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 mathsMaths is great for foodMathematicians 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

dQTkH

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 firstThe middle starts coolAnd 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

upuutu 2).(

0. u

p ˆ

er

u

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