Non-Gaussian chain statistics and finite extensibility in liquid crystal elastomers

In this work we will derive an anisotropic generalisation of the finitely extensible chain model, due to Kuhn and Gr\"un, which is well known in rubber elasticity. This provides a chain energy that couples elastic behaviour to a probability distribution describing the orientations of liquid crystal monomers within a main chain elastomer. The key point is to invoke a maximum relative entropy assumption on the distribution of bond angles in an observed chain. The chain energy's fourth order Taylor expansion is also given, which couples to the second and fourth moments of the nematic distribution function only

'Just Let Them Play':Complex dynamics in youth sport, why it isn't so simple

This ethnographic case study examines the long-term impact of youth sport coaching within tennis, using observations, field notes, and interviews as data sources. We highlight the complexities that youth sport coaches face in their role in developing young players within, in this example, tennis, but suggest that these issues are transferable across the youth sport context. There are some key messages for youth sport coaches and sporting organisations arising from this study, particularly around the role of a youth sport coach. We advocate an expertise approach to developing youth sport coaches due to the many roles, within their sport and from a biopsychosocial perspective, that they have to navigate. Additionally, we suggest that simplistic narratives in youth sport coaching are misplaced

Convex Integration Arising in the Modelling of Shape-Memory Alloys: Some Remarks on Rigidity, Flexibility and Some Numerical Implementations

We study convex integration solutions in the context of the modelling of shape-memory alloys. The purpose of the article is two-fold, treating both rigidity and flexibility properties: Firstly, we relate the maximal regularity of convex integration solutions to the presence of lower bounds in variational models with surface energy. Hence, variational models with surface energy could be viewed as a selection mechanism allowing for or excluding convex integration solutions. Secondly, we present the first numerical implementations of convex integration schemes for the model problem of the geometrically linearised two-dimensional hexagonal-to-rhombic phase transformation. We discuss and compare the two algorithms from [RZZ16] and [RZZ17].Comment: 35 pages, 14 figure

Student Involvement & Growth: A Case Study on Student Stories of Agency & Adulthood

Often students face their most challenging life decisions and periods of growth during college. Engagement and involvement with their institution helps students develop socially and academically; some research shows that involvement can support other students’ needs as well. The goal of this project is to explore the ways in which students perceive their agency or sense of freedom of choice relative to their college engagement. Using multi-level data collection, consisting of a background recruitment survey and two interview sessions, the data generated in this layered approach came from the third-year student cohort at one state university in the southeastern US. Analysis of the data highlights the difficulty of transitions to college, building decision-making skills, learning about themselves and their identities, and developing communities. Details about college engagement pathways from high school to and through the first years of college were all analyzed to explore students’ perceptions of feelings of agency, decision-making capabilities, identity and personal awareness, and movement toward adulthood. Although not the focus of study, additional questions were asked regarding the students’ experiences with involvement and personal development during the turbulent period of their fourth semester when forced to leave campus as a result of COVID-19 prevention policies. Increased sense of agency and development toward adulthood occurred throughout the students’ pathways to and through college; however, students’ first engagements when they arrived on campus often had a huge impact on this growth and on establishing their plans for the future