Session A24: GSNP Dissertation, Graduate Student, and Post-doctoral Speaker Awards

Geometry and Topology in Motion

Topological and geometric ideas are now a mainstay of condensed matter physics, underlying much of our understanding of conventional materials in terms of defects and geometric frustration in ordered media, and protected edge states in topological insulators. In this talk, I will argue that such an approach successfully identifies the relevant physics in metamaterials and active matter as well, even when traditional techniques fail. Novel topological phenomena acquire unique realizations in active fluids that pose a particular challenge to conventional statistical mechanics, by virtue of being far from equilibrium. I will present some recent results to illustrate this and show how spontaneous flow on complex substrates can mimic synthetic gauge fields allowing them to be fruitfully viewed using topological ideas and analogies with superconductors.
  

Minimal Model for Intermittent Dynamics and "Turbulence" in Many-Body Systems

Complex systems are known to exhibit emergent properties that are missing on the constituent level. One particular property shared by many seemingly unrelated complex systems is intermittent switching between distinct dynamical states. Inspired by our previous experimental findings [1], here we present computational results for a particle-based system that exhibits intermittent switching between two distinct phases. The emergent dynamics are a direct consequence of coupling between structural disorder arising from particle polydispersity, inertial dynamics, and external forcing. Modelling the orthogonal mechanical energies of the system using ODEs with both noise and coupling terms based on kinetic arguments surprisingly results into predator-prey-like interactions. Such equations have recently been employed to describe intermittent turbulence in a pipe flow [2]. The only non-dimensional number derived from our equations resembles the Reynolds number in fluid flow and accurately predicts where intermittent dynamics are manifested.
1. G.Gogia, and J. C. Burton. PRL,119.17 (2017):178004
2. H-Y. Shih, T-L. Hsieh, and N.Goldenfeld. Nat.Phys. 12.3 (2016):245   

Vortices, space-time braids and loops in the membrane of a living cell

Topological defects determine the structure and function of matter over a wide range of scales. Many advances have been made in understanding and controlling the defect dynamics in active and passive non-equilibrium fluids. Yet, it remains unknown whether the statistical laws which govern the dynamics of defects in classical or quantum fluids extend to active living matter. Here, we show a defect-mediated turbulence underlies the complex wave propagation patterns of Rho-GTP signaling proteins on the membrane of starfish oocytes. Our experiments reveal that the phase-velocity field extracted from Rho-GTP concentration patterns exhibits vortical defect motions and annihilation dynamics reminiscent of those seen in quantum systems. Space-time analyses of defect trajectories reveal the existence of two characteristic types of braids: loops braided by multiple pairwise creation and annihilation events, and long-lived defect pairs that wiggle and form braid groups. Several key statistics and scaling laws of the defect dynamics, braids and loops can be captured by a generic complex Landau-Ginzburg continuum theory, suggesting space-time braids and loops are useful topological measures for unraveling information scrambling and transmission in dissipative living systems.   

A mechanical model for supervised learning

A broad goal of engineering is to make functional machines with specific, programmed input-output responses. When inputs are specified in advance and few in number, this goal is sought through rational design, changing the system elements to obtain desired responses. In the supervised learning framework of computer science, system parameters (synapses) are modified in response to observed examples of the correct input-output mapping (classification).
In this work, we apply the supervised learning framework to self-folding sheets, using a physically motivated learning rule. The trained sheet classifies labeled forces by folding into discrete folded states. These sheets succeed in classifying real-world data like Iris flowers, and also generalize, similar to other learning algorithms. As learning provides a straightforward framework to programming complex input-output relationships, we hope that implementing these ideas in engineering could usher in new classes of machines, that have so far eluded design.   

Ecological mechanisms of direct and indirect bacteriotherapies in generalized Lotka-Volterra systems

Over the last two decades, an association between microbiome composition and some human diseases has been unambiguously established. The correlation between gut microbe composition and these diseases has prompted medical interest into bacteriotherapies, which seek to modify the gut microbiome composition in the hopes of treating the correlated disease. In this work we use generalized Lotka-Volterra (gLV) models to probe the ecological mechanisms through which these bacteriotherapies function. We first describe direct bacteriothapies, which drive a microbiome to a target state via an instantaneous influx of foreign microbes (e.g. probiotics or fecal microbiota transplantation). Then, we present a novel control framework for indirect bacteriotherapies, which drive a microbiome to a target state by deliberately modifying its environment (e.g. diet, acidity, or nutrients). These dual control methods for gLV systems, interpreted as bacteriotherapies, could eventually inform personalized medicine for the microbiome.   

Noisy driven oscillators: Adaptive drives break the fluctuation-dissipation theorem

The steady-state dynamics of complex nonlinear systems include limit cycles in which the dynamic variables trace a closed path in phase space. Biological systems are replete with examples of such driven oscillators in a diverse range of systems including circadian rhythms, neuronal central pattern generators, and the active mechanics of hearing. These biological systems are inherently noisy, and they are typically controlled by active feedback. We explore the fluctuations and response functions of intrinsically noisy limit-cycle oscillators starting with models of stereocilium dynamics in the inner ear. We show that one can obtain a generalized fluctuations-dissipation theorem (GFDT) for the system in a reference frame comoving with the mean dynamical state moving about the limit cycle. However, in the presence of adaptive drives where there is feedback so that the energy input driving the oscillator depends on the state of the system, as in the driven stereocilium, even these generalized fluctuation theorems fail. We further explore the essential role of these feedback mechanisms in breaking GFDTs in noisy driven systems using a combination of simple computational models, analytical calculations, and stereocilium dynamics data.   

Diffusive behavior in walking droplets

Fluid droplets walking on a vibrating fluid bath have been observed to display deterministic diffusion. We present an experimental and theoretical investigation of such droplets. In our experiments a droplet is placed into an annular region on a vibrating fluid bath. The droplet motion becomes increasingly diffusive as the bath vibration is intensified above the Faraday wave threshold. This is also captured in our hydrodynamic – kinematic models, which shows close agreement between theory and experiments. Since the model can be studied at a much higher spatio-temporal resolutions than experiments, we use the model to numerically investigate bifurcations and chaotic dynamics suggested by experiments. Finally, we briefly discuss the possibility of model reduction to mitigate computational costs.   

Exotic Soft Modes in 2D Mechanical Metamaterials Yield Powerful New Analytic Prediction Methods

Maximally Auxetic behavior, where Poisson’s ratio is the most negative, has been explored and identified in 2D perforated elastic sheets in which rigid square elements are connected at the corners by comparatively flexible elastic “hinges”. While these metamaterials are designed to emulate a uniform zero-energy motion of the free hinge material (mechanism), experiments have revealed qualitatively different non-uniform mechanical response. To understand this, we utilize a coarse graining approach, combined with highly detailed finite element simulations and experiments, to reveal that the perforated elastic sheet mechanics is controlled by a novel set of soft modes that correspond precisely to the well-studied planar Conformal Maps. We exploit this very convenient result to demonstrate new and highly accurate methods of analytically solving for linear and non-linear deformations of real materials. This includes a powerful holographic approach, in which large non-linear deformations may be predictably controlled by simple actuation at the boundary. Finally, we introduce a more general methodology for identifying and controlling the soft modes associated with a broad class of 2D mechanisms including the Miura and Eggbox origami patterns.   

Low frequency vibrations of deformable particles

Disk packings at jamming onset exhibit an excess of low-frequency vibrational modes compared to the number predicted by Debye scaling. The excess number of modes, which controls the mechanical response of packings, decreases as the packings are compressed above jamming onset. In this work, we calculate the spectrum of vibrational modes from the eigenvalues of the dynamical matrix for truly deformable particles at jamming onset as a function of the shape parameter A = p²/(4πa), where p is the perimeter and a is the area of the particle. We show that there is an excess number of low frequency, collective modes in the density of vibrational modes for jammed packings of deformable particles over a wide range of particle shape both above and below the characteristic value A ≈ 1.15 at which the system is confluent.   

Hydrodynamic memory and driven microparticle transport: hedging against fluctuating sources of energy

In a viscous fluid, the motion of an accelerating particle is retained as an imprint on the vorticity field, giving rise to the famous t^-3/2 decay of the velocity autocorrelation. For nonuniform particle motion at low Reynolds number, this hydrodynamic memory effect is captured by the Basset-Boussinesq-Oseen (BBO) equation, which can be derived from various physical perspectives, including (fluctuating) hydrodynamics and kinetic theory. Moreover, finite-temperature dynamics can be modeled by using fluctuation-dissipation to reincorporate (correlated) thermal noise, turning BBO into a generalized Langevin equation. In this work, we numerically solve the BBO equation to simulate driven microparticles and show that hydrodynamic memory generally reduces transport friction, particularly when driving forces do not vary smoothly. Remarkably, this enables coasting over uneven potentials that otherwise trap particles modeled by pure Stokes drag. Our results are germane to questions surrounding intracellular transport efficiency and, more generally, provide direct physical insight into the role of particle-fluid coupling in microparticle transport.   

Landscapes, nonlinearity, and optimality of ion transport in sub-nanoscale pores

Biological ion channels evolved to have high transport rates and high selectivity, among other functional characteristics. Synthetic nanoscale pores aim to mimic these properties for applications such as desalination and osmotic power generation.¹ In these systems, ion-ion and ion-channel interactions occur at sub-nanometer distances which entails large electrostatic and dehydration energies.² The balance of these energies determines selectivity and permeation rates. Importantly, the susceptibility of transport and selectivity to minute changes in distances—changes on the order of picometers—is enormous resulting in highly-nonlinear behavior. Biological systems can exploit this susceptibility via variations in protein structure that steer the local electrostatic and structural conditions. We demonstrate how this works in a synthetic selectivity filter and discuss how to probe this system, which will help to experimentally quantify optimal transport conditions and will give the foundation for a robust understanding of more complex biological pores.
[1] S. Sahu & M. Zwolak, Rev. Mod. Phys. 91, 021004 (2019).
[2] S. Sahu, J. Elenewski, C. Rohmann, & M. Zwolak, Sci. Adv. 5, eaaw5478 (2019).