# Statistics, Probability, Analysis and Applied Mathematics

SPAAM student seminar series
Organisers: Hanson Bharth, Connah Johnson, Jaromir Sant and Jack Thomas

#### Cathie Wells, University of Reading Reducing Aviation Emissions and Fuel Burn by Re-routing Transatlantic Flights

Introduction: Commercial long haul flight is at the brink of major change. After decades of limited communications across the North Atlantic, full satellite coverage will soon be available. At the same time, airlines are facing increasing pressure to ensure their flights are more fuel efficient and thus less polluting. Here we show that changes to current fixed track trajectories could significantly reduce fuel use for aircraft making the journey between London and New York.

Methods: Each simulation is completed for a constant air speed and at FL 350, an altitude of 35 000 feet. Optimal Control Theory is used to minimise time of flight in routing aircraft through actual wind fields obtained from a global atmospheric re-analysis dataset. New formulae are then applied to calculate fuel burn rate at the given air speed and the fuel used for the trajectory is found. Applying this method to routes obtained at a variety of air speeds, the most fuel efficient simulation can be chosen.

Results:Total fuel burned in simulations was compared with actual flight data. Three different models of fixed wing aircraft were considered, the Boeing 747-436, 777-236 and 787-9. Each has a unique physical profile leading to different fuel burn rates. This is reflected in the varied levels of savings possible. The importance of the change to air speed, compared with the re-routing of the flight, was also considered.

Conclusions: By making use of the available wind fields, this low cost method not only allows punctual arrivals, but also reduces fuel use and emissions, ensuring a solution that is for once both good for business and for the environment.

#### Phil Herbert | MASDOC | The membrane mediated force on point attachments with application to a near spherical biomembrane

Abstract: We consider a hybrid model of a biomembrane with attached particles. The membrane is represented by a near spherical continuous surface, attached proteins are described by rigid bodies which are free to move tangentially and rotate in the axis normal to a reference point. As the standard energy for a membrane is highly non-linear, we consider a quadratic energy which may be shown to be an approximation of the Canham-Helfrich energy with a volume constraint and the deformations due to the attached proteins are imposed by point Dirichlet constraints. We show differentiability of the membrane energy with respect to parameterisation of these embedded particles and provide illustrative numerical examples.

#### Dom Brockington | MASDOC | Sticky Flows and KPZ Universality

Abstract: We shall introduce stochastic flows, and stochastic flows of kernels, before moving to the special case of sticky flows and their fluctuations. On the large deviation scale these fluctuations turn out to be Tracey-Widom GUE distributed, thus the sticky flows lie in the KPZ universality class.