent in the unpolarised case. The remaining observables depend on the same short distance contributions as the unpolarised observables, but with different dependence on hadronic form-factors. These relations provide possibilities for novel tests of the SM that could be carried out with the data that will become available at the LHC or a future e+e− collider.
This thesis explores how embodying Shakespeare's language through theatre-based practice can connect young people to the plurality of human perspectives, and develop their skills of communication.
I review the evolution of Shakespeare's value in formal education as literary heritage, and the tension that persists between his roles as literary icon and living artist. Peter Brook warns that Shakespeare is particularly in danger of becoming 'deadly theatre': admired and respected, but not alive to the moment of its production and reception. A parallel can exist with 'deadly' classrooms, where Shakespeare is taught with reverence but students find no relevance in his plays to their own lives.
I construct a theoretical framework using key concepts from education and theatre along with findings from linguistics and cognitive science to explore the pedagogical value of Shakespeare as a cultural heritage with which young people can critically and creatively interact. I explore the relationship between language, thought and learning, and how theatre-based practice creates meaning through a dialogic process of collaborative negotiation and close study of the text. This practice acknowledges the role narrative and analogy play in how we learn, and allows young people to be both emotionally engaged in and intellectually critical of how Shakespeare creates situations of human experience.
I conclude that the musicality and metaphorical nature of language is critical in how we express, share and shape our sense of the world and suggest that as performance texts Shakespeare's plays provide a site of continually evolving cultural metaphors. I propose that embodying Shakespeare's text allows young people to explore the possibilities of sense behind the meaning of words, and to reflect metacognitively on their experiences to build understanding of how language works and what it achieves in a search for the quality of truth.