I'm going to be talking about.

Now because it worked we've been doing
with the press and even Michael on

mechanics of fire and aggregations but
I'm going to give you a theoretical

perspective on on the way that it's
the way they behave the way they do

so we start with a simple description
of what I mean by dynamic networks.

They have these.

They have what elastic properties and
fluid properties and

they can be called correlated with
the chains that are in the dam and

indeed in the denim in a group
having a Spring Lake stiffness

that gives them their mass to city and
their ability to.

Detach and to get that and that gives them
the ability to reconfigure themselves

which we attribute to the fluidity
of the network so this is not.

Exactly new in the sense that we have been
seen in synthetic polymers in them in

the molecule a scale for example with
ironic bonds that are pretty weak or

adaptable networks that have been
recently been studying light so

I want to give you an example of the the
dynamic nature of the network actually.

Many first macroscopically this is.

A video of silly body at two
different time scales and

you see and six scale of second
Sibby of that a solid so

you can pretty much bunch of of off
the surface but then if you lead just

by gravity for up more than a few minutes
and actually scan see the flow so.

The question is this video is going to
be here really in different genes and

the aspect of these two elasticities
including coming from the wind.

Characteristics can explain these periods
and they're one they're short below

is actually an example of sort of healing
of these videos where they were able to do

for two different pieces actually being
coming and going to hear themselves so

the question again dancer is sort
of these are synthetic systems and

and Legations are biological
examples of active networks saw.

The people of found them to actually
be the way the inverse of by use.

Their body to link each other and
actually form these really nice structures

they where they agree that it helps them
survive for example of After all if they

can morph into a tower or even to build
a bridge program they want to put it.

So what I'm going to be talking
about today is calculating these

aggregation as we give us and trying
to explain some of the experiment and

work that that might be less done
in twenty fifteen in their paper so

as you see here what I'm showing here is
supplied of stress was strangely it and

the dotted line actually spawns
to a new turn in fluid and

clearly these aggregations
were tested by in a yarmulke.

Shown there and then the.

Shit in the sponge was actually a quarter
so it's clearly not a simple fluid.

It seems to shear thin at large and
it's and then go back to the beginning and

classical in pretty good models like
a string and dashboard systems that

have been used again are actually
explain this type of behavior saw what

the approach that we took was actually
to use a statistical mechanics approach.

To try and

explain if we can go from the behavior of
individual ants to the coral aggregation.

So.

To start with that to put to get the sense
of the statistical theory that I'm talking

about it let's look at a system
of Cedar Springs connected

connecting two plates and a and a deformed
the plate on the top it's of the force F.

and it's being assisted by the springs
that are a dash to it so all the or all

force actually the summation of all the
spring forces the attach spring force and

the spring force is given by the stretch
so when you have a lot of these springs we

can give a character a stem of the
population behavior which is shown there.

In terms of just the tip if you've got
a distribution function and that is

describing the frequency or the number
of scenes in different stretch values so

the OR ARE force actually the the integral
of that fear with the force of

that crest wants to a certain stretch in
the spring so the idea is that you can get

if you nor the distribution function
at a coffee in Bang then or

the order of course in the in the system
so OP can extend this to Do D.

and you can talk about
stress in that network and

instead offer a distribution function that
looks like that you have a point good.

Of that character characterizes
the direction of the stretches when

you have these iso going to is that so
in a.

Stress free network he did action
is pretty much isotropic So

if you start stretching them you will
see more direction and dependence so

then you can take the street.

Expression road it can take the stress
again in terms of the feet but

now as a dancer with the directional.

So the question is if we can get
the force from the distribution functions

how does the distribution
function change in took So

that's the question we asked and
then sought to understand that

what contributes to the change in the
distribution function first we start with.

The defamation So if we are if
I am playing the last of the V.

or in this case the velocity of lead in L.

then I D.
form the chains at the same rate as

the change in the distribution function or
the function that describes the stretching

all the chains would be affected by
the needed to be said to form it and

then there is a Sync TERM where some of
these chains are unable to break and then

that and it uses the number of IT that
change so I have a sync term and let it.

Sit in which the.

Brick and then I have a source of them
where the chains that Bree unable to

deform and a stress free country nation
because you know so this was sort of.

Evolutionary question of the of the
distribution of these the Stritch in that

and the legs so it's a it's similar
to the boards men equation for

in the kinetic theory of gases and
saw that they have a similar to

evolution equation for the last thirty
of the of the molecules so it's.

So to.

See how that transforms to
describe lastic or aggregation

here let's look at creep response
when the rate at which the form and

brick is constant in name so
it's a characteristic of the idea so

what I defined here this one dimensional
number called the ways in but

a number where to become a doctor
represents that it a sheer them and

kid he is a pretty brick So
what I'm showing here this

four different ways in book numbers
what happens to the leg stretch and

the leg alignment in average so
these distributions sure that the average

orientation of the legs is is almost
zero in the sense the isotropic and

as I said start stretching the more and
more and W.

becomes closer to one meaning a shear
them a defeat at which they can break so

if I go beyond that they don't have
time to be an inch themselves they're

going to stretch a lot as you see here.

When I go or close to double eagles one
I share them in a really frustrated

competitive again before be Dutch and

a stretch most of them so
the average leg stretch and

the alignment goes up as a close go
closer and closer to to that same scale.

So Or the question is.

If I use a constant don't know what rates

I see that when I try
to match stresses she.

It seems today words.

At the gum are because one which is sort
of a she had taken in behavior which is

not exactly what we see in experiments for
the for the an aggregation so.

That's why this has happened so clearly
the assumption that the constant turnover

rate and the kid being constants
may not necessarily be true so

he hypothesized that since the ants
actually better themselves the born it's

the nature of the Born This is
coming from their tires implies

that have these frictional force us so we
have but so is that what if they can sense

if they're being stretched a lot and
detach faster so if they're so

good he said can the detachment
lead now be a function of course.

So Or do you have a model for
that we said OK So

we have a bellows law in
the microscopic scale for cells where

the detachment is a function of force and
it goes up exponentially like that so we.

Model that is macroscopic in nature
now for the ants where the dash

in a similar equation and as you see
it EVER seen as a sensitivity but

I mean that meaning how sensitive are the
force you've ever seen a small even for

a small force needed to actually diversity
the sense of really easy when you ever see

those large in there really less sensitive
of the force the they need a lot of force

before they can start responding to it so
clearly in the question that I was shown

before now kiddie is not constant anymore
but a function of the stretch in the next.

So to actually test if this this works we
went back to the experimental results and

started out playing.

Here and first and showing again what
happens if I have constant put it and

then you see thickens But
then as a piece the sensitivity.

Decrease.

I see it starting to shit then
because as a play I'm faster and

faster sure it's the ants are the model
predicts that they sense them and

the respond by betting faster so

you see that it's the cross it
goes down and then you get a fit.

And as you know that's twenty two
times the weight of the end so

what we see there I'm showing is
the distribution of the leg stretch So

initially when there were not considered
a force if you stretch them really fast

they're going to be at a large lead
they're going to be stretched and

are going to be elastic going
up showing a shift to get in but

then when I have a stretch
sensitive detachment

I see that the distribution
is able to rearrange itself.

So to summarise.

Look at the basic aspects of dynamic
networks and I played them to the case of

the ant educations and the simple feedback
mechanisms Lake sensing the tension and

increasing the don't know of it and
then to decrease the density Reus and

so actually seem to explain
how they are here so.

This is a really good
inspiration to sort of.

Understand the individuals
be here to to do.

Short collective emergent behavior
which we can learn a lot from and

play two different.

Synthetic it up with matter to have
self healing or morphogenesis and

swarm intelligence and so on so
of thank you and begin to question.