Brazil Nut Effect in Avalanches and Cereal

The brazil nut effect describes the movement of large particles to the top of a container after shaking. The same effect also occurs in avalanches where large blocks of ice and rocks are seen on the surface, and in a box of cereal where the large pieces migrate to the top and the smaller dusty particles remain at the bottom. In this video, Nathalie Vriend and Jonny Tsang from the University of Cambridge explain how the granular fingering instability causes granular convection and particle segregation, with examples of experiments and numerical simulations from their research.


This video is part of a collaboration between FYFD and the Journal of Fluid Mechanics featuring a series of interviews with researchers from the APS DFD 2017 conference. Sponsored by FYFD, the Journal of Fluid Mechanics, and the UK Fluids Network. Produced by Tom Crawford and Nicole Sharp with assistance from A.J. Fillo.

How high can bees count?

Bees are not only able to build fantastic hexagonal honeycombs they’re apparently also able to count! But do they deserve their reputation as nature’s mathematicians? Georgia Mills spoke to Srini Srinivasan from the University of Queensland to find out how they discovered counting bees…

  • Bees were trained to fly down a tunnel with a reward of sugar water at the end, and a series of identical landmarks labelled 1, 2, 3, 4, etc. along the route.
  • One of the landmarks contained the reward and the bees had to test each one to discover its location. This was repeated several times until the bees learned the location of the reward.
  • The spacing of the landmarks was then changed, but the reward remained at the same landmark, and the bees had to find it once again.
  • They were able to ‘count’ the number of landmarks and would go straight to the correct location bypassing the others that did not contain a reward.
  • The highest number of sequential landmarks the bees were able to ‘count’ was 4.
  • Four is a universal number as when briefly presented with an image containing a number of objects, the largest amount most animals can recognise accurately is 4-5. This process is called subitising.
  • Counting to 4 is useful for bees when for example deciding whether or not to land on a flower to collect pollen. If there are 3-4 bees already there then it is probably not worth their effort.
  • Counting has also been looked at in fish birds and chimpanzees, and in each case the number four keeps cropping up, suggesting universality.
  • The tunnel experiment was actually designed to investigate how bees navigate and the corresponding ‘waggle dance’ that they use to communicate information.

You can listen to the full interview with the Naked Scientists here.

How do tissues grow?

Interview with Edouard Hannezo from the University of Cambridge for the Naked Scientists. You can listen to the full interview here.

This year marks the 100th anniversary since the landmark publication On Growth and Form by D’Arcy Wentworth Thompson, which describes the mathematical patterns seen across the natural world including in shells, seeds and bees. Now, a new study from the University of Cambridge has used the same ideas of self-organisation to give an elegant solution to a problem that has taxed biologists for centuries: how complex branching patterns arise in tissues such as the lungs, kidneys and pancreas. The answer involves some very simple maths…

Edouard – We are a team of physicists and we’ve been working with developmental biologists in order to understand how complex organs are formed during development. And what we’ve found is by using real organ reconstructions and mathematical modelling is that there are incredibly simple mathematical rules that are conserved among several organs, that allow organs to self-organise in a fundamentally random manner. Which means that organs don’t follow a precise blueprint, but rather each cell making up an organ behaves in a very random manner and is able to communicate with its neighbours in a simple way in order to generate a mature organ.

Tom – So in some sense each cell is kind of doing its own thing and then somehow all of the cells together give you your organ?

Edouard – Exactly, that’s something that has been widely studied in physics. For example, if you think about a tsunami wave, individual water molecules do not know that they’re forming a tsunami wave that’s moving cohesively. Each molecule just goes randomly around and it sonly if you put a lot of water molecules in a very specific way that you can form suddenly these self-reinforced structures that make up tsunami waves. And this is an exactly similar example in biology in which each cell behaves randomly and its through very simple interaction with the neighbours that they’re able to self-organise into complex patterns.

Tom – How do we end up with these incredibly complicated structures such as the lungs and the kidneys?

Edouard – What we found is that even though the global appearance of tissues such as kidneys and mammary glands is broadly similar, actually if you look in detail its actually like snowflakes – no two organs can be superposed and are exactly similar. And that’s a signature of the fact that the underlying mechanism is fundamentally random and that from random disorder these cells are able to self-organise into something that is almost robust, but never exactly the same.

Tom – A lung roughly speaking is about the same between most people. If it is as random as your suggesting, how do these cells know when to stop when they reach a certain size or how to form a lung?

Edouard – That’s the key rule that we’ve proposed in this article. So what we think is that cells proliferate, they grow randomly in all directions and of course they need to know when to stop – you want your organs to have a given size and not too much less and not too much more. And so the rule that we’ve shown is that even though each cell explores space completely randomly and divides randomly, we’ve shown that it’s able to measure the local density, so if it arrives in a place that’s a bit too crowded, it doesn’t try to keep growing it just stops. And stops growing forever. Therefore, with this density sensing of cells the organ is able to know the regions which are already dense enough – it shouldn’t grow anymore – and the regions which are not dense enough and it should grow additionally. And it’s this intrinsic self-correcting tool that allows for the self-organisation of organs and that allows organs to robustly develop from a series of random interactions between cells.

Tom – So can we imagine for a second that we are one of these tissues growing and can you talk me through the process that that tissue would undergo and how it develops into an organ.

Edouard – You can imagine a tree, and one of these trees starts with a single bud on top of a single trunk. This bud is going to start growing, it’s going to explore a random direction. And rather frequently these buds are going to divide and give rise to two branches, four branches and then eight branches, exactly as you can imagine in a tree. Therefore, this alone would never stop and it’s only thanks to this crowding induced termination that some of the tips turn off and stop growing, while other tips that are at the outer edges of the organ have access to low density regions and continue growing. There’s actually a pretty strong resemblance to what you can think about with a real tree, where you can imagine that the tips that have access to the sun will continue growing whereas tips that are overshadowed will stop.

Tom – And in terms of other applications of this kind of work beyond just understanding how our tissues develop, have you given any thought to other ways this could be used?

Edouard – One thing that we’ve started to look at in the paper is the question of developmental disorders. In particular, in the kidney, there are quite a few conditions in which unfortunately the kidneys stop growing before they are fully mature and so patients end up with at birth kidneys which are much smaller compared to normal. Therefore, we wonder if the fundamental randomness in organ development couldn’t explain pathological cases such as these developmental disorders.

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