Sphere packings
Sphere packings - Dr Fabien 8/10/25
Ever wondered what the best way to pack spheres in a container? Well it turns out that hexagonally packing them is the most optimum. Famously this was known as the Kepler conjecture, originally stated in 1611, and was later proved by exhaustion in 1998 by Hales and Ferguson. It was shown that hexagonal packing in 3D has a density of 32 (pi / 3 root 2 because unicode does not work) or roughly 0.74. This packing density means that roughly 74% of the space is actually taken up by the objects meaning that 26% of the space is unoccupied.
But what if you don’t want to spend the time organising the spheres? Well it turns out there is a best way to randomly place spheres in a container, simulations in the presentation show that tapping vertically on the container can increase the packing efficiency of spheres when dropped randomly into the container. Scott, Nature 188, 908 Found that when tapping vertically the packing efficiency approaches but does not exceed 0.64. The study also says it’s “unlikely that there are other stable random packing arrangements for equal spheres which have packing densities outside these limits”, referring to the random packing density not exceeding 0.64.
Yu et al., PRL 97, 265501 found that the limit of tapping horizontally on the container can actually increase the packing efficiency above the previously shown limit of 0.64.This method however cannot beat the hexagonal packing shown earlier. Calixtro Yanqui “An average model for disordered sphere packings” states that random packing could even approach 0.72 when “pouring the spheres layer by layer into a box subjected to horizontal vibration”.
In conclusion if you want to pack spheres into a cylinder without spending a large amount of time and effort you should tap lightly on the side of the cylinder to improve the efficiency of the packing.
60795
1, Blogs overall presentation: relevant information that is given clearly. The use of grammar is good and the data and title are included. 3/3
2, Accuracy of reporting the seminar’s take home message: Blog is very clear on the message and why the research matters. 3/3
3, Accuracy of contextualisation of research: does a very good job of contextualising at the end of the blog but could have done more to contextualise within the main body of writing. 2/3
4, Additional research: Good use of external sources and how they relate to the research. 3/3
5, suitability for audience: Relatively easily legible for the average person. 2/3
26801
Presentation: 11/15
You have followed the criteria of including the speaker’s name, title and date of the seminar, shown clearly at the start of the blogpost.
Content: 12/15
Explained the main topics and message of packing spheres referring to the content in the Fabien’s seminar.
Context: 13/15
Informed us of the Kepler conjecture and its by referring to the content in the Fabien’s seminar.
Style: 12/15
It is very easy to read as blogpost doesn’t focus on complex structure or terminology.
Other sources: 14/15
Referenced additional sources for readers to explore for the factuality of the blogpost content including direct quotes.
Overall Mark: 12/15
Feedback:
A small issue is not including the speaker’s surname (Paillusson) when labelling the speakers name. Some grammatical mistakes; “Found “should be lowercase in “Scott, Nature 188, 908 Found that…”; and there should be a spacing between these sentences “limit of 0.64.This method”. From the the way it has been worded, I find that it is hard to understand what information is from the seminar apart being evidence that tapping a container vertically helps improve packing efficiency. As well as it feels like the blog post is just telling us information with brief explanations to why. References could have been linked at the end as footnote or bibliography.