ֱ̽ of Cambridge - flow /taxonomy/subjects/flow en Sand dunes can ‘communicate’ with each other /research/news/sand-dunes-can-communicate-with-each-other <div class="field field-name-field-news-image field-type-image field-label-hidden"><div class="field-items"><div class="field-item even"><img class="cam-scale-with-grid" src="/sites/default/files/styles/content-580x288/public/news/research/news/crop1_10.jpg?itok=CFKzXXi1" alt="Sand dune" title="Sand dune, Credit: Karol Bacik, Nathalie Vriend" /></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>Using an experimental dune ‘racetrack’, the researchers observed that two identical dunes start out close together, but over time they get further and further apart. This interaction is controlled by turbulent swirls from the upstream dune, which push the downstream dune away. ֱ̽<a href="https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.124.054501">results</a>, reported in the journal <em>Physical Review Letters</em>, are key for the study of long-term dune migration, which threatens shipping channels, increases desertification, and can bury infrastructure such as highways.</p> <p>When a pile of sand is exposed to wind or water flow, it forms a dune shape and starts moving downstream with the flow. Sand dunes, whether in deserts, on river bottoms or sea beds, rarely occur in isolation and instead usually appear in large groups, forming striking patterns known as dune fields or corridors.</p> <p>It’s well-known that active sand dunes migrate. Generally speaking, the speed of a dune is inverse to its size: smaller dunes move faster and larger dunes move slower. What hasn’t been understood is if and how dunes within a field interact with each other.</p> <p>“There are different theories on dune interaction: one is that dunes of different sizes will collide, and keep colliding, until they form one giant dune, although this phenomenon has not yet been observed in nature,” said Karol Bacik, a PhD candidate in Cambridge’s Department of Applied Mathematics and Theoretical Physics, and the paper’s first author. “Another theory is that dunes might collide and exchange mass - sort of like billiard balls bouncing off one another - until they are the same size and move at the same speed, but we need to validate these theories experimentally.”</p> <p>Now, Bacik and his Cambridge colleagues have shown results that question these explanations. “We’ve discovered physics that hasn’t been part of the model before,” said Dr Nathalie Vriend, who led the research.</p> <p>Most of the work in modelling the behaviour of sand dunes is done numerically, but Vriend and the members of her lab designed and constructed a unique experimental facility which enables them to observe their long-term behaviour. Water-filled flumes are common tools for studying the movement of sand dunes in a lab setting, but the dunes can only be observed until they reach the end of the tank. Instead, the Cambridge researchers have built a circular flume so that the dunes can be observed for hours as the flume rotates, while high-speed cameras allow them to track the flow of individual particles in the dunes.</p> <p>Bacik hadn’t originally meant to study the interaction between two dunes: “Originally, I put multiple dunes in the tank just to speed up data collection, but we didn’t expect to see how they started to interact with each other,” he said.</p> <p> ֱ̽two dunes started with the same volume and in the same shape. As the flow began to move across the two dunes, they started moving. “Since we know that the speed of a dune is related to its height, we expected that the two dunes would move at the same speed,” said Vriend, who is based at the BP Institute for Multiphase Flow. “However, this is not what we observed.”</p> <p>Initially, the front dune moved faster than the back dune, but as the experiment continued, the front dune began to slow down, until the two dunes were moving at almost the same speed.</p> <p>Crucially, the pattern of flow across the two dunes was observed to be different: the flow is deflected by the front dune, generating ‘swirls’ on the back dune and pushing it away. “ ֱ̽front dune generates the turbulence pattern which we see on the back dune,” said Vriend. “ ֱ̽flow structure behind the front dune is like a wake behind a boat, and affects the properties of the next dune.”</p> <p>As the experiment continued, the dunes got further and further apart, until they form an equilibrium on opposite sides of the circular flume, remaining 180 degrees apart.</p> <p> ֱ̽next step for the research is to find quantitative evidence of large-scale and complex dune migration in deserts, using observations and satellite images. By tracking clusters of dunes over long periods, we can observe whether measures to divert the migration of dunes are effective or not.</p> <p><em><strong>Reference:</strong></em><br /> <em>Karol A. Bacik et al. ‘<a href="https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.124.054501">Wake-induced long range repulsion of aqueous dunes</a>.’ Physical Review Letters (2020). DOI: 10.1103/PhysRevLett.124.054501</em></p> </div></div></div><div class="field field-name-field-content-summary field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><p>Even though they are inanimate objects, sand dunes can ‘communicate’ with each other, researchers have found. A team from the ֱ̽ of Cambridge has found that as they move, sand dunes interact with and repel their downstream neighbours.</p> </p></div></div></div><div class="field field-name-field-content-quote field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even">We’ve discovered physics that hasn’t been part of the model before</div></div></div><div class="field field-name-field-content-quote-name field-type-text field-label-hidden"><div class="field-items"><div class="field-item even">Nathalie Vriend</div></div></div><div class="field field-name-field-media field-type-file field-label-hidden"><div class="field-items"><div class="field-item even"><div id="file-156952" class="file file-video file-video-youtube"> <h2 class="element-invisible"><a href="/file/156952">Sand dunes can ‘communicate’ with each other.</a></h2> <div class="content"> <div class="cam-video-container media-youtube-video media-youtube-1 "> <iframe class="media-youtube-player" src="https://www.youtube-nocookie.com/embed/fvO5u7WM2sQ?wmode=opaque&controls=1&rel=0&autohide=0" frameborder="0" allowfullscreen></iframe> </div> </div> </div> </div></div></div><div class="field field-name-field-image-credit field-type-link-field field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/" target="_blank">Karol Bacik, Nathalie Vriend</a></div></div></div><div class="field field-name-field-image-desctiprion field-type-text field-label-hidden"><div class="field-items"><div class="field-item even">Sand dune</div></div></div><div class="field field-name-field-cc-attribute-text field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p><a href="http://creativecommons.org/licenses/by/4.0/" rel="license"><img alt="Creative Commons License" src="https://i.creativecommons.org/l/by/4.0/88x31.png" style="border-width:0" /></a><br /> ֱ̽text in this work is licensed under a <a href="http://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution 4.0 International License</a>. Images, including our videos, are Copyright © ֱ̽ of Cambridge and licensors/contributors as identified.  All rights reserved. We make our image and video content available in a number of ways – as here, on our <a href="/">main website</a> under its <a href="/about-this-site/terms-and-conditions">Terms and conditions</a>, and on a <a href="/about-this-site/connect-with-us">range of channels including social media</a> that permit your use and sharing of our content under their respective Terms.</p> </div></div></div><div class="field field-name-field-show-cc-text field-type-list-boolean field-label-hidden"><div class="field-items"><div class="field-item even">Yes</div></div></div> Tue, 04 Feb 2020 01:00:00 +0000 sc604 211152 at How the kettle got its whistle /research/news/how-the-kettle-got-its-whistle <div class="field field-name-field-news-image field-type-image field-label-hidden"><div class="field-items"><div class="field-item even"><img class="cam-scale-with-grid" src="/sites/default/files/styles/content-580x288/public/news/news/131018-tea-kettle-whistle-kaitlin-foley-flickr-attribution-noncommsharealike.jpg?itok=Y0HrrddO" alt="Tea kettle whistle. Homepage banner image: Dwayne Bent (Att-SA)" title="Tea kettle whistle. Homepage banner image: Dwayne Bent (Att-SA), Credit: Kaitlin Foley, via Flickr" /></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>It may come as a surprise to some, but in all the years that people have been brewing tea, no-one has ever quite been able to work out why kettles whistle. In a basic sense, of course, the reasons are pretty clear, but the physical source of the noise and the specific reason for the whistling sound have both remained elusive.</p>&#13; <p>Elusive, that is, until now. Writing in the October issue of the academic journal, <a href="http://scitation.aip.org/content/aip/journal/pof2/25/10/10.1063/1.4821782"> ֱ̽Physics Of Fluids</a>, two Cambridge ֱ̽ researchers claim to have solved the conundrum, and in the process developed the first accurate model for the whistling mechanism inside a classic stove kettle.</p>&#13; <p>Perhaps reassuringly for those who never felt that this was a significant problem, the ramifications reach far beyond kettles themselves. Using the knowledge gained from the study, researchers could potentially isolate and stop similar, but far more irritating whistles - such as the noise made when air gets into household plumbing, or damaged car exhausts.</p>&#13; <p>“ ֱ̽effect we have identified can actually happen in all sorts of situations - anything where the structure containing a flow of air is similar to that of a kettle whistle,” Ross Henrywood, from the ֱ̽ of Cambridge Department of Engineering, and the study’s lead author, explained.</p>&#13; <p>“Pipes inside a building are one classic example and similar effects are seen inside damaged vehicle exhaust systems. Once we know where the whistle is coming from, and what’s making it happen, we can potentially get rid of it.”</p>&#13; <p>Henrywood carried out the research for his fourth-year project as part of his engineering degree, under the guidance of his supervisor, Dr Anurag Agarwal, a lecturer in aeroacoustics. Drawing on previous research by Agarwal, which identified the source of noise in jet engines, the pair were able to show how sound is created inside a kettle as the “flow” of steam comes up the spout.</p>&#13; <p>Having identified the source of the sound itself, they were then able to pinpoint two separate mechanisms, which not only create the sound but specifically cause a kettle to whistle, rather than making the rushing noise a flow might create in other household items, such as a hairdryer.</p>&#13; <p><a href="/sites/www.cam.ac.uk/files/inner-images/131022-whistle-mechanism-credit-henrywood.jpg"><img alt="" src="/sites/www.cam.ac.uk/files/inner-images/131022-whistle-mechanism-credit-henrywood.jpg" style="width: 400px; height: 228px; float: right;" /></a></p>&#13; <p>A basic kettle whistle consists of two plates, positioned close together, forming a cavity. Both plates have a hole in the middle, which allows steam to pass through.</p>&#13; <p>Although the sound of a kettle is understood to be caused by vibrations made by the build-up of steam trying to escape, scientists have been trying for decades to understand what it is about this process that makes sound.</p>&#13; <p>As far back as the 19th century, John William Strutt, 3rd Baron Rayleigh and author of the foundational text, ֱ̽Theory Of Sound, was trying to explain it. In the end, he posited an explanation that Henrywood and Agarwal have proven to be flawed. And Lord Rayleigh was forced to concede that “much remains obscure as regards the manner in which the vibrations are excited.”</p>&#13; <p>Henrywood and Agarwal started by making a series of slightly simplified kettle whistles, then tested these in a rig, in which air was forced through them at various speeds and the sound they produced was recorded.</p>&#13; <p>This enabled them to plot the frequency and amplitude of the sound, and the data was then subjected to a non-dimensional analysis, effectively a set of calculations using numbers without any units, which allowed them to identify trends in the data. Finally, they used a two-microphone technique to determine frequency inside the spout.</p>&#13; <p>Their results showed that, above a particular flow speed, the sound itself is produced by small vortices – regions of swirling flow – which at certain frequencies can produce noise.</p>&#13; <p>As steam comes up the kettle’s spout, it meets a hole at the start of the whistle, which is much narrower than the spout itself. This contracts the flow of steam as it enters the whistle and creates a jet of steam passing through it. ֱ̽steam jet is naturally unstable, like the jet of water from a garden hose that starts to break into droplets after it has travelled a certain distance. As a result, by the time it reaches the end of the whistle, the jet of steam is no longer a pure column, but slightly disturbed.</p>&#13; <p>These instabilities cannot escape perfectly from the whistle and as they hit the second whistle wall, they form a small pressure pulse. This pulse causes the steam to form vortices as it exits the whistle. These vortices produce sound waves, creating the comforting noise that heralds a forthcoming cup of tea.</p>&#13; <p>Henrywood and Agarwal also explain why this effect makes a whistle, rather than another noise, by showing that the mechanism is similar to that seen in an organ pipe or flute. A specific frequency dominates among the sound waves because the note is determined by the size and shape of the opening, and the length of the spout. ֱ̽longer the spout, the lower the note will be.</p>&#13; <p> ֱ̽researchers also found, however, that kettles will whistle below the flow-rate at which the vortices emerge. Just as the water begins to boil, they found an entirely different mechanism, which also makes a sound. ֱ̽difference was that the tone at this stage was fixed at one frequency.</p>&#13; <p>“ ֱ̽fixed frequency was intriguing and not something that we had expected to see,” Henrywood said. “We eventually established that below a particular flow rate the whistle behaved like a Helmholtz resonator – the same mechanism which gives you a tone when you blow over an empty bottle.”</p>&#13; <p>When air is blown over the open neck of a bottle, the Helmholtz resonator mechanism causes sound to radiate from the neck. ֱ̽air just inside the neck is bouncing up and down – the air in the main body of the bottle being compressed and released each time like a spring.</p>&#13; <p>For the kettle, the spring is the air inside the whistle, while the air within the whistle opening reverberates like the air in the neck of a bottle. “In a kettle, of course, the air is blown through, rather than over, the neck – the effect is similar to whistling by mouth,” Henrywood added. “In some kettles, both these mechanisms are happening. Because our study enables us to assess the mechanisms in action, we can potentially make modifications to stop the noise – if we want to.”</p>&#13; <p>Henrywood and Agarwal are now working on a project to make quieter high-speed hand-dryers, by looking at how the jet of air released by these devices creates noise. Their paper on kettles  - ֱ̽Aeroacoustics Of A Steam Kettle – can be found in the October issue of ֱ̽Physics Of Fluids.</p>&#13; <p>For more information about this story, please contact Tom Kirk, Tel: +44 (0)1223 332300, <a href="mailto:thomas.kirk@admin.cam.ac.uk">thomas.kirk@admin.cam.ac.uk</a></p>&#13; </div></div></div><div class="field field-name-field-content-summary field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><p>Researchers have finally worked out where the noise that makes kettles whistle actually comes from – a problem which has puzzled scientists for more than 100 years.</p>&#13; </p></div></div></div><div class="field field-name-field-content-quote field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even">Once we know where the whistle is coming from, and what’s making it happen, we can potentially get rid of it</div></div></div><div class="field field-name-field-content-quote-name field-type-text field-label-hidden"><div class="field-items"><div class="field-item even">Ross Henrywood</div></div></div><div class="field field-name-field-image-credit field-type-link-field field-label-hidden"><div class="field-items"><div class="field-item even"><a href="https://www.flickr.com/photos/foshow/3305317732/" target="_blank">Kaitlin Foley, via Flickr</a></div></div></div><div class="field field-name-field-image-desctiprion field-type-text field-label-hidden"><div class="field-items"><div class="field-item even">Tea kettle whistle. Homepage banner image: Dwayne Bent (Att-SA)</div></div></div><div class="field field-name-field-cc-attribute-text field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p><a href="http://creativecommons.org/licenses/by-nc-sa/3.0/"><img alt="" src="/sites/www.cam.ac.uk/files/80x15.png" style="width: 80px; height: 15px;" /></a></p>&#13; <p>This work is licensed under a <a href="http://creativecommons.org/licenses/by-nc-sa/3.0/">Creative Commons Licence</a>. If you use this content on your site please link back to this page.</p>&#13; </div></div></div><div class="field field-name-field-show-cc-text field-type-list-boolean field-label-hidden"><div class="field-items"><div class="field-item even">Yes</div></div></div><div class="field field-name-field-license-type field-type-taxonomy-term-reference field-label-above"><div class="field-label">Licence type:&nbsp;</div><div class="field-items"><div class="field-item even"><a href="/taxonomy/imagecredit/attribution-noncommercial-sharealike">Attribution-Noncommercial-ShareAlike</a></div></div></div><div class="field field-name-field-related-links field-type-link-field field-label-above"><div class="field-label">Related Links:&nbsp;</div><div class="field-items"><div class="field-item even"><a href="http://scitation.aip.org/content/aip/journal/pof2/25/10/10.1063/1.4821782">Article in Physics of Fluids</a></div></div></div> Thu, 24 Oct 2013 07:28:57 +0000 tdk25 106712 at BP Institute for Multiphase Flow /research/news/bp-institute-for-multiphase-flow <div class="field field-name-field-news-image field-type-image field-label-hidden"><div class="field-items"><div class="field-item even"><img class="cam-scale-with-grid" src="/sites/default/files/styles/content-580x288/public/news/research/news/bpi-institute.jpg?itok=9HoM_oAt" alt="BP Institute" title="BP Institute, Credit: ֱ̽ of Cambridge" /></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div>&#13; <div>&#13; <p>Endowed by a £22 million donation from BP, the BP Institute for Multiphase Flow (BPI) was created in 2000 with the explicit intent of hosting research teams from five departments within the ֱ̽: Applied Maths and Theoretical Physics, Chemical Engineering, Chemistry, Earth Sciences and Engineering.</p>&#13; &#13; <p>Today, a multidisciplinary team of almost 40 academics and students is working to understand how gases and fluids move. Multiphase flow is an area of great interest to BP as it underpins all parts of its business: from enhancing oil recovery to delivering it to customers, and from refining hydrocarbons to investing in a low carbon future.</p>&#13; &#13; <p>For the BPI, engagement with BP enriches research in a very practical sense, as Professor Andy Woods, Director, explained: ‘Our close working relationship with BP gives us in-depth exposure to technical challenges in the industry as well as unparalleled access to field data that would be impossible for us to collect. This means that we can frame research directions that are fundamentally interesting to us as academics and can also solve problems that are of relevance to the industry.’</p>&#13; &#13; <p>Currently, a large pan-Institute project is analysing the interactions between fluids and solids in oil fields to understand the physical chemistry that controls how much oil can be recovered as a function of the salinity of the water used to pump it from the well. Other projects vary from analysing the molecular basis of how lubricants work to understanding how volcanoes erupt, and from addressing questions about the long-term storage of CO<sub>2</sub> in redundant oil wells to determining how you can control heat transfer in buildings through natural convection. This latter research theme led in 2006 to the spin-out company E-Stack, which was set up to commercialise a low energy ventilation system that uses natural convection to keep the interior temperature of buildings buffered from exterior changes.</p>&#13; &#13; <p>Professor Woods sees the link between basic research and industrial applications as key to research at BPI. ‘We determine our own research programme and our prime interest is in answering fundamental questions about flow. But we’re also looking at how this impacts on ‘real world’ applications because this in turn informs a whole new set of fundamental questions and, if we’re lucky, the development of unforeseen applications.’</p>&#13; </div>&#13; &#13; <div>&#13; <p>For more information, please contact Professor Andy Woods (<a href="mailto:andy@bpi.cam.ac.uk">andy@bpi.cam.ac.uk</a>) or visit <a href="https://www.bpi.cam.ac.uk/">www.bpi.cam.ac.uk/</a></p>&#13; </div>&#13; </div>&#13; </div></div></div><div class="field field-name-field-content-summary field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><p>Understanding flow – whether it’s of oil, air, lubricants, lava, seawater or CO2 – lies at the heart of Cambridge’s BP Institute.</p>&#13; </p></div></div></div><div class="field field-name-field-content-quote field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even">Our prime interest is in answering fundamental questions about flow. But we’re also looking at how this impacts on ‘real world’ applications because this in turn informs a whole new set of fundamental questions and, if we’re lucky, the development of unforeseen applications.</div></div></div><div class="field field-name-field-content-quote-name field-type-text field-label-hidden"><div class="field-items"><div class="field-item even">Professor Andy Woods</div></div></div><div class="field field-name-field-image-credit field-type-link-field field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/" target="_blank"> ֱ̽ of Cambridge</a></div></div></div><div class="field field-name-field-image-desctiprion field-type-text field-label-hidden"><div class="field-items"><div class="field-item even">BP Institute</div></div></div><div class="field field-name-field-panel-title field-type-text field-label-hidden"><div class="field-items"><div class="field-item even">BP</div></div></div><div class="field field-name-field-panel-body field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>Energy giant BP looks to its engagement with universities like Cambridge to help stay connected to cutting-edge research in science and technology.</p>&#13; &#13; <p>‘As head of BP’s research and technology portfolio, my job is to ensure that BP has the technology it needs to contribute to the world’s future energy demands,’ said David Eyton, BP Group Head of Research &amp; Technology and Executive Sponsor for Cambridge. ‘As part of this, we work closely with a handful of excellent academic centres like Cambridge to keep us plugged into the fast-changing world of science and technology.’</p>&#13; &#13; <p>BP’s relationship with the ֱ̽, which stretches back through the past century, was recently formalised by the signing of a Memorandum of Understanding (MoU). ‘ ֱ̽MoU,’ David Eyton explained, ‘embraces all of our current interactions with Cambridge at a strategic level – from research activities, through policy development and training, to recruitment – as well as laying the groundwork for mutual support and development so that the relationship can fulfil its greatest potential.’ These interactions are being overseen by Andy Leonard in his role as BP’s Vice-President for Cambridge.</p>&#13; &#13; <p><strong>Valuing research</strong></p>&#13; &#13; <p>BP’s annual spend for 2009 across the ֱ̽ is £3.6 million, of which approximately £1 million is funding technical research and the remainder is principally funding endowments and scholarships.</p>&#13; &#13; <p> ֱ̽company’s main channels of engagement are the BP Institute for Multiphase Flow, established in 2000 with a £22 million endowment from BP, and Judge Business School through the Centre for India and Global Business and the Cambridge Centre for Energy Studies. BP has also had long and fruitful collaborations elsewhere in the ֱ̽, especially with the Bullard Laboratories within the Department of Earth Sciences.</p>&#13; &#13; <p>Several areas of applied research activities in Cambridge have brought world-class expertise to bear on practical issues that have reaped immediate benefits for BP, from exploration through to fuels and lubricants. But BP also views fundamental research as strategically important: ‘Although fundamental research can take years from invention to commercialisation, it also has the potential to yield something truly significant,’ said Eyton. ‘ ֱ̽ ֱ̽ has a fabulous track record of creating important knowledge and that is one of the reasons we are investing in Cambridge. As a business, we have to stay competitive and invest in areas that we believe will benefit our shareholders.’</p>&#13; &#13; <p><strong>Recruiting the best</strong></p>&#13; &#13; <p>Recruitment is very much part of the strategic relationship with Cambridge. ‘ ֱ̽people we recruit today could have a profound impact on the company over many decades,’ explained Andy Leonard, ‘so we need to ensure that the highest quality students are exposed to the range of employment opportunities within BP.’ Also of importance, partly from a recruiting perspective, is the large number of scholarship programmes BP runs for research students, mainly in collaboration with the Cambridge Commonwealth and Overseas Trusts. This year, BP has made job offers to 20 graduates and 17 interns in Cambridge, as well as partially funding 49 research scholarships.</p>&#13; &#13; <p><strong>Recognising opportunities</strong></p>&#13; &#13; <p>‘ ֱ̽key to success in strategic relationships is to create situations where there is genuine mutuality,’ said Eyton. ‘We want the relationship with Cambridge to achieve its greatest potential and to progress the strategic aims of the ֱ̽ and BP.’ ֱ̽company is also keen to support the strengthening of links between universities such as Cambridge, the Massachusetts Institute of Technology (MIT) and Tsinghua ֱ̽ in Beijing, predominantly with regard to finding new forms of low carbon energy and moving towards a more sustainable energy landscape in the world.</p>&#13; &#13; <p>‘I am a big believer in investing in places like Cambridge that have a proven record of success,’ explained Eyton. ‘I also think that we have even more to discover in terms of opportunities for productive interactions. I’m delighted to say that we are on this journey.’</p>&#13; &#13; <p>For more information about BP, please visit <a href="http://www.bp.com/">www.bp.com/</a></p>&#13; </div></div></div><div class="field field-name-field-cc-attribute-text field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p><a href="http://creativecommons.org/licenses/by-nc-sa/3.0/"><img alt="" src="/sites/www.cam.ac.uk/files/80x15.png" style="height:15px; width:80px" /></a></p>&#13; &#13; <p>This work is licensed under a <a href="http://creativecommons.org/licenses/by-nc-sa/3.0/">Creative Commons Licence</a>. If you use this content on your site please link back to this page.</p>&#13; </div></div></div><div class="field field-name-field-show-cc-text field-type-list-boolean field-label-hidden"><div class="field-items"><div class="field-item even">Yes</div></div></div> Sat, 01 Aug 2009 15:10:59 +0000 lw355 25891 at