Bounds and estimates on the effective properties for nonlinear composites

summary:In this paper we derive lower bounds and upper bounds on the effective properties for nonlinear heterogeneous systems. The key result to obtain these bounds is to derive a variational principle, which generalizes the variational principle by P. Ponte Castaneda from 1992. In general, when the Ponte Castaneda variational principle is used one only gets either a lower or an upper bound depending on the growth conditions. In this paper we overcome this problem by using our new variational principle together with the bounds presented by Lukkassen, Persson and Wall in 1995. Moreover, we also present some examples where the bounds are so tight that they may be used as a good estimate of the effective behavior

Experiences of nursing students in a Bachelor of Nursing program as they transition from enrolled nurse to registered nurse

Background A substantial number of Enrolled Nurses (ENs) undergo the conversion to Registered Nurse (RN) within Bachelor of Nursing (BN) programs in Australia. However, unlike the majority of undergraduate nursing students, ENs enter BN programs as health professionals and are offered a range of advanced standing in recognition of their previous learning and experience. This positions ENs as a unique sub-cohort of students and it is therefore important that tertiary institutions recognise and understand the challenges that these students experience. The global literature available on the conversion experiences of the EN equivalent to RN offers some insight into these challenges, however an in-depth understanding of the transition experience within the Australian context is currently limited. Aims The aim of this research is to contribute to the understanding of the EN experience as they make the conversion to RN within a BN program. A comprehensive understanding of these conversion experiences within the Australian context is required to inform the development and introduction of educational and institutional strategies to enhance the quality of their experience, to not only encourage more ENs to undergo the conversion to RN but also minimise the attrition for those ENs who enrol in BN programs. Method This study used a qualitative interpretive descriptive research design that incorporated Schlossberg’s Transition Theory as a framework to guide the understanding of the experiences of ENs enrolled in a BN University program in Western Australia. The EN’s lived experiences were privileged by the collection of data through individual semi-structured interviews conducted with seven ENs who were recruited during their final year of study. A focus group of four academic staff with experience teaching in the BN program was also conducted to provide additional context for the ENs’ experiences. This approach enabled triangulation of data from the two sources and thematic analysis to be undertaken. Findings Five themes were identified from analysis of the ENs’ and academics’ data: ‘standing out from the crowd’, ‘seeking personal and professional balance’, ‘struggling with academic demands’, ‘moving beyond the constraints of being an EN’ and ‘growing within the program’. These findings revealed how the ENs were primarily motivated to undertake the conversion to RN to broaden their career opportunities and scope of practice. However, many related how they had difficulty fitting in with, and being accepted by, the main BN student cohort. Trying to balance study with their other life responsibilities was discussed along with various academic difficulties; the latter reportedly exacerbated by their 12 months of advanced standing. Also highlighted was their struggle to maintain confidence in their professional EN skills when faced by academic challenges. Other difficulties were identified with academic writing and clinical assessments, although the development of strategies such as personal commitment and the use of support groups assisted students to manage these issues. As the ENs overcame challenges and progressed through the program they experienced academic success, which then engendered a feeling of personal empowerment as their goal came within reach. Conclusion Enrolled Nurses’ experiences of transitioning to RN within the BN program can be explained within the stages of Schlossberg’s Transition Theory. It was evident from the participants’ experiences that adaption was required at each stage of the transition process, including the development of individual coping strategies that allowed them to successfully navigate their journey. Varying degrees of challenge and success were evident as the ENs used strategies to adapt to tertiary education and their aspired to RN role. Notably, these challenges were increased for the EN because they entered the BN in its second year. Providing transparent information of the potential challenges prior to enrolment and introducing individualised advanced standing and bridging programs specifically designed for the EN converting to RN could assist to improve the transition for these students

Modelling Cavitation in (Elasto)Hydrodynamic Lubrication

In this chapter we will present a derivation of a mathematical model describing how cavitation influences the pressure distribution in a thin lubricant film between two moving surfaces. The main idea in the derivation is to first describe the influence of cavitation on the mass flow and thereafter using a conservation law for the mass. This leads to a nonlinear system with two complementary variables: one is the pressure distribution and the other is related to the density, i.e. a nonlinear complementarity problem (NLCP). The proposed approach is used to derive a mass conserving cavitation model considering that density, viscosity and film thickness of the lubricant depend on the pressure. To demonstrate the applicability and evaluate the proposed model and the suggested numerical implementation, a few model problems are analysed and presented

Higher order intersection numbers of 2-spheres in 4-manifolds

This is the beginning of an obstruction theory for deciding whether a map f:S^2 --> X^4 is homotopic to a topologically flat embedding, in the presence of fundamental group and in the absence of dual spheres. The first obstruction is Wall's self-intersection number mu(f) which tells the whole story in higher dimensions. Our second order obstruction tau(f) is defined if mu(f) vanishes and has formally very similar properties, except that it lies in a quotient of the group ring of two copies of pi_1(X) modulo S_3-symmetry (rather then just one copy modulo S_3-symmetry). It generalizes to the non-simply connected setting the Kervaire-Milnor invariant which corresponds to the Arf-invariant of knots in 3-space. We also give necessary and sufficient conditions for moving three maps f_1,f_2,f_3:S^2 --> X^4 to a position in which they have disjoint images. Again the obstruction lambda(f_1,f_2,f_3) generalizes Wall's intersection number lambda(f_1,f_2) which answers the same question for two spheres but is not sufficient (in dimension 4) for three spheres. In the same way as intersection numbers correspond to linking numbers in dimension 3, our new invariant corresponds to the Milnor invariant mu(1,2,3), generalizing the Matsumoto triple to the non simply-connected setting.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol1/agt-1-1.abs.htm

The future of genomics in pathology

The recent advances in technology and the promise of cheap and fast whole genomic data offer the possibility to revolutionise the discipline of pathology. This should allow pathologists in the near future to diagnose disease rapidly and early to change its course, and to tailor treatment programs to the individual. This review outlines some of these technical advances and the changes needed to make this revolution a reality