Reactive Boundary Conditions as Limits of Interaction Potentials for Brownian and Langevin Dynamics

A popular approach to modeling bimolecular reactions between diffusing molecules is through the use of reactive boundary conditions. One common model is the Smoluchowski partial absorption condition, which uses a Robin boundary condition in the separation coordinate between two possible reactants. This boundary condition can be interpreted as an idealization of a reactive interaction potential model, in which a potential barrier must be surmounted before reactions can occur. In this work we show how the reactive boundary condition arises as the limit of an interaction potential encoding a steep barrier within a shrinking region in the particle separation, where molecules react instantly upon reaching the peak of the barrier. The limiting boundary condition is derived by the method of matched asymptotic expansions, and shown to depend critically on the relative rate of increase of the barrier height as the width of the potential is decreased. Limiting boundary conditions for the same interaction potential in both the overdamped Fokker-Planck equation (Brownian Dynamics), and the Kramers equation (Langevin Dynamics) are investigated. It is shown that different scalings are required in the two models to recover reactive boundary conditions that are consistent in the high friction limit where the Kramers equation solution converges to the solution of the Fokker-Planck equation.Comment: 23 pages, 2 figure

Carbon assessment of wind power

The Earth is facing huge implications from Anthropogenic Global Warming and peaks in the production of finite fossil fuels. Decision-makers have to choose strategies for combating these dual problems whilst ensuring minimal costs to society and the environment. Unfortunately, renewable technologies in particular have doubt associated with their ability to reduce total life cycle greenhouse gas (GHG) emissions of electricity due to uncertainty in estimates. This thesis analyses historic associated GHG estimates of wind farms, the largest renewables contributor to electricity generation in the UK, to reduce the uncertainty inherent in estimates and better understand critical factors that influence estimation. Through harmonisation of published life cycle GHG emissions estimates, they are reduced by 56% to between 2.9 and 37.3gCO2e/kWh. Average values for onshore and offshore wind power are calculated as 16 and 18.2gCO2e/kWh respectively and exhibit similar characteristics in their life cycle GHG emissions. Ormonde Offshore Wind Farm is analysed using a novel hybrid approach and gives total baseline GHG emissions of 17.5gCO2e/kWh and is the largest wind power installation to be analysed to date. Finally, an estimate of the effect of load variability of wind on thermal plant in the UK system is calculated. It is shown that this effect may reduce the net emissions saving from wind power relative to the whole UK system’s savings when wind power is included

Second-Order Coverage Control for Multi-Agent UAV Photogrammetry

Unmanned Aerial Vehicles equipped with cameras can be used to automate image capture for generating 3D models via photogrammetry. Current methods rely on a single vehicle to capture images sequentially, or use pre-planned and heuristic imaging configurations. We seek to provide a multi-agent control approach to capturing the images required to 3D map a region. A photogrammetry cost function is formulated that captures the importance of sharing feature-dense areas across multiple images for successful photogrammetry reconstruction. A distributed second-order coverage controller is used to minimise this cost and move agents to an imaging configuration. This approach prioritises high quality images that are simultaneously captured, leading to efficient and scalable 3D mapping of a region. We demonstrate our approach with a hardware experiment, generating and comparing 3D reconstructions from image sets captured using our approach to those captured using traditional methods.Comment: 8 pages, 4 figure