Jumping random walks: a stochastic description for the modelling of glass-like materials
Glass has always been an important material throughout history, with evidence of glassmaking dating as far back as 4000 years ago in Mesopotamia. [1] Despite its extensive history, glass is not usually intuitively understood. In his seminar titled “Jumping random walks: a stochastic description for the modelling of glass-like materials” delivered on the 26th of November 2025, Dr. Bart Vorselaars presents his research providing a stochastic perspective on the understanding of glass-like materials.
Before “jumping” into stochastic processes and modelling, Dr. Vorselaars starts the seminar by explaining glass as a material. Materials can be described by their viscosity, in simpler terms you can imagine viscosity as the “thickness” of a liquid, water has a very low viscosity for example, and it visibly flows. However, glass is visibly solid, so its viscosity must be much higher than water. But what exactly is glass? Dr. Vorselaars explains that on a structural level, glass is disordered, resembling a liquid, however it shows long relaxation times, meaning atoms take longer to return into equilibrium due to the glass’s high viscosity, and hence visibly resembling a solid. More specifically, to transition into glass, materials must have a viscosity higher than one trillion pascal-seconds! At such viscosities, the atomic structure of the material essentially appears frozen, appearing solid.
After contextualising the structure of glass, Dr. Vorselaars introduces a glass-like class of materials, called polymers. Polymers are essentially large chains of molecules joined together, and they provide applications in various fields, such as textiles, medicine and technology. [2] Dr. Vorselaars continues by explaining that, during his research, he performed molecular modelling of polymer chains, modelling the deformation of the chains to determine the polymer’s mechanical properties, with the aim of creating a simpler mathematical model that explains the properties of the polymer, essentially. But how can we model glass-like materials?
Random walk is a mathematical model that, as the name suggests, defines a path of steps with random direction. Since it is a random process, it may not be intuitive how it can be modelled, however there are multiple types of random walks, with properties such as the probability of taking a step in the same direction and taking a step in the opposite direction are the same. But how can we characterize each random walk? Dr. Vorselaars explains that we can take the average displacement of the random walk as zero, as it is the sum of the average of the steps, and since it is a random process, all directions of the steps are equally probable. We can characterise the random walks even further by looking at the averaged displacement squared. The averaged displacement squared is equal to the number of steps taken times the individual distance of each step squared, therefore characterising the size of the random walk. By defining the size of the random walk, we can define its dimensions.
Random walks are useful when modelling glass-like materials as they resemble the trajectory of particles moving within a liquid. Random walk-like motion is observable under a microscope in the molecular dynamics of particles and the motion of milk fat in globules of water, for example. Dr. Vorselaars continues the seminar by explaining how to model the motion of the particles mathematically, modelling the particles using equations of motion, drag force and the random fluctuating force. After extensive mathematics, Dr. Vorselaars highlights the resemblance of the results with those of a random walk, since it shows square root behaviour. Additionally, Dr. Vorselaars highlights that, these particles not only move around but also jump, therefore modelling this jumping in terms of the random walks too. Since we are talking about glass-like materials, particles typically repel each other, and in order to jump the “barrier” formed by its neighbour particles, a particle must reach an effective potential. Although analytical solutions are not possible when accounting for the motion of the particle in the effective potential, numerical solutions show the trajectory of the particle resembling a random walk at different timescales, with intermittent jumps.
Dr. Vorselaars concludes the seminar by highlighting the results of using stochastic models when modelling glass-like materials, particularly in their motion. The caged and jumping phenomena of the particles can be modelled by diffusive motion within a sinusoidal, or periodic, potential. Similar models can be applied to different areas, such as laser physics and electric circuits, with many scientists acknowledging that “random walks have found widespread applications in physics, chemistry, biology and beyond.” [3]
[1] History Facts, “How and When Did People Started Making Glass?” - https://historyfacts.com/science-industry/article/how-and-when-did-people-start-making-glass/
[2] Evergreen Chemical, “Types of Polymers and Their Applications in Your Daily Life” - https://evergreenthailand.com/blog/types-of-polymers-and-applications-in-daily-life/
[3] R. Metzler and J. Klafter, “The random walk’s guide to anomalous diffusion: a fractional dynamics approach.” - https://www.researchgate.net/publication/270451279_The_random_walk’s_guide_to_anomalous_diffusion_a_fractional_dynamics_approach_Phys_Rep
67384
Presentation 3/3: The date, title and name of the speaker are present at the beginning, and the blog is written in good English and grammar.
Content 3/3: The content covers a great amount of information from the seminar in a good amount of words.
Context 3/3: There is a lot of evidence of societal and research contexts which have been well explored and explained. For example, the brief history of glass at the beginning, and the applications of random walk models.
Style 3/3: Very suitable for a lay audience and engaging to read. I liked the use of rhetorical questions throughout.
External source 3/3: It is clear that external sources and references have been used. You have even included a direct quote from an external source towards the end, which is great.
Final grade: 15/15
Feedback: Everything about the work aligns with the mark scheme, and it is written very well. The only thing to mention is the word count. I thought it had to be ~500 words or a page length, but it’s a minor detail because there was nothing else to comment on; it shouldn’t be a problem because it doesn’t feel like too much.
42890
This is a good piece of writing, it is clear you understand the content and you have used multiple sources including a direct quote. However some things might get misunderstood by a lay person as there are some undefined terminologies. Apart from that, looks good.
46422
- Blog overall presentation (3/3)
The seminar title, speaker and date all clearly stated. The report is well structured and generally well written, with good clarity.
- Accurate report of the seminar’s take home message (3/3)
The main aim of the seminar is clearly and accurately communicated throughout the whole report.
- Contextualisation of the research topic (2/3)
The research content is well explained, particularly in relation to the research of the field. Broader societal implications could be developed further.
- Use of external sources with a direct quote (3/3)
Relevent and quality external sources are used appropriately, including a direct quote that supports the discussion of random walks and their applications in different disciplines.
- Writing style & technical level for a lay audeince (2/3)
The report is mostly accesible to a lay audience, but some terminology could do with an intuitive explanation on what it actually means. e.g. more explanation on what the average displacement squared actually means, what ‘effective potential’ is.
Overall a great blog, some explanations could improve clarity for a lay reader.