Maths in Medicine: How to Survive a Science Fair

When talking to secondary school students, first impressions are crucial. Accidentally say something that sounds boring and you'll lose them in seconds. A physical demonstration can be an eye-catching way to begin an activity or spark off a conversation about mathematics. This is especially true in the context of an event like a science fair where there are hundreds of other exhibitors and stands, possibly involving loud music and/or dancing robots! In this article we describe three devices that were built to illustrate specific physical phenomena that occur in the human body. Each device corresponds to a simple mathematical model which contains both elements that are accessible to pupils in the early years of secondary education and more challenging mathematical concepts that might appeal to A-level students. Two of the devices relate to the Windkessel effect, a physical phenomenon that regulates blood flow, and the third demonstrates the elastic properties of ligaments and tendons

Re-defining upstream fish passage

In efforts to re-establish populations of migratory fish in areas previously blocked by man-made barriers, upstream migration of adults needs to be facilitated past those barriers. Passage solutions need to meet the standards of being safe, timely, efficient and effective. While traditional upstream adult passage solutions may meet these agency standards, the upfront planning and implementation costs associated with these solutions severely impacts the timing and financial viability of these programs. In an environment of increasing pressures on fish populations caused by climate change and habitat degradation, solutions that are cheaper and quicker to deploy are needed. In this talk we describe a pilot adult volitional passage system that took less than 3 months to install in 2017 at a high head dam in Washington State, USA, and the results from that system. This pilot was made possible by collaboration of private industry, tribal interests and the federal government. We will look at the technology used and additional testing that has been performed to make sure that the solution meets the acceptable standards. Biologists and engineers may be able to use this project as an example to accelerate other passage implementations with industry and government participation

Employing pre-stress to generate finite cloaks for antiplane elastic waves

It is shown that nonlinear elastic pre-stress of neo-Hookean hyperelastic materials can be used as a mechanism to generate finite cloaks and thus render objects near-invisible to incoming antiplane elastic waves. This approach appears to negate the requirement for special cloaking metamaterials with inhomogeneous and anisotropic material properties in this case. These properties are induced naturally by virtue of the pre-stress. This appears to provide a mechanism for broadband cloaking since dispersive effects due to metamaterial microstructure will not arise.Comment: 4 pages, 2 figure

Well-posed continuum equations for granular flow with compressibility and μ(I)-rheology

Continuum modelling of granular flow has been plagued with the issue of ill-posed equations for a long time. Equations for incompressible, two-dimensional flow based on the Coulomb friction law are ill-posed regardless of the deformation, whereas the rate-dependent $\mu(I)$-rheology is ill-posed when the non-dimensional strain-rate $I$ is too high or too low. Here, incorporating ideas from Critical-State Soil Mechanics, we derive conditions for well-posedness of PDEs that combine compressibility with $I$-dependent rheology. When the $I$-dependence comes from a specific friction coefficient $\mu(I)$, our results show that, with compressibility, the equations are well-posed for all deformation rates provided that $\mu(I)$ satisfies certain minimal, physically natural, inequalities

The relative compliance of energy-storing tendons may be due to the helical fibril arrangement of their fascicles

T.S. acknowledges funding for this work from the EPSRC through grant no. EP/L017997/1

MyRun: balancing design for reflection, recounting and openness in a museum-based participatory platform

Cultural organisations are increasingly looking towards using digital technologies to supplement, augment and extend visitors' experiences of exhibits and museums. In this paper, we describe the design and evaluation of MyRun, a 'participatory platform' for a museum. Our goal with MyRun was to use experience-centered design principles of reflecting, recounting and openness as a basis for engaging visitors in sharing stories about experiences related to a nationally significant cultural event. We undertook a qualitative evaluation of the system based upon observations of its use, the contributions visitors made to the platform, and interviews with 10 visitors. We discuss how visitors approached MyRun, contributed and browsed stories, and the challenges associated with the expectations visitors and curators placed on cultural exhibits. We close by identifying a series of design opportunities for future participatory platforms in museum settings

The inflation of viscoelastic balloons and hollow viscera

For the first time, the problem of the inflation of a nonlinear viscoelastic thick-walled spherical shell is considered. Specifically, the wall has quasilinear viscoelastic constitutive behaviour, which is of fundamental importance in a wide range of applications, particularly in the context of biological systems such as hollow viscera, including the lungs and bladder. Experiments are performed to demonstrate the efficacy of the model in fitting relaxation tests associated with the volumetric inflation of murine bladders . While the associated nonlinear elastic problem of inflation of a balloon has been studied extensively, there is a paucity of studies considering the equivalent nonlinear viscoelastic case. We show that, in contrast to the elastic scenario, the peak pressure associated with the inflation of a neo-Hookean balloon is not independent of the shear modulus of the medium. Moreover, a novel numerical technique is described in order to solve the nonlinear Volterra integral equation in space and time originating from the fundamental problem of inflation and deflation of a thick-walled nonlinear viscoelastic shell under imposed pressure. EPSRC Grant EP/R014604/