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Eat, drink and be merry with maths Chris Budd Chris Budd

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A common scenario You meet someone at a party and (foolishly) Tell them you are a mathematician Their immediate reaction is to … Panic Leave quickly Tell you that.. Mathematics is completely useless Mathematicians are souless geeks All mathematicians are mad!

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In response you can … Deny that you are a mathematician Not go to any more parties Agree that mathematicians are evil or …. Say that The modern world would not exist without maths Maths is great for food Mathematicians organise great parties

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From Farm to Fork and Beyond Maths and the food industry We use maths to help grow, store, freeze, defrost, transport, cook, eat and digest food Maths can do lots of what if? experiments in complete safety

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Microwave cooking (CCFRA)

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How safe is microwave cooking? If you cook a potato in a microwave cooker what gets hotter? The outside The middle Somewhere else? What is the best design of a microwave cooker? Mode stirred Turntable

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What happens in a microwave oven? L: Length : 2-14cm d: Penetration depth : 8mm Microwaves Potato Magnetron

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Electric Field Calculations (Maxwell) Small oscillations about an exponential decay Lambert

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Use the heat equation to find the food temperature T 10cm 2cm FOOD

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650W Oven, Mode stirrer Temperature

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650W Point Temperatures

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Thermal image of cross section after 3 minutes heating

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750W turntable oven

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Turntable oven, thermal image taken after 5 minutes heating Cold Spot

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Conclude: The corners of the food get hot first The middle starts cool And stays cool in a turntable oven

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What happens when we eat the food? [Unilever] Stomach Small intestine: 7m x 1.25cm Intestinal wall: Villi and Microvilli

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Process: Food enters stomach and leaves as Chyme Nutrients are absorbed through the intestinal wall Chyme passes through small intestine in 4.5hrs Stomach Intestinal wall Colon, illeocecal sphincter Peristaltic wave Mixing process

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Objectives Model the process of food moving through the intestine Model the process of nutrient mixing and absorption

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Navier Stokes Slow viscous Axisymmetric flow Velocity & Stokes Streamfunction The equations for poo The equations are a bit sticky to solve!!!

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Illeocecal sphincter open

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Without peristalsis With peristalsis Food concentration

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Illeocecal sphincter closed

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Without peristalsis With peristalsis Food concentration

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Food absorbed With peristalsis Without peristalsis Peristaltic waves greatly enhance mixing and the absorption of food

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You have five friends, Annabel, Brian, Colin, Daphne, Edward Want to invite three to a party Annabel hates Brian and Daphne Brian hates Colin and Edward Daphne hates Edward Who do you invite? A C EA C E What have mathematicians done for parties?

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Now have 200 friends and want 100 to come to a party Have a book saying who hates who Who do you invite? Parties to check Takes a high speed computer Years to check them 9000000000000000000000000000000000000000000 00000000000000000000000 6000000000000000000000000000000000000000

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Works for a party and many other problems Using maths we can solve it in seconds SATNAV devices! Simulated annealing

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Conclusion …. your Life Food Party Are safe in the hands of a mathematician

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