So defects in shape.

The relationship is complex
they say it's complicated OK So

we've got several different cases
case one defects are immobile but

the shape changes that's a programmable
solid second case the shape is fixed but

the defects can move OK third case both
the shape and the defect structures

can evolve at the same time which is the
case for most materials for case I'm going

to tell you a little fun story of a little
collaboration that said that I did and

I did that involves defects in tiling
on curved surfaces that's again it's.

Where the shape is fixed but we can
put the defects where we want OK And

just as a list of examples.

OK so for defects in mobility of changes
we're going to talk about liquid

crystal polymers they're stretchy polymers
we're going to call them elastomer liquid

crystal blasphemers and then for the shape
fix case where defects can move will

look at some statistical physics models
of defects and we'll also look at active

liquid crystals rather like what Alberto
for an end to this is working on in

the case three like I said most materials
have defects in microstructure both

evolving with time but we're going to look
at a really interesting problem involving

a loop it best to call where the kinetic
competition between these two processes

determines what the final state is and
in the fourth case I'm going to show you

a dress that's made out of top
logical tile it sounds like fun.

OK OK So

I mentioned dislocations before have
you seen dislocations I know that this

is a very interdisciplinary department but
not everybody learns materials physics so

in a crystal structure if you have say
an extra half layer of material the place

where that half layer ends is an edge
dislocation there's also something called

a screw dislocation it's another kind
of top logical defect in a crystal and

solid So if you want to know what is the
nature of your scope of your dislocation

you have to take a walk around the block
so if you start here and you go one two

three four steps East one two three four
one two three four one two three four you

don't end up where you started if there's
a defect inside this is also true when you

walk blocks in the city right if you walk
four blocks for about four blocks and

you'll come back where you started one
of those streets ended in the middle

that's an education and that thing is
called the burgers effect or it's a kind

of top a logical charge to defects compare
an aisle eight if their burgers vectors

are opposite OK and if you nucleate a pair
their burgers vectors have to add up to

zero so inside the bulk of the total
burgers back there is fixed but

from a free surface you can nucleate or
lose the top logical charts or

here's a little movie little cartoon
showing you how an education can enter

from the edge OK and also an education
can annihilate at the edge in this

case it leaves a mechanical
scar it leaves an atomic step

on the surface where it came in OK So
top a logical charge can enter and

leave through the surface but it otherwise
cannot be generated inside that's why we

call it a charge it has nothing to
do with electrical charge except

that it is conserved so this is the nature
of top a logical defects in general and

many kinds of condensed matter.

Let's also talk about top logical defects
in non Crystal and solids in particular in

soft materials made up of Rod
shaped molecules OK so here we have

the phases this is just a cartoon version
of the phases of liquid crystals although

in the cold side you might have a crystal
phase all the way on the hot side will.

An isotropic phase where both
the centers of mass are disordered and

the orientations are disordered but
in between we have what's called

the mezzo phases these don't exist for
sphere like molecules they only exist for

an isotropic molecules that
are the long gaited like a rod or

flat like a cracker and in particular we
can have a magic phase where the long axis

of the molecules is aligned and has long
range order we can have a smack tick phase

where we have layered sort of stacked two
dimensional oriented liquids we can also

have tilted phases in
the phase you have layers but

within each layer the molecules have a
tilt with respect to the layer we're going

to need that when a little later so don't
forget that when so these are mezzo phases

if you have a cell phone in your
pocket and it's not the new i Phone.

It might have a liquid
crystal display in it and

chances are it's in the magic phase
it will have a car rolled up and

added to it so it has a tendency to twist
that's called a cola staircase didn't put

it in my picture but you should know it
exists OK So top logical defects can also

arise in oriented liquids in particular
in a magic liquid crystal if you think of

the rod like molecule as having a head and
tail that are equivalent to each other so

there's no difference between the two
ends then the lowest form of top

logical defect is the lowest energy
one is called a plus one half or

minus one half defect if you have a smack
succeed it has a tilt it's a plus one or

a minus one so I need to borrow
a pattern maybe I'll just here's one.

OK So just like with the burghers vector
you have to take a walk around the block

to find it you have to do the same
thing with the defect in oriented.

Liquids So here if I take my pencil and
point it along this axis and

I make a walk around the defect
my pen rotated by to pry OK And

in this case it rotated in
the plus direction but for

this one the pen rotates in the minus two
pide direction so this is a plus one and

a minus one if I were a little
bit taller I could do.

Same thing for the ones on the top and
you'd see a plus one half and

a minus one half OK so
you can do it two dimensions

you can nucleate a pair plus what happened
minus one house or annihilate a pair or

you could nucleate a pair of plus one and
minus one or annihilate a pair but

you can only imbalance the net top logical
charge if you bring it in from a free

surface if you have a system of
periodic boundary conditions or

otherwise closed boundary conditions no
defect charge can be generated You can

also put closed boundary conditions
that capture a defect So for

instance if I had a circular system and
I said all my spins need to point parallel

to the wall on the edge of my circle I
would be trapping a plus one defect inside

so top logical charge is it
conserves quantity in the bowl.

OK now we're going to start talking about
how these top logical defects make shapes

So let's first talk about what is
a liquid crystal elastomer it's a polymer

that has liquid crystal molecules attached
to the main chain they can be dangling

off the main chain or they can actually be
part of the main chain like a string of

sausages here I've just shown you
a picture of the side chain varieties so

these long ride like molecules we call the
mezzo gens because they form mezzo phases

OK And in these materials so
in this little video do you see

this little thin almost transparent thing
in the middle what's going on is the coil

is heating when currents running through
it and not heating when currents not

running through it and the material is
stretching and shrinking spontaneously in

response to changes of temperature what's
going on is that when the material is cold

the molecules form that pneumatic phase
and they actually stretch the polymer

chains out and when you heat them
up they go to a less ordered

state in her case I visualized it as
fully isotropic it doesn't have to be all

the way isotropic it actually
makes the material shrink so

in this case the cold state is the long
state the hot state is the short state

material shrinks when heated and I don't
know when I was growing up my mind.

Told me that everything expanded when he
did so I was come surprise to learn that

OK and the other issue is that the
material shrinks and contracts along than

a magic director so it's a differential
shrinkage in the different direction so

it's going to shrink and grow along
that one axis OK but that axis can be

patterned it doesn't have to be uniform in
the sample So here's a picture where that

special axis has been patterned to
make a bull's eye make a circle that's

a plus one defect OK And there's two ways
to make something like that the way that

experimenters have been using for
a long time is called blue printing and

the idea is this we can pattern
a glass substrate to align

a liquid crystal parallel to a special
direction that's done chemically and with.

A thin beam of polarized light that's used
pixel by pixel to write the pattern on

the glass so we write that same pattern
on the front and the back surfaces put

the rod like molecules monomers
the cross-linking agent in between.

And lo and behold poof after the material
is fully cross-linked you remove

it from the glass and then the magic
director has been patterned so that it's

not uniform in the body and then when you
heat it it's going to change shape just

very recently that same young man Taylor
where now a faculty member at University

of Texas at Dallas figured out how to make
patterns in the magic director by three D.

printing all they call it in
reference to Sabbat is where four D.

printing because the material changes
shape with time when heated and

so here is for instance a material
that he fabricated in the shape

it's got some positive curvature
some negative curvature and

when he did change the shape OK So
the question is I want to

model how you go from a pattern of
the pneumatic director to a shape

of the sample this is now a problem at the
lab scale it's a macroscopic problem we

can't get an answer from doing
molecular scale simulator.

And so what can we do so we're going
to do finite element simulation

how many people here have ever written
a finite element code yet a we have one

to how many people have ever used a finite
element called code like console.

OK So writing I find it on the code is
not easy so we decided to write our

own because we wanted to be able to do
any kind of multi physics we wanted so

what we did is we started with an energy
that depends on the strain right because

it cost energy to stretch the material we
have to have a description of them out of

order and then coupling between the strain
and the State of them out of order so

what happens in this material is that we
have a blueprint of pneumatic director and

when we heat the material the state
of pneumatic order changes

in particular the scalar order
parameter that is a measure of how

well aligned the liquid crystal is
drops when you heat the material.

And it goes to zero at the Mattick
isotropic transition so

this is what we call dancing tofu this is
just to show you that we know how to model

the dynamics of an elastic body.

OK So
what happens when you heat this thing

when you heat it the plus
defect turns into a cone.

Right because the material is expanding

along in a magic director sorry it's
shrinking along the magic director and

it's growing slightly in the other
two directions What do you think

will happen with the plus one defect
when you cool it the other way and

the answer is it develops negative
Gaussian curvature it becomes a saddle.

Right OK So just as another
example here's another simulation

one of my other students and you can you
did showing how the material goes through

a transition from flat to a cone but
it goes through a somewhere

a state first that's because the material
in the simulation has a finite thickness

which gives rise to that funny in between
state and this is an experiment from

the broker group at University Technical
University and in the Netherlands showing

what the shape is this is a similar
experiment from the group there for slab.

So.

What if we have higher order defects there
is more to top logical defects than just

plus one and minus one what other
types of shapes could we get

well the group at the airports lab decided
to try to do all these exotic more

complicated defects there's the plus one
but three plus two plus five halves and

these are their artist rendering of
what they think it would look like but

if you look at the actual
pictures they look like you took

the plastic that your sandwich was wrapped
in and laid it on top of a glass of water

it's really hard to see any structure
there they look kind of disordered looking

it's not really easy to tell what's going
on so we decided to simulate these so

here's actually a minus two defect this
is what a minus two defect looks like

if I take my pen and
runnin around you'll see it goes around.

For pi times.

And it makes this really interesting
shape that looks like something you would

maybe make orange juice in.

Or serve deviled eggs I'm not sure which
OK but look at this and look at this and

you say wow those testings
are really really different How come

the experiment doesn't look like
the model and I will tell you why because

this material has the director
uniform through the thickness so

there's nothing to break the symmetry
between the top and the bottom so

every little section of the sample
could pop up or it could pop down and

if in the experiment half of them pop
up and half of them pop down it'll be

all disordered in our case they have all
popped in one direction so we decided.

To explore that to figure out
what could the experimenters do

in order to make that happen so
here's a minus four defect and

even more convoluted thing has many little
sections each of which can pop up or

pop down and some fraction of them popped
up and some fraction of them pop down and

it's all disordered looking so
we said maybe we can break the symmetry

simply by heating from one side so here's
the simulation where we heated one side

first and then the other and then it
always uniformly Pops in one direction and

we can get a symmetric
lower energy structure.

OK so that the case where the material
can pop up or pop down has also been seen

in experiment and actually you can just
take your hands and pop them up and

down right so this is you can say it's
a bug because it looks disordered or

you can see it's a feature because it has
many medicine able States to fence what

you're trying to build OK And

then the other question is whenever
anybody talks about shape transformations

we always talk about origami but
it's really hard to make origami

at this point we're just trying to fold
a box just have the four edges come up so.

Lawrence Don from the group
said Well we're making plus one

defects we're all that magic directors
point out in a circle that's a radio plus

one defect sometimes we make one where
where we have that bull's eye and

then a magic director is known as a
musical stage he said well what if we just

made one will make those two pieces of
glass to make one of them radio and

one of them as a musical he called it the
rather musical It seemed like a silly idea

you know a drunk graduate student on
a Saturday night with nothing better to do

and they discovered that
it folded really nicely so

we decided to use the same design in
a simulation to see if he was right and in

fact he was we can make so this is radio
on one surface as in you fly on the other

with the gradual twist in between and
it folds very nicely into a box

OK I'm a statistical physicist by training
has anybody here studied the X.Y.

model it got a lot of press because

you know the Nobel Prize was awarded
was that last year the year before.

The year before so what we know about
the X.Y. model it has top logical

defects right it has more to see so this
is just a little money Carlo simulation.

You might remember so
if you're above the K.T.

transition the transition you'll have
a population of the facts in this case

the materials being quenched below
the cost of that stylus temperature but

it's been quenched fast enough that
the defects couldn't all paranoia late and

a few of them are still stuck in a bed
of stable state are you familiar with

the concept of the barrier from metallurgy
that tells you the energy barrier for

a dislocation to move through a crystal
has to overcome a little energy barrier to

get from one local minimum to the next
the same barrier exists in the X.-Y.

model there's a little energy barrier for
defects for top logical defects

to move from one spot in the lattice
to the next spot to the next spot and

so paranoid elation can actually fail
to occur if you quench the system

too fast because the defects are trapped
in their little local minima OK so.

It's not what I wanted to do here we go
question what happens if you put the X.

Y.
model on a curved surface so

here's a picture of an X.

Y.
model on a sphere.

If I ran the system you know
raise the temperature and

then quench it down do you think we
could get a state that has no defects

no not going to happen why is that.

Because.

There OK so the gas beneath there I'm
also known as the hairy coconut theorem

the nettop a logical charge for
top a logical defects in a curved tree

depends on connectivity of the shape of
the genus of the shape genus is roughly

something like the number of handles
a sphere has no handles that's genus G.

equals zero but we can have a donut or
Taurus which will have to equal one or

we can make a figure eight
like if your niece or

nephew was celebrating
their eighth birthday and

you gave them a stuffed animal eight that
would be a figure eight has to handle so

would have a genus minus two so we can
calculate the number of defects that there

would have to be so for
a sphere two minus two D.

gives you plus two for
a donut you get zero and for

a thick figure eight you get minus
two Can you guess where the defect.

It would go in each case.

OK for a tourist it's easy because
there aren't any what about for

a sphere the two defects repel from each
other so they should go on opposite sides

of the sphere how about for
the thick figure eight where do you think

the defects would go I think they would go
in the hips of the eight because that's

where the curvature is negative the local
curve curvature is negative OK So

here's the coconut you can see that
Coconut has hair where the special points

on the coconut one at the top right
there one at the bottom right there.

Those are places where
the hair comes together

Did anybody here ever watch the old
television show The Addams Family.

Do you remember there is a character
called cousin it who has a lot of hair

the hair is so much that it goes
in front of Cousin its face

I think Cousin It was gender indeterminate
non-binary cousin it is non-binary.

So the question is there's that special
point at the top of Cousin its head and

what it type of top logical
charge is that what's the charge.

Plus one plus one OK and
if Cousin It called himself into a book or

herself into a ball and the hair was
meeting on the other side with that

what would the sign of that be where all
the hair comes together when you think

it's another plus one right it
can't be mine it can't be minus one

that would be odd OK and
back on the theme of old television

shows who watches the original
Star Trek series but Captain Kirk and

Mr Spock Do you remember the famous
episode The Trouble With Tribbles OK So

here's the Tribble you can see the special
point there with a Harris pointing out so

if the Tribble is really frightened
because a Romulan is close by and

all that Tara standing on and it has
no top logical defects it's completely

uniform and shape right there's no special
points but if the Romulans go away and

the trouble comes down and
you comb its hair it would be just like

you would have a special point
where all the hairs going out and

you could have another special point
where all the hair is going in both Plus

when the facts what if you decided to
comb the hair going from east to west

around the sphere and you have one defect
on top that winds around like this and

went to effect on the bottom
still both plus ones OK Could

you make a minus one defect on the sphere
and the answer is yes you can but you also

have to make an extra plus one defect
because they have to add up to zero OK.

The logic of the Fix OK So
when we put the X.

Y.
model on a rigid sphere so

the sphere is not going to
change the shape when the system

first comes down from high temperature and
we're quenching we see some.

Net number of defects so let's see if you
can see these pictures can you identify

which one is positive and which one is
negative Can you see the lines well enough

that once definitely a plus
one what about this one.

That's definitely a minus
one what about this one.

That's right so they've got to be some on
the other side because the net charge has

to be plus two after a to Neils
there's a plus one there and

there's another one on the other side so
why aren't they next to each other and

the answer is because it's like
two angry people on a small planet

they hate each other and
they go to opposite sides.

OK what if we put the actually
model on a Taurus remember

that top logical charge is now is zero
we could have a defect free state but

when we find when we heat the system up
high temperature all disordered cool it

down below the key transition to fix
don't parent I away they get stuck OK So

what happens is positive defects claiming
to the region a positive gassing

curvature negative defects cling
to the region of negative Gaussian

curvature OK And Alberto is seeing
this also in his experiments on active

matter so the moral of the story is

surface curvature acts as an external
potential for top a logical defects so

the defects will move to regions
that minimize their energy.

And positive defects have a lower

energy in regions of positive Gaussian
curvature and vice versa for negative.

OK Let's talk about active matter this
is a simulation of spaghetti that.

This is a flex of
flexible active elements.

On a flat surface and

what can you see from that you can see top
logical defects what charges do you see.

This isn't a magic so
we tend to see plus one half and

minus one half the facts they're moving
fast so it's kind of hard to see them but

for instance I see a plus one
half right there moving around.

The minus one hops tend to
move much less quickly and

the question is what happens if
you put that on a curved surface.

So like if you're taking your pet
snake for a walk in the hills

what well in this case
many many pet snakes.

I'm sorry what.

Fish worms.

It could be worms.

So the question is what happened so

this the shape of the surface looks like
this sign can't sign K.Y. kind of shape.

This is the work of my grad
student Michael Farkas So

this is the non Act This is
the non active system it's just

a magic liquid crystal on a curved
geometry here's the same system active.

Can you tell the difference.

OK So in this case again

the shape of the substrate represents
an extra no potential for the D.

Fax it also it just acts as an extra
potential for the system anyway

that the particles are avoiding the tops
of the mountains so if you had a pet snake

I'll name him Seymour if you took your pet
snake Seymore for a walk in the mountains

the pet snake might say please don't take
me to the top of the mountain it bends my

back so much I don't like this I don't
like to call their OK so they tend to

avoid the tops of the mountains they avoid
regions of high grass and curvature and

what they really like is the flat
pathways in between See like.

So there those are showing.

The flat places and so

you can see where the the top of the
mountains are the pneumatic liquid crystal

stays away from there because there really
is a chemical potential for the crystal

to bend on the top surface and likewise
here you can see they also have way.

And so this is a graph just showing
the density as a function of position and

you can see that the at
the the taller the mountains.

The more the active liquid crystal
avoids the top of the mountains so

again the shape is here controlling
the density of the particles all together

from my conversation with Alberto for

us today we're also going
to analyze the simulations.

To show that the defect density is also
affected that the positive effects go

to regions of more positive
Gaussian curvature and

the negative ones to more negative.

OK What about stripes stripe
patterns like this phase.

Can also form on curved surfaces this is
just a little toy model I fould around

with it's a lattice gas with a separation

fifty fifty materials and
in this case the.

Interaction occurs over a distance
out to length five if you don't mind.

The heterosexual metaphor if every
man wanted to be surrounded by

five by women out to a distance five and
every woman wanted to be surrounded by men

out to a distance five this is how they
would pattern themselves on the planet.

And you can see that in this case we have
a defect free Taurus but you can also

have a Taurus with defects so striped
phases here there's a plus one defect and

the end of the yellow brick road on the
other side is another plus one defect for

stripes again the Taurus
can be defect free but

if you have a fat enough Taurus
you'll definitely get the facts.

OK if you look at that X.

Y.
model with just arrows it gets really hard

to visualize when there are very dense
it's hard to see those little arrows So

another way to visualize them as if we
were looking at a liquid crystal through

crossed polarizers Has anybody here
looked at a liquid crystal through cross

polarizers you see the thing called
the texter OK so the defects.

If you're looking through two to cross

a plus one defect would have four
dark brushes as you go in and.

Out of range for each polarizer but
you can't tell from just looking through

the cross polarizers without moving
them whether a defect is positive or

negative you actually have
to rotate the polarizers and

I just wanted to teach you that also
here I've shown in the plus defects in

green the minus defects in red you can see
that kind of daisy chain positive negative

positive negative opposites attract like
signs repel the energy goes like a log.

Actually minus log and the force goes like
whenever are so attractive between defects

of opposite sign repulsive between
the effects of the same sign so

here is just a little movie
in the texture visualisation.

Starting at a high temperature and
coming down.

So you see many many defects and then they
will start to paranoia late so the number

of the effects drops I think there is
one last annihilation that happens maybe

around here somewhere maybe that pair
maybe that pair that's this one there.

OK And then I rotate the polarizers
you see what's happening

it's a virtual polarizers because
this is a simulation so the defects

that rotate in the same direction are plus
ones when you rotate the polarizer

if they opt rotate the opposite way that
means they're the negative points so

that's how you can see top
the logical defects in an attic OK so

now I'm going to tell you case three
a situation where both shape and

microstructure are bobbing
at the same time and

this is a story about another
kind of oriented liquid.

A little bit.

Single you need it so
it's you need a limb our.

Best of all.

This is experimental work by Linda Hurst
from the University of California Merced

said this is from some work we did
together in two thousand and three so

this is this nice beautiful
smooth water balloon of

a union Mellor best of all it's a material
called D.P.C. it's a single Lippitt

it's not a mixture of lifted and
then she cools it off it makes the shapes.

Those don't look smooth and round anymore
they look all complicated they are kind of

crumpled and we're trying to figure out
why these materials have the shapes OK So

the nice round smooth one is an un

tilted liquid crystal phase called
El alpha phase so in this face.

Both leaves of the by layer have
these long liquid molecules

aligned on average parallel
to the layer normal OK so

it's completely defect free there's no
special points it's just a water balloon

OK when it's cooled off it's going into
the gel phase also called the elevator

problem phase which is tilted and now that
tilt erection is rather like doesn't it's

hair it has a direction OK it has
a direction has a happy action and

there's no way to comb the hair on a
sphere with a uniform without any defects

we know there have to be defects OK but
i still doesn't explain the.

Structure.

OK So here's what D.P.P. looks like at the
molecular scale here is that alpha phase

here is the elevator prime so you can see
it's tilted there's no way I can simulate

that system at the molecular scale you
know something that's microns across so

someone has thought about this before
some very smart people in fact

including Tommy Bensky And
Fred Macintosh who thought about

what happens if you have a vested call and
it's an insult to phase two it has to have

two defects Well if each defect makes the
material want to curve a little bit more

then it's a bit of a sphere I should
get something shaped like I don't know

a watermelon a cucumber something
a long gain it right and

my friend great Cooper working with
Bob and I think with their student.

Also calculated shapes like that and that
seems like what you should definitely get

OK but if you compare that to Linda's
actual experiment it just doesn't match

but this doesn't look like a cucumber it
looks more like Australia I mean it looks

like something OK So the question is
what's wrong with this picture well

maybe when the defects form to actually
change the shape of the material OK so

it's not just that the material goes to
its ground state something has to happen

so maybe something about that interaction
with the shape actually stops them

from paranoia leading So the system traps
some defects so when I look at this

I might say hey maybe there's a positive
defect on the nose of that pretrial and

maybe there's a negative defect you
know in the trough of this of this

curved region there so we wanted to figure
out whether that's a mechanism that could

really work and we wanted to simulate it
so our idea was that there are competing

timescales if defect motion is really
really fast so you take the system

from the UNTIL to phase into the tilted
phase defect to call over the place

just like that simulation
I showed you of the X.

Y.
model defects or call over this place and

they start paranoid elating if they're
paranoid I only really really fast

we would get to the state like that
sphere that just had to defects and then

the whole system would stretch out and
make something probably OK So that's it.

Defect motion is fast but if the effect
motion is slow compared to the rate at

which the whole the whole shape of the
best are called to forms then those extra

defect pairs can get trapped so lots of
defects would form initially yes just.

As far as I know they are always paired.

And that is a good question it is that
there is such a strong interaction

between the two leaflets that their angle
of orientation is always the same and

I can only say that because
Linda Hurst visualize by putting.

A dye in there that she could look
with polarizers So I think they're

always the same so our idea then is
that we could trap those defects and

they would be in a medicine able state and

the system would never get to the ground
state which is a long ellipsoid.

OK so
how can you say experiment to look for

defects so Linda Hurst put a dye
called large van in the system and

she looked with polarizers and she
convinced herself that there were actually

irregularities in the dye
orientation to tell her that where

this was a vessel that was fused onto
a mica surface and she saw these pointy.

Prichard engines and
she convinced me that they were in fact

top logical defects there in
the orientation of the lids OK but

if I wanted to see that in a simulation I
know how to do molecular simulation I mean

molecular dynamics is not that hard but if
you have something that's microns in size

that would be an awful
lot of molecules and

I need something really really
REALLY course grained so

with molecular dynamics is great for
looking at a little patch of molecules or

a very small assembly but a big best
of coal is beyond our ability to do

even course grain models OK so I needed a
really really REALLY course brain model so

I found a good course brain model in
the literature from Julie who I think

is at MIT and so
he was trying to model the make

a model of biological cells and
he wanted a really simple model for

the cell membrane he didn't even want to
model two layers he said let's just make

a coarse grained fluid and his model
looked like a tomato with a toothpick in

it it's a point mass with
a vector degree of freedom and

those two Things like to
assemble like this and

they don't like to assemble like that.

Or like that so you put him in space and
they will self assemble into a pancake He

even added another term in the potential
that said I want my vectors to have some

angle with each other and then they would
spontaneously assemble into spheres

which is just an awesome model so the
point is if you take here your toothpick.

What I wanted to do is say OK this is
a nice model of a liquid membrane but

now I need to have a tilt direction I need
another factor degree of freedom and so

we did is if you've ever been to a Fourth
of July picnic you might have your

your cherry tomato with your toothpick and

then a flag the flag is that extra
degree of freedom that's like an X.

Y.
model superimposed on a two dimensional

liquid OK so now the system can
have top logical defects so

that extra spin is defining here a plus
when defect in here a minus one defects

OK so now I think I will skip
I will just say about for

anybody here who's a simulation geek I
tried doing this with Leonard Jones and

the winner Jones potential are familiar
six twelve potential just crystallizes so

easily in two dimensions that if I was
able to get the system to stabilize it

would just crystallize too fast the genius
of Julie and his coworkers as they came up

with actually a softened potential that's
eight for so it stays liquid in the plane

it's a really great course green
model of the liquid membrane.

And adding that extra

degree of freedom lets us have these top
illogical defects so this is the initial

state here is the quench state with
all these defects Let me show you.

I need to see the video.

You will skip all the details so
here is the best to cope with X.

Y.
order Linda Hurst was

making her visualisations with just
one polarizer instead of two and so

a plus one defect here only has two
dark brushes instead of four so

here you can see two
different visualizations

this one is showing orientation this one
is just showing color that tells you.

How far from the center each
part of the vessel is OK and

this is again a single
layer thick simulation and

where you see a red spot
here that's a protrusion and

there are little black dots those
are the defects so what happens is

wherever there's a plus one defect to
the material protrudes a little bit

where there are there is a minus one
defect the membrane flattens a little bit

that inhibits paranoia elation OK so why
can't the positive defect and the negative

defect paranoia late it's just like on
the tourists right the positive effects

like to live on the outside the negative
effects like to live on the inside so

I like to say it's like if a bird fell
in love with the fish it's very nice but

where would they live the positive
effects can go in the negative

effect area the negative effects can't go
in the positive gassing curvature area so

they don't paranoia late so
here's the difference is that the defects

themselves are generating the defamation
now for a sphere the Gaussian curvature is

always already positive so the negative
defects don't actually make a saddle they

just flatten it a bit but
again that repels the positive effect so

you can see when we're done we have
appreciation here and a protrusion here

there are several of them so we ended up
trapping a total of ten defects which is

not a lot so we didn't get anything so
disordered as Linda her six parents but

we demonstrated the principle
that the system can get stuck in

a medicine able state because of the shape
of pollution around the defects.

OK And I'll skip that I will also say
other materials also showed this kind of

case three where are defects move and
she moves this is another simulation

of a liquid crystal elastomer but one that
has the phenomenon of soft elasticities

which is to say under the influence of
strain the pneumatic director can also.

Rotate and you get a very large
plateau in the stress strain curve so

in this particular case the material
starts with the name and

Matic director north south and
as you stretch the material east west.

It breaks into stripes where one which
one stripe the material rotates left and

the next minute rotates right OK so
that striping instability is

just another example of the material
where the shape changes and

the micro structure
changes it can also be.

A poly domain to Mama
domain simulation OK so

what I would say about this general case
three where both effects can move and

straight can change is that it
represents the holy grail of material

science if you can predict the evolution
of the micro structure and

overall macroscopic shape change that's
really the goal of theoretical material

science these days OK case for it this
is desert my friends OK so I heard.

A wonderful talk about a at a science cafe
in Santa Barbara where I learned this

thing about fabrics equal lateral hexagons
can be sewn together to make a flat sheet.

OK no problem they fit beautifully you
know you can't tile the floor Pentagons

but you can tile the floor with toxic
ons no problem you can add Pentagons and

you can get positive gas in
curvature to make a soccer ball.

Right that's familiar but I learned
from Sabet is wonderful talk was this

amazing thing that she built called the
Klein quartic Is that how you say it it's

twenty four have to go on seven together
into an object that has negative gas and

curvature everywhere OK So we really
enjoyed learning about the geometry of

fabric with us at the science cafe was
a costume designer named Andrea Hsu it

she happens to be married to a physicist
and was in residence at the care T.P.

her husband was so she came to
the talk and so I turned to Andrea and

said hey Andrea if we could mix
together hexagons Pentagons and

how to guns and put them in just the right
places could we customize a quilt address

that would print that would that
would fit a woman of arbitrary shape.

OK So
this is a very specific tiling problem

can we fit a human form OK So
Andrea brought.

A dress form to the CAN T.

P.

we had a wine and cheese party
where we had many many shapes and

we made a pattern for
the dress out of paper and

I don't know can you see the numbers
there is kind of small That's a seven.

That's a six that's a five so there's all
fives and sixes and sevens we tried adding

some squares didn't help we tried adding
octagons didn't help we decided five six

and seven was the best combination and
then Andrea Hsu we went home and

she started cutting out the pieces and
she made the dress and there it is.

OK So this is just a little
demonstration of tiling but

let's try to do a little bit more thinking
about where this project would go.

We can get a shape of a human
from using a body scanner

as it happens Kent State has a fashion
school and a tech fashion lab and

I just contacted the head of the fashion
lab and he sent me a point cloud for

the shape of a volunteer who went in
the scanner then you can analyze you know

do in Monte Carlo simulation to figure out
where to put the equal Admiral polygons to

best fit that shape then we could
manufacture a kid that people could put

together their own dresses from parts
these days people don't like to use sewing

machines so
this is coming soon to a science fun.

Store near you.

OK so here are some of the students
who've worked with me on these projects

Andrew Konya is one of those people that
made the transition from statistical

physics or in this case materials
physics into artificial intelligence

he started a wonderful
company called rematch

based in New York City by stuck by
stock trust me he's going places

him in his Pinto is just finishing up post
stock at Columbia but Dell and bonga.

Also made the transition into a I work for
a large bank and

is probably monitoring your transactions
right now to make sure they're not

trouble and my carcass still in school
Gendang went to a hedge fund so

my students are all wealthier than I am my
husband Jonathan Salinger is a co-author

on some of these papers and Linda Hirst I
mentioned did the experiments said there's

a complete list of references at
this U.R.L. If you're interested and

I will just say my conclusions are OK
interactions between defects and curvature

on a rigid substrate gassing curvature
serves as a chemical potential for

defects right so we expect that positive
defects migrate to regions of positive

curvature and might vice versa.

On a blueprinted Matic polymer where
the defects can diffuse or annihilate

the positive effects induce the gas in
curvature positive gas from curvature

negative effects induce a decrease in gas
in curvature this gives us a programmable

solid so that your trajectory is
encoded in the director field.

So that it also pointed out today
that when you knit or crochet or

weave a structure you can put top logical
defects there to that also in code

a shape so there's all kinds of ways that
top logical defects hitting coach shape

OK on the flexible membrane with tilt
order which was our Are you Neil Mellor

best to call kinetic competition between
defect and aisle ation and shape change

can determine whether the system ends up
in a ground state with just two defects or

in a disordered state with
lots of medicine able States.

Many defects present and in general this
idea that predicting the simultaneous

evolution of microstructure and

macroscopic defamation is the holy
grail of material science and

I trust that the rising generation that
here that is here especially people doing.

Materials theory computational
material science

are going to make great
progress on that and

your career thank you very much I'll
be happy to answer your questions.

It was relatively low you may have
noticed that there was some faint

separation right.

So that if we can just write we
can put more worms or fewer worms.

That particular project was done by
Michael Varga in residence with Luca Geo

me and Biden in the Netherlands so
I wasn't there

to say hey add more liquid crystal but
that project's not finished yet so I think

we will probably increase the density so
we can cover it but active matter tends

to say to have these giant density
fluctuations so matter how full you make

it there will always be a moment in time
when they face separate a little bit.

Yes.

I guess I

would say it is a local
energy minimum I mean in

the simulation we ran the heck out
of it millions of times steps and

it never it never reverted to
the ground state I would only.

That's a very interesting question I think
it might be that there is a magic number

and it's not clear that the magic
number has to be two but

you would you would think that the lowest
energy the state with just two.

Would be extremely stable so for instance
if we if I could get Linda Hurst to take

that defect rich structure and then use
optical tweezers to stretch it a little

bit first of all it would probably pop so
I don't know if it's even possible but

it might actually then annihilate
all the rest of the defects I mean

we could also just swallow it and then and
then see if it got rid of the defects.

But I would say it's certainly in
a very deep med is stable state

I just don't I don't know if I
can call it a ground state but

it's a very interesting question
well thank you very much.