Stability of Fixed Points in an Approximate Solution of the Spring-Mass Running Model

We consider a classical spring-mass model of human running which is built upon an inverted elastic pendulum. Based on our previous results concerning asymptotic solutions for large spring constant (or small angle of attack), we construct analytical approximations of solutions in the considered model. The model itself consists of two sets of differential equations - one set describes the motion of the centre of mass of a runner in contact with the ground (support phase), and the second set describes the phase of no contact with the ground (flight phase). By appropriately concatenating asymptotic solutions for the two phases we are able to reduce the dynamics to a onedimensional apex to apex return map. We find sufficient conditions for this map to have a unique stable fixed point. By numerical continuation of fixed points with respect to energy, we find a transcritical bifurcation in our model system.MSC 2020 Classification: 34C20, 34D05, 37N25, 70K20, 70K42, 70K50, 70K60

Analysis of the Nicolaus Copernicus Airport Activity in Terms of the Flight Operations Impact on Air Pollution

The dynamic development of aviation is associated with many benefits, but also, unfortunately, with negative effects. One of the adverse consequences is the exhaust emissions that have a negative impact on human health. It particularly affects the residents of areas neighboring airports, as airport activity deteriorates local air quality. Using the Emissions and Dispersion Modeling System, the activity of the Nicolaus Copernicus Airport was assessed in terms of the flight operations’ contribution to air contamination in the area adjacent to the airport. Emissions from three sources were compared: aircraft, ground support equipment and auxiliary power units. The concentrations of pollutants in inhabited areas located in three different directions in relation to the airport were also estimated. In addition, the effect of distance from the airport on contaminant concentrations was assessed as a function of wind direction. It was noticed that small values of pollutant concentrations, originating from airport activity, appeared within a few kilometers from the airport, even if the prevailing wind direction on a given day was opposite to the analyzed dispersion direction.

P-B04 Restarting bariatric surgery after the Covid-19 pandemic: a template for safe practice

Background Bariatric surgery virtually ceased with the advent of the Covid-19 pandemic and has been amongst the last sector of operative practice to restart. There have been understandable concerns about restarting bariatric surgery including the risks to patients of contracting Covid infection in the peri-operative period, potential de-skilling of surgeons and theatre teams and the appropriateness of directing scarce and limited resources to bariatric surgery when every surgical specialty is experiencing rapidly rising waiting times and ever lengthening waiting lists. This study describes the restart programme at our NHS bariatric unit and offers a template for safe commencement of complex benign surgeries in the current era. Methods In the months after the pandemic started, our Bariatric MDT reviewed every case on the waiting list and contacted each patient to explain the current waiting times and the importance of not gaining weight to be eligible for surgery when surgical practice resumed. Group education and Support Group sessions were moved from face-to-face appointments to online classrooms and regular input was sought from specialist dieticians, nurses and psychologists. The expected waiting times for patients was pro-actively submitted to the Executive Board of the Trust with details about >104-week waiting patients being clearly articulated. Once approval was given to restart bariatric surgery, every patient was assessed and prioritised in terms of waiting time and clinical need. A bariatric theatre team was brought together and engaged in pre-operative training and a local refresher course on equipment and the planned surgeries. There was engagement with industry to provide on-the-ground support for the first lists to ensure proper and safe use of energy and stapling devices. Each list had two consultant surgeons assigned to it and just two cases per day were planned and patients were managed on an entirely green pathway within the NHS hospital . Results The bariatric restart programme commenced in May 2021; between May 2021 and August 2021, there have been 27 operations carried out (25 Roux-en-Y gastric bypass, 2 sleeve gastrectomy) and two cancellations on the day (both due to patient choice). Each operating list finished between two and three hours before the planned finish time. Formal debrief sessions after each list identified no problems with the operations of the equipment and none of the patients had any post-operative complications. Length of stay was between 1 to 2 days for the entire cohort. Since the restart programme commenced, the requirement for dual consultant operating has ceased and the last 5 cases have been entirely training cases for the operating registrar, again without complication. Each list is now planned to increase to pre-pandemic levels of activity with four cases per list. Conclusions Restarting complex benign surgical practice is complicated and requires engagement with management, theatre and nursing colleagues to ensure that cases are not ‘left behind'. It is important to reduce the risk of complications and of peri-operative covid-19 infection in bariatric patients and development of a pathway that all members of the theatre team have input in to meant that there were few problems or issues with either the planning of the lists or the running of the lists. Such an approach could be considered for restarting any high volume, complex benign surgical practice.

Model-driven system-level validation and verification on the space software domain

The development process of on-board software applications can benefit from model-driven engineering techniques. Model validation and model transformations can be applied to drive the activities of specification, requirements definition, and system-level validation and verification according to the space software engineering standards ECSS-E-ST-40 and ECSS-Q-ST-80. This paper presents a model-driven approach to completing these activities by avoiding inconsistencies between the documents that support them and providing the ability to automatically generate the system-level validation tests that are run on the Ground Support Equipment and the matrices required to complete the software verification. A demonstrator of the approach has been built using as a proof of concept a subset of the functionality of the software of the control unit of the Energetic Particle Detector instrument on-board Solar Orbiter.