Student Poster Abstracts

Confined Rayleigh-Taylor Instability

The interface between two stratified layers of fluids is stable when the denser fluid is on the bottom. The inverted situation, with the denser fluid on top, gives rise to the Rayleigh-Taylor instability. Setting up the unstable situation with clean initial conditions can be experimentally challenging. Here we take advantage of the inherent stratification of fluids formed by a different instability – the viscous fingering of miscible fluids inside a thin gap – to achieve controlled initial conditions for the Rayleigh-Taylor instability. By varying the thickness of the gap between two plates, b, we find that the instability is completely suppressed below a critical gap bc. As b is increased, the instability changes from this mass-diffusion dominated regime of stability, through an intermediate regime where the dynamics are set strictly by the gap, λ ∼ b, to the limit where the boundaries no longer affect the dynamics. In this last regime, the instability is governed by a competition between momentum diffusion and buoyancy as predicted by theory in the unconstrained limit. DOI: 10.1126/sciadv.abd6605

Studying the active collective motions of flexible filaments using Brownian Dynamics simulations

Ordered, collective motions commonly arise spontaneously in systems of many interacting, active particles, such as self-propelled colloids. Examples of active phases range from the flocking behavior seen in Active Brownian particles to anisotropic particle systems of active nematics where liquid crystalline order emerges. To understand the active phases formed in these anisotropic particle systems, understanding collective motion of active flexible chains is necessary. We use Brownian Dynamics simulations to study the collective motions of flexible chains that can ‘self-propel’. Depending on the energy cost of overlap of these chains and their flexibility, our model predicts that the active global state transitions between an active polar state and an active nematic state. Our model also suggests that the active global nematic state is only transient and eventually the system orders into an active global polar state. These global active states can be realized in gliding microtubule assay experiments.

Thermodynamics of microdroplet phase in elastic phase separation

We study the thermodynamics of binary mixtures with the volume fraction of the minority component less than the amount required to form a flat interface and show that the surface tension dominated equilibrium phase of the mixture forms a single macroscopic droplet. Elastic interactions in gel-polymer mixtures stabilize a phase with multiple droplets. Using a mean-field free energy we compute the droplet size as a function of the interfacial tension, Flory parameter, and elastic moduli of the gel. Our results illustrate the role of elastic interactions in dictating the phase behaviour of biopolymers undergoing liquid-liquid phase separation.

A model for the infection dynamics of a urinary catheter

Catheter associated urinary tract infections (CAUTI) constitute up to 40% of hospital acquired infections, yet there is still limited understanding of how CAUTI develops. By combining population dynamics and fluid dynamics, I construct a mathematical model to find new insight. Within this model, bacteria spread as a wave on the external surface of the catheter. On reaching the bladder they proliferate within the urine, before being swept down the inside of the catheter by the urine flow. Some bacteria stick to the inside surface of the catheter, where they grow just as on the outside. From this model, the rate of urine production by the kidneys emerges as a critical parameter, governing a pseudo second-order phase transition. Low urine production rates give rise to an infected bladder state, transitioning, as the rate increases, into a washed-out state where the catheter can still be infected but there is no detectable growth within the urine.

Leidenfrost effect as a directed percolation phase transition

Volatile drops deposited on a hot solid can levitate on a cushion of their own vapor, without contacting the surface. We propose to understand the onset of this so-called Leidenfrost effect through an analogy to non-equilibrium systems exhibiting a directed percolation phase transition. When performing impacts on superheated solids, we observe a regime of spatiotemporal intermittency in which localized wet patches coexist with dry regions on the substrate. We report a critical surface temperature, which marks the upper bound of a large range of temperatures in which levitation and contact coexist. In this range, with decreasing temperature, the equilibrium wet fraction increases continuously from zero to one. Also, the statistical properties of the spatio-temporally intermittent regime are in agreement with that of the directed percolation universality class. This analogy allows us to redefine the Leidenfrost temperature and shed light on the physical mechanisms governing the transition to the Leidenfrost state.

Weakly nonlinear evolution of stochastically driven nonnormal systems

We consider nonlinear dynamical systems driven by a stochastic forcing. It has been largely evidenced in the literature that the linear response of nonnormal systems may exhibit a large variance amplification even in a linearly stable regime. It is typically the case for some parallel or nonparallel fluid flows, governed by the Navier-Stokes equations [1,2,3]. However, the linear response is relevant only in the limit of vanishing forcing intensity. As the latter increases, the spectrum and the variance of the response may be strongly modified, owing to nonlinear effects [4]. To go beyond this limitation, we propose a theoretical approach to derive an amplitude equations governing the weakly nonlinear evolution of these systems. This approach, contrarily to classical ones, does not rely on the presence of an eigenvalue close to the neutral axis, and the Fourier components of the response are allowed to be arbitrarily different from any eigenmode. It applies to any sufficiently nonnormal operator, and reconciles the nonnormal nature of the growth mechanisms with the need for a center manifold to project the leading-order dynamics. The methodology is outlined for a generic nonlinear dynamical system, and the application case highlights a common [2] nonnormal mechanism in hydrodynamics: the convective nonnormal amplification in the flow past a backward-facing step. At low numerical cost, the amplitude equation quantifies the respective contribution of each dominant nonlinear interaction, thus bringing insight on the saturation mechanisms of the stochastic amplification.

[1] Farrell and Ioannou, Phys. Fluids A 5, 11 (1993).
[2] Dergham et al., J. Fluid Mech. 719, (2013).
[3] Fontane et al., J. Fluid Mech. 613, (2008).
[4] Mantic-Lugo et al., Phys. Rev. Fluids 1, (2016)

The small-amplitude dynamics of spontaneous tropical cyclogenesis

Spontaneous tropical cyclogenesis over a uniform sea surface temperature is an idealized setup for studying the formation of tropical cyclones. While the longwave radiation feedback and surface flux feedback have been identified as the main mechanisms for the growth of the perturbation at the early stage, there is no theoretical model for the growth rate and length scale of the perturbation. In this paper, we develop a theoretical framework based on Fourier analysis to understand the small-amplitude dynamics revealed in the cloud-permitting simulations. Initially, the random stretching of planetary vorticity by the stochastic convection produces an initial vorticity perturbation that is proportional to the square root of the domain-averaged accumulated rainfall. The perturbation then kicks off a mesoscale hydrodynamic instability that features an exponential growth. The mesoscale instability has a clear most unstable mode, which is theoretically shown to be below the Rossby deformation radius and above a convective spreading length scale. This convective spreading length scale is considered to depend on the spread of convective activity by cold pools and the nonlocal longwave radiative heating by the anvil clouds. These hypotheses are confirmed by cloud-permitting simulations that modify the sub-cloud rain evaporation rate and horizontally filter the longwave radiative heating tendency respectively.

Wavelength selection in transitional turbulence

The transition to turbulence in plane shear flows is characterized by coexisiting turbulent and laminar zones. Unlike in the case of pipe flow, these zones appear in the form of regular patterns, oblique in the streamwise-spanwise plane. The mechanism explaining how those statistically steady structures arise from uniform turbulence is still unclear: is it due to a random nucleation of laminar gaps; or to a long-wavelength instability of the uniform turbulent flow?

We first address this question by using periodic domains of restricted lengths and fixed tilt, where patterns of fixed wavelengths can exist, over a limited range in Reynolds number. The stability of such fixed-wavelength patterns is studied as a function of Reynolds number, showing that there is a prefered wavelength (around 40 half-gaps) for which the pattern is most stable.

We secondly study the impact of the mean flow along those turbulent bands. We therefore introduce a Modified Plane Couette flow, in which the large-scale spanwise velocity is suppressed, while still allowing modulations of the streamwise velocity, necessary for the existence of turbulent bands. We show that in the absence of large-scale spanwise flow, laminar gaps appear at random locations in space and time (like the puffs in pipe flow). This suggests that the regular patterned appearance of gaps is related to large-scale spanwise flow but not essential to the evolution of bands in Plane Couette Flow.

Transport of a passive rod in an active nematic film

Suspended particles offers a means to measure the transport and rheological properties in many turbulent flows in industrial and natural environments. A class of internally-driven, biologically inspired fluids, called active nematics, demonstrate large scale turbulent-like flows at low Reynolds numbers. Motivated by experimental work, we study the transport of passive colloidal rods suspended in water above an active nematic film via a coarse-grained MPCD algorithm. We find that the rods respond to the active flows to preferentially advance towards stagnation points in the flow field. Further, the rods orientation couples to the hydrodynamic stresses of the film, to maintain alignment with the underlying local director. These results may shed light of the interplay between passive and active constituents in hybrid systems.

Noise thermometry in electron hydrodynamics

Johnson noise thermometry, based on the Johnson-Nyquist theorem, offers a powerful primary thermometry technique to access the electron temperature at the nanoscale. In practical situations, one needs to generalize the Johnson-Nyquist theorem to handle spatially inhomogenous temperature profiles. This was previously done for Wiedemann-Franz-obeying ohmic devices, where it was found that Joule heating leads to a geometry-independent increase in Johnson noise. However, there has been great recent interest in strongly-interacting electron hydrodynamic systems which do not admit a local conductivity nor obey the Wiedemann-Franz law, signatures of which have even been observed in previous thermometry experiments. In this paper, we study low-frequency Johnson noise in the hydrodynamic setting for a rectangular geometry. As opposed to the ohmic setting, we find that the Johnson noise is no longer geometry-independent due to non-local viscous gradients. Despite this, ignoring the geometric correction only leads to an error of at most 40% as compared to naively using the ohmic result.

Stokes flows in three-dimensional fluids with odd and parity-violating viscosities

The Stokes equation describes the motion of fluids when inertial forces are negligible compared to viscous forces. In this presentation, we explore the consequence of parity-violating and non-dissipative (i.e. odd) viscosities on Stokes flows in three dimensions. Parity-violating viscosities are coefficients of the viscosity tensor that are not invariant under mirror reflections of space, while odd viscosities are those which do not contribute to dissipation of mechanical energy. These viscosities can occur in systems ranging from synthetic and biological active fluids to magnetized and rotating fluids. We first systematically enumerate all possible parity-violating viscosities compatible with cylindrical symmetry, highlighting their connection to potential microscopic realizations. Then, using a combination of analytical and numerical methods, we analyze the effects of parity-violating viscosities on the Stokeslet solution, on the flow past a sphere or a bubble, and on many-particle sedimentation. In all the cases we analyze, parity-violating viscosities give rise to an azimuthal flow even when the driving force is parallel to the axis of cylindrical symmetry. For a few sedimenting particles, the azimuthal flow bends the trajectories compared to a traditional Stokes flow. For a cloud of particles, the azimuthal flow impedes the transformation of the spherical cloud into a torus and the subsequent breakup into smaller parts that would otherwise occur. The presence of azimuthal flows in cylindrically symmetric systems (sphere, bubble, cloud of particles) can serve as a probe for parity-violating viscosities in experimental systems.

Steady State Thermal Blooming with Convection

The modeling, simulation, and analysis of high energy laser propagation remains a research topic of pertinent interest to the defense community. In particular, steady-state thermal blooming is detrimental to the propagation of lasers over long distances and through atmospheric conditions with significant aerosol presence. The simulation of thermal blooming in the present literature relies on wave optics models and a priori averaging of aerosol effects. Since thermal blooming is a product of natural convection, however, there is a need for simulating this coupled fluid-beam effect using a first principles approach. We introduce a coupled method to solve the steady-state Boussinesq Navier–Stokes equations for fluid behavior with the paraxial equation for beam propagation. We consider three distinct schemes for solving the forced Boussninesq equations in stream function-vorticity variables in two dimensions: a fixed-point approach, a perturbation series expansion, and a Pade approximant. The functions governing fluid behavior at 2D slices along the propagation path are then used to determine index of refraction fluctuations as a result of laser-driven temperature fluctuations. Pertinent results include a proof of the existence of steady solutions for small laser intensities through the fixed-point method along with a convergence proof for the perturbation series of solutions in a laser intensity parameter. The Pade approximant is used to arrive at higher laser intensity solutions, and we discuss the analysis of the complex pole distribution of rational approximants to the fluid functions.

How does a material make memories?

Jammed systems which are cyclically sheared will often find periodic orbits after just a few cycles, thus encoding a memory of their drive amplitude. Aspects of these periodic orbits can be captured by models of interacting hysteretic regions (“hysterons”) that represent particle rearrangements in the jammed packings. However, there remains a gap between hysterons as a model and the rearrangements they aim to describe. Here, we study small jammed systems — on the order of 10 particles — to probe the nature of rearrangements. For packings with one pair of rearrangements (one hysteron) in their periodic orbit, we examine the two-state nature of the strain region between the rearrangements and begin to paint a more robust picture of the extent to which these systems behave like model hysterons.

Anomaly-induced transport regime in Weyl semimetals

We study propagation of an oscillatory electromagnetic field inside a Weyl semimetal. In conventional conductors, the motion of the charge carriers in the skin layer near the surface can be diffusive, ballistic, or hydrodynamic. We show that the presence of chiral anomalies, intrinsic to the massless Weyl particles, leads to a hitherto neglected transport regime, in which the relation between the current and the electric field becomes nonlocal as a result of the diffusion of the valley charge imbalance into the bulk of the material. We propose to use this novel regime as a diagnostic of the presence of chiral anomalies in optical conductivity measurements. These results are obtained from a generalized kinetic theory which includes various relaxation mechanisms, allowing us to investigate different transport regimes of Weyl semimetals.

Metachronal waves in swarms of nematode Turbatrix aceti

There is a recent surge of interest in the behavior of active particles that can at the same time align their direction of movement and synchronize their oscillations, known as swarmalators. I will present an experimental investigation of the collective motion of the nematode Turbatrix aceti, which self-propel by body undulation. I will show that under favorable conditions these nematodes can synchronize their body oscillations, forming striking traveling metachronal waves that, similar to the case of beating cilia, produce strong fluid flows.

I will demonstrate that the location and strength of this collective state can be controlled through the shape of the confining structure; in our case the contact angle of a droplet. This opens a way for producing controlled work such as on-demand flows or displacement of objects. I will illustrate this by a practical example: showing that the force generated by the collectively moving nematodes is sufficient to change the mode of evaporation of fluid droplets, by counteracting the surface-tension force, which allow us to estimate its strength.

Exact solution for the thermalization transition in a model fracton system

In fracton systems, the dynamics is constrained by higher-order conservation laws, such as the conservation of both charge and dipole moment. In certain situations, these constraints prevent the system from thermalizing by causing a “fragmentation” of the Hilbert space into many dynamically disconnected sectors. In this work we consider a simple one-dimensional lattice of charges that evolve under the influence of random local operators that conserve both charge and dipole moment. This system exhibits a thermalization transition as a function of the total charge, such that only systems with sufficiently large charge density are able to thermalize. We construct an exact solution for this transition by mapping the dynamics to two different problems in combinatorics. Our solution allows us to identify the critical charge density as a function of the gate size, as well as the critical scaling and certain critical exponents.

Active Extensile Stress Promotes 3D Director Orientations and Flows

We use numerical simulations and linear stability analysis to study an active nematic layer where the director is allowed to point out of the plane. Our results highlight the difference between extensile and contractile systems.

Contractile stress suppresses the flows perpendicular to the layer and favors in-plane orientations of the director. By contrast, extensile stress promotes instabilities that can turn the director out of the plane, leaving behind a population of distinct in-plane regions that continually elongate and divide. Our results suggest a mechanism for the initial stages of layer formation in living systems and explain the propensity of dislocation lines in three-dimensional active nematics to be of twist-type in extensile, or wedge-type in contractile, materials.

Turbulent Relaxation to Equilibrium in a Two-Dimensional Quantum Vortex Gas

We experimentally study the emergence of microcanonical equilibrium states in the turbulent relaxation dynamics of a two-dimensional chiral vortex gas. Same-sign vortices are injected into a quasi-two-dimensional disk-shaped atomic Bose-Einstein condensate using a range of mechanical stirring protocols. The resulting long-time vortex distributions are found to be in excellent agreement with the mean-field Poisson Boltzmann equation for the system describing the microcanonical ensemble at fixed energy H and angular momentum M. The equilibrium states are characterized by the corresponding thermodynamic variables of inverse temperature β and rotation frequency ω. We are able to realize equilibria spanning the full phase diagram of the vortex gas, including on-axis states near zero temperature, infinite temperature, and negative absolute temperatures. At sufficiently high energies, the system exhibits a symmetry-breaking transition, resulting in an off-axis equilibrium phase at negative absolute temperature that no longer shares the symmetry of the container. We introduce a point-vortex model with phenomenological damping and noise that is able to quantitatively reproduce the equilibration dynamics.

Flow around topological defects in active nematic films

Jonas Rønning¹, M. Cristina Marchetti², Mark J. Bowick³ and Luiza Angheluta¹

1. Njord Centre, Department of Physics, University of Oslo, P. O. Box 1048, 0316 Oslo, Norway
2. Department of Physics, University of California Santa Barbara , Santa Barbara, CA 93106, USA
3. Kavli Institute for Theoretical Physics, University of California Santa Barbara, Santa Barbara, CA 93106, USA

The hydrodynamics of active nematics is characterized by an active turbulence regime whereby topological defects proliferate and interact with each other. The nematic state corresponds to orientational order, which is punctuated by half integer disclinations, as lowest energy defects. We study the flow induced by the active stress around isolated ±1/2 defects in an active nematic film in the presence of both viscous dissipation (η) and friction with the substrate (Γ). The interplay between the two dissipation mechanisms gives rise to a length scale〖 l〗_d^2=η/Γ, which sets the scale of the self-propulsion velocity for the +1/2 defect, and the scale for the decay of flow velocity and vorticity. Spanning vortices with alternating vorticity are formed around the defect in an active nematic film confined to a disk. The shape of these vortices, in addition to the self-propulsion of the positive defect, is determined by the relation between the discs radius R and〖 l〗_d. For small systems, in units of l_d, the velocity is proportional to the radius. As the size become larger the velocity become set by the dissipation length and the vortices become elongated. In the limit of R→∞ the vortices closes at infinity.

Triangular Pair-Density Wave in Confined Superfluid 3-He

Recent advances in experiment and theory suggest that superfluid 3He under planar confinement may form a pair-density wave (PDW) whereby superfluid and crystalline orders coexist. While a natural candidate for this phase is a unidirectional stripe phase predicted by Vorontsov and Sauls in 2007, recent nuclear magnetic resonance measurements of the superfluid order parameter rather suggest a two-dimensional PDW with noncollinear wavevectors, of possibly square or hexagonal symmetry. In this work, we present a general mechanism by which a PDW with the symmetry of a triangular lattice can be stabilized, based on a superfluid generalization of Landau’s theory of the liquid-solid transition. A soft-mode instability at finite wavevector within the translationally invariant planar-distorted B phase triggers a transition from uniform superfluid to PDW that is first order due to a cubic term generally present in the PDW free-energy functional. This cubic term also lifts the degeneracy of possible PDW states in favor of those for which wavevectors add to zero in triangles, which in two dimensions uniquely selects the triangular lattice.

*P.S.Y. was supported by the Alberta Innovates Graduate Student Scholarship Program. R.B. was supported by Département de physique, Université de Montréal. J.M. was supported by NSERC Discovery Grants Nos. RGPIN-2014-4608, RGPIN-2020-06999, RGPAS-2020-00064; the CRC Program; CIFAR; a Government of Alberta MIF Grant; a Tri-Agency NFRF Grant (Exploration Stream); and the PIMS CRG program.

Both colonization and competition abilities determine the fitness at the frontier of an expanding population

Bacteria colonize new territory in a process known as range expansion. This expansion is driven by the division of bacteria, allowing for the expanding population to accrue mutations resulting in evolution at the expansion front. In most cases, evolution will select for a faster expansion rate. However, there have been reported cases where a mutant evolves which expands slower than the wildtype and yet is able to out-compete the wildtype strain in coculture. This competition between fast and slow expanders generates dented fronts which we study in this work. We present a theory describing the competition at the boundary of a growing front between two populations. In typical one-dimensional competition, invasion generates a travelling wave which can be either ”pulled” or ”pushed”. We generalize these cases to competition on a growing front in both pulled and pushed regimes. We then demonstrate how coupling competition to the morphology of the expansion can have large effects on both the invasion velocity and the outcome of competition.

Are all two-dimensional turbulent flows born equal? -- A study of two-dimensional turbulence driven by an instability

Instabilities of fluid flows often generate turbulence. Using extensive direct numerical simulations, we study two-dimensional turbulence driven by a wavenumber-localised instability superposed on stochastic forcing, in contrast to previous studies of state-independent forcing. As the instability growth rate increases, the system undergoes two transitions. For growth rates below a first threshold, a regular large-scale vortex condensate forms. Above this first threshold, shielded vortices (SVs) emerge and coexist with the condensate. At a second, larger value of the growth rate, the condensate breaks down, and a gas of weakly interacting vortices with broken symmetry spontaneously emerges, characterised by preponderance of vortices of one sign only and suppressed inverse energy cascade. The number density of SVs in this broken symmetry state slowly increases via a random nucleation process. Bistability is observed between the condensate and mixed SV-condensate states. Our findings provide new evidence for a strong dependence of two-dimensional turbulence phenomenology on the forcing.

Stochastic model for the laminar-turbulent transition in pipe flow

In transitional pipe turbulence, a sequence of phases is observed experimentally in the range of Reynolds numbers between 1900 and 5000, passing through the laminar-turbulent transition at Re ~ 2040. These phases are characterized by transient decay of puffs (Re < 2040), puff-splitting and propagation (2040 < Re < 2250), expansion of turbulent regions via “weak slugs” (asymmetric upstream and downstream fronts, 2250 < Re < 4500), and via “strong slugs” (symmetric upstream and downstream fronts, Re > 4500). In earlier work, an intrinsically stochastic model for puff-decay and splitting accounted for the corresponding single-puff super-exponential timescales. This model focused on the dynamics and fluctuations within a single puff and described the near-critical behavior of transitional pipe flow. Here we extend this model by considering the previously neglected energy balance and turbulence-shear flow interaction. The resulting model recapitulates the full phase diagram of the transition, successfully capturing the mechanism of puff splitting and pushing and the puff-slug transition. Structural stability analysis on the model also shows the deep connection between the subcritical bifurcation picture and the directed percolation picture of the transition. The model is not restricted to pipe flow geometry and is extendable to other transitional shear flows like quasi-one-dimensional Taylor-Couette flow.

Topological Signature of Stratospheric Poincare -- Gravity Waves

The rotation of the earth breaks time-reversal and parity symmetries in an opposite sense north and south of the equator, leading to a topological origin for certain atmospheric and oceanic equatorial waves. Away from the equator the shallow water and stably-stratified primitive equations show that Poincaré-gravity waves have nontrivial topology as evidenced by a phase singularity in frequency-wavevector space.  This non-trivial topology then predicts, via the principle of bulk-boundary correspondence, the existence of two equatorial waves, the Kelvin and Yanai waves.  To verify the existence of these topological properties, we examine ERA5 reanalysis data to study cross-correlations between the wind velocity and geopotential height in the mid-latitude stratosphere at the 50 hPa level, and find the expected vortex and anti-vortex in the phase of the correlations at the frequencies of the Poincaré-gravity waves. These results demonstrate a new way to deepen understanding of waves in the stratosphere, and this approach provides a new tool for investigating waves in other components of the climate system.