As a function of connectivity, spring networks exhibit a critical transition between floppy and rigid phases at an isostatic threshold. For connectivity below this threshold, fiber networks were recently shown theoretically to exhibit a rigidity transition with corresponding critical signatures as a function of strain. Experimental collagen networks were also shown to be consistent with these predictions. We develop a scaling theory for this strain-controlled transition. Using a real-space renormalization approach, we determine relations between the critical exponents governing the transition, which we verify for the strain-controlled transition using numerical simulations of both triangular lattice-based and packing-derived fiber networks.

Turbulence is ubiquitous in nonequilibrium systems, and it has been noted that even dense granular flows exhibit characteristics that are typical of turbulent flow, such as the power-law energy spectrum. However, studies on the turbulentlike behavior of granular flows are limited to two-dimensional (2D) flow. We demonstrate that the statistics in three-dimensional (3D) flow are qualitatively different from those in 2D flow. We also elucidate that avalanche dynamics can explain this dimensionality dependence. Moreover, we define clusters of collectively moving particles that are equivalent to vortex filaments. The clusters unveil complicated structures in 3D flows that are absent in 2D flows.

We numerically simulate the uniform athermal shearing of bidisperse, frictionless, two-dimensional spherocylinders and three-dimensional prolate ellipsoids. We focus on the orientational ordering of particles as an asphericity parameter $\alpha \to 0$ and particles approach spherical. We find that the nematic order parameter $S_2$ is nonmonotonic in the packing fraction $\varphi$ and that, as $\alpha \to 0$, $S_2$ stays finite at jamming and above. The approach to spherical particles thus appears to be singular. We also find that sheared particles continue to rotate above jamming and that particle contacts preferentially lie along the narrowest width of the particles, even as $\alpha \to 0$.

Kinesins are molecular motors that carry cellular cargoes. While the mechanics of single kinesins are well characterized experimentally, the behavior of multiple kinesins varies considerably among experiments. The basis for this variability is unknown. Here, we resolve single-motor force measurements into a vertical component, which accelerates kinesin detachment, and a horizontal component, which decelerates the detachment when resisting the motor. This directionality, when the different experimental geometries are considered, can account for much of the variation in multiple motor dynamics.

We numerically investigate nonlocal effects on inhomogeneous flows of soft athermal disks close to but below their jamming transition. We employ molecular dynamics to simulate Kolmogorov flows, in which a sinusoidal flow profile with fixed wave number is externally imposed, resulting in a spatially inhomogeneous shear rate. We find that the resulting rheology is strongly wave-number-dependent, and that particle migration, while present, is not sufficient to describe the resulting stress profiles within a conventional local model. We show that, instead, stress profiles can be captured with nonlocal constitutive relations that account for gradients to fourth order. Unlike nonlocal flow in yield stress fluids, we find no evidence of a diverging length scale.

The universality class of the avalanche behavior in plastically deforming crystalline and amorphous systems has been commonly discussed, despite the fact that the microscopic defect character in each of these systems is different. In contrast to amorphous systems, crystalline flow stress increases dramatically at high strains and/or loading rates. We perform simulations of a two-dimensional discrete dislocation dynamics model that minimally captures the phenomenology of nanocrystalline deformation. In the context of this model, we demonstrate that a classic rate dependence of dislocation plasticity at large rates ($>{10}^3/\mathrm{s}$) fundamentally controls the system’s statistical character as it competes with dislocation nucleation: At large rates, the behavior is statistically dominated by long-range correlations of “dragged” mobile dislocations. At small rates, plasticity localization dominates in small volumes and a spatial integration of avalanche behavior takes place.

Using video microscopy and simulations, we study the diffusion of probe particles in a wide range of complex backgrounds, both crystalline and disordered, in quasi-2D colloidal systems. The dimensionless diffusion coefficients $D^{*}$ from different systems collapse to a single master curve when plotted as a function of the structural entropy of the backgrounds, confirming the universal relation between diffusion dynamics and the structure of the medium. A new scaling equation is proposed with consideration for the viscous friction from the solvent, which is absent in previous theoretical models. This new universal law quantitatively predicts the diffusion coefficients from different systems over several orders of magnitude of $D^{*}$, with a single common fitting parameter.

Surfactant molecules have been extensively used as emulsifying agents to stabilize immiscible fluids. Droplet stability has been shown to be increased when ordered nanoscale phases form at the interface of the two fluids due to surfactant association. Here, we report on using mixtures of a cationic surfactant and long chained alkenes with polar head groups [e.g., cetylpyridinium chloride (CPCl) and oleic acid] to create an ordered nanoscale lamellar morphology at aqueous-oil interfaces. The self-assembled nanostructure at the liquid-liquid interface was characterized using small-angle x-ray scattering, and the mechanical properties were measured using interfacial rheology. We hypothesize that the resulting lamellar morphology at the liquid-liquid interface is driven by the change in critical packing parameter when the CPCl molecules are diluted by the presence of the long chain alkenes with polar head groups, which leads to a spherical micelle-to-lamellar phase transition. The work presented here has larger implications for using nanostructured interfacial material to separate different fluids in flowing conditions for biosystems and in 3D printing technology.

We investigate the turbulent dynamics of a two-dimensional active nematic liquid crystal constrained to a curved surface. Using a combination of hydrodynamic and particle-based simulations, we demonstrate that the fundamental structural features of the fluid, such as the topological charge density, the defect number density, the nematic order parameter, and defect creation and annihilation rates, are approximately linear functions of the substrate Gaussian curvature, which then acts as a control parameter for the chaotic flow. Our theoretical predictions are then compared with experiments on microtubule-kinesin suspensions confined on toroidal droplets, finding excellent qualitative agreement.

The availability of large datasets requires an improved view on statistical laws in complex systems, such as Zipf’s law of word frequencies, the Gutenberg-Richter law of earthquake magnitudes, or scale-free degree distribution in networks. In this Letter, we discuss how the statistical analysis of these laws are affected by correlations present in the observations, the typical scenario for data from complex systems. We first show how standard maximum-likelihood recipes lead to false rejections of statistical laws in the presence of correlations. We then propose a conservative method (based on shuffling and undersampling the data) to test statistical laws and find that accounting for correlations leads to smaller rejection rates and larger confidence intervals on estimated parameters.

The structural and functional organization of biological tissues relies on the intricate interplay between chemical and mechanical signaling. Whereas the role of constant and transient mechanical perturbations is generally accepted, several studies recently highlighted the existence of long-range mechanical excitations (i.e., waves) at the supracellular level. Here, we confine epithelial cell monolayers to quasi-one-dimensional geometries, to force the establishment of tissue-level waves of well-defined wavelength and period. Numerical simulations based on a self-propelled Voronoi model reproduce the observed waves and exhibit a phase transition between a global and a multinodal wave, controlled by the confinement size. We confirm experimentally the existence of such a phase transition, and show that wavelength and period are independent of the confinement length. Together, these results demonstrate the intrinsic origin of tissue oscillations, which could provide cells with a mechanism to accurately measure distances at the supracellular level.

We experimentally investigate the statistical behavior of a model two-dimensional granular system undergoing stationary sedimentation. Buoyant cylindrical particles are rotated in a liquid-filled drum, thus confined in a harmonic centripetal potential with tunable curvature, which competes with gravity to produce various stationary states: though heterogeneous, the packing fraction of the system can be tuned from fully dispersed to crystallized as the rotation rate is increased. We show that this dynamical system is in mechanical equilibrium in the confining potential and exhibits a thermal-like behavior, where the granular pressure and the packing fraction are related through an equation of state. We obtain an expression of the equation of state allowing us to probe the nature of the hydrodynamic interactions between the particles. This description is valid in the whole range of the physical parameters we investigated and reveals a buoyant energy scale that we interpret as an effective temperature. We finally discuss the behavior of our system at high packing fractions and the relevance of the equation of state to the liquid-solid phase transition.

Fröhlich discovered the remarkable condensation of polar vibrations into the lowest frequency mode when the system is pumped externally. For a full understanding of the Fröhlich condensate one needs to go beyond the mean field level to describe critical behavior as well as quantum fluctuations. The energy redistribution among vibrational modes with nonlinearity included is shown to be essential for realizing the condensate and the phonon-number distribution, revealing the transition from quasithermal to super-Poissonian statistics with the pump. We further study the spectroscopic properties of the Fröhlich condensate, which are especially revealed by the narrow linewidth. This gives the long-lived coherence and the collective motion of the condensate. Finally, we show that the proteins such as bovine serum albumin and lysozyme are most likely the candidates for observing such collective modes in THz regime by means of Raman or infrared spectroscopy.

Cities, wealth, and earthquakes follow continuous power-law probability distributions such as the Pareto distribution, which are canonically associated with scale-free behavior and self-similarity. However, many self-similar processes manifest as discrete steps that do not produce a continuous scale-free distribution. We construct a discrete power-law distribution that arises naturally from a simple model of hierarchical self-similar processes such as turbulence and vasculature, and we derive the maximum-likelihood estimate (MLE) for its exponent. Our distribution is self-similar, in contrast to previously studied discrete power laws such as the Zipf distribution. We show that the widely used MLE derived from the Pareto distribution leads to inaccurate estimates in systems that lack continuous scale invariance such as branching networks and data subject to logarithmic binning. We apply our MLE to data from bronchial tubes, blood vessels, and earthquakes to produce new estimates of scaling exponents and resolve contradictions among previous studies.

Daily precipitation time series are composed of null entries corresponding to dry days and nonzero entries that describe the rainfall amounts on wet days. Assuming that wet days follow a Bernoulli process with success probability $p$, we show that the presence of dry days induces negative correlations between record-breaking precipitation events. The resulting nonmonotonic behavior of the Fano factor of the record counting process is recovered in empirical data. We derive the full probability distribution $P(R,n)$ of the number of records $R_n$ up to time $n$, and show that for large $n$, it converges to a Poisson distribution with parameter $\ln (pn)$. We also study in detail the joint limit $p\to 0$, $n\to \infty$, which yields a random record model in continuous time $t=pn$.

Complex nonlinear models are typically ill conditioned or sloppy; their predictions are significantly affected by only a small subset of parameter combinations, and parameters are difficult to reconstruct from model behavior. Despite forming an important universality class and arising frequently in practice when performing a nonlinear fit to data, formal and systematic explanations of sloppiness are lacking. By unifying geometric interpretations of sloppiness with Chebyshev approximation theory, we rigorously explain sloppiness as a consequence of model smoothness. Our approach results in universal bounds on model predictions for classes of smooth models, capturing global geometric features that are intrinsic to their model manifolds, and characterizing a universality class of models. We illustrate this universality using three models from disparate fields (physics, chemistry, biology): exponential curves, reaction rates from an enzyme-catalyzed chemical reaction, and an epidemiology model of an infected population.

The number of units of a network dynamical system, its size, arguably constitutes its most fundamental property. Many units of a network, however, are typically experimentally inaccessible such that the network size is often unknown. Here we introduce a detection matrix that suitably arranges multiple transient time series from the subset of accessible units to detect network size via matching rank constraints. The proposed method is model-free, applicable across system types and interaction topologies, and applies to nonstationary dynamics near fixed points, as well as periodic and chaotic collective motion. Even if only a small minority of units is perceptible and for systems simultaneously exhibiting nonlinearities, heterogeneities, and noise, exact size detection is feasible. We illustrate applicability for a paradigmatic class of biochemical reaction networks.