OCT4 expression in human embryonic stem cells: spatio-temporal dynamics and fate transitions.

The improved in vitro regulation of human embryonic stem cell (hESC) pluripotency and differentiation trajectories is required for their promising clinical applications. The temporal and spatial quantification of the molecular interactions controlling pluripotency is also necessary for the development of successful mathematical and computational models. Here we use time-lapse experimental data of OCT4-mCherry fluorescence intensity to quantify the temporal and spatial dynamics of the pluripotency transcription factor OCT4 in a growing hESC colony in the presence and absence of BMP4. We characterise the internal self-regulation of OCT4 using the Hurst exponent and autocorrelation analysis, quantify the intra-cellular fluctuations and consider the diffusive nature of OCT4 evolution for individual cells and pairs of their descendants. We find that OCT4 abundance in the daughter cells fluctuates sub-diffusively, showing anti-persistent self-regulation. We obtain the stationary probability distributions governing hESC transitions amongst the different cell states and establish the times at which pro-fate cells (which later give rise to pluripotent or differentiated cells) cluster in the colony. By quantifying the similarities between the OCT4 expression amongst neighbouring cells, we show that hESCs express similar OCT4 to cells within their local neighbourhood within the first two days of the experiment and before BMP4 treatment. Our framework allows us to quantify the relevant properties of proliferating hESC colonies and the procedure is widely applicable to other transcription factors and cell populations.

Knot spectrum of turbulence.

Streamlines, vortex lines and magnetic flux tubes in turbulent fluids and plasmas display a great amount of coiling, twisting and linking, raising the question as to whether their topological complexity (continually created and destroyed by reconnections) can be quantified. In superfluid helium, the discrete (quantized) nature of vorticity can be exploited to associate to each vortex loop a knot invariant called the Alexander polynomial whose degree characterizes the topology of that vortex loop. By numerically simulating the dynamics of a tangle of quantum vortex lines, we find that this quantum turbulence always contains vortex knots of very large degree which keep forming, vanishing and reforming, creating a distribution of topologies which we quantify in terms of a knot spectrum and its scaling law. We also find results analogous to those in the wider literature, demonstrating that the knotting probability of the vortex tangle grows with the vortex length, as for macromolecules, and saturates above a characteristic length, as found for tumbled strings.

Quantum Ferrofluid Turbulence.

We study the elementary characteristics of turbulence in a quantum ferrofluid through the context of a dipolar Bose gas condensing from a highly nonequilibrium thermal state. Our simulations reveal that the dipolar interactions drive the emergence of polarized turbulence and density corrugations. The superfluid vortex lines and density fluctuations adopt a columnar or stratified configuration, depending on the sign of the dipolar interactions, with the vortices tending to form in the low-density regions to minimize kinetic energy. When the interactions are dominantly dipolar, the decay of the vortex line length is enhanced, closely following a t^{-3/2} behavior. This system poses exciting prospects for realizing stratified quantum turbulence and new levels of generating and controlling turbulence using magnetic fields.

Regimes of turbulence without an energy cascade.

Experiments and numerical simulations of turbulent 4He and 3He-B have established that, at hydrodynamic length scales larger than the average distance between quantum vortices, the energy spectrum obeys the same 5/3 Kolmogorov law which is observed in the homogeneous isotropic turbulence of ordinary fluids. The importance of the 5/3 law is that it points to the existence of a Richardson energy cascade from large eddies to small eddies. However, there is also evidence of quantum turbulent regimes without Kolmogorov scaling. This raises the important questions of why, in such regimes, the Kolmogorov spectrum fails to form, what is the physical nature of turbulence without energy cascade, and whether hydrodynamical models can account for the unusual behaviour of turbulent superfluid helium. In this work we describe simple physical mechanisms which prevent the formation of Kolmogorov scaling in the thermal counterflow, and analyze the conditions necessary for emergence of quasiclassical regime in quantum turbulence generated by injection of vortex rings at low temperatures. Our models justify the hydrodynamical description of quantum turbulence and shed light into an unexpected regime of vortex dynamics.

Stability of model flocks in a vortical flow.

We investigate the stability of self-propelled particle flocks in the Taylor-Green vortex, a steady vortical flow. We consider a model in which particles align themselves to a combination of the orientation and the acceleration of particles within a critical radius. We identify two distinct regimes: If alignment with orientation is dominant, the particles tend to be expelled from regions of high vorticity. In contrast, if anticipation is dominant, the particles accumulate in areas of large vorticity. In both regimes, the relative order of the flock is reduced. However, we show that there can be a critical balance of the two effects that stabilizes the flock in the presence of external fluid forcing. This strategy could provide a mechanism for animal flocks to remain globally ordered in the presence of fluid forcing, and it may also have applications in the design of flocking autonomous drones and artificial microswimmers.

Visualizing Pure Quantum Turbulence in Superfluid 3He: Andreev Reflection and its Spectral Properties.

Superfluid 3He-B in the zero-temperature limit offers a unique means of studying quantum turbulence by the Andreev reflection of quasiparticle excitations by the vortex flow fields. We validate the experimental visualization of turbulence in 3He-B by showing the relation between the vortex-line density and the Andreev reflectance of the vortex tangle in the first simulations of the Andreev reflectance by a realistic 3D vortex tangle, and comparing the results with the first experimental measurements able to probe quantum turbulence on length scales smaller than the intervortex separation.

Model flocks in a steady vortical flow.

We modify the standard Vicsek model to clearly distinguish between intrinsic noise due to imperfect alignment between organisms and extrinsic noise due to fluid motion. We then consider the effect of a steady vortical flow, the Taylor-Green vortex, on the dynamics of the flock, for various flow speeds, with a fixed intrinsic particle speed. We pay particular attention to the morphology of the flow, and quantify its filamentarity. Strikingly, above a critical flow speed there is a pronounced increase in the filamentarity of the flock, when compared to the zero-flow case. This is due to the fact that particles appear confined to areas of low vorticity; a familiar phenomena, commonly seen in the clustering of inertial particles in vortical flows. Hence, the cooperative motion of the particles gives them an effective inertia, which is seen to have a profound effect on the morphology of the flock, in the presence of external fluid motion. Finally, we investigate the angle between the flow and the particles direction of movement and find it follows a power-law distribution.

Quantum turbulent velocity statistics and quasiclassical limit.

Two research groups have measured turbulent velocity statistics in superfluid helium using different techniques. The results were in conflict: one experiment revealed Gaussian distributions (as observed in ordinary turbulence), the other experiment determined power laws. To solve the apparent puzzle, we numerically model quantum turbulence as a tangle of vortex filaments, and conclude that there is no contradiction between the two experiments. The transition from Gaussian to power law arises from the different length scales which are probed using the two techniques. We find that the average distance between the quantum vortices marks the separation between quantum and quasiclassical length scales.