Thank you very much. My presentation is about GPU powered molecular dynamic simulations of

liquids and I will show a couple of examples where we use graphics processing units to look

into dynamic phenomena in liquids and at the end I would like to say also a little bit about the

technical aspects of GPUs. So my first example is about friction which is a very prominent example.

How does it emerge? So at the hydrodynamic scale we know the Stokes drag so if you have sedimentation

experiment this is a well-known formula that the drag force is given by 6 pi times the viscosity

times the radius of the sphere times velocity and but there's more to it if there's an oscillating

sphere then Stokes calculated in an impressive paper how this friction depends on the frequency

that's all hydrodynamics on large scales. If you take a magnifying glass and look at the small

scales we see that we have atoms that make the liquid so and these atoms in our classic picture

they follow Newton's equations and so this gives trajectories that are smooth and time reversible

there is no obvious source of entropy production and so there's no friction. So how can we combine

the two pictures and the idea is to use the this frequency dependent friction as magnifying glass

at high frequencies we look at small scales and at low frequencies we look at the hydrodynamic scales.

So we have run extensive simulations of liquids for different liquids a monoatomic liquid water

in the middle and a supercooled slightly supercooled liquid on the right. On the left part of each panel

you see the hydrodynamic regime we have so this is friction versus frequency so small frequencies

is hydrodynamic and look at the red data there we see that frequency dependence is predicted by Stokes

matches nicely it looks pretty different for water and again different for supercooled liquid

but what was most interesting almost striking for us is at high frequencies that friction drops down

so rapidly here actually exponentially fast so towards the atomistic regime friction is suppressed

quickly and so this matches with the idea that at very high frequencies there's no friction

but it was surprising it's suppressed it falls off so quickly. So to give you some ideas how much

the simulation effort went into that is the system with hundreds thousand particles and

10 runs over 10 to the 8 NbE steps a water system and then the supercooled system of similar size here. That's the first example.

Second example is about binary liquids which undergo a phase separation so we have a generic

mixture again it's a symmetric mixture of nanotrons particles but you can think of water and oil if

you want to have some more practical thing and below a certain temperature so that's the phase

diagram here, a resistance curve, if one goes lower certain temperature then the region is unstable and it

separates into oil and water if you like and so we quantified here this phase diagram and also

the different densities there should be a video hopefully it's running.

So Acrobat decided to not support videos anymore so we start from a mixed phase quench it and then

we can observe very neatly just demixing almost as it was in a continuum description but still

with atomistic resolution. We then went and calculated critical properties of this

critical dynamics the divergences of transport coefficients divergence of the correlation

lengths and could verify that this matches very nicely with this general theoretical expectations

but here we could quantify pre-factors which is yeah gives some extra information.

There is in the context of critical phenomena if one wants to locate critical temperature or

critical point there is something known as finite size scaling this goes back to the 80s

to the work of Kurt Binder mostly and the observation is that if we cannot have an

infinitely large system so the correlation links diverges in these systems at the critical point

and you can never have a system which encompasses the correlation links

so and the idea is that one controls the size of the system and sees how the quantity for example

the susceptibility diverges with this controlled size and then one can infer the critical point

from that in a certain way. The idea now is that it's relatively easy to do large simulations

of large systems and can we divide the big system into small subvolumes and of different sizes so

that in one run we have simultaneous access to all different sizes of subvolumes then the scaling is

the same so this but the capital L for the box size is now replaced by the subvolume size

and this subvolume size should be much larger than the particle size but still sufficiently small

compared to the system size so this is a finite range and so some corrections to scaling come into