Components of learning and assessment in linear algebra

Linear algebra provides theory and technology that are the cornerstones of a range of cutting edge mathematical applications, from designing computer games to complex industrial problems, as well as more traditional applications in statistics and mathematical modelling. Once past introductions to matrices and vectors, the challenges of balancing theory, applications and computational work across mathematical and statistical topics and problems are considerable, particularly given the diversity of abilities and interests in typical cohorts. This paper considers two such cohorts in a second level linear algebra course in different years. The course objectives and materials were almost the same, but some changes were made in the assessment package. In addition to considering effects of these changes, the links with achievement in first year courses are analysed, together with achievement in a following computational mathematics course. Some results that may initially appear surprising provide insight into the components of student learning in linear algebra.

The mechanics of disc degeneration from an engineering and computational modelling viewpoint

The anatomy and microstructure of the spine and in particular the intervertebral disc are intimately linked to how they operate in vivo and how they distribute loads to the adjacent musculature and bony anatomy. The degeneration of the intervertebral discs may be characterised by a loss of hydration, loss of disc height, a granular texture and the presence of annular lesions. As such, degeneration of the intervertebral discs compromises the mechanical integrity of their components and results in adaption and modification in the mechanical means by which loads are distributed between adjacent spinal motion segments.

Computational fluid dynamics of a centrifugal heart pump as biventricular assist device(BVAD)

The results of a recent study have shown that there is a severe shortage of donor hearts to meet the demand of patients suffering from acute heart failures, and patients who received a left ventricular assist device (LVAD) have extended lives. However, some of them develop right heart failure syndrome, and these patients required a right ventricular assist device (RVAD). Hence, current research focus is in the development of a bi-ventricular assist device (Bi-VAD). Computational Fluid Dynamics (CFD) is useful for estimating blood damage for design of a Bi-VAD centrifugal heart pump to meet the demand of the left and right ventricles of a normal hearts with a flow rate of 5 lit/min and the supply pressure of 100 mmHg for the left ventricle and 20 mmHg for the right ventricle. Numerical studies have been conducted to predict pressure, flow rate, the velocity profiles, and streamlines in a continuous flow Bi-VAD using. Based on the predictions of numerical simulations, only few flow regions in the Bi-VAD exhibited signs of velocity profiles and stagnation points, thereby signifying potentially low levels of thrombogenesis.

Computational power meets human contact

This chapter traces the development of the global digital storytelling movement from its origins in California to its adoption by the BBC in the UK and its subsequent dispersal around the world. It identifies the foundational practices, uneven development and diffusion, and emergent practices internationally.

Computational approach to localization using global energy minimization

Damage localization induced by strain softening can be predicted by the direct minimization of a global energy function. This article concerns the computational strategy for implementing this principle for softening materials such as concrete. Instead of using heuristic global optimization techniques, our strategies are a hybrid of local optimization methods with a path-finding approach to ensure a global optimum. With admissible nodal displacements being independent variables, it is easy to deal with the geometric (mesh) constraint conditions. The direct search optimization methods recover the localized solutions for a range of softening lattice models which are representative of quasi-brittle structures

Mechanobiology of Bone Development and Computational Simulations

Bone is important because it provides the skeleton structural integrity and enables movement and locomotion. Its development and morphology follow its function. It adapts to changes of mechanical loading and has the ability to repair itself after damage or fracture. The processes of bone development, bone adaptation, and bone regeneration in fracture healing are regulated, in part, by mechanical stimuli that result when the bone is loaded.