Session S51: Emergent self-organization in Active Matter II

Membrane rotors: from Euler vorticity dynamics to quasi-geostrophic flows

We show that the dynamics of rotors embedded in a quasi 2D membrane exhibit a power law transition in their interactions, from Euler fluid at small distances (1/r) , to quasi-geostrophic at large distances (1/r^2). We derive a Hamiltonian for a discrete system of rotors and describe the conserved quantities. We develop a coarse-grained description for a density field of rotors. Theory and simulations for both the discrete and the continuous cases are presented.   

The Effect of Scaffold Morphology on Tissue Growth

Cell proliferation within a porous tissue-engineering scaffold depends on a sensitive choice of pore geometry and flow rates: regions of high curvature encourage cell proliferation while a critical flow rate is required to promote growth for certain cell types. When the flow rate is too slow the nutrient supply is limited; too fast and cells may be damaged by the high shear. As a result, determining appropriate tissue engineering construct geometries and operating regimes poses a significant challenge that cannot be addressed by experimentation alone. In this work, we present a mathematical theory for the fluid flow within a pore of a tissue-engineering scaffold, which is coupled to the growth of cells on the pore walls. We exploit the slenderness of a pore that is typical in such a scenario, to derive a reduced model that enables a comprehensive analysis of the system to be performed. We derive analytical solutions in a particular case and compare this with numerical solutions of the reduced model. We demonstrate how the simplified system may be used to make predictions on the design of a tissue-engineering scaffold and the appropriate operating regime, and present an example in which such a prediction can be made.   

Experimental modeling of fluid homeostasis in the mammalian hearing organ

The mammalian hearing organ (cochlea), contains a long microfluidic channel where the ion concentration must be homogenized to enable the sensor cells that allow hearing. We hypothesize that homeostasis is achieved not only through diffusion, but by advective mixing caused by peristaltic flow in the cochlea. By determining the relevant physical parameters in the cochlea and applying fluid mechanics scaling laws, we design an apparatus that replicates conditions in the cochlea. Our apparatus consists of a square channel with a flexible wall what can be actuated to induce a flow in the channel. We seek to characterize the induced flow by using a particle imaging velocimetry system and calculating particle paths. Theory suggests that at the Reynolds number in the cochlea (Re ≈ 80) mixing will occur. We experimentally test a spectrum of parameters to verify theory predictions. The parameter region we study is also relevant for understanding other biophysical phenomena, as peristalsis is a common mechanism found in biological systems.   

Traveling waves in a hydrodynamic model for schooling swimmers

We construct and analyze a continuum model of a 1D school of flapping swimmers, which interact through their collectively generated fluid flows. Our model is is motivated by ongoing experiments in the Applied Math Lab at NYU, in which heaving wings self-propel and interact in a water tank. We investigate the properties of our evolution equations both analytically and numerically, and find that a uniform density of swimmers destabilizes into a traveling wave. Generally, our model indicates that hydrodynamics may play a role in organizing densely packed schools and flocks.   

Fluctuating Hydrodynamics in the 13-moment Approximation for Simulating Biomacromolecular Nanomachines

Proteins are nanomachines largely existing in ionic aqueous conditions that perform mechanicochemical work and whose dynamics span femtosecond timescales (i.e., covalent bond oscillations) to beyond the millisecond regime (e.g., glucose transport across a lipid membrane). All-atom molecular dynamics (MD) can fully capture solute-solvent interactions but is currently limited to microsecond timescales—orders of magnitude short of many biophysical timescales of interest. One viable means of overcoming this timescale problem is the hybrid atomistic-continuum (HAC) method where, for example, MD is used in a subdomain requiring atomistic detail while a hydrodynamic representation is used elsewhere to capture solvent dynamics. We are developing a 13-moment fluctuating hydrodynamics model that goes beyond Landau-Lifschitz Navier-Stokes theory—popular in HAC methods. Our numerical model is based on Grad's 13-moment approximation and can capture nonlinear, nanoscale transport phenomena such as emergent viscoelasticity and thermoacoustic effects arising in dense fluids like water. With a view toward understanding large proteins like molecular motors, potential advantages are described and preliminary results are presented.   

Self-driven phase transitions in living matter

The soil dwelling bacterium Myxococcus xanthus is an amazing organism that uses collective motility to hunt in giant packs when near prey and to form beautiful and protective macroscopic structures comprising millions of cells when food is scarce. I will present an overview of how these cells move and how they regulate that motion to produce different phases of collective behavior. Inspired by recent work on of active matter, I will discuss experiments that reveal how these cells generate nematic order and how they actively tune the Péclet number of the population to drive a phase transition from a gas-like flocking state to an aggregated liquid-droplet state during starvation.   

Hydrodynamic Clustering of Oriented Magnetotactic Bacteria at Solid-Liquid Interfaces

Magnetotactic bacteria are a group of motile prokaryotes that synthesize chains of membrane bound intracellular magnetic nanoparticles called magnetosomes. These particles endow the cells with a magnetic moment, which in general lie parallel to the direction of propulsion that is controlled by their rotating flagellar. Thus, the swimming behavior and orientation of the cell relative to surfaces is readily controlled by external magnetic fields. This property makes them an ideal system to investigate the many-body dynamics of self-propelled colloids. In this talk, the self-organization of magnetic bacteria into rotating clusters arising from hydrodynamic cell-cell interactions at solid-liquid interfaces is discussed. The pairwise hydrodynamic interactions are experimentally measured and compared with theoretical calculations. These findings lay the foundation for understanding the many-body dynamics of the clustering process. These hydrodynamically formed clusters are further manipulated by weak in-plane external fields which direct along them along well-defined trajectories and controllably confined with patterned micro-magnetic structures. The implications of these field-controlled phenomena for biology- based applications are discussed.
  

Collective gradient sensing in fish schools

Throughout the animal kingdom, animals frequently benefit from living in groups. Models of collective behavior show that group morphologies (swarms, flocks and mills) found in nature can be generated via local social interactions. However, individuals also interact with the complex noisy environment in which they live. In this work, we experimentally investigate the performance in navigating a noisy light gradient of two unrelated freshwater species, golden shiners (Notemigonus crysoleucas) and rummy nose tetra (Hemigrammus bleheri). We find that tetras outperform shiners due to their innate individual ability to sense the environmental gradient. Using numerical simulations, we examine how group performance depends on the relative weight of social and environmental information. Our results highlight the importance of individuals using a balanced weight of social and environmental information which promotes an optimal group morphology and performance.   

Ironing Out The Wrinkles: The Role of Buckling and Delamination in Structuring Rugose Biofilms

In nature, almost all biofilm constituents secrete extracellular products, which give biofilms many of their advantages over their single-celled constituents. One of the primary functions of these extracellular secretions is to structure the biofilm. However, the specifics of this structuring—and thus the degree to which it is valuable—depend strongly on material properties of the substrate on which is grows. Previous work [Nolte et al.] has shown that in thin polymer films on compliant substrates, both surface wrinkling and buckle delamination can occur. Here, we examine the presence and relative prevalence of wrinkling and delamination of rugose V. cholerae biofilms on agar substrates of difference stiffnesses using confocal microscopy, and argue that the secretion of EPSes in natural environments is a favorable strategy for structuring and survival.   

Active Matter with Intent: Clog Control in Excavating Collectives

Ensembles of self-propelling elements can form clusters, clogs and jams. In certain biological and robotic systems, clog mitigation is important for collective task completion. To discover principles by which individual and group behaviors facilitate clog control in such “task-oriented” active matter, we studied tunnel excavation in granular media using fire ants, autonomous robots and two models: cellular automata (CA) and a one worker model. We used tools from the study of dense particulate ensembles to provide insight into how different excavation strategies modulate congestion dynamics. These tools elucidated how participant idleness in robots and modelled ant systems reduced tunnel density and decreased the frequency of catastrophic clogs and how selective “retreats” reduced jam dissolution time for large clogs. In simulations, the maximum flux in an experimentally derived tunnel width (2 ant body width(BW)) occurred at a particular tunnel density. Experiments with ants in tunnels(2 BW) excavated by them in laboratory revealed that the ants selected a similar density, suggesting that the ants optimize the tunnel flux and thus excavation efficiency by implementing workload inequality and retreats, without need for global control.   

An Algorithmic Approach to Flocking Behavior: Reaching beyond Global Phases

We present a flocking model which is able to create a collective time-dependent
behavior (termed dynamic emergence in this work) which is seen to naturally occur in a group of hundreds of real birds. The model is based on the ideas of consensus and frustration, where consensus is a nonlinear topological averaging that drives the particles towards one of three unique phases, and frustration is a perturbation that pushes the particles beyond these simple phases. The nonlinearity merged with these two rules produces characteristics which go beyond the dynamic interplay of global phase transitions. The emergent results are interpreted in terms of global and local order parameters, and correlation functions. In this work, three consensus rules are considered namely metrical, topological, and fixed topological neighbors, while the frustration rule follows a simple U-turn. To elucidate the exchange of information among members of the flock, a network analysis is performed. In particular, a comparison between networks arosed in a consensus rule based on metrical, topological, and fixed topological neighbors interactions is made.   

Investigating Schooling Behavior with Statistical Mechanics

Collective behavior is ubiquitous in living systems. While there are several current models that successfully describe qualitative features of collective structures in animal behavior, the dynamical behavior of these systems in response to perturbation is not well understood. We examine the response of laboratory schools of negatively phototaxic freshwater fish to a variety of projected light fields. We observed laboratory schooling events of rummy nose tetra (Hemigrammus bleheri) in a shallow tank using a high-speed camera and particle-tracking setup. We employed both static light fields and dynamic light fields which were used to apply a normal stress on the school increasing the density of the system with time. Our results highlight how a materials and thermodynamic approach can give insights to current models.   

Collective motion in heterogeneous drone swarms

One of the main reasons for the broad interest in the collective motion of active systems derives from its natural origins in the form of flocks, swarms and crowds. In general, these natural systems are composed of single, autonomous organisms that communicate only locally but form extended collective mobile groups. capable of collective decision-making and displaying highly nontrivial dynamics over a wide range of length and time scales. This sort of decentralized, leaderless decision making and collective action has also inspired efforts especially in the area of robotic drones, where such systems could operate autonomously in groups to execute search and rescue or surveillance operations in a robust fashion without the need for active communication and feedback from a central command. What happens, however, when a certain fraction of the drones begin to malfunction and display more erratic behavior and are there strategies to mitigate the effects of malfunctioning agents? We answer these questions by implementing simple rules for collective motion in a system consisting of 100 Kilobots that are only 33 mm in diameter, easily programmable and equipped with differential drive vibration powered locomotion, neighbor-to-neighbor communication and distance sensing.