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Flocking behavior is observed in biological systems from the cellular to superorganismal length scales, and the mechanisms and purposes of this behavior are objects of intense interest. In this paper, we study the collective dynamics of bovine sperm cells in a viscoelastic fluid. These cells appear not to spontaneously flock, but transition into a long-lived flocking phase after being exposed to a transient ordering pulse of fluid flow. Surprisingly, this induced flocking phase has many qualitative similarities with the spontaneous polar flocking phases predicted by Toner-Tu theory, such as anisotropic giant number fluctuations and nontrivial transverse density correlations, despite the induced nature of the phase and the clearly important role of momentum conservation between the swimmers and the surrounding fluid in these experiments. We also find a self-organized global vortex state of the sperm cells, and map out an experimental phase diagram of states of collective motion as a function of cell density and motility statistics. We compare our experiments with a parameter-matched computational model of persistently turning active particles and find that the experimental order-disorder phase boundary as a function of cell density and persistence time can be approximately predicted from measures of single-cell properties. Our results may have implications for the evaluation of sample fertility by studying the collective phase behavior of dense groups of swimming sperm. 

Under decompression, disordered solids undergo an unjamming transition where they become under-coordinated and lose their structural rigidity. The mechanical and vibrational properties of these materials have been an object of theoretical, numerical, and experimental research for decades. In the study of low-coordination solids, understanding the behavior and physical interpretation of observables that diverge near the transition is of particular importance. Several such quantities are length scales (ξ or l) that characterize the size of excitations, the decay of spatial correlations, the response to perturbations, or the effect of physical constraints in the boundary or bulk of the material. Additionally, the spatial and sample-to-sample fluctuations of macroscopic observables such as contact statistics or elastic moduli diverge approaching unjamming. Here, we discuss important connections between all of these quantities and present numerical results that characterize the scaling properties of sample-to-sample contact and shear modulus fluctuations in ensembles of low-coordination disordered sphere packings and spring networks. Overall, we highlight three distinct scaling regimes and two crossovers in the disorder quantifiers χz and χμ as functions of system size N and proximity to unjamming δz. As we discuss, χX relates to the standard deviation σX of the sample-to-sample distribution of the quantity X (e.g., excess coordination δz or shear modulus μ) for an ensemble of systems. Importantly, χμ has been linked to experimentally accessible quantities that pertain to sound attenuation and the density of vibrational states in glasses. We investigate similarities and differences in the behaviors of χz and χμ near the transition and discuss the implications of our findings on current literature, unifying findings in previous studies. 

Under applied shear strain, granular and amorphous materials deform via particle rearrangements, which can be small and localized or organized into system-spanning avalanches. While the statistical properties of avalanches under quasi-static shear are well-studied, the dynamics during avalanches is not. In numerical simulations of sheared soft spheres, we find that avalanches can be decomposed into bursts of localized deformations, which we identify using an extension of persistent homology methods. We also study the linear response of unstable systems during an avalanche, demonstrating that eigenvalue dynamics are highly complex during such events, and that the most unstable eigenvector is a poor predictor of avalanche dynamics. Instead, we modify existing tools that identify localized excitations in stable systems, and apply them to these unstable systems with non-positive definite Hessians, quantifying the evolution of such excitations during avalanches. We find that bursts of localized deformations in the avalanche almost always occur at localized excitations identified using the linear spectrum. These new tools will provide an improved framework for validating and extending mesoscale elastoplastic models that are commonly used to explain avalanche statistics in glasses and granular matter. 

In amorphous solids subject to shear or thermal excitation, so-called structural indicators have been developed that predict locations of future plasticity or particle rearrangements. An open question is whether similar tools can be used in dense active materials, but a challenge is that under most circumstances, active systems do not possess well-defined solid reference configurations. We develop a computational model for a dense active crowd attracted to a point of interest, which does permit a mechanically stable reference state in the limit of infinitely persistent motion. Previous work on a similar system suggested that the collective motion of crowds could be predicted by inverting a matrix of time-averaged two-particle correlation functions. Seeking a first-principles understanding of this result, we demonstrate that this active matter system maps directly onto a granular packing in the presence of an external potential, and extend an existing structural indicator based on linear response to predict plasticity in the presence of noisy dynamics. We find that the strong pressure gradient necessitated by the directed activity, as well as a self-generated free boundary, strongly impact the linear response of the system. In low-pressure regions the linear-response-based indicator is predictive, but it does not work well in the high-pressure interior of our active packings. Our findings motivate and inform future work that could better formulate structure-dynamics predictions in systems with strong pressure gradients. 

The introduction of transient degrees of freedom into a system can lead to novel material design and training protocols that guide a system into a desired metastable state. In this approach, some degrees of freedom, which were not initially included in the system dynamics, are first introduced and subsequently removed from the energy minimization process once the desired state is reached. Using this conceptual framework, we create stable jammed packings that exist in exceptionally deep energy minima marked by the absence of low-frequency quasilocalized modes; this added stability persists in the thermodynamic limit. The inclusion of particle radii as transient degrees of freedom leads to deeper and much more stable minima than does the inclusion of particle stiffnesses. This is because particle radii couple to the jamming transition, whereas stiffnesses do not. Thus, different choices for the added degrees of freedom can lead to very different training outcomes.