1
00:00:18,660 --> 00:00:23,730
Thank you, Alan. So there was a lot of meticulous planning that went into this so that everything would go nice

2
00:00:23,730 --> 00:00:28,830
and slick and as you can see, nothing has gone slick. But that's quite a nice way to start off, because now I don't

3
00:00:28,830 --> 00:00:33,870
have high expectations. I'm as Alan

4
00:00:33,870 --> 00:00:39,180
said, I'm an industrial mathematician, having quite a lot of us in here. And

5
00:00:39,180 --> 00:00:44,310
what we do is we work with lots of industries who bring along problems and then we work on these and

6
00:00:44,310 --> 00:00:49,350
find solutions that can help to advance society or technology. And what I'd like

7
00:00:49,350 --> 00:00:54,570
to do in this talk today is tell you some stories about some of the industries that I've worked

8
00:00:54,570 --> 00:01:00,880
with and the kinds of techniques that we use to solve some of the problems that might present.

9
00:01:00,880 --> 00:01:06,130
So what I want to do to start with is motivate

10
00:01:06,130 --> 00:01:11,350
this idea of going backwards in time. That is in to title.

11
00:01:11,350 --> 00:01:16,500
So let me try and switch to the. Come

12
00:01:16,500 --> 00:01:21,830
on. OK. So what we have here is a

13
00:01:21,830 --> 00:01:27,200
container cylinder container and it's full of glycerol. So this is the kind of stuff if you've

14
00:01:27,200 --> 00:01:32,210
ever had a sore throat and gone to the pharmacy, you get honey lemon in glycerine. It's that kind of thing. So it's a

15
00:01:32,210 --> 00:01:38,120
sugar solution and is quite discussed, quite sticky. And that's inside the container. And then inside

16
00:01:38,120 --> 00:01:43,370
the centre of here, we have a cylinder. And when I turn this dial here, the handle,

17
00:01:43,370 --> 00:01:48,380
it spins the list of all around. And hopefully you can see that this place of all is clear. So

18
00:01:48,380 --> 00:01:53,390
you can't see anything going on at the moment. So what I'm gonna do is I'm going to inject some colour dye

19
00:01:53,390 --> 00:01:58,570
in so that when I move the handle, you can see how it how it smells.

20
00:01:58,570 --> 00:02:03,600
OK, so let's have a guy try and inject some blue dye. First of all,

21
00:02:03,600 --> 00:02:13,000
inject it and then have a look and see if it's in the shot on it.

22
00:02:13,000 --> 00:02:21,270
You can see it, it's a little bit faint, but you can see it. And then I'll try some Medina.

23
00:02:21,270 --> 00:02:28,100
Now, try and be a bit more creative with this.

24
00:02:28,100 --> 00:02:33,560
Well. That's supposed to be an aim. But

25
00:02:33,560 --> 00:02:38,600
we we've got a little bit of a pattern there. OK. So what I'm going to do now

26
00:02:38,600 --> 00:02:44,040
is I'm going to mix this, Oola. As many.

27
00:02:44,040 --> 00:02:50,990
And we should hopefully see this, you see the camera biting and I mix and makes.

28
00:02:50,990 --> 00:02:56,300
And then I think we need to go too far before it's all the way come round and actually you can't see much

29
00:02:56,300 --> 00:03:02,300
here. You can still see me as on here. So now we ask the question, what if I go in the other direction?

30
00:03:02,300 --> 00:03:07,610
So in some mix, as you mix in one direction, then you mix in the other direction and it makes things

31
00:03:07,610 --> 00:03:12,830
up even more. So the options are here. It's going to mix even more. It'll stay

32
00:03:12,830 --> 00:03:18,170
about the same or it'll completely on mix. So just and the blogs

33
00:03:18,170 --> 00:03:23,330
will go back to how they were again. So that's an option. So just to cheque hands. I'll give you

34
00:03:23,330 --> 00:03:28,430
three options. So mix more, stay the same or complete your mix. So 100. If you think you'll makes

35
00:03:28,430 --> 00:03:34,860
more. Quite a lot. Stay about the same.

36
00:03:34,860 --> 00:03:39,960
And completely unmixed. OK. So we have a big, big

37
00:03:39,960 --> 00:03:45,090
number of people who say it's going to completely omic. So if I spin this round now,

38
00:03:45,090 --> 00:03:50,670
the other way turning. Tony.

39
00:03:50,670 --> 00:03:55,720
Turning like this, then, sure enough, a

40
00:03:55,720 --> 00:04:00,940
completely on mixes. And actually, you can. It's pretty robust that you can flip this man and go back

41
00:04:00,940 --> 00:04:06,010
with any and you can do this pretty fast and unmake his every single time. So

42
00:04:06,010 --> 00:04:11,200
this is perhaps perhaps not to this audience, but perhaps to the other audience,

43
00:04:11,200 --> 00:04:16,230
quite unexpected. You know, when you give a mass talk

44
00:04:16,230 --> 00:04:21,510
in the maths department, you're always going to get people who know the answer. But this is kind of surprising.

45
00:04:21,510 --> 00:04:26,610
And you can have a go at this if you didn't believe me until I was doing a bit of a trick. You can either go yourself. You can just

46
00:04:26,610 --> 00:04:31,830
take a break again by the UK. But another baker inside like a cylinder and get some glycerine

47
00:04:31,830 --> 00:04:37,170
from a pharmacist and then put the column in and turn it round and turn it back and you'll get this kind of feature.

48
00:04:37,170 --> 00:04:42,180
That's kind of interesting. And so that's the idea. And we want to kind of tap

49
00:04:42,180 --> 00:04:47,250
into this notion of going backwards in time to see if we can solve

50
00:04:47,250 --> 00:04:53,010
some industrial problems using this.

51
00:04:53,010 --> 00:04:58,020
So if you're interested in looking this up, it's called the reversible Stokes flow experiment. If you look this up

52
00:04:58,020 --> 00:05:03,600
on Google and have a look on YouTube, there are some nice videos of this.

53
00:05:03,600 --> 00:05:08,710
So how is this going to help us with the kinds of industry problems that we're working on? Well, here's a box of

54
00:05:08,710 --> 00:05:13,980
Samuel's disco Nesquik cereal. And if any of you have

55
00:05:13,980 --> 00:05:18,990
young children, then you might be familiar with this because they might be making their name when you're trying to get them

56
00:05:18,990 --> 00:05:25,440
off to school in the morning. So the idea with this is

57
00:05:25,440 --> 00:05:30,480
that you take you make these things in a similar way to a play doh fun factory. And

58
00:05:30,480 --> 00:05:35,520
again, if you have small children, you might be familiar with this thing as well. So what you have here is

59
00:05:35,520 --> 00:05:40,720
some play dough that you inject into this. This device here. And then you squish

60
00:05:40,720 --> 00:05:45,990
in tanks and you can make stars. We can make coarsest or you can make these wholely shapes.

61
00:05:45,990 --> 00:05:51,450
And then this funny shape here. Now, the good thing about Plato is that it's quite

62
00:05:51,450 --> 00:05:56,550
it's almost solid, which means that when you squishy tanked the hole, when it comes out of this

63
00:05:56,550 --> 00:06:01,830
nozzle, it's pretty much the shape of the thing you get. Now, with Nesquik

64
00:06:01,830 --> 00:06:06,930
cereal, what you're squeezing out. It's the same kind of idea. You squeeze it out of a hole.

65
00:06:06,930 --> 00:06:12,210
But the Nesquik S.A.M. is a hot, bubbly liquid.

66
00:06:12,210 --> 00:06:18,160
So when it squeeze it out, it doesn't behave lightly. So

67
00:06:18,160 --> 00:06:23,260
this is a simulation done by Michael Holmes there to give us

68
00:06:23,260 --> 00:06:29,270
an idea of exactly what does happen. So here Michael has been trying to make Mickey Mouse

69
00:06:29,270 --> 00:06:34,520
see that we start off with Mickey Mouse at the start here. But because it's a serial

70
00:06:34,520 --> 00:06:41,300
molton mixture, it uses eggs and you actually lose Mickey as you go along.

71
00:06:41,300 --> 00:06:46,360
So this is no good. This is no good because it means that if you

72
00:06:46,360 --> 00:06:51,820
want to try and make particular letters, then you're not actually clear what hole you should.

73
00:06:51,820 --> 00:06:57,310
This scenario makes Jeff way because, for instance, if you pump it through an R shape

74
00:06:57,310 --> 00:07:02,380
because of this evolution, you don't end up with an R. In fact, one of the features you notice

75
00:07:02,380 --> 00:07:08,080
here is that the hole closes off and another feature is that they're not very regular.

76
00:07:08,080 --> 00:07:13,120
All of the letters. So we have another experiment over here. This is where the overhead

77
00:07:13,120 --> 00:07:18,430
projector, this is very old school that hopefully we can rely on the old school

78
00:07:18,430 --> 00:07:23,890
kind of stuff. So what we've got here

79
00:07:23,890 --> 00:07:29,280
is a cookie cutter. And I understand to put some

80
00:07:29,280 --> 00:07:34,390
more, I like my sugary solution. This is Golden State. I'm just going to squeeze the Golden State

81
00:07:34,390 --> 00:07:43,590
into the cookie cutter. Like, say.

82
00:07:43,590 --> 00:07:49,340
And then I'm just going to take it out. So

83
00:07:49,340 --> 00:07:54,470
what you see here is that quite quickly, remember

84
00:07:54,470 --> 00:07:59,710
what the thing looked like. It's like a star shape. It had quite pointy edges quite quickly.

85
00:07:59,710 --> 00:08:04,730
You lose the points and you get something like they said. This is exactly the kind of thing that's going on with the

86
00:08:04,730 --> 00:08:09,740
Nestlé problem. It's coming out and it's changing. So you don't get the star that you started

87
00:08:09,740 --> 00:08:14,930
with. Now, if we were to try and model this mathematically, this is what Michael did

88
00:08:14,930 --> 00:08:20,360
with this. He just took what are the Stokes flow experiments? That's exactly Stokes flow equations.

89
00:08:20,360 --> 00:08:25,430
That's exactly what we used to model this here. Then if I give you an initial

90
00:08:25,430 --> 00:08:30,770
shape, you can tell me how it evolved. So I could say, what does it look like 10 seconds later?

91
00:08:30,770 --> 00:08:35,810
A minute later? That's called of well posed a problem. Now, if I take this

92
00:08:35,810 --> 00:08:40,940
shape here and if you hadn't watched me do that experiment and I said, what did that look like?

93
00:08:40,940 --> 00:08:46,010
When I started, you wouldn't be able to tell me it's lost all of the features. So if I

94
00:08:46,010 --> 00:08:51,050
want to go backwards in time. This is what's called an imposed problem.

95
00:08:51,050 --> 00:08:56,060
And this means it's mathematically challenging and impossible to solve because

96
00:08:56,060 --> 00:09:01,250
we can't just one time backwards to work out what shape we need to start. But this

97
00:09:01,250 --> 00:09:06,350
is exactly the challenge that Nestlé won't say. They say we want to make Anar. What shape should

98
00:09:06,350 --> 00:09:11,930
we start with? And you can't say, well, let's start with an arm and just one time backwards. So the kinds of mathematical

99
00:09:11,930 --> 00:09:17,090
tools that we're going to introduce in this talk will be to see how

100
00:09:17,090 --> 00:09:22,670
this how we can get around this problem and work out

101
00:09:22,670 --> 00:09:27,710
how we can make this kind of cereal's. So this is the idea

102
00:09:27,710 --> 00:09:33,470
that we have. We want to try and make better. Let us have.

103
00:09:33,470 --> 00:09:38,900
Now, this is quite a hard problem because, as I said, it's a bubble, see, and we mixture. So I'm going to take

104
00:09:38,900 --> 00:09:44,240
a step back and consider a glass manufacturer instead. Now, glass manufacture is exactly

105
00:09:44,240 --> 00:09:49,460
the same process. It's an extrusion process. But glass is easier to work with than

106
00:09:49,460 --> 00:09:54,650
a molten say, a real mixture. So if you want to make all

107
00:09:54,650 --> 00:09:59,810
of these products here, anything from these optical fibres to test tubes and

108
00:09:59,810 --> 00:10:05,800
medicine vials here, they're all made in exactly the same process, these extrusion process.

109
00:10:05,800 --> 00:10:10,880
And you take your molten glass and you pump it through the hole here and you pull vertically downwards. Now, notice,

110
00:10:10,880 --> 00:10:16,490
all of these are circular and that's good because that means that it doesn't matter how much you pull.

111
00:10:16,490 --> 00:10:23,240
It's never going to evolve from a star. Well, everything wants to end up as a circle. If you look at this here,

112
00:10:23,240 --> 00:10:28,490
it's going towards a circle. Now, this was working

113
00:10:28,490 --> 00:10:33,560
with a company called Shots. Shot makes glass for lots of different companies such as

114
00:10:33,560 --> 00:10:39,080
Samsung in Hawaii Way. And they asked a very similar question. I said we don't want to make

115
00:10:39,080 --> 00:10:44,240
circular capillary tubes. We want to make square ones like this. I wanted

116
00:10:44,240 --> 00:10:50,320
to make square Maddieson vials and they wanted to make square a test tube so they don't want to weigh in on the table.

117
00:10:50,320 --> 00:10:55,330
So their question was exactly the same. What hole should we pump this through so

118
00:10:55,330 --> 00:11:00,840
that we end up with the square? Here's my schematic. But we're going to try and find out what that is.

119
00:11:00,840 --> 00:11:05,930
Now, we use the Stokes equations again, which are exactly what would describe this, exactly what would

120
00:11:05,930 --> 00:11:11,090
describe Michael's problem. But the forward problem is well posed. I give you a shape. I go

121
00:11:11,090 --> 00:11:16,610
forwards in time. You can tell me what the shape looks like at any given light point.

122
00:11:16,610 --> 00:11:21,710
The inverse problem is ill posed. I give you a shape at the lifetime. You can't tell me how

123
00:11:21,710 --> 00:11:28,660
that evolves backwards in time. So this is a challenge that we want to try and overcome.

124
00:11:28,660 --> 00:11:33,810
And the way in which we do this is by making various simplifying steps. And the first

125
00:11:33,810 --> 00:11:39,540
one is we look at this problem and this is a complicated, three dimensional problem of drawing.

126
00:11:39,540 --> 00:11:44,820
I choose. Now, the first thing we do is say, let's convert this into slices.

127
00:11:44,820 --> 00:11:50,010
So just like I showed you on here, this was on a plane. Two dimensional problem.

128
00:11:50,010 --> 00:11:55,440
And we looked at evolution of this blob with time. So let's say we'll consider

129
00:11:55,440 --> 00:12:00,900
a time evolution problem in two dimensions with the idea that each of these

130
00:12:00,900 --> 00:12:05,940
snapshot in time corresponds to a different axial position. So we can imagine

131
00:12:05,940 --> 00:12:12,180
stacking these up like Coaster's to reconstruct a three dimensional shape.

132
00:12:12,180 --> 00:12:17,630
That's the first simplification that turns it from a 3-D problem into a Tudi. The next

133
00:12:17,630 --> 00:12:22,730
simplification is we say, let's just look at a little bit of this

134
00:12:22,730 --> 00:12:27,740
glass tubing here. This zoomed picture

135
00:12:27,740 --> 00:12:32,840
here and we model this using the angle data

136
00:12:32,840 --> 00:12:38,120
and the arc lens. So that's X as we go round and time to see if I tell you the angle

137
00:12:38,120 --> 00:12:43,220
every single point on this glass and every single time. That's enough to reconstruct

138
00:12:43,220 --> 00:12:48,320
the problem. Now, what we've done here is we've taken a complicated, three dimensional problem that

139
00:12:48,320 --> 00:12:53,420
he's ill posed for negative time and turned it into a tiny little piece

140
00:12:53,420 --> 00:12:58,550
that we're going to reconstruct the evolution of this tiny little piece. We can run backwards

141
00:12:58,550 --> 00:13:03,660
in time that's well posed. So that is exactly what we do. We we

142
00:13:03,660 --> 00:13:08,690
construct our picture by doing lots of tiny little pieces. And then we start with the square and

143
00:13:08,690 --> 00:13:14,060
run it backwards in time. And we get our two dimensional slices, which then

144
00:13:14,060 --> 00:13:19,160
allow us to reconstruct the three dimensional picture. And the interesting

145
00:13:19,160 --> 00:13:24,380
things about this are that you can do it for any shape you like. And I've done it for a square. You can do whatever

146
00:13:24,380 --> 00:13:30,080
you like. And what was a very complicated problem to solve mathematically

147
00:13:30,080 --> 00:13:35,420
or to solve using experiments can be written in this little box here. This encapsulates

148
00:13:35,420 --> 00:13:40,550
all of the information about this. And they speak to as naughtier tells you the shape that you want

149
00:13:40,550 --> 00:13:45,740
to start with. Think of it whatever you like into this as an example.

150
00:13:45,740 --> 00:13:51,110
Here's a funny shape that we might want to start with the whole shape. What do you think that ends up

151
00:13:51,110 --> 00:13:56,570
evolving to? Does anybody know? Once the triangle

152
00:13:56,570 --> 00:14:04,110
and the other guest is Mickey Mouse again. Looks like Mickey Mouse.

153
00:14:04,110 --> 00:14:09,580
It's the heart. It's Valentine's Day tomorrow and we have to have something.

154
00:14:09,580 --> 00:14:14,590
So for those of you who have not yet bought a Valentine's Day present for your loved one,

155
00:14:14,590 --> 00:14:21,240
you can come and talk to me and we can make you a Valentine's shaped, heart shaped tube.

156
00:14:21,240 --> 00:14:27,310
For those of you who didn't know, it's Valentine's Day tomorrow. I have just saved your relationship.

157
00:14:27,310 --> 00:14:32,770
But this generalises a lot more than just what we've shown here. It generalises into

158
00:14:32,770 --> 00:14:37,930
multi structured optical fibres. And these are pretty big business nowadays as we're trying

159
00:14:37,930 --> 00:14:43,390
to transmit more and more data around. We need to transmit lots of signals

160
00:14:43,390 --> 00:14:48,670
in one fibre. So here are two examples. This one here

161
00:14:48,670 --> 00:14:53,680
looks a bit like a Mercedes Benz. It's quite hard to see, but it's got three struts. So you can send

162
00:14:53,680 --> 00:14:58,990
three times the amount of signals down this tube. This one here

163
00:14:58,990 --> 00:15:04,090
is surrounded by a honeycomb. And this prevents the signal from leaks.

164
00:15:04,090 --> 00:15:09,100
And we can do exactly the same kind of idea with this. How do we make a Mercedes-Benz

165
00:15:09,100 --> 00:15:14,710
shape? Well, this one is a lot harder, actually. It's perhaps not what you would expect.

166
00:15:14,710 --> 00:15:19,880
It also doubles up as a really nice thing to keep your flowers in. So

167
00:15:19,880 --> 00:15:25,770
I'll keep those out so you can kind of see this stays in my office. Nice flowers.

168
00:15:25,770 --> 00:15:30,940
This has been 3D printed on our lands 3D printer. So this is a nice way to visualise these

169
00:15:30,940 --> 00:15:36,120
kinds of products when you've made them.

170
00:15:36,120 --> 00:15:41,630
OK, so let's stick with the idea of glass manufacture

171
00:15:41,630 --> 00:15:46,670
for the moment. But what you can see and what I've shown you is that this all translates

172
00:15:46,670 --> 00:15:51,680
to making the Nesquik cereal. These kinds of ideas, these multi structured optical fibres are

173
00:15:51,680 --> 00:15:57,470
exactly what you need to make the Nesquik cereal, albeit in a more complicated fashion.

174
00:15:57,470 --> 00:16:02,550
Now, we're going to move on and we're going to ask a question. How do you make glass sheets for

175
00:16:02,550 --> 00:16:07,640
mobile phones? This is a glass sheet that this guy has got in his hand here, and it's so

176
00:16:07,640 --> 00:16:12,710
thin. You're watching a minute and squish squishier and it flexes. And I find this incredible,

177
00:16:12,710 --> 00:16:18,150
this glass. You have this idea that glass is very brittle.

178
00:16:18,150 --> 00:16:24,930
This during F is glass, and we've got some here might be able to see at the back, but it really is flexible.

179
00:16:24,930 --> 00:16:30,030
Now, what we did once is my P actually finished a student handed this angrist for people to have

180
00:16:30,030 --> 00:16:35,040
play around with. But the trouble is it has a limit of how much you can flex it. So you could

181
00:16:35,040 --> 00:16:40,490
hear this cracking sound as it was going round the audience and then what came back was dust

182
00:16:40,490 --> 00:16:45,540
or. Oh I guess sun. Sand is the more material of that glass. You can see

183
00:16:45,540 --> 00:16:50,940
just how flexible this stuff really is. And this is used for flexible electronics.

184
00:16:50,940 --> 00:16:56,230
Something released their first flexible device last year and Glena.

185
00:16:56,230 --> 00:17:01,290
And to release one. So we were interested in trying to

186
00:17:01,290 --> 00:17:06,900
make this kind of glass sheet. And the way in which this is made

187
00:17:06,900 --> 00:17:12,300
is called the withdrawal process. The glass tubes were made using what's called the down draw process.

188
00:17:12,300 --> 00:17:17,490
This is called the withdrawal process. Now, what you do here is you start off with a rectangular

189
00:17:17,490 --> 00:17:22,590
block here and you feed down to this heat zone here and

190
00:17:22,590 --> 00:17:27,600
you pull it on the bottom with the moment. As you pull in, you stretch and gets thinner and thinner until

191
00:17:27,600 --> 00:17:33,180
the product that comes out is the product that you just saw. Now, the downside of doing this

192
00:17:33,180 --> 00:17:38,310
is if you've ever had a go at making pizza, when you're trying to pull your structural pizza

193
00:17:38,310 --> 00:17:43,410
wanked, when you're done, you have a look at this and you've got Fat Ed June, the white man. That's your pizza

194
00:17:43,410 --> 00:17:48,480
crust. Pizza crust is nice on a pizza pizza crust. Not so nice on a piece

195
00:17:48,480 --> 00:17:53,940
of glass. So here you get exactly the same kind of thing when I pull my glass

196
00:17:53,940 --> 00:17:59,510
downwards. You get these fat edges. This is a 3-D print of

197
00:17:59,510 --> 00:18:05,070
of this kind of thing. Perhaps you can't see. But I've started with a rectangle here. And when I pull,

198
00:18:05,070 --> 00:18:10,470
I get fat edges at either side. And if you're interested in looking at any of these things at the end, then you can come down

199
00:18:10,470 --> 00:18:16,150
equally if you want to play around with this at the end. So

200
00:18:16,150 --> 00:18:22,390
this is a similar kind of question we want to know. How do we make glass?

201
00:18:22,390 --> 00:18:28,390
That is completely flat at the end. No fat edges. And these strategies are bad for two reasons.

202
00:18:28,390 --> 00:18:33,520
One is that if you have a mobile phone and got fat edges on it, it'll distort your

203
00:18:33,520 --> 00:18:39,040
picture. Two is if you have these fat edges, it won't flex.

204
00:18:39,040 --> 00:18:44,100
It'll fracture. This is called fracture. But the problem,

205
00:18:44,100 --> 00:18:49,650
just like the other one, the overclass problem, the forward problem is well posed. I can take a rectangle here

206
00:18:49,650 --> 00:18:55,140
and I can pull and stretch and I can tell you exactly what the shape will be at the end.

207
00:18:55,140 --> 00:19:00,240
But if I give you a final shape, very hard to work out what shape I should

208
00:19:00,240 --> 00:19:05,500
have started with to get. So here's the question.

209
00:19:05,500 --> 00:19:10,870
Rectangle, Mike, flatted, rectangle. What shape should we start with? To make

210
00:19:10,870 --> 00:19:16,060
a flat rectangle. And we need to come up with another creative idea, because

211
00:19:16,060 --> 00:19:21,250
we can't just one time backwards. Same equations as we've used everywhere else

212
00:19:21,250 --> 00:19:26,330
to stokes equations. But we're now going to do something a bit different.

213
00:19:26,330 --> 00:19:31,450
What we're going to do is say if we put this GLASSINE and then we pull it

214
00:19:31,450 --> 00:19:36,820
out faster, then it stretches. What happens if we put the GLASSINE ampoule

215
00:19:36,820 --> 00:19:41,920
at a lower speed than the glass is going in? So physically, that doesn't make sense. It's almost like

216
00:19:41,920 --> 00:19:47,350
you're trying to push the glass back up into the heat zone. But mathematically,

217
00:19:47,350 --> 00:19:52,540
we can choose our pulling speed to be whatever we like. So if we choose a pulling

218
00:19:52,540 --> 00:19:57,670
speed to be 20 times slower than the input speed

219
00:19:57,670 --> 00:20:04,180
with a rectangle. And what we find is we get this funny shape coming out of the bottom.

220
00:20:04,180 --> 00:20:09,550
And what that means is if we were to start with this shape at the top, this type

221
00:20:09,550 --> 00:20:14,850
of shape and pull at 20 times the input speed, we should in principle

222
00:20:14,850 --> 00:20:19,930
recover the rectangle. So does this work? Let's have a try.

223
00:20:19,930 --> 00:20:25,090
It does. So here's another thing. So, again, you may not be able to say it back, but we start

224
00:20:25,090 --> 00:20:30,130
off with this type of rectangle now a pool. And what you get out to the bottom here is

225
00:20:30,130 --> 00:20:35,500
perfectly flat glass. And so these ideas now

226
00:20:35,500 --> 00:20:40,540
are used on your Samsung or your Hawaiian way phone products. So this

227
00:20:40,540 --> 00:20:46,540
is how they make the flat glass that goes on the front and also goes on the back and covers your camera.

228
00:20:46,540 --> 00:20:51,730
So it's nice to see that the mathematical models that we develop are actually implemented

229
00:20:51,730 --> 00:20:56,880
in industry. OK, so that's been a lot

230
00:20:56,880 --> 00:21:02,160
about glass manufacture. I meant to switch topics now to

231
00:21:02,160 --> 00:21:07,560
filtration. Still keeping the idea of this. Can we go backwards

232
00:21:07,560 --> 00:21:13,100
in time to what? Some guy. Is it made at home

233
00:21:13,100 --> 00:21:18,510
doing my vacuuming because I'm quite proud. But I'm frowning

234
00:21:18,510 --> 00:21:24,480
as I'm looking at the vacuum cleaner. And the reason I'm frowning is because it's not picking up the dust.

235
00:21:24,480 --> 00:21:30,150
So you might say always because the bags full Dyson have no banks and they

236
00:21:30,150 --> 00:21:35,820
have no loss of suction. That's my sales pitch for Dyson. That's what gives my half price. Dyson, I'm

237
00:21:35,820 --> 00:21:41,770
so the reason it's blocked is because the filter is blocked.

238
00:21:41,770 --> 00:21:47,230
That's not picking up the dead. Now, what we're working on with Dyson is trying to make a film

239
00:21:47,230 --> 00:21:52,240
that lasts longer, ideally lasts the lifetime of vacuum cleaner, so

240
00:21:52,240 --> 00:21:57,700
you never need to clean it. In principle, you're supposed to change or clean your filter

241
00:21:57,700 --> 00:22:02,910
about every three months. How many of you actually change your filter? Everything.

242
00:22:02,910 --> 00:22:08,260
How many of you actually vacuum every three months? Well, that's the idea.

243
00:22:08,260 --> 00:22:13,930
So if you are doing as you're told, then you should change or clean this filter every three months.

244
00:22:13,930 --> 00:22:19,100
If we could extend this so we never needed to change it, that's a good idea.

245
00:22:19,100 --> 00:22:24,170
Now to understand what's going on in a field. So this is an example of a Dyson film.

246
00:22:24,170 --> 00:22:29,210
They're quite fluffy. It's like hot and warm effectively. And I've illustrated

247
00:22:29,210 --> 00:22:34,750
this cotton movie. Film. In this picture here. So imagine all of the blue circles here

248
00:22:34,750 --> 00:22:39,920
are fibres that are sticking out of the page. Then I'm going to

249
00:22:39,920 --> 00:22:45,380
put some dirt into my favourite coming in the top black.

250
00:22:45,380 --> 00:22:50,420
And see where it sticks. Here comes my dust. And what we say, I'm changing the

251
00:22:50,420 --> 00:22:55,490
colours here and the colour change corresponds to how much dust has been trapped by

252
00:22:55,490 --> 00:23:00,710
each of these fibres. And what you see is that the colours at the top change a lot

253
00:23:00,710 --> 00:23:05,960
more than the colours at the bottom. And this is dynamic in filters. If you've ever actually

254
00:23:05,960 --> 00:23:11,120
looked at your filter in your column or your vacuum cleaner and you take it out,

255
00:23:11,120 --> 00:23:16,190
you'll find that it's really dirty on the one side, black. And you flip it over on the other side and

256
00:23:16,190 --> 00:23:22,760
it's a white. It's all clean. And actually, even if you look in the depth, it's own clean as well.

257
00:23:22,760 --> 00:23:28,170
So that's indicative of a filter that's not working to its full capacity, because when the top surface

258
00:23:28,170 --> 00:23:33,220
is blocked, then it's all over. So we asked the question, could we

259
00:23:33,220 --> 00:23:38,290
make a porosity graded film? And by that I mean, could we open the top I

260
00:23:38,290 --> 00:23:43,990
to be so that it lets more of the way so that the filter

261
00:23:43,990 --> 00:23:49,000
down here is also trapping. And really what we're after

262
00:23:49,000 --> 00:23:54,010
is a filter that traps that uniformly for wanked so that when it blocks at the

263
00:23:54,010 --> 00:23:59,530
top, it blocks in the middle and it blocks at the bottom, it blocks everywhere at once and it's trapped

264
00:23:59,530 --> 00:24:04,860
all the dust. Now, how do we mount the leaks? Well,

265
00:24:04,860 --> 00:24:10,200
it's a really complicated problem to model. All of these particles, all of these dust particles

266
00:24:10,200 --> 00:24:15,330
wiggling a man in your felt. But that's not what Dyson cares about anyway. They just care

267
00:24:15,330 --> 00:24:21,230
about what concentration of dust do we have? How dirty is your house

268
00:24:21,230 --> 00:24:26,850
and what concentration of dust is coming out of the other side, which we hope is zero.

269
00:24:26,850 --> 00:24:31,980
So what we want to do here is use a technique called homogenisation failing.

270
00:24:31,980 --> 00:24:37,800
And what we do in this is we take this complicated problem on the micro scale

271
00:24:37,800 --> 00:24:43,020
and upscale it so that we look at this on the macro scale. This is a bit like looking

272
00:24:43,020 --> 00:24:49,260
at the picture go into the back of the room and screaming your eyes up a bit and getting a bit early picture out there.

273
00:24:49,260 --> 00:24:54,480
So that's the idea. And in doing that,

274
00:24:54,480 --> 00:24:59,880
what we can do is we can model the macro scale picture that we care about.

275
00:24:59,880 --> 00:25:04,980
That's for the fluid flow. In this case, the fluid is a gas and the dust transport

276
00:25:04,980 --> 00:25:10,140
within our filter. But then this is coupled to the micro scale, so we don't

277
00:25:10,140 --> 00:25:15,660
lose that micro scale behaviour. So here we zoom in and we have the little fibres

278
00:25:15,660 --> 00:25:21,630
on the micro scale. And what we say is when this filter has blocked

279
00:25:21,630 --> 00:25:26,650
these fibres, I'm all touching one another. And ideally,

280
00:25:26,650 --> 00:25:33,300
we want to make sure that these fibres of all touching one another everywhere in AFL.

281
00:25:33,300 --> 00:25:38,370
Here and we have at Green Box again that we're becoming quite familiar with. Now the forward

282
00:25:38,370 --> 00:25:43,380
problem is well posed. I give you a filter. I say this is your dust concentration. You can run it.

283
00:25:43,380 --> 00:25:48,540
You can see where the dust will stay. If I gave you a filter, you would not be able to tell

284
00:25:48,540 --> 00:25:53,640
me how this thing to go into this current state. But that's what we want. We

285
00:25:53,640 --> 00:25:58,950
want to say here we have a filter that is blocked everywhere at once.

286
00:25:58,950 --> 00:26:06,450
How should I run this backwards? What filter should I have started with to end up with a.

287
00:26:06,450 --> 00:26:11,520
So this is what we want. If I plot a graph and graph that I'm going to

288
00:26:11,520 --> 00:26:16,800
show, this is the filter depth here. And what we want to say

289
00:26:16,800 --> 00:26:21,870
is that at the end point, every way it looks like this. So if

290
00:26:21,870 --> 00:26:27,510
I plot the function of the free volume, which is the whitespace hand compared with the total volume,

291
00:26:27,510 --> 00:26:33,010
then I want this to be uniform as I go from the top of the filter through to the bottom.

292
00:26:33,010 --> 00:26:38,370
And now I just want to run this backwards in time. And what helps us in this problem

293
00:26:38,370 --> 00:26:44,070
to go backwards in time is the fact that we have two distinct timescale.

294
00:26:44,070 --> 00:26:49,310
We have the time scale over which a little piece of dust wiggles its way through the filter.

295
00:26:49,310 --> 00:26:54,320
And that's about a millisecond. No. And then we have the timescale over which

296
00:26:54,320 --> 00:26:59,390
the film, two blocks, that's about three months or so. So this disparity

297
00:26:59,390 --> 00:27:04,550
in timescales that allows us to work on these longer time scale of blocking, which is the one that we are actually interested

298
00:27:04,550 --> 00:27:09,590
in, and we can run time backwards on this timescale. So that's what we're going to

299
00:27:09,590 --> 00:27:16,130
do one time backwards. And these are snapshots of the fraction at different points.

300
00:27:16,130 --> 00:27:21,170
And this is what we end up with. So sure enough, we want it to be quite separated at the top because that's

301
00:27:21,170 --> 00:27:26,850
where the concentration of dust is the highest. Less so in the middle.

302
00:27:26,850 --> 00:27:32,220
I'm quite close together at the bottom. And with this filter, if we went it forwards

303
00:27:32,220 --> 00:27:37,230
in time, then if a block everywhere at once, which is exactly what we want. So we

304
00:27:37,230 --> 00:27:42,450
these kinds of filters, you can get about four or five times the lifetime after this. And this is pushing

305
00:27:42,450 --> 00:27:47,850
to the limit of the lifetime of a vacuum cleaner. So this is something that we're exploring

306
00:27:47,850 --> 00:27:53,300
with Dyson.

307
00:27:53,300 --> 00:27:58,330
OK. So everything on Shamone so far has been going backwards in time. In

308
00:27:58,330 --> 00:28:07,560
a quite nice way. We'll go back over to these RHP again.

309
00:28:07,560 --> 00:28:12,570
I'm going to do one final experiment here, which is kind of similar to the other experiments,

310
00:28:12,570 --> 00:28:17,770
and that is I'm going to blow up some more golden syrup.

311
00:28:17,770 --> 00:28:23,060
On to this thing here. One of the things you notice

312
00:28:23,060 --> 00:28:28,900
is that it quite quickly forms a circle and which you sharing surface tension, tension.

313
00:28:28,900 --> 00:28:33,920
And then I'm going to drop another perspective plate on top.

314
00:28:33,920 --> 00:28:39,240
And I'm going to ask we. It's incredible

315
00:28:39,240 --> 00:28:44,490
how secular this is. Right now, I'm going to start

316
00:28:44,490 --> 00:28:49,830
to pull these plates apart again. I'm going to go back in time and you have to think, well,

317
00:28:49,830 --> 00:28:55,080
what is going to happen in this case? Is it going to just shrink? And we go backwards

318
00:28:55,080 --> 00:29:07,840
in time again. Well, let's see what happens. I promise very carefully.

319
00:29:07,840 --> 00:29:12,980
It's quite tricky to do. I also don't want to get it on the overhead projector. So you get something completely

320
00:29:12,980 --> 00:29:18,680
different. You get this quite pretty pattern. And if I push against it, don't regularises

321
00:29:18,680 --> 00:29:24,330
again and you go back to the circle. I see. Repeatable.

322
00:29:24,330 --> 00:29:29,790
You can get some really quite nice patterns coming after this.

323
00:29:29,790 --> 00:29:36,200
She's got Becka's fingering. So this is an example. I can't see anything. Now I have to step in Diamond

324
00:29:36,200 --> 00:29:41,380
Quest to the stage. So this is an example

325
00:29:41,380 --> 00:29:46,900
where where you can't go backwards in time. The inverse

326
00:29:46,900 --> 00:29:52,140
problem is very different to the forward problem. And this is a big

327
00:29:52,140 --> 00:29:57,600
issue in the oil industry. So let's imagine that I've got some oil down here.

328
00:29:57,600 --> 00:30:02,610
I'm actually we're running out because we've used up a lot of this. So this guy is looking by side

329
00:30:02,610 --> 00:30:07,650
because there's not so much oil. And then someone else comes along and says, I can help you. What I'm gonna

330
00:30:07,650 --> 00:30:12,690
do is I'm going to pump some carbon dioxide down here. And the carbon dioxide is

331
00:30:12,690 --> 00:30:17,910
going to push the oil and you're going to get more oil out of here. That's the idea. So

332
00:30:17,910 --> 00:30:23,250
this guy starts doing that. But you get exactly the same picture that we got over here

333
00:30:23,250 --> 00:30:28,620
because this is a going into oil. Just like here, we had a pushing into golden

334
00:30:28,620 --> 00:30:33,720
syrup. So these air pushes CO2. And it just

335
00:30:33,720 --> 00:30:39,090
pushes straight past the oil and goes straight to pay. So you've got this one guy here,

336
00:30:39,090 --> 00:30:44,150
one guy here. So this guy here is pumping CO2 down. This guy who is collecting all the CO2 that this guy is

337
00:30:44,150 --> 00:30:49,290
from Dan. And then after a day of work, I go home and think they've done a good job. But this is

338
00:30:49,290 --> 00:30:54,930
a really difficult issue in the oil industry because of this idea

339
00:30:54,930 --> 00:31:00,130
of this fiscus fingering, trying to push a less Becka's fluid, in this case,

340
00:31:00,130 --> 00:31:06,350
the CO2 into a more Becka's fluid. You always get these Becka's fingers.

341
00:31:06,350 --> 00:31:12,330
So this is an instance where you can't go backwards in time and we need to think more creatively

342
00:31:12,330 --> 00:31:17,350
about how we solve these.

343
00:31:17,350 --> 00:31:22,780
OK. So that's all I really wanted to say about going forwards and backwards in time. What I wanted to end with

344
00:31:22,780 --> 00:31:27,910
is something that Alan touched on, and that's the more humanitarian

345
00:31:27,910 --> 00:31:33,000
aspect of some of the things that I work on. So some of you

346
00:31:33,000 --> 00:31:38,670
might be aware. About 25 years ago now or so, UNICEF launched an initiative

347
00:31:38,670 --> 00:31:43,920
to provide clean, safe water for residents in Bangladesh. And the idea

348
00:31:43,920 --> 00:31:49,050
was that they would do a boreholes into the ground so that the Bangladeshis could tap

349
00:31:49,050 --> 00:31:55,260
into the ground water and drink this ground water rather than the contaminated surface water.

350
00:31:55,260 --> 00:32:00,660
In principle, this was a great idea in practise. It turned out to be a disaster

351
00:32:00,660 --> 00:32:05,750
because the groundwater is naturally contaminated with arsenic. This

352
00:32:05,750 --> 00:32:11,100
is being described as the largest global mass poisoning affected more than three million people.

353
00:32:11,100 --> 00:32:16,970
So far. But there may be a solution

354
00:32:16,970 --> 00:32:22,650
and the solution comes in quite a simple form. It comes in this readily available

355
00:32:22,650 --> 00:32:27,850
laterite soil. Laterite is very ayane, which you can see that Mrs.

356
00:32:27,850 --> 00:32:32,880
Wedd very wet soil here. Now, iron absorbs arsenic,

357
00:32:32,880 --> 00:32:38,040
which means that you can take a filter. I can fill up a cylinder like this full

358
00:32:38,040 --> 00:32:44,090
of this laterite soil. I can take some contaminated water in this dustbin at the top here.

359
00:32:44,090 --> 00:32:49,570
And this is contaminated to 100 times over the safe limit of arsenic.

360
00:32:49,570 --> 00:32:54,700
And it filters through just through percolation. And what you get out to the bottom here is pure

361
00:32:54,700 --> 00:32:59,750
water. So it's incredibly effective. But we ask

362
00:32:59,750 --> 00:33:04,880
some questions here, such as how do we know when this photo has expired? It's not like your bitter

363
00:33:04,880 --> 00:33:09,890
water filters that you replace every three months or so. But if you don't replace them, it's OK. The

364
00:33:09,890 --> 00:33:15,500
water just doesn't taste so good here. If you don't replace this, then you're drinking contaminated

365
00:33:15,500 --> 00:33:20,570
water that could potentially kill you. And you don't know until a year or so later

366
00:33:20,570 --> 00:33:26,300
down the line. And how do we upscale for a school or a community?

367
00:33:26,300 --> 00:33:31,420
This is a home filter. And this is the filter that's actually in my stocks

368
00:33:31,420 --> 00:33:36,950
in India. But if we wanted to upscale, we need to have some mathematical models to understand

369
00:33:36,950 --> 00:33:43,240
how much material we might need to use. So

370
00:33:43,240 --> 00:33:48,280
I should cheque the volume on this. But you've you've had me talking quite a lot. So I'm going

371
00:33:48,280 --> 00:33:54,610
to give you a rest by me talking. I mean, show you a video. And the video is of me talking.

372
00:33:54,610 --> 00:33:59,620
What we're trying to do really is develop mathematical models that can help purify water all

373
00:33:59,620 --> 00:34:04,930
over the world. Arsenic contamination and other content. It's been described

374
00:34:04,930 --> 00:34:10,090
as the largest global mass poisoning. It's affected more than three million people using a very

375
00:34:10,090 --> 00:34:15,130
simple, readily available laterite soil, which is just off hand because it's

376
00:34:15,130 --> 00:34:20,320
readily available. That makes it very cheap. And then you take the contaminated water. Then it passes through

377
00:34:20,320 --> 00:34:25,540
this column of laterite soil, which is about a meat torso high. And

378
00:34:25,540 --> 00:34:30,640
what you get out of the bottom is almost pure water. If you run this filter for a long time,

379
00:34:30,640 --> 00:34:35,710
eventually that filter cannot soak up any more arsenic. It

380
00:34:35,710 --> 00:34:40,810
becomes saturated. And so the key question that we're trying to address is how long before

381
00:34:40,810 --> 00:34:45,910
we need to replace this film? You cannot run an experiment for six or seven years to work

382
00:34:45,910 --> 00:34:50,980
out how long this this filter would last. So we need to have accelerated tests

383
00:34:50,980 --> 00:34:55,990
and winning them on a computer give you that. That's what we wanted to do with our mathematical

384
00:34:55,990 --> 00:35:01,150
modelling, is take something that is a very complicated problem and reduce it down to something

385
00:35:01,150 --> 00:35:06,160
very simple. But what you want to know ultimately is what is the concentration of arsenic in the water that comes

386
00:35:06,160 --> 00:35:11,920
out? That's when you really want to know. Ideally, we wanted to be able to explain the whole problem

387
00:35:11,920 --> 00:35:17,320
in terms of a single parameter. So this number relates to how much mass of soil you're using

388
00:35:17,320 --> 00:35:23,110
and the required flow rate and the absorption capacity of that facility itself. The typical

389
00:35:23,110 --> 00:35:28,420
exchange rate at the moment is about five or six years. Our predictions say they can last maybe seven

390
00:35:28,420 --> 00:35:33,430
or eight. So it gives you a little bit of extra time for these factors. The key point of

391
00:35:33,430 --> 00:35:38,680
our models is that now if you want to make another film for a particular size school

392
00:35:38,680 --> 00:35:43,690
or something, then anybody who comes in and says, I want to film with a particular flow, why do we

393
00:35:43,690 --> 00:35:48,910
just give them the number and say, this is this is how you would make that film? So what we're trying to make something

394
00:35:48,910 --> 00:35:54,070
that that alleviate some of the complications in the end, the problem

395
00:35:54,070 --> 00:35:59,380
for me, innovation is very important. Time is very applied mathematician.

396
00:35:59,380 --> 00:36:04,480
And that means that I interact with a lot of different industries. And that's a good way to find

397
00:36:04,480 --> 00:36:09,550
out exactly what the key questions are. I think as as mathematician, we can get a bit

398
00:36:09,550 --> 00:36:14,740
caught up on some of the fine detail that we find interesting. That might not necessarily be the key

399
00:36:14,740 --> 00:36:19,810
questions. So working with industries, working with experimentalists and

400
00:36:19,810 --> 00:36:24,850
the money, the scientific community is a good way to keep us grounded and make sure that

401
00:36:24,850 --> 00:36:30,200
we are innovating.

402
00:36:30,200 --> 00:36:35,360
So what's the state of play with these now? Well, we have some

403
00:36:35,360 --> 00:36:40,370
filters in family homes. We have filters providing schools.

404
00:36:40,370 --> 00:36:45,440
That's an order of magnitude of water per day. And another order of magnitude higher

405
00:36:45,440 --> 00:36:50,540
is in communities as well. And now we're looking into the removal of flow lines as well.

406
00:36:50,540 --> 00:36:55,880
And reactive dye to most of you are wearing clothing that has been made using reactive

407
00:36:55,880 --> 00:37:01,160
dye. And once this has been made, it makes a lot of wastewater, which is then just pumped straight

408
00:37:01,160 --> 00:37:06,680
out into the water stream. So trying to remove this dye is pretty complicated and it's carcinogenic

409
00:37:06,680 --> 00:37:12,070
as well. OK. So before my show, my somebody slide,

410
00:37:12,070 --> 00:37:17,590
I should acknowledge some people and all of this stuff that I do is in collaboration with lots of different

411
00:37:17,590 --> 00:37:22,810
people, as is all of the work that we do here in Oxford.

412
00:37:22,810 --> 00:37:28,030
So we that I would like to conclude. And this is kind of a broad

413
00:37:28,030 --> 00:37:33,130
picture of the sorts of things that we have looked at here and how you can go backwards in

414
00:37:33,130 --> 00:37:38,230
time with all of these. And I hope you don't want to go backwards in time for the last hour,

415
00:37:38,230 --> 00:37:43,390
which you want to go somewhere else. But I hope you've actually learnt something from what I've talked about today. Thank

416
00:37:43,390 --> 00:37:59,440
you.