Transcript Eat, drink and be merry with maths

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
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?
Microwaves
Magnetron
Potato
L:
d:
Length: 2-14cm
Penetration depth: 8mm
Electric Field Calculations (Maxwell)
Small oscillations
about an exponential
decay Lambert
Use the heat equation to find the food
temperature T
kTy  hc (T (0, t )  Ta )   (T (0, t ) 4  Ta4 )
y
2cm
FOOD
H t  k 2T 
Q0
( a ( y ) e  x / d  b ( y ) e  ( L  x ) / d  c ( x )e  y / d  d ( x )e  ( h  y ) / d )
d
10cm
x
650W Oven, Mode stirrer
Temperature
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
Intestinal wall
Stomach
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
The equations for poo
• Navier Stokes
• Slow viscous
Axisymmetric flow
u
 (u.)u  p   2u
t
.u  0
ˆ    u  e ,   ˆ  p
• Velocity & Stokes
Streamfunction
    (e / r )  e
 
u     e 
r 
    (e )  0
The equations are a bit sticky to solve!!!
Illeocecal sphincter open
Food concentration
Without peristalsis
With peristalsis
Illeocecal sphincter closed
Food concentration
Without peristalsis
With peristalsis
Food absorbed
With peristalsis
Without peristalsis
Peristaltic waves greatly enhance mixing
and the absorption of food
What have mathematicians done for parties?
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?
ACE
Now have 200 friends and want 100 to come to a party
Have a book saying who hates who
Who do you invite?
9000000000000000000000000000000000000000000
00000000000000000000000
Parties to check
Takes a high speed computer
6000000000000000000000000000000000000000
Years to check them
Using maths we can solve it in seconds
Simulated annealing
Works for a party and many other problems
SATNAV devices!
Conclusion …. your
• Life
• Food
• Party
Are safe in the hands of a mathematician