differential equation
https://plus.maths.org/content/category/tags/differential-equation
enMartin Hairer: at the interface
https://plus.maths.org/content/mh
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<p>Martin Hairer's is being honoured for a major breakthrough that gives a way of attacking problems that had previously been impenetrable.</p>
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<p><em> Martin Hairer has been awarded the <a href="http://www.mathunion.org/general/prizes/fields/details/">Fields Medal</a>, the most prestigious prize in maths, at this year's <a href="http://www.icm2014.org">International Congress of Mathematicians</a> in Seoul.</em></p>
<p><em>Listen to our <a href="https://plus.maths.org/content/fields-medals-2014-interview-martin-hairer">interview with Martin Hairer</a> recorded yesterday before the ICM 2014.</em></p>
<p>Martin Hairer is being honoured for a major breakthrough that gives
a way of attacking problems that had previously been impenetrable.</p><p><a href="https://plus.maths.org/content/mh" target="_blank">read more</a></p>https://plus.maths.org/content/mh#commentsdifferential equationfields medalFields Medal 2014ICM 2014Wed, 13 Aug 2014 00:49:31 +0000mf3446157 at https://plus.maths.org/contentBeneath the waves
https://plus.maths.org/content/waves
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Marianne Freiberger </div>
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<p>Ocean waves are not moving walls of water. Instead, it's some kind of energy that moves along. But then, what happens to the water itself? This isn't just an idle question to ponder while watching the ocean — its answer may help protect us from it too. And it requires some sophisticated maths.</p>
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<div class="rightimage" style="width: 426px"><iframe width="426" height="255" src="https://plus.maths.org/content/sites/plus.maths.org/files/articles/2012/waves/swell.mov?autoplay=1" frameborder="1" allowfullscreen ></iframe><p>Swell coming into a beach in Australia. Click to play movie.</p><p><a href="https://plus.maths.org/content/waves" target="_blank">read more</a></p>https://plus.maths.org/content/waves#commentsdifferential equationEuler's equationfluid dynamicsfluid mechanicswaveThu, 15 Nov 2012 13:31:24 +0000mf3445787 at https://plus.maths.org/contentCareer interview: Biomedical engineer
https://plus.maths.org/content/career-interview-biomedical-engineer
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Marianne Freiberger </div>
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<div class="rightimage" style="width: 300px;"><img src="https://plus.maths.org/content/sites/plus.maths.org/files/careers/March2012/kiran.jpg" alt="Kiran" width="277" height="518" /><p>Kiran Dellimore at the door of the <a href="http://stbweb02.stb.sun.ac.za/berg/index.php">Biomedical Engineering Research Group</a> at the University of Stellenbosch.</p><p><a href="https://plus.maths.org/content/career-interview-biomedical-engineer" target="_blank">read more</a></p>https://plus.maths.org/content/career-interview-biomedical-engineer#commentscareer interviewdifferential equationengineeringHealth & Societymedicine and healthnavier-stokes equationsWed, 07 Mar 2012 14:31:58 +0000mf3445672 at https://plus.maths.org/contentEat, drink and be merry: making it go down well
https://plus.maths.org/content/eat-drink-and-be-merry-0
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Chris Budd </div>
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<p>This article is part of a series of two articles exploring two ways in which mathematics comes into food, and especially into food safety and health. In this article we will take a dive into the rather smelly business of digesting food, and how a crazy application of chaos theory shows the best way to digest a medicinal drug.</p>
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<div style="position: relative; left: 50%; width: 70%"><font size="2"><i>Back to the <a href="https://plus.maths.org/content/do-you-know-whats-good-you-maths-next-microscope">Next microscope package </a><p><a href="https://plus.maths.org/content/eat-drink-and-be-merry-0" target="_blank">read more</a></p>https://plus.maths.org/content/eat-drink-and-be-merry-0#commentschaosdifferential equationdiffusionfractalmathematical modellingmedicine and healthMon, 13 Sep 2010 11:37:25 +0000mf3445309 at https://plus.maths.org/contentEat, drink and be merry: making sure it's safe
https://plus.maths.org/content/eat-drink-and-be-merry
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Chris Budd </div>
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<p>This article is part of a two-part series exploring ways in which mathematics comes into food, and especially into food safety and health. In this part we'll look at how maths can tell us the safest way to cook food.</p>
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<div style="position: relative; left: 50%; width: 70%"><font size="2"><i>Back to the <a href="https://plus.maths.org/content/do-you-know-whats-good-you-maths-next-microscope">Next microscope package </a><p><a href="https://plus.maths.org/content/eat-drink-and-be-merry" target="_blank">read more</a></p>https://plus.maths.org/content/eat-drink-and-be-merry#commentsdifferential equationFourier analysismathematical modellingmedicine and healthMon, 13 Sep 2010 09:51:11 +0000mf3445308 at https://plus.maths.org/contentModelling cell suicide
https://plus.maths.org/content/os/issue55/features/barhu/index
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Martino Barenco and Mike Hubank </div>
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<b>Martino Barenco</b> and <b>Mike Hubank</b> shed light on suicidal cells and a mathematical model that could help fight cancer. </div>
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<div style="position: relative; left: 50%; width: 70%"><font size="2"><i>Back to the <a href="https://plus.maths.org/content/do-you-know-whats-good-you-unravelling-genetic-secrets">Unravelling genetic secrets package</a><p><a href="https://plus.maths.org/content/os/issue55/features/barhu/index" target="_blank">read more</a></p>https://plus.maths.org/content/os/issue55/features/barhu/index#comments55cancerdifferential equationDNAGenesmathematical modellingmedicine and healthFri, 09 Jul 2010 15:53:55 +0000mf3445220 at https://plus.maths.org/contentUncoiling the spiral: Maths and hallucinations
https://plus.maths.org/content/uncoiling-spiral-maths-and-hallucinations
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Think drug-induced hallucinations, and the whirly, spirally, tunnel-vision-like patterns of psychedelic imagery immediately spring to mind. But it's not just hallucinogenic drugs that conjure up these geometric structures. People have reported seeing them in near-death experiences, following sensory deprivation, or even just after applying pressure to the eyeballs. So what can these patterns tell
us about the structure of our brains? </div>
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<div class="pub_date">December 2009</div>
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<div style="position: relative; left: 50%; width: 70%"><font size="2"><i>Back to the <a href="https://plus.maths.org/content/do-you-know-whats-good-you-maths-next-microscope">Next microscope package </a><p><a href="https://plus.maths.org/content/uncoiling-spiral-maths-and-hallucinations" target="_blank">read more</a></p>https://plus.maths.org/content/uncoiling-spiral-maths-and-hallucinations#comments53differential equationmathematical modellingmedicine and healthreaction-diffusion equationsTue, 01 Dec 2009 00:00:00 +0000plusadmin2372 at https://plus.maths.org/contentKelvin's bubble burst again
https://plus.maths.org/content/kelvins-bubble-burst-again
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A new foam with medical potential </div>
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<div class="pub_date">24/09/2009</div>
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<div style="position: relative; left: 50%; width: 70%"><font size="2"><i>Back to the <a href="https://plus.maths.org/content/do-you-know-whats-good-you-maths-next-microscope">Next microscope package </a><br>Back to the <a href="https://plus.maths.org/content/do-you-know-whats-good-you-0">Do you know what's good for you package</a>
<p><a href="https://plus.maths.org/content/kelvins-bubble-burst-again" target="_blank">read more</a></p>https://plus.maths.org/content/kelvins-bubble-burst-again#commentsbubbledifferential equationkelvin's problemmedicine and healthminimal surfacepacking problemspartial differential equationWed, 23 Sep 2009 23:00:00 +0000plusadmin2820 at https://plus.maths.org/contentSupersonic Bloodhound
https://plus.maths.org/content/supersonic-bloodhound
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Ben Evans </div>
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In 1997 Andy Green was the first to break the sound barrier in his car Thrust SSC, which reached speeds of over 760mph. Now he and his team want to push things even further with a car called Bloodhound, designed to reach the dizzy heights of 1,000mph, about 1.3 times the speed of sound. <b>Ben Evans</b> explains how maths is used to build this car. </div>
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<h3>The land speed record</h3>
<p>The first vehicles that today we might describe as cars were steam powered and used primarily for transporting large heavy loads back in the 18th century. Ever since, engineers have been pushing boundaries to try and get them to go faster.<p><a href="https://plus.maths.org/content/supersonic-bloodhound" target="_blank">read more</a></p>https://plus.maths.org/content/supersonic-bloodhound#comments52aerodynamicscomputational fluid dynamicsdifferential equationengineeringfinite elementsmathematical modellingmathematics in sportnavier-stokes equationsMon, 31 Aug 2009 23:00:00 +0000plusadmin2368 at https://plus.maths.org/contentRestoring profanity
https://plus.maths.org/content/restoring-profanity
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Carola Schönlieb </div>
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In 1979 decorating work in a house in Vienna revealed a set of medieval frescoes depicting a cycle of songs by a 13th century poet, who was particularly fond of satirising the erotic relationships between knights and peasant maidens. The frescoes are of great historical significance, but they are badly damaged. In this article <b>Carola Schönlieb</b> explores how mathematicians use the heat
equation to fill in the gaps. </div>
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<p>In the late 14th century Michel Menschein, a wealthy Viennese cloth merchant, commissioned local artists to paint a series of frescoes on the walls of his banqueting hall. The paintings depicted a cycle of songs by <a href="http://en.wikipedia.org/wiki/Neidhart_von_Reuental">Neidhart von Reuental</a>, a 13th century <i>minnesinger</i>, who was particularly fond of satirising the erotic
relationships between knights and peasant maidens.<p><a href="https://plus.maths.org/content/restoring-profanity" target="_blank">read more</a></p>https://plus.maths.org/content/restoring-profanity#comments50CMSdifferential equationdigital photographyImage analysismathematics and artpartial differential equationSun, 01 Mar 2009 00:00:00 +0000plusadmin2355 at https://plus.maths.org/contentA risky business: how to price derivatives
https://plus.maths.org/content/risky-business-how-price-derivatives
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Angus Brown </div>
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In the light of recent events, it may appear that attempting to model the behaviour of financial markets is an impossible task. However, there are mathematical models of financial processes that, when applied correctly, have proved remarkably effective. <b>Angus Brown</b> looks at one of these, a simple model for option pricing, and explains how it takes us on the road to the famous Black-Scholes
equation of financial mathematics, which won its discoverers the 1997 Nobel Prize in Economics. </div>
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<p><i>In the light of recent events, it may appear that attempting to model the behaviour of financial markets is an impossible task. However, there are mathematical models of financial processes that, when applied correctly, have proved remarkably effective. In this article we look at one of these, a simple model for option pricing, and see how it takes us on the road to the famous Black-Scholes
equation of financial mathematics, which won its discoverers the 1997 Nobel Prize in Economics.</i></p><p><a href="https://plus.maths.org/content/risky-business-how-price-derivatives" target="_blank">read more</a></p>https://plus.maths.org/content/risky-business-how-price-derivatives#comments49Black-Scholes equationdifferential equationfinancial mathematicsfinancial modellingoptionMon, 01 Dec 2008 00:00:00 +0000plusadmin2344 at https://plus.maths.org/contentUniversal pictures
https://plus.maths.org/content/universal-pictures
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Marianne Freiberger </div>
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<b>Peter Markowich</b> is a mathematician who likes to take pictures. At first his two interests seemed completely separate to him, but then he realised that behind every picture there is a mathematical story to tell. <i>Plus</i> went to see him to find out more, and ended up with a pictorial introduction to partial differential equations. </div>
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<p><i>Beautiful photography is not what you usually find on a mathematician's website, but this is just what Plus recently came across while idly browsing the Web. Intrigued, we went to see the website's owner, and ended up with an introduction to some high-powered mathematics through the means of pictures.</i></p>
<p><i>Parts of this interview are also available as a <a href="/podcasts/PlusPodcastSept08.mp3">podcast</a>.</i></p><p><a href="https://plus.maths.org/content/universal-pictures" target="_blank">read more</a></p>https://plus.maths.org/content/universal-pictures#comments48Alan Turinganimal patterningBoltzmann equationCMSdifferential equationmathematics and artnavier-stokes equationsoptimal transportationpartial differential equationreaction-diffusion equationsSun, 31 Aug 2008 23:00:00 +0000plusadmin2343 at https://plus.maths.org/contentCareer interview: Systems engineer
https://plus.maths.org/content/career-interview-systems-engineer
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<div style="position: relative; left: 50%; width: 70%"><font size="2"><i>Back to the <a href="https://plus.maths.org/content/ingenious-constructing-our-lives">Constructing our lives package</a></i></font></div><br clear="all">
<p><i>A version of this interview is also available as a <a href="/podcasts/PlusCareersPodcastSep08.mp3">podcast</a>.</i></p><p><a href="https://plus.maths.org/content/career-interview-systems-engineer" target="_blank">read more</a></p>https://plus.maths.org/content/career-interview-systems-engineer#comments48aerodynamicscareer interviewdifferential equationellipseengineeringheat diffusion equationKepler's three laws of planetary motionmathematical modellingpartial differential equationphysicssatelliteScience & Engineeringspace explorationstatisticsuncertaintySun, 31 Aug 2008 23:00:00 +0000plusadmin2437 at https://plus.maths.org/contentSaving lives: the mathematics of tomography
https://plus.maths.org/content/saving-lives-mathematics-tomography
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Chris Budd and Cathryn Mitchell </div>
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Not so long ago, if you had a medical complaint, doctors had to open you up to see what it was. These days they have a range of sophisticated imaging techniques at their disposal, saving you the risk and pain of an operation. <b>Chris Budd and Cathryn Mitchell</b> look at the maths that isn't only responsible for these medical techniques, but also for much of the digital revolution. </div>
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<div style="position: relative; left: 50%; width: 70%"><font size="2"><i>Back to the <a href="https://plus.maths.org/content/do-you-know-whats-good-you-maths-next-microscope">Next microscope package </a><br>Back to the <a href="https://plus.maths.org/content/do-you-know-whats-good-you-0">Do you know what's good for you package</a><p><a href="https://plus.maths.org/content/saving-lives-mathematics-tomography" target="_blank">read more</a></p>https://plus.maths.org/content/saving-lives-mathematics-tomography#comments47CAT scandifferential equationFourier analysisFourier transformfrequencyImage analysismedicine and healthwaveSat, 31 May 2008 23:00:00 +0000plusadmin2328 at https://plus.maths.org/contentMaths and climate change: the melting Arctic
https://plus.maths.org/content/maths-and-climate-change-melting-arctic
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The Arctic ice cap is melting fast and the consequences are grim. Mathematical modelling is key to predicting how much longer the ice will be around and assessing the impact of an ice free Arctic on the rest of the planet. <i>Plus</i> spoke to <b>Peter Wadhams</b> from the Polar Ocean Physics Group at the University of Cambridge to get a glimpse of the group's work. </div>
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<p>The Arctic ice cap is in trouble. Due to global warming, summer sea ice cover has been disappearing at approximately 70,000 km<sup>2</sup> per year, an area the size of Scotland. Measurements from submarines indicate that the ice has grown thinner by at least 40% over the last two decades. Predictions of if and when the permanent ice will disappear from the Arctic vary widely, but few models
give it longer than 100 years and many predict that a total melt-down of the Arctic will occur within our lifetimes.</p><p><a href="https://plus.maths.org/content/maths-and-climate-change-melting-arctic" target="_blank">read more</a></p>https://plus.maths.org/content/maths-and-climate-change-melting-arctic#comments46accelerationCMSCoriolis forcedifferential equationmathematical modellingmathematics and climate changemathematics and the environmentNewtonian mechanicsstefan problemvectorSat, 01 Mar 2008 00:00:00 +0000plusadmin2326 at https://plus.maths.org/content