Barbara Mahler: 15+5 min

Thomas Woolley: 15+5 min

Julian A. Garcia Grajales: 15+5 min
 

Respiratory illnesses, such as asthma and chronic obstructive pulmonary disease, account for one in five deaths worldwide and cost the UK over £6 billion a year. The main form of treatment is via inhaled drug delivery. Typically, however, a low fraction of the inhaled dose reaches the target areas in the lung. Predictive numerical capabilities have the potential for significant impact in the optimisation of pulmonary drug delivery. However, accurate and efficient prediction is challenging due to the complexity of the airway geometries and of the flow in the airways. In addition, geometric variation of the airways across subjects has a pronounced effect on the aerosol deposition. Therefore, an accurate model of respiratory deposition remains a challenge.

High-fidelity simulations of the flow field and prediction of the deposition patterns motivate the use of direct numerical simulations (DNS) in order to resolve the flow. Due to the high grid resolution requirements, it is desirable to adopt an efficient computational strategy. We employ a robust immersed boundary method developed for curvilinear coordinates, which allows the use of structured grids to model the complex patient-specific airways, and can accommodate the inter-subject geometric variations on the same grid. The proposed approach reduces the errors at the boundary and retains the stability guarantees of the original flow solver.

A Lagrangian particle tracking scheme is adopted to model the transport of aerosol particles. In order to characterise deposition, we propose the use of an instantaneous Stokes number based on the local properties of the flow field. The effective Stokes number is then defined as the time-average of the instantaneous value. This effective Stokes number thus encapsulates the flow history and geometric variability. Our results demonstrate that the effective Stokes number can deviate significantly from the reference value based solely on a characteristic flow velocity and length scale. In addition, the effective Stokes number shows a clear correlation with deposition efficiency.

G’s Growers supply salad and vegetable crops throughout the UK and Europe; primarily as a direct supplier to supermarkets. We are currently working on a project to improve the availability of Iceberg Lettuce throughout the year as this has historically been a very volatile crop. It is also by far the highest volume crop that we produce with typical weekly sales in the summer season being about 3m heads per week.

In order to continue to grow our business we must maintain continuous supply to the supermarkets. Our current method for achieving this is to grow more crop than we will actually harvest. We then aim to use the wholesale markets to sell the extra crop that is grown rather than ploughing it back in and then we reduce availability to these markets when the availability is tight.

We currently use a relatively simple computer Heat Unit model to help predict availability however we know that this is not the full picture. In order to try to help improve our position we have started the IceCAM project (Iceberg Crop Adaptive Model) which has 3 aims.

1. Forecast crop availability spikes and troughs and use this to have better planting programmes from the start of the season.
2. Identify the growth stages of Iceberg to measure more accurately whether crop is ahead or behind expectation when it is physically examined in the field.
3. The final utopian aim would be to match the market so that in times of general shortage when price are high we have sufficient crop to meet all of our supermarket customer requirements and still have spare to sell onto the markets to benefit from the higher prices. Equally when there is a general surplus we would only look to have sufficient to supply the primary customer base.

We believe that statistical mathematics can help us to solve these problems!!

Already Serre's "Cohomologie Galoisienne" contains an exercise regarding the following condition on a field F: For every finite field extension E of F and every n, the index of the n-th powers (E*)^n in the multiplicative group E* is finite. Model theorists recently got interested in this condition, as it is satisfied by every superrosy field and also by every strongly2 dependent field, and occurs in a conjecture of Shelah-Hasson on NIP fields. I will explain how it relates to the better known condition that F is bounded (i.e. F has only finitely many extensions of degree n, for any n - in other words, the absolute Galois group of F is a small profinite group) and why it is not preserved under elementary equivalence. Joint work with Franziska Jahnke.

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