Dynamics of Conformal Maps for a Class of Non-Laplacian Growth Phenomena

Time-dependent conformal maps are used to model a class of growth phenomena limited by coupled non-Laplacian transport processes, such as nonlinear diffusion, advection, and electro-migration. Both continuous and stochastic dynamics are described by generalizing conformal-mapping techniques for viscous fingering and diffusion-limited aggregation, respectively. A general notion of time in stochastic growth is also introduced. The theory is applied to simulations of advection-diffusion-limited aggregation in a background potential flow. A universal crossover in morphology is observed from diffusion-limited to advection-limited fractal patterns with an associated crossover in the growth rate, controlled by a time-dependent effective Peclet number. Remarkably, the fractal dimension is not affected by advection, in spite of dramatic increases in anisotropy and growth rate, due to the persistence of diffusion limitation at small scales.Comment: 4 pages, 2 figures (six color plates

Learning to learn in supported parent and toddler groups : a sociocultural investigation

Over the last 50 years research has consistently suggested that some types of adult\ud guidance can improve upon 'pure discovery learning' (Mayer, 2004). In the preschool\ud age group studies have suggested that pedagogical strategies identified with\ud Scaffolding, Sustained Shared Thinking, and Co-construction can be advantageous to\ud children's later educational success (Siraj-Blatchford & Sylva, 2004). This thesis\ud examines the cultural practices of adults supporting children's learning in 'free play'\ud during practitioner facilitated 'Parent and Toddler Group' sessions to consider the\ud extent to which these children are being guided towards participating in collaborative\ud learning interactions (Rogoff 1998) by both practitioners and parents.\ud The investigative approach adopted is informed by Socio-cultural theory (Hedegaard\ud & Fleer, 2008, Rogoff, 1998) and develops the complementary use of affordance\ud theory (Gibson, 1979) to investigate the learner as part of a system of mutually\ud effective elements. The thesis draws on observations of 12 children's interactions in\ud two ethnographic case studies set in context by interview and survey data. The thesis\ud identifies and describes a range of modes of interaction employed in the case study\ud parent and toddler groups. The thesis shows how children's experiences vary as a\ud result of the balance of modes that they experience. It suggests strategies to broaden\ud parents' and practitioners' awareness of promoting children's learning through a\ud range of modes of interaction.\ud The study findings echo those of international studies suggesting that early education\ud contexts may encourage individual and peer-learning much more frequently than\ud collaborative learning with adults (Pramling-Samuelsson & Fleer, 2009, Rogoff,\ud 1998)

Elastic Metrics on Spaces of Euclidean Curves: Theory and Algorithms

A main goal in the field of statistical shape analysis is to define computable and informative metrics on spaces of immersed manifolds, such as the space of curves in a Euclidean space. The approach taken in the elastic shape analysis framework is to define such a metric by starting with a reparameterization-invariant Riemannian metric on the space of parameterized shapes and inducing a metric on the quotient by the group of diffeomorphisms. This quotient metric is computed, in practice, by finding a registration of two shapes over the diffeomorphism group. For spaces of Euclidean curves, the initial Riemannian metric is frequently chosen from a two-parameter family of Sobolev metrics, called elastic metrics. Elastic metrics are especially convenient because, for several parameter choices, they are known to be locally isometric to Riemannian metrics for which one is able to solve the geodesic boundary problem explictly -- well-known examples of these local isometries include the complex square root transform of Younes, Michor, Mumford and Shah and square root velocity (SRV) transform of Srivastava, Klassen, Joshi and Jermyn. In this paper, we show that the SRV transform extends to elastic metrics for all choices of parameters, for curves in any dimension, thereby fully generalizing the work of many authors over the past two decades. We give a unified treatment of the elastic metrics: we extend results of Trouv\'{e} and Younes, Bruveris as well as Lahiri, Robinson and Klassen on the existence of solutions to the registration problem, we develop algorithms for computing distances and geodesics, and we apply these algorithms to metric learning problems, where we learn optimal elastic metric parameters for statistical shape analysis tasks

The physical and mental health of acute psychiatric ward staff, and its relationship to experience of physical violence

To evaluate and describe the physical and mental health of staff on acute psychiatric wards and examine whether violence exposure is linked with health status. We undertook a cross-sectional survey with 564 nursing staff and healthcare assistants from 31 psychiatric wards in nine NHS Trusts using the SF-36, a reliable and valid measure of health status and compared summary scores with national normative data. Additional violence exposure data were collated simultaneously and also compared with health status. The physical health of staff was worse, and their mental health was better than the general population. Physical health data were skewed and showed a small number of staff in relatively poor health while the majority were above average. Better physical health was associated with less time in the current post, a higher pay grade, and less exposure to mild physical violence in the past year. Better mental health was associated with being older and from an ethnic minority background. Violence exposure influenced physical health but not mental health when possible confounders were considered. Mental health was strongly influenced by ethnicity, and further research might highlight the impact on own-group ethnic density on the quality of care. The impact of staff whom are physically unwell or impaired in the workplace needs to be considered as the quality of care may be compromised despite this being an example of inclusiveness, equal opportunities employment, and positive staff motivation

The effect of the introduction of Nile tilapia ( Oreochromis niloticus , L.) on small indigenous fish species (mola, Amblypharyngodon mola , Hamilton; chela, Chela cachius , Hamilton; punti, Puntius sophore , Hamilton)

This is the first controlled experiment to quantify the effect of introduced tilapia on indigenous species. This experiment was conducted in small earthen ponds (100 m 2 ) to assess the impact of mixed-sex or all-male Nile tilapia ( Oreochromis niloticus ) on small indigenous species (SIS) commonly found in south Asia, mola ( Amblypharyngodon mola ), chela ( Chela cachius ) and punti ( Puntius sophore ). Ponds were fertilized, then stocked with 0.56 fish m −2 of water surface area in the mixed-sex and all-male tilapia treatments and 0.42 fish m −2 in the treatment without tilapia. No additional nutritional inputs were applied after stocking. Treatments were: mixed-sex tilapia with SIS, mono-sex male tilapia with SIS and SIS without tilapia (control). All treatments were stocked with 14 fish per species. All species reproduced during the 21-month culture duration. The number of recruits varied by species, Tilapia reproduced in greater numbers than SIS. Tilapia numbers at harvest were the highest (451 ± 25/100 m 2 ) in the mixed-sex treatment compared with mola (221 ± 22/100 m 2 ), chela (94 ± 8/100 m 2 ) and punti (100 ± 7/100 m 2 ). The number of mola was higher (399 ± 33/100 m 2 ) in the all-male tilapia treatment. There was reduction in the number of mola and chela in the treatment containing mixed-sex tilapia. Gut content analysis combined with water sampling revealed that all fish species fed selectively. Significant interspecies dietary overlap was found between Nile tilapia and SIS and among SIS. Thus, there is potential for tilapia to compete with indigenous fish species when space and other resources are limiting, but a longer duration study with varying level of management is needed to determine how successfully tilapia competes with locally adapted SIS.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/79201/1/j.1365-2109.2009.02372.x.pd