1,488 research outputs found
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
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