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Eat, drink and be merry with maths Chris Budd. 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 - PowerPoint PPT Presentation
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Eat, drink and be merry with mathsEat, drink and be merry with maths
Chris BuddChris Budd
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!
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
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
Microwave cooking (CCFRA)
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
What happens in a microwave oven?
L: Length: 2-14cm
d: Penetration depth: 8mm
Microwaves
Potato
Magnetron
Electric Field Calculations (Maxwell)
Small oscillations about an exponential decay Lambert
Use the heat equation to find the food temperature T
)),0(()),0(( 44aacy TtTTtThkT
))()()()(( /)(//)(/02 dyhdydxLdxt exdexceybeya
d
QTkH
10cm
2cm
FOOD
x
y
650W Oven, Mode stirrerTemperature
650W Point Temperatures
Thermal image of cross section after 3 minutes heating
750W turntable oven
Turntable oven, thermal image taken after 5 minutes heating
Cold Spot
Conclude:
The corners of the food get hot first
The middle starts cool
And stays cool in a turntable oven
What happens when we eat the food? [Unilever]
Stomach
Small intestine:
7m x 1.25cm
Intestinal wall:
Villi and Microvilli
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
Objectives
• Model the process of food moving through the intestine
• Model the process of nutrient mixing and absorption
• Navier Stokes
• Slow viscous Axisymmetric flow
• Velocity & Stokes Streamfunction
upuut
u 2).( 0. u
p ˆ
e
ru
ere )/( 0)( e
,ˆ eu
The equations for poo
The equations are a bit sticky to solve!!!
Illeocecal sphincterIlleocecal sphincter openopen
Without peristalsis With peristalsis
Food concentration
Illeocecal sphincter Illeocecal sphincter closedclosed
Without peristalsis With peristalsis
Food concentration
Food absorbed
With peristalsis
Without peristalsis
Peristaltic waves greatly enhance mixing
and the absorption of food
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 E
What have mathematicians done for parties?
Now have 200 friends and want 100 to come to a partyHave a book saying who hates who Who do you invite?
Parties to check
Takes a high speed computer
Years to check them
900000000000000000000000000000000000000000000000000000000000000000
6000000000000000000000000000000000000000
Works for a party and many other problems
Using maths we can solve it in seconds
SATNAV devices!
Simulated annealing
Conclusion …. your
• Life
• Food
• Party
Are safe in the hands of a mathematician