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What is multiscale modelling?

It is a scientific approach of using separate models describing phenomena occurring on different length and time scales and linking these models together so they can exchange relevant information and work together to predict materials properties.

Quantum mechanics is a great tool to study a dozen of atoms, but make it a hundred and it will really struggle unless some system details are thrown away to make things work. How about a thousand atoms? A droplet of water? Apparently, a water drop contains about 100 times more molecules than there are grains of sand on Earth. Do we really, have to know the whereabouts of every single molecule to tell, for example, the shape of the droplet? Evidently not.



So how do we predict the shape of the water droplet using the bottom-up multiscale modelling approach? We start with quantum mechanics to study the forces between a pair of water molecules. Then, take these forces, take a few thousands of molecules interacting via these forces and work out the structure of bulk water and the properties of its interface with air. Check it against the available experimental data and refine the model if needed. We will have to do similar calculations for the substrate supporting the droplet to decide how well water wets the surface. Equipped with this information, we can already tell what the contact angle will be, but to work out the exact shape of the droplet will need to set up another calculation. This time we forget about single atoms, treat water as a continuous substance and concentrate on the balance between gravitational and surface forces.

How does it work?

Simple models can sometimes be solved analytically with only pen and paper and/or simulated on an average desktop computer within minutes or hours. These models are usually the ones with the highest level of abstraction with no explicit microscopic details. They are based on some averaged mascroscopic parameters (like surface tension in the example above) which in turn originate from the intermolecular interactions.

A typical atomistic simulation will have about 10,000 atoms interacting via relatively simple physics laws and the computer will move the atoms around while obeying these interaction laws. This simulation is basically a movie that is only a 10,000,000 part of a second long but it took about a week to produce using a mid-range parallel computer. Therefore, additional techniques are required to predict system's behaviour over longer time scales. There is also a chance that this brute-force method might get stuck in the configuration you have started from, so no new information about the system can be collected. Part of my work is to develop and implement numerical methods which would get around such "bottle-neck" problems and make the simulation meaningful.

Collaborations with experimental chemists, physicists, biologists and material scientists are essential to make good progress as these collaborations provide an essential feedback mechanism. We constantly compare the results of the computer simulations to the theoretical predictions and experimental observation of the same phenomenon. This results in a better understanding of how things actually work and tells us how we can make them work better.