Jumping Random Walks: A Stochastic Description for the Modelling of Glass-like Materials
I’m sure we have all dropped a glass before. Shattered on the kitchen floor or off a table at the pub. Knowing this we would assume glass to be solid. However, in Bart Volselaars’ seminar, ‘Jumping random walks: a stochastic description for the modelling of glass-like materials’, he explains to us how science contradicts the common belief that glass is sloid.
Bart states in the seminar, “A glass is a disordered material whose viscosity exceeds about 10 pascal-seconds, meaning it flows, but only on extremely long timescales”. What this means for the non-scientific community is that glass is actually a liquid that moves unimaginably slowly. At the microscopic level, the molecules inside glass never form neat crystals. Instead, they are trapped in a kind of crowded mess. Each molecule is stuck in a small space, jostled by its neighbours and very occasionally jump to new positions. This pattern is called “caging and hopping”, tiny movements followed by sudden jumps. Scientists see this in computer simulations and experiments on materials like plastics and rubber [1].
Physicists use the idea of a random walk to try help visualise what’s going on here. We can think of it like a drunken person stumbling their way home after a long night. Bart explains this random walk process a bit more scientifically: “A random walk is a process where each step is taken in a completely random direction, and the average displacement is zero, but the mean-square displacement grows with time”. “Diffusion and Brownian motion are continuous versions of a random walk”, which relate to everyday atomic and molecular processes such as how perfume spreads in air or how ink diffuses in water.
To model this mathematically, scientists use something called the Langevin equation, which balances friction and random thermal kicks. This approach is explained in detail in the classic physics textbook Stochastic Processes in Physics and Chemistry [2].
But glass isn’t just free diffusion. The molecules sit in little energy valleys, like marbles stuck between hills. To move, they must climb over a barrier. When scientists add this idea into their models, we really start to see the whole picture: “By adding a periodic potential to the Langevin equation, we can model how particles become trapped in cages and occasionally hop between them”. This simple idea recreates everything we see in real glass; slow motion, aging, and sudden rearrangements.
A modern theory of this behaviour is reviewed by Berthier and Biroli [3]. Their work shows how microscopic trapping leads to the strange properties of glass we experience every day.
So, the simple vessels we use to drink from and see through are actually far more complex and interesting than either you or I could ever imagine.
References:
[1] Chaudhuri et al., 2007
[2] van Kampen, 2007
https://www.researchgate.net/publication/313574118_Stochastic_Processes_in_Physics_and_Chemistry
[3] Berthier & Biroli, 2011
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Blog overall presentation (3/3) Well presented in terms of the specification, all relevant information is included and grammar looks good.
Accurate reporting of the seminar’s take-home message (3/3) The seminar message is well covered.
Accurate contextualisation of the research topic (3/3) Good information is provided around the topic of research.
Additional assessment using external sources with a direct quote (2/3) The included references are okay, but I feel they may be lacking depth into the original topic of the seminar.
Writing style and technical level for a lay audience (3/3) Perfect and consistent writing style for a more complicated scientific area of study