L1

This talk is about the mathematics behind an artistic project focusing on the vibrations of soap films.

Latent Dirichlet Allocation (LDA) is capable of analyzing thousands of documents in a short time and highlighting important elements, recurrences and anomalies. It is generally used in linguistics to study natural language: its word analysis reveals the theme(s) of a document, each theme being identified by a specific vocabulary or, more precisely, by a particular statistical distribution of word frequency.
In the climatologists' use of LDA, the document is a daily weather map and the word is a pixel of the map. The theme with its corpus of words can become a cyclone or an anticyclone and, more generally, a 'pattern'  that the scientists term motif. Artificial intelligence – a sort of incredibly fast robot meteorologist – looks for correlations both between different places on the same map, and between successive maps over time. In a sense, it 'notices' that a particular location is often correlated with another location, recurrently throughout the database, and this set of correlated locations constitutes a specific pattern.
The algorithm performs statistical analyses at two distinct levels: at the word or pixel level of the map, LDA defines a motif, by assigning a certain weight to each pixel, and thus defines the shape and position of the motif;  LDA breaks down a daily weather map into all these motifs, each of which is assigned a certain weight.
In concrete terms, the basic data are the daily weather maps between 1948 and nowadays over the North Atlantic basin and Europe. LDA identifies a dozen or so spatially defined motifs, many of which are familiar meteorological patterns such as the Azores High, the Genoa Low or even the Scandinavian Blocking. A small combination of those motifs can then be used to describe all the maps. These motifs and the statistical analyses associated with them allow researchers to study weather phenomena such as extreme events, as well as longer-term climate trends, and possibly to understand their mechanisms in order to better predict them in the future.

The preprint of the study is available as:
 Lucas Fery, Berengere Dubrulle, Berengere Podvin, Flavio Pons, Davide Faranda. Learning a weather dictionary of atmospheric patterns using Latent Dirichlet Allocation. 2021. ⟨hal-03258523⟩ https://hal-enpc.archives-ouvertes.fr/X-DEP-MECA/hal-03258523v1
 

Bacteria represent the major component of the world’s biomass. A number of these bacteria are motile and swim with the use of flagellar filaments, which are slender helical appendages attached to a cell body by a flexible hook. Low Reynolds number hydrodynamics is the key for flagella to generate propulsion at a microscale [1]. In this talk I will discuss two projects related to swimming of a model bacterium Escherichia coli (E. coli).

E. coli has many flagellar filaments that are wrapped in a bundle and rotate in a counterclockwise fashion (if viewed from behind the cell) during the so-called ‘runs’, wherein the cell moves steadily forward. In between runs, the cell undergoes quick ‘tumble’ events, during which at least one flagellum reverses its rotation direction and separates from the bundle, resulting in erratic motion in place. Alternating between runs and tumbles allows cells to sample space by stochastically changing their propulsion direction after each tumble. In the first part of the talk, I will discuss how cells reorient during tumble and the mechanical forces at play and show the predominant role of hydrodynamics in setting the reorientation angle [2].

In the second part, I will talk about hydrodynamics of bacteria near walls in visco-elastic fluids. Flagellar motility next to surfaces in such fluids is crucial for bacterial transport and biofilm formation. In Newtonian fluids, bacteria are known to accumulate near walls where they swim in circles [3,4], while experimental results from our collaborators at the Wu Lab (Chinese University of Hong Kong) show that in polymeric liquids this accumulation is significantly reduced. We use a combination of analytical and numerical models to propose that this reduction is due to a viscoelastic lift directed away from the plane wall induced by flagellar rotation. This viscoelastic lift force weakens hydrodynamic interaction between flagellated swimmers and nearby surfaces, which results in a decrease in surface accumulation for the cells. 

References

[1] Lauga, Eric. "Bacterial hydrodynamics." Annual Review of Fluid Mechanics 48 (2016): 105-130.

[2] Dvoriashyna, Mariia, and Eric Lauga. "Hydrodynamics and direction change of tumbling bacteria." Plos one 16.7 (2021): e0254551.

[3] Berke, Allison P., et al. "Hydrodynamic attraction of swimming microorganisms by surfaces." Physical Review Letters 101.3 (2008): 038102.

[4] Lauga, Eric, et al. "Swimming in circles: motion of bacteria near solid boundaries." Biophysical journal 90.2 (2006): 400-412.

Preparing for Prelims and Part A exams with Dr Vicky Neale

Description: This session will offer guidance for Prelims and Part A students preparing for closed-book, in-person exams this summer, with tips on revision and information about practical arrangements. If you have questions, please send them in advance (by 28 February) via https://vevox.app/#/m/170975861 and we'll try to address as many as possible during the session.

A separate session in Week 6 will be aimed at students doing Part B, Part C and MSc exams.

Great progress has been made recently in exploiting categorical/topological/higher symmetries in quantum field theory. I will explain how the same structure is realised directly in the lattice models of statistical mechanics, generalizing Kramers-Wannier duality to a wide class of models. In particular, I will give an overview of my work with Aasen and Mong on using fusion categories to find and analyse lattice topological defects in two and 1+1 dimensions.  These defects possess a variety of remarkable properties. Not only is the partition function is independent of deformations of their path, but they can branch and fuse in a topologically invariant fashion.  The universal behaviour under Dehn twists gives exact results for scaling dimensions, while gluing a topological defect to a boundary allows universal ratios of the boundary g-factor to be computed exactly on the lattice.  I also will describe how terminating defect lines allows the construction of fractional-spin conserved currents, giving a linear method for Baxterization, I.e. constructing integrable models from a braided tensor category.