Structural Covariance in the Hard Sphere Fluid

Hard spheres are one of the simplest model of fluid. When the density is increased, the motion is slowed down and non-trivial local arrangements of particles characteristic of the liquid emerge. We call these local structural motifs.

In hard spheres, special role is played by structures with pentagonal rings, such as icosahedra or pentagonal pyramids.

In collaboration with Pierre Ronceray (Princeton), to appear on the Journal of Chemical Physics, we have shown that if we study the cross-correlations between the variation of populations of different motifs we can understand more of the phase behaviour of this model liquid: for example, we can predict its propensity to form more motifs of a given type if an external field is applied; or, we can understand and classify different motifs that coexist in the liquid phase.

More details can be found in the JCP Editor’s Pick:

B. Carter, F. Turci, P. Ronceray, C.P. Royall, Structural Covariance in the Hard Sphere Fluid, The Journal of Chemical Physics 148, 204511 (2018); https://doi.org/10.1063/1.5024462

Filtering long sentences with regular expressions

It happens often to me that in order to make an article clearer or more incisive, I may need to identify very long sentences in a draft and break them down to smaller, simpler units.

In \LaTeX  editors, there may not be an option by default to identify long sentences. However, using regular expressions, it is possible to circumvent this issue.

In editors that allow to search for regular expressions (such as Sublime Text or Texpad or others) the following snippet would allow us to search for sentences with more that 20 words:

<br>
((\w+,\s+)|(\w+\s+)){20,}(\w+[\.|?|!])<br>

It is not too hard to break this regular expression down to its elementary constituents. Let us just recall a few ideas concerning regular expressions

  • remember that () enclose groups
  • | indicates the OR operation
  • \w+ corresponds to a series of one or more occurrences of an alphanumeric character (a word)
  • \s+ corresponds to a series of one or more occurrences of spaces
  • \. is the dot character
  • {number_1, number_2} looks for at least number_1 repetitions of the previous element (with at most number_2 repetitions)

Therefore, in plain language, the above regular expression is

(a word followed by a comma followed by some space) OR (a word followed by some space) REPEATED AT LEAST 20 TIMES (a word followed by a full stop OR a question mark OR an exclamation mark)

This clearly allows us to detect sentences that may be long, very long, very very long, at least as long as this very sentence!

Screen Shot 2018-03-31 at 11.43.49
An example of a match in Sublime Text. Notice that the regular expression button .* on the bottom left corner of the search field is pressed.

Experimental determination of configurational entropy in a two-dimensional liquid under random pinning

A glass is (broadly speaking) mostly composed of particles that very slowly move due to surrounding cages formed by the disordered structure of the neighbouring particles. A way to study the glass transition is to actually freeze-in a subset of the particles and observe how this induces changes to the slow relaxation and how this relates to the emergence of local order.

The freezing-in procedure (also called pinning) has a secondary important effect: the pinned liquid has a “simplified” configurational space, as many configurations become forbidden. The number of available configurations (and hence the configurational entropy of the liquid) is therefore reduced by the simple pinning procedure and if a thermodynamic origin of dynamical arrest is to be surmised, such a reduction would be a necessity.

Some years ago, Ian Williams designed a novel, clever way to pin large two-dimensional colloidal supercooled liquids. In an article recently accepted in the Journal of Physics: Condensed Matter we have shown that the technique allows us to observe the crossover from a free-flowing liquid to a pinned glass and that this is accompanied by very limited structural changes. However, if we map the configurational entropy of the experiments with the entropy measured from model numerical simulations, we do observe that accounting for the fraction of pinned particles leads to a reduction in the estimated configurational entropy.

Full reference:

I. Williams, F. Turci et al. (2018) Experimental determination of configurational entropy in a two-dimensional liquid under random pinning, J. Phys.: Condens. Matter in press https://doi.org/10.1088/1361-648X/aaa869

Segmenting 3d biological data

I have recently been given the opportunity to study the segmentation of 3D data.  The group of Dr. C. Hammond of the School of Physiology, Pharmacology and Neuroscience in Bristol studies malformation in tissues of  Zebrafish  a model organism which can be genetically manipulated relatively easily .

A major task is to identify bone malformation or osteoarthritis. Hammond’s group manages to image hundreds of Zebrafish in three dimensions so that bone structures can be visualised. Identifying bone deformations in the spine, for example, is key to associate them to specific genetic marker. To do so, a quantitative analysis of the structure of the individual vertebrae is necessary.

It turned out that it is possible to do this via image analysis techniques that are publicly available in Python: the key libraries that I employed are scipy. ndimage and scikit-image.  Identifying the vertebrae in 3d means to perform  a segmentation of volumes and surfaces in 3d images.

An example of the vertebrae, individually resolved, can be visualised in 3d here below:

Long-lived non-equilibrium interstitial solid solutions in binary mixtures

We just published on the Journal of Chemical Physics the experimental and computer simulation work of a Ioatzin Rios de Anda (PhD student in the Royall group) on kinetically arrested crystalline phases in colloidal binary mixtures.

Despite slightly different conditions (presence/absence of confinement or polydispersity in the particle sizes) the experiments and simulations match in the fundamental message of the work: when we have two species rather different in sizes, crystallisation of the bigger species can occur before the reordering of the smaller species, forming long-lived kinetically arrested structures (interstitial solid solutions), characterised by a high density of imperfections and vacancies. This shows how challenging the formation of a well ordered binary crystal is and, on the other hand, how they can potentially be considered for the realisation of partially ordered porous matrices.

Full reference:
Rios de Anda, I., Turci, F., Sear, R., & Royall, P.  Journal of Chemical Physics, 147, 124504 (2017).

Weak temperature dependence of ageing of structural properties in atomistic model glassformers

We have just published in the Journal of Chemical Physics the simulation work of a brilliant former master student of the School of Physics at the University of Bristol (Thomas Jenkinson) on the local structural changes occurring during ageing in two atomistic glass formers with Lennard-Jones interactions (the Kob-Andersen and Wahnström mixtures).

We find some expected results (local order steadily increases as the out-of-equilibrium liquid ages) and some more surprising ones (for example, the rate at which such increase occurs changes weakly for temperatures above the apparent dynamical divergence of viscosities, T0). We also investigate the effect of transient deep quenches, finding very moderate traces of so-called rejuvenation.

The reference to the work is J. Chem. Phys. 147, 054501, (2017).

Nonequilibrium Phase Transition in an Atomistic Glassformer: the Connection to Thermodynamics

One central piece of the problem of dynamic arrest is whether the phenomenology of slow relaxation, increasing dynamical length scales, mild (or dramatic) structural changes are somewhat related to the existence of a zero entropy amorphous state emerging at a non-zero temperature.

A comprehensive theory would need on the one hand to take into account of the well established phenomenon of dynamical heterogeneitiesi.e. the non-homogenous patterns of diffusion that emerge together with the glassy dynamics itself; on the other hand, it should also rationalise the many findings that point (for several model systems) to a dramatic reduction of the so-called configurational entropy as one approaches a finite temperature (sometimes termed Kauzmann temperature) at which also the relaxation times appear to diverge.

In our recent work (Physical Review X 7, 031028) Thomas Speck,  C. Patrick Royall and I discuss a unified scenario that combines dynamical aspects to structural ones in order to sample very low energy and entropy states, employing dynamical large deviations.

We find that the equilibrium supercooled liquid competes with a secondary metastable  amorphous liquid rich in long-lived structural motifs, hidden in the tails of probability distributions in trajectory space. We also show that sampling the tails of such probabilities at a single moderate temperature allows us to retrieve the thermodynamic properties of the ordinary liquid in much wider range of temperatures, down to very low temperatures. We can then draw a diagram for the stable and metastable phase, pointing towards critical-like fluctuations in the region where the Kauzmann temperature is normally located, and allowing us to review currently proposed scenarios from an alternative point of view, rooted in the large deviation theory of metastability.

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