Publications

We consider the Saintillan--Shelley kinetic model of active rodlike particles in Stokes flow (Saintillan & Shelley 2008a,b), for which the uniform, isotropic suspension of pusher particles is known to be unstable in certain settings. Through weakly nonlinear analysis accompanied by numerical simulations, we determine exactly how the isotropic steady state loses stability in different parameter regimes. We study each of the various types of bifurcations admitted by the system, including both subcritical and supercritical Hopf and pitchfork bifurcations. Elucidating this system's behavior near these bifurcations provides a theoretical means of comparing this model with other physical systems which transition to turbulence, and makes predictions about the nature of bifurcations in active suspensions that can be explored experimentally.

Many active biological particles, such as swimming microorganisms or motor-proteins, do work on their environment by going though a periodic sequence of shapes. Interactions between particles can lead to the phase-synchronization of their duty cycles. Here we consider collective dynamics in a suspension of such active particles coupled through hydrodynamics. We demonstrate that the emergent non-equilibrium states feature stationary patterned flows and robust unidirectional pumping states under confinement. Moreover the phase-synchronized state of the suspension exhibits spatially robust chimera patterns in which synchronized and phase-isotropic regions coexist within the same system. These findings demonstrate a new route to pattern formation and could guide the design of new active materials.

We present a statistical learning framework for robust identification of differential equations from noisy spatio-temporal data. We address two issues that have so far limited the application of such methods, namely their robustness against noise and the need for manual parameter tuning, by proposing stability-based model selection to determine the level of regularization required for reproducible inference. This avoids manual parameter tuning and improves robustness against noise in the data. Our stability selection approach, termed PDE-STRIDE, can be combined with any sparsity-promoting regression method and provides an interpretable criterion for model component importance. We show that the particular combination of stability selection with the iterative hard-thresholding algorithm from compressed sensing provides a fast and robust framework for equation inference that outperforms previous approaches with respect to accuracy, amount of data required, and robustness. We illustrate the performance of PDE-STRIDE on a range of simulated benchmark problems, and we demonstrate the applicability of PDE-STRIDE on real-world data by considering purely data-driven inference of the protein interaction network for embryonic polarization in Caenorhabditis elegans. Using fluorescence microscopy images of C. elegans zygotes as input data, PDE-STRIDE is able to learn the molecular interactions of the proteins.

We present data structures and algorithms for native implementations of discrete convolution operators over Adaptive Particle Representations (APR) of images on parallel computer architectures. The APR is a content-adaptive image representation that locally adapts the sampling resolution to the image signal. It has been developed as an alternative to pixel representations for large, sparse images as they typically occur in fluorescence microscopy. It has been shown to reduce the memory and runtime costs of storing, visualizing, and processing such images. This, however, requires that image processing natively operates on APRs, without intermediately reverting to pixels. Designing efficient and scalable APR-native image processing primitives, however, is complicated by the APR’s irregular memory structure. Here, we provide the algorithmic building blocks required to efficiently and natively process APR images using a wide range of algorithms that can be formulated in terms of discrete convolutions. We show that APR convolution naturally leads to scale-adaptive algorithms that efficiently parallelize on multi-core CPU and GPU architectures. We quantify the speedups in comparison to pixel-based algorithms and convolutions on evenly sampled data. We achieve pixel-equivalent throughputs of up to 1TB/s on a single Nvidia GeForce RTX 2080 gaming GPU, requiring up to two orders of magnitude less memory than a pixel-based implementation.

The cytoskeleton -- a collection of polymeric filaments, molecular motors, and crosslinkers -- is a foundational example of active matter, and in the cell assembles into organelles that guide basic biological functions. Simulation of cytoskeletal assemblies is an important tool for modeling cellular processes and understanding their surprising material properties. Here we present aLENS, a novel computational framework to surmount the limits of conventional simulation methods. We model molecular motors with crosslinking kinetics that adhere to a thermodynamic energy landscape, and integrate the system dynamics while efficiently and stably enforcing hard-body repulsion between filaments -- molecular potentials are entirely avoided in imposing steric constraints. Utilizing parallel computing, we simulate different mixtures of tens to hundreds of thousands of cytoskeletal filaments and crosslinking motors, recapitulating self-emergent phenomena such as bundle formation and buckling, and elucidating how motor type, thermal fluctuations, internal stresses, and confinement determine the evolution of active matter aggregates.

Continuum kinetic theories provide an important tool for the analysis and simulation of particle suspensions. When those particles are anisotropic, the addition of a particle orientation vector to the kinetic description yields a dimensional theory which becomes intractable to simulate, especially in three dimensions or near states where the particles are highly aligned. Coarse-grained theories that track only moments of the particle distribution functions provide a more efficient simulation framework, but require closure assumptions. For the particular case where the particles are apolar, the Bingham closure has been found to agree well with the underlying kinetic theory; yet the closure is non-trivial to compute, requiring the solution of an often nearly-singular nonlinear equation at every spatial discretization point at every timestep. In this paper, we present a robust, accurate, and efficient numerical scheme for evaluating the Bingham closure, with a controllable error/efficiency tradeoff. To demonstrate the utility of the method, we carry out high-resolution simulations of a coarse-grained continuum model for a suspension of active particles in parameter regimes inaccessible to kinetic theories. Analysis of these simulations reveals that inaccurately computing the closure can act to effectively limit spatial resolution in the coarse-grained fields. Pushing these simulations to the high spatial resolutions enabled by our method reveals a coupling between vorticity and topological defects in the suspension director field, as well as signatures of energy transfer between scales in this active fluid model.

We present a spectrally accurate embedded boundary method for solving linear, inhomogeneous, elliptic partial differential equations (PDE) in general smooth geometries, focusing in this manuscript on the Poisson, modified Helmholtz, and Stokes equations. Unlike several recently proposed methods which rely on function extension, we propose a method which instead utilizes function `intension', or the smooth truncation of known function values. Similar to those methods based on extension, once the inhomogeneity is truncated we may solve the PDE using any of the many simple, fast, and robust solvers that have been developed for regular grids on simple domains. Function intension is inherently stable, as are all steps in the proposed solution method, and can be used on domains which do not readily admit extensions. We pay a price in exchange for improved stability and flexibility: in addition to solving the PDE on the regular domain, we must additionally (1) solve the PDE on a small auxiliary domain that is fitted to the boundary, and (2) ensure consistency of the solution across the interface between this auxiliary domain and the rest of the physical domain. We show how these tasks may be accomplished efficiently (in both the asymptotic and practical sense), and compare convergence to several recent high-order embedded boundary schemes.

We demonstrate the utility of the bispectrum, the Fourier three-point correlation function, for studying driving scales of magnetohydrodynamic (MHD) turbulence in the interstellar medium. We calculate the bispectrum by implementing a parallelized Monte Carlo direct measurement method, which we have made publicly available. In previous works, the bispectrum has been used to identify non-linear scaling correlations and break degeneracies in lower-order statistics like the power spectrum. We find that the bicoherence, a related statistic which measures phase coupling of Fourier modes, identifies turbulence driving scales using density and column density fields. In particular, it shows that the driving scale is phase-coupled to scales present in the turbulent cascade. We also find that the presence of an ordered magnetic field at large-scales enhances phase coupling as compared to a pure hydrodynamic case. We, therefore, suggest the bispectrum and bicoherence as tools for searching for non-locality for wave interactions in MHD turbulence.

Changes in the geometry and topology of self-assembled membranes underlie diverse processes across cellular biology and engineering. Similar to lipid bilayers, monolayer colloidal membranes have in-plane fluid-like dynamics and out-of-plane bending elasticity. Their open edges and micron length scale provide a tractable system to study the equilibrium energetics and dynamic pathways of membrane assembly and reconfiguration. Here, we find that doping colloidal membranes with short miscible rods transforms disk-shaped membranes into saddle-shaped surfaces with complex edge structures. The saddle-shaped membranes are well-approximated by Enneper's minimal surfaces. Theoretical modeling demonstrates that their formation is driven by increasing positive Gaussian modulus, which in turn is controlled by the fraction of short rods. Further coalescence of saddle-shaped surfaces leads to diverse topologically distinct structures, including catenoids, tri-noids, four-noids, and higher order structures. At long time scales, we observe the formation of a system-spanning, sponge-like phase. The unique features of colloidal membranes reveal the topological transformations that accompany coalescence pathways in real time. We enhance the functionality of these membranes by making their shape responsive to external stimuli. Our results demonstrate a novel pathway towards control of thin elastic sheets' shape and topology -- a pathway driven by the emergent elasticity induced by compositional heterogeneity.

We introduce a closure model for coarse-grained kinetic theories of polar active fluids. Based on a thermodynamically consistent, quasi-equilibrium approximation of the particle distribution function, the model closely captures important analytical properties of the kinetic theory, including its linear stability and the balance of entropy production and dissipation. Nonlinear simulations show the model reproduces the qualitative behavior and nonequilibrium statistics of the kinetic theory, unlike commonly used closure models. We use the closure model to simulate highly turbulent suspensions in both two and three dimensions in which we observe complex multiscale dynamics, including large concentration fluctuations and a proliferation of polar and nematic defects.