The pattern of raindrops has been bugging me for years and perhaps a model could be construct for it. One can easily observe the phenomenon when travelling on a train/bus and let us be grateful that we are based in UK that we do not need a huge budget for performing raining experiments. It impressed me the most when a raindrop runs down and leaves a track of tiny drops, which may affect some later raindrop's trajectory. Due to friction, different sizes of raindrops run at different speeds and some may stand still but eventually another runs, literally, into it; they merge and fall as one. The pattern would be dramatically changed, when the vehicle accelarates or slows down, or when the rain suddenly becomes more heavy or the opposite. I believe there are various ways to model the phenomenon. The one I am keeping in my mind is to apply ant colony algorithm, which is an agent-based model, and I know for such swarm intelligence things, there are many experts in the centre -- any advice is appreciated.
Warwick Annual Retreat Projects
As you should be aware, the format of the retreat is slightly different this year. Parts of the timetable are dedicated to the Warwick Annual Retreat Projects (WARPs) where you will collaborate with others on a chosen project in a study group style atmosphere.
The aim of these projects is to foster a collaborative atmosphere within the department, particularly between year groups. Therefore it is hoped that this format change will be both enjoyable and informative.
If you wish to propose a potential project then please add a brief problem description as a topic in the forum below, where others can express their interest and give other comments on your ideas.
This could just be a vague idea which others can help you form.
Warwick Annual Retreat Projects
Project: Raindrops on the window of a moving train
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Colm recently presented some work (Phys. Rev. Lett. 109, 168304 (2012)) on the kinetics of the Smoluchowski equation, one application of which is the aggregation of raindrops in a cloud. As far as I understand it (i.e. very little), the Smoluchowski equation assumes the raindrops are all well mixed, so the probablity of two drops of masses m1 and m2 doesn't depend on where they are in a cloud.
This problem seems like a very nice extension of that because it takes into account the spatial distribution of the raindrops on the window, the history of past mergers (tracks) and external factors (gravity and train speed, i.e. an effective gravity vector).
It would be nice to see whether/how a spatial Smoluchowski approach and an ant colony algorithm approach converge (although I have no idea how to approach either).
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At the BAMC conference Eugene Benilov gave a talk 'A thin drop sliding down an inclined plate' in which he cited this paper; might be useful.
Ho-Young Kim, Heon Ju Lee, Byung Ha Kang, Sliding of Liquid Drops Down an Inclined Solid Surface, Journal of Colloid and Interface Science, Volume 247, Issue 2, 15 March 2002, Pages 372-380, ISSN 0021-9797
http://dx.doi.org/10.1006/jcis.2001.81560 likes
Details:
-The problem should not be part of your PhD!
- It is encouraged that the problem proposed be sufficiently simple so that someone without domain specific knowledge could contribute.
- ~6 hours are allocated for these projects so some progress should be possible within this time-frame.
- Groups will be expected to give an informal summary at the end of the retreat and will give a presentation the Wednesday following the retreat (12:30, 11th May).