OK so.

So I'd like to tell you a little bit about
some of the work that we've been doing

trying to exploit disorder and
the idea here is to design function

into mechanical networks and so this has
been a project that has been going on for

a few years of spearheaded
by Andrew you and

collaborators at University of
Pennsylvania and some people at University

of Chicago my student kneedeep Machina and
postdoc and our bishop Berger and

then some people from the engineering
department had Chicago Daniel Reed in one

to Pablo and I'll tell you about
their work as we go along.

So what I want to ask is

does disorder matter to the material
properties of the system and

so what I want to compare for
example is what happens for

jam glasses in comparison to
what you get in a crystal and so

up why I'm interested in this is that you
know we study glasses all the time but

if you know when I was a kid and

I was told by a glass was one to
the window and knocked on the glass and

it was solid just like everything else but
they told me this is very different and

so when well why is it so different
I mean and so well if you go to an X.

ray machine and you take X.

rays of it you'll see that
the structure is different and

somehow this was supposed to be so
terribly deep and

I never understood why I should care
if that was the subtle thing that

is the difference is just that
the particles weren't in organized places.

Organized in a Christian way then
why is the glass interesting and so

the idea here has been to try and
find out other ways in which glasses or

jam systems are more physis tems are
actually different from what you get in

the crystals and so there are a couple
of things that we know are somewhat

different between crystals and
glasses and so one thing is.

That the exit patients that you get
in crystals you know those very well

they're the by law for
the specific heat at low temperatures T.Q.

case it's just saying that the low
frequency modes are normal modes of

a long wavelength plane waves and
what we know is that for.

A game systems or
glasses that you have many more X.

A Taishan particularly at low frequencies
and so this is one thing that

makes things different between glasses and
crystals but are there other things that

are special and so what I'm interested
in asking Is Ken thought or.

Provide some unique functionality that you

wouldn't easily be able to
get in a crystal and so

what are some of the things that we know
about well we know that if you have a.

You know a glass or amorphous material
that there are certain things that

it has that is because
it doesn't have this.

Perfect structure we
don't really know what a.

Defect is and we have grain boundaries and
so this provides certain kind weaknesses

for the crystal that you don't necessarily
get in the glass and so this is.

You know.

This water is more forgiving
in that way that is you don't

have failure due to those kind of modes.

Another thing that we know about glasses
and jam systems is that your many many

quibbling ground states many more than you
get in a crystal and so this can lead to.

Adaptable features of the system
that there are multiple paths for

creating a certain kind of function this
is the kind of thing I want to explore

today and then there's one thing that
I just want to mention because it

came up in a lot of things that we've
heard about during this this conference is

that there's a common feature that
seems to appear in all sorts of.

Disordered systems which is this
idea of constraint counter.

And so we've seen that in case of
the origami that we've heard about we also

hear back in faint counting when you talk
about jamming or networks or glasses that

cetera and so this kind of idea is
throughout a lot of disordered systems and

so one question is well is this
something that you can grab ahold of and

therefore make some kind of
functionality out of this aspect and so

what I want to ask here is can this kind
of flexibility that you have in the glass

be harnessed in certain ways and

so there are two things on
the talk about global features and

also local features and so these
are the two things I want to mention.

And so here I want to focus
specifically on networks and so

I think networks I'm going to talk about
are derived from jampacked things and

so I don't think this is
actually necessary for the.

Conclusions I'm going to reach but they
are but that is actually what the studies

were and so that's what I can tell you
about concretely and I think a lot of

these things can probably be generalized
to more general kinds of disordered

materials so how do we make these
networks so we take a system of box

filled with frictionless shears that
are soft that you can squeeze together and

so you put these particles in a box
randomly and then you let them.

Go to their push each other apart because
they have repulsive interactions between

them until they no longer interact if
they can or if the vine is too small

then they will end up in some kind
of mechanical equilibrium and

this mechanical equilibrium will be
disordered in so this is what we have on

the left hand side here is that
these are the spheres that for

two dimensional jam packing and then what
we do to make this into a network is we.

The centers of those fears and
we put nodes at those points and

wherever there's an overlap that means
an interaction between two particles we

replace that overlap with an unstretched
spring between the two parties and

so this is what we get on the right so
we are racist for

years as fears are no longer there and
we have just this network

of unstretched Springs between nodes and
so that's the system that I want to talk

about today and see what we can what kind
of functionality we can have in that case.

So as I said I want to talk about
two things global response and

the local response and so the global
response I want to just talk about

the module lie of the system so
the bulk modulus and

the sheer margin so want to remind
you briefly about what those are so

the bulk modulus is if I take
a system of the bulk system

the bulk modulus is I squeeze
it in all directions equally and

that cost a certain amount of energy
to do that the energy cost to squeeze

is a measure of the book market should
book on just as a measure of the energy

cost to squeeze this thing
compressed in all directions so

that's one of the modulus the other
modulus is the sheer modules that

I want to talk about and so
this is I take this system and I.

Find shear it in this case
it's just simple sheer and

again moving it in this direction
is going to cost some energy and

that energy one way of characterizing
the energy is that your Majesty math

the energy it takes to give it
a unit here in that direction so

these are the two kinds of modular life
that we're interested in in this case and

one of the things that you should.

Think is well how big
are these two modules I.

And the two module I are typically in
crystals comparable to one another and

why is that well simply that I have to
if I look at the microscopic I have

two atoms and I'm pushing them together
this way well they have to come up against

potentials of their nearest neighbors and
so that one energy scale the other thing

is if I do it your mind just will maybe
I'm coming at this direction instead and

while still going up against that same
potential between the two particles so

it's going to be the same order of
magnitude it may be off by a cosigned

theta I don't care about or
close on data here the direction which I'm

moving these things that's of order
unity so that your module and

bulk of crystals are typically comparable
to one another and so this is the.

What we typically get for
Crystal and behavior and then

I've been talking about these two things
because the one thing that we heard about.

In the first day was the side
DIA of the possums ratio until

I just want to remind you what the possums
ratio is possums ratio is a measure of

you know if I take a material and
an ordinary material and I

pull it in one direction it gets narrower
in the direction just as you showed us on.

Wednesday and so
this is the normal material and so

this has a positive possums ratio I
pulled in this direction and it squeezes

down in the other two directions and in
the ideal case it would be incompressible

that is the volume of this thing would
not change in that particular case now.

That is what you have for
normal materials and

then the word I learned
from Martin was that

the other end of this is weird right
that was your characterization of.

A negative plus on ratio of materials and
so this is the case of negative possums

racial material I call it in one direction
and it expands equally in all these other

directions so OK and so
material that does that is not common and

we found I mean this is so it's a weird
material and one of the things is could we

make materials like that and it would that
be something generic that you could find

in if you could make this in
three dimensions this could be a.

Something that you could say well we
can actually begin to make materials

that are not normal.

And so

typically if you think about it what
materials that you do you have that are.

Negative plus one ratio and.

There are probably only two that
you're commonly familiar with one is.

It's only barely negative which
would be cork that you have for

your wine bottles and so
you don't want something that has a.

Positive ratio which puts a cork in and
it breaks the neck of the bottle and

you don't want with native POS on
ratio because then as you know if you.

You know push in from the bottom it
squeeze in from the sides and it will go

out too easily so you you want something
that has essentially zero Possum's ratio

and so cork is very good it has zero near
zero percent ratio the other thing that

you may know that has negative parts
of ratio if you complicate a paper and

you couple of paper and this as you have
in Him Paul you pull in one direction and

somehow expands in all these
other directions and so

this is the two materials that
you typically see there you go

if you raise it up high so we can
all see that look at that brilliant.

Experimentalist.

Par Excellence OK.

Now I raise this regard.

To the well of the module I of
the system because in elasticities.

There's a one to one relationship
between the Possum's ratio and this.

Ratio of the bloke and it's your module so

if you have a very very low value of shear
compared to the bulk of the shear of

essentially goes to zero compared to the
bulk then you have a normal material and

so it's easy to shear the same hard
to compress it and so this is.

Something which would have a normal
positive Possum's ratio and

if you go to the other regime where this
your module is much much much much greater

than the bulk modulus then
you go into this organic

case the negative passant ratio you did
and so that's what I want to explore.

It so what I want to ask now
if one of these networks

is I've measured the bulk monitors
I've measured the shear modulus and

now what I want to ask you suppose
I go in to this network and

I grab a bond at random and
I pull it out of the system.

What's going to happen to the module well.

It will change by a small amount
because there's one Bond missing now so

there will be a delta be.

Labeled I for
that bond there we moved a delta G.

The change in the bulk money
in the sheer amount just

due to that one bomb being removed so
there's a delta G.

and there's a Delta B.

for that one bond and so
I want to measure what those that is for

that bond but
now want to put those that bond back and

I want to now take another bond at random
out of this network pull that one out and

I do the same thing I measure what is
Delta be for that bond and Delta G.

for that bond and now I do this for
all the bonds in the system and

I now am going to get a distribution of.

How many bonds.

How many.

Bonds will give a contribution Delta B I

how many bonds will give a contribution
to the G.I. and so to see how this works

I want to start off by looking at what
you would get if you had a crystal.

And so a crystal is really a very boring
system that is I have a unit cell

which I repeat in term an ability over and
over and over again in all directions and

if I think of the very simplest case of
a crystal so I'm going to have one and

impune itself then it's a very simple
thing that is what does the distribution

of these B I's and geodes look like well
it'll just be a delta function that is

if I take this bond out it'll have
a value of Dell to be I I put it back and

because his next Bond that I choose is
identical to the first one I take it away

it will also have that same contribution
to the book munchers for this year modules

so all module I own the all bonds
contributes to the bulk modulus and

sure modules in an identical way and so
what I have is this is distribution of B.

eyes here still to be eyes will just
be a delta function everything will do

the same thing Bill nothing will
do more nothing will do less.

OK And so
what I want to ask is Well what happens to

this property of a material
when I make it disordered and

so typically what I would
have thought is that if I.

Go and I make a make the same disorder
I put disorder into mine a material

that I would get a blurring out of
that delta function that it would just

spread out a little bit and you know some
bonds will create a little more time with

create a little bit different less change
to the July but it will be basically.

Centered around that average value.

And so what I want to ask now is
well what happens if I do this for.

Or a jam system so
something that's fully disordered and.

As disorders as I can make it OK And
so what you're going to see

here is now I'm going to show you
this distribution function for

the bulk of my just if your mind to
light of this thing for these this.

These distribution function for Delta
beyond but the first thing you're going

to see is this dirty work at the foot
because the axes are going to change

from linear axes to log axes which means
something funny is happening OK and

so themselves this is not
what disorder does and

it this is the distribution
functions that we get and so

what you see about this is that first of
all the actually says changelog axes so

that means that I have an incredibly
broad distribution of how

a bond will affect either the book
knowledge of the few modules and

that's one thing it goes all the way
it's very broad it goes all the way it's

continuous It goes all the way down
to as low a value as we can find in

our simulations and so this goes all the
way down to zero as close as we can get.

The other thing about this is that it's
basically universal that it's the same

distribution here for
Delta B I N for Delta G.I.

both have the same behavior so it's.

Still something is you know kind
of universal about this and.

What of.

Then you'll have post-doc was able to show
is that this distribution function which

is sweeping something under the rug here
about how universal it is it's not exactly

universal to begin with but after a few
pruning things it becomes universal for

the bookmark to so once you've done that
then this distribution function has this

simple form of a power law cut
off by this exponential and

so this is something
we can show where the.

This country and so we have these
distributions that are broad and

continuous and universal OK So
now having gotten this far what I want

to ask you is well you know if you have
a bond over at the right hand side so.

You don't have a point there but.

Of Days of well of two I take
the side way over here OK and.

Well I thought you can give me your arm
is going to use your arm to the point.

So if I take this pond here and
that was a bond that made

a very big difference to the both modulus
I would have guessed that that would have

had a very big effect on the shear margin
says Well that is if it's an important

bond to the system is that
important bond to the system but

what we find is that that's
not true at all that is these.

Distributions are nearly completely
uncorrelated with one another so

the distribution of what you get for
the shear module and for the bulk on July

are less than one percent correlated so
they're completely uncorrelated So

if I took this pond away for
the bulk month list.

Its contribution to this year much is
could have come from anywhere in this

distribution it doesn't matter what
its value was to the book modules and

so this is.

These two properties are somehow very
different from what I would have

expected from a crystal and
this is what I want to use now in.

In order to do things and

so what I want to do is first go
back to something that Martin did.

Way back in two thousand and
nine which was if you took a.

Network of the kind that I mention and
I reach in and

pull a bond out at random I can ask well
what does it do to the bulk margins and

what does it do this year modulus and.

Basically if I keep doing this
taking bombs out over and

over again I'm just doing
rigidity percolation And

at that point I know that both
the two mothers and the both

modules are going to drop in tandem
with one another and so the ratio of G.

over B.

remains constant and so
nothing much happens when I take the.

Things at random but notice that what
I'm plotting here is the ratio of

this year to the book modules and I just
told you that I have a broad distribution

of both your module and
contributions so I can reach in and

pull out a bond that has a very big effect
on one modules but not on the other or

vice versa and so
this is what I want to do now and

I'm going to take out the bond
which has the largest

contribution to the vault much less so

I know what all the bonds are I can ask
the computer to tell me which Bond if I

take it away has the largest effect
on the book modulus I go in and

I pulled up on the way what that's
going to do is it's going to make B.

drop as fast as it can because I've taken
the way the bond that created it was most

important for that whereas modulus is just
going to drop by an average amount and

as I do this I do this over and over and
over again so I'm starting up here at.

The disease just measuring
how many bonds extra over

rigidity threshold that I have so
out here I have a lot of extra

bonds in the system and now I take them
away one time and that means that Delta Z.

is dropping so I start here and
I take away one bond and

move up one little bit here I keep doing
it over and over and over again and

this thing just continues to increase G.

over be increases dramatically and this
is now again a log scale and so this Geo

would be is up to ten to the ten I mean so
ten orders of magnitude in that case.

Now I can do.

Something else I could have gone and
asked So let's prune the bonds

that has a minimum effect on
the book modulus Now if I do that.

Going to.

Be will not change at all but Delta G.

is going to change by its
average amount each time and so

that means this ratio of G.

over B.
is going to drop so

I start from the same point for
the same network and

I just keep pruning in that way and now.

Will be dropped and
this goes down to about ten minus four and

so just by pruning.

A few percent of the bonds in the system I
can tune this shear to the bulk modulus by

something like fourteen orders of
magnitude and so that's a large change and

what that's telling me is I can go from
something that's completely or exact that

is with a possible ratio
of negative one all the way

to one is completely incompressible which
is Possum's ratio in well in three D.

would be cause for issue of plus
a half in to do you be a plus one.

OK And so this is what we could
do fight pruning the Delta B.S.

I could have also done the same
thing by pruning on the shear

Montreux I instead of the book my choice
and here again I get another set of.

Curves that I can go I can make something
or that it by putting a minimum value

of Delta G.I. or make it incompatible
by tuning the maximum value Delta G.

Od so I have all these different ways of
getting to the end point that I want.

OK So this is.

These different algorithms produce
different kind of pruning.

Behavior and so I get different
lattices I can get the same.

Possums ratio by tuning in.

Riding of ways as a many
many ways of achieving this

the desired property of the system
the Possum's ratio by pruning.

In many different ways I
can get the same thing.

OK And so then what we try to do
with we want to make these things in

the laboratory and so we go in and so we
can do this either in two dimensions and

so in two dimensions we
take a sheet of rubber and

we take it to a laser cutter and we cut
out everything that doesn't look like

a network and
that's what we have on the left and

on the right we can do the see in three
dimensions by building this up by three D.

printer and so
we print these things in three D.

in two you can make.

Systems that are three D.

or two D..

And so this is.

One way that we test whether
we're actually doing something

correct in the system now.

What I'm not going to show
you the behavior for the.

Organic networks here are five
shows something in the.

For the local thing in a minute so

having said that with making these things
in the laboratory of now I want to ask

what else can we do with these networks
and so the question is can we make.

Other things that are on
a more local scale so

I told you about the bulk module the bulk
module I were the only things that

happened I would be kind of interesting
but it would be somewhat limited and so

what we want to do is take a lesson
from biology and ask about what do

what does biology do in biology makes
use of proteins in a way that is very.

Very important to the biology in this
is what's called protein Alistair E.

and so here this is.

Pulled from the biology website and
so you take.

A protein and
what this idea of Alistair does is

that if you have one side
on the protein where you.

Add your bind to something here then.

At a site way over on the other side of
the protein it now has the ability to bind

this substrate over here whereas
if you didn't have this.

Bond here it would lose the ability
to find something far away and so

this is an important way of the proteins
control their behavior their dynamics and

so what we wanted to ask is well can
we do the same thing in the case of.

Of our networks or
mechanical networks and so here is what

we were doing in so we take so
the idea is I ask you

please come up to this network that
we've just made this network and.

I ask you to please choose at random Your
choice of where you want to source and

so this was where you happen to choose
a source that I ask you to come back in

please choose another place on this
network that you want to be the target and

so you chose this thing far
away to be on the target so

this is totally random is your choice and
then I ask you Do you want this target

when I pull the source apart so
I want to target to pull apart or

do I want to go together so it's your
choice precisely where you source where

the target and what you want the active
action to be and so the question is can we

can we tune the same to that case and
so we using the same idea and

this is what I wanted to be able
to show you if we had had the.

Overhead projector of so
this is the idea so here we have a.

View so the This Is It OK so you can see
it and so what you actually see here is

are two separate networks
there's one on top of the other.

What if I pull them apart you'll see that
these two networks really were almost

identical and what I can show you here
because I don't have four hands but

is that if I pull on the source
I can make in one case

the target come apart and the case of how
you come together and so I will show that

to you if anyone's interested they
DID WE CAN I can show that you.

Directly but but
this actually works OK and so.

This kind of behavior so this is.

We didn't know you could do this and
now the fact that you can do this and

you can do this with nearly
one hundred percent.

Success rate is something that we
didn't expect to be so easy to do and

so this kind of work has also done by two
other groups who ran the same time so

I met you group and.

See TO SEE THE has also done some related
work in the same the same general ideas.

Can you design out a star response.

So what.

I want to ask now was well how
complicated can that task be that is.

What I told it beginning is we have
one source and one target could I'm

now ask you to have one source but
more target so the sources

over at the upper left and I have three
things which I've asked the system to.

Create So if I pull on the source
I want those three other targets

to move in the direction and with the
amplitude that I've put right there and

the question is can you do that and
the answer is yes and.

What we're showing here is at the on
the bottom left is how many targets can I.

Have.

The the function that I prescribe at
random how what's the probability

of being able to get all of those
to work and so what you see here.

Is.

So for a system the size of an In this
case with a size eight system what we

can do with you can have asked will see if
I can tune one yes I can tune one can or

two to yes I can tune to but
pretty soon I can tune that many because

I only have eight particles in the system
but if I make the system bigger and bigger

YOU SEE THAT CAN TOO MANY MANY MANY sites
here many targets with that one source so

the complexity of the task is increasing
so there's a number of targets I'm asking

system to tune and each different color is
for a system of a different size and so

if I make the system larger and larger and
larger I can tune many many many more

sites almost uniformly so
there is a probability of success and so

I can get nearly one hundred percent
success of with many many targets if if I

make the system large and the question is
Well how does a number of targets increase

with the number of nodes I have in
the system and at least the present

behavior is the algorithm that we have
is a little bit sub linear it still

says that if I have an infinite system I
can prune an infinite I can to an infinite

number of sites but it doesn't scale
with the size of the system so

it says that in the infinite
size limit I can

tune zero percentage of the sides but
still be an infinite number but.

But this is depends on the algorithm that
we're choosing to tune this thing in so

that we may be able to
do better than that.

OK but
it also tells us one other thing which is

that what how many ways
could I have two and one.

Site right that is and
well since I can tune any of them and T.

of them then the number of ways
of getting that one function.

Is going to be some exponential.

You know it's a.

Whatever that thing is called the.

The Benefactor Oriel thing with a factor
of me that's lots so it's not one and.

So.

What it's saying is that this is
really a very easy thing to to create

five minutes OK so.

And so this is the.

Kind of showing the power of the said is.

We started with asking what.

Was biology doing and could we mimic it
and then what we found out was very easy

to do it and part of the reason so easy to
do it is that there are so many different

ways in which you can do it and
that's what this is basically telling us.

Until now I just want to end with one
last thing which is talking about aging.

Behavior and so this is now a little
bit different that is what I'm

thinking about is suppose I have
a sand pile you know and so

it's a big heap of sand and
down in the middle of the sense

of it's feeling the weight from
everything on top of it and so

these particles are under a lot of
force between the grains of sand.

So what's going to happen here is well
the grains that are under the most force

they're going to do form plastically
over time not a lot but over time a long

enough time you will see that these grains
are no longer going to be nice little

fears they'll be little flat top guides
and so they're going to distort over time.

And so
the bonds that are the under the most

stress most force are going to form
faster than those that are under

less force and so this is the idea so
it's a little bit different from

the pruning that is this is a weaker form
of pruning I'm just allowing the system to

evolve under its own steam
it's measuring its own.

As on it and
then responding with a memory of what it.

Learned about.

From all the weight that's
been on top of it so

that it has memory in it it's also
a greedy algorithm so in the sense that.

What it's doing is it's no longer asking
pulling the bond away asking which Bond

was the most important I'm just asking
which Bond has most stress on it and

that's something that
the system just knows and

it responds to what that stress is so
it's a very greedy algorithm it's not

having to do any complicated computations
and it just goes down hill and

so this is the results that we def
of this so the idea here is that.

The bonds are in the most stress
to form classically faster than

those with less stress and so what I mean
by that so the energy of this pile is

the sum of the energies of each of
the bombs separately minus a lot

a lot is the unstretched length and I'm
going to let the unstretched length relax

very slowly depending on how much force
there is on that actually and so L.

I zero changes slowly in time and
we feed that back in and this is

what the ageing of the system does and
what you see is well the bulk modest drops

this year modulus doesn't do very much and
so after time in two dimensions or

three dimensions you get that the ratio
of geo be it gets larger and larger and

you get some of this really it drives
itself towards inorganic behavior

automatically on its own and so this is
something called directed ageing that is

you usually think of ageing is just some
bad thing that happens you don't typically

think of aging into this directed in
one pathway to a particular place and

this is a ageing that you somehow knows
it wants to make a weird material items.

OK And so that's where I basically
want to end so I just want to.

Conclude that.

Designing function into
disordered networks there is

what I've tried to present here is a new
paradigm for designing punctual materials

based on the idea of using the disorder
in the material to make it

possible to design the functionality I've
shown that you can do this globally and

you can select the passant ratio you can.

Do locally and get action at a distance
Alistair effect in the system.

But as I've said many times before no
good talk is really finished until

you have the both feet line and so this is
a bullshit line so everything above this

line I hope you believe in I mean I
think that's all facts everything below

the bullshit line you have to believe it
all OK And so this is what I want to.

See them the picture if you will and

so what I've tried to show here is
that there's a new principle for

disordered matter and this principle
is that this independent of Bond

level response that you have these very
broad distributions for the Delta bialys

in the Delta G.I. they're very very broad
They go all the way down to zero and

these distributions are uncorrelated with
each other and this allows a new kind of

functionality to be tuned into disordered
materials that is not available for

their order can't counterpart the second
thing that I want to make is OK so

what does this have to do with real things
and so can you do this in situ and so

on in our lab we're working on doing this
in situ those we're trying to figure out

whether we can actually measure without
going to the computer which Panjandrum

most stress and then flip them and make
the systems do do stuff on their own so

that's one thing could we do this
microscopically so that you go down into.

Design interactions between particles at
the microscopic scale which you could then

if they're under stress a laser could.

Come in and zap them those bonds that
are in distress where as it would

leave the other ones alone that would be
a different kind of thing that you could

you could do and so this would be so that
we can dream of happening one thing is

biology which is you know we
started with the South stuff having

to do with biology but what does it
really part about biology that's kind of.

You know those great you bristle on our
part to think that what we have to say

has anything to do with biology but you
can at least say that well since it's so

easy to do in these mechanical
networks perhaps that's why biology

can make use of it so easily and so
that was one idea that of how we can

return to biology something that we took
from biology to begin with and finally you

know the idea is that you might be able
to use this stuff in architecture I'm so

buildings no longer have to have
rectilinear walls I mean we have you know

you look at a Frank Gehry building and
they are all doing all sorts of things and

what this allows you to do is OK so
you have this disordered structure and

so if my colleague across
the way pisses me off

what I want to be able to do is go to
my window push it a little bit and

have the window fall out OK And so
this would be how I could get even with.

The.

People in mind but my my last OK
with that I thank you very much

I should just say want to hear all
the people who did all the work and

so and really who was involved
in all of this and then

Goodrich started this work out on
the organic materials and they.

Took that over improve all
these various things about it

Jason rocks has done the work
on the Alice Terry and

then you'll read in one the Pablo
from engineering group.

Has applied this to actually show how you
can add on bendy constraints into these

materials and then the machine and
Berger did the making the.

In the lab and then Elaine it headed for
E N N Rick run Ellen Fitch

who did the work on many you know
how many different ways you can.

Create the same kind of how
complex your function can be

without Thank you very much thank you.