The bicontinuous double gyroid phase is one of the nature’s most symmetric and complex structures, the electron density map of which was established long ago. By utilizing small-angle x-ray scattering, resonant soft x-ray scattering at the carbon $K$ edge and model-dependent tensor-based scattering theory, we have not only elucidated morphology but also identified molecular packing in the double gyroid phases formed by molecules with different shapes, i.e., rodlike vs taper shaped, thus validating some of the hypothetical packing models and disproving others. The spatial variation of molecular orientation through the channel junctions in the double gyroid phase can be either continuous in the case of anisotropic channels or discontinuous in the case of isotropic channels depending on the molecular structure and shape.

It is shown that vibrated packings of frictional disks self-organize cooperatively onto a rotational-transport state where the long-time angular velocity ${\overline{\omega }}_i$ of each disk $i$ is nonzero. Steady rotation is mediated by the spontaneous breaking of local reflection symmetry, arising when the cages in which disks are constrained by their neighbors acquire quenched disorder at large packing densities. Experiments and numerical simulation of this unexpected phenomenon show excellent agreement with each other, revealing two rotational phases as a function of excitation intensity, respectively, the low-drive (LDR) and the moderate-drive (MDR) regimes. In the LDR, interdisk contacts are persistent and rotation happens due to frictional sliding. In the MDR, disks bounce against each other, still forming a solid phase. In the LDR, simple energy-dissipation arguments are provided, that support the observed dependence of the typical rotational velocity on excitation strength.

We propose an analytically tractable neural connectivity model with power-law distributed synaptic strengths. When threshold neurons with biologically plausible number of incoming connections are considered, our model features a continuous transition to chaos and can reproduce biologically relevant low activity levels and scale-free avalanches, i.e., bursts of activity with power-law distributions of sizes and lifetimes. In contrast, the Gaussian counterpart exhibits a discontinuous transition to chaos and thus cannot be poised near the edge of chaos. We validate our predictions in simulations of networks of binary as well as leaky integrate-and-fire neurons. Our results suggest that heavy-tailed synaptic distribution may form a weakly informative sparse-connectivity prior that can be useful in biological and artificial adaptive systems.

Many types of cells require the ability to pinpoint the location of an external stimulus from the arrival of diffusing signaling molecules at cell-surface receptors. How does the organization (number and spatial configuration) of these receptors shape the limit of a cell’s ability to infer the source location? In the idealized scenario of a spherical cell, we apply asymptotic analysis to compute splitting probabilities between individual receptors and formulate an information-theoretic framework to quantify the role of receptor organization. Clustered configurations of receptors provide an advantage in detecting sources aligned with the clusters, suggesting a possible multiscale mechanism for single-cell source inference.

Suspensions of rear- and front-actuated microswimmers immersed in a fluid, known respectively as “pushers” and “pullers,” display qualitatively different collective behaviors: beyond a characteristic density, pusher suspensions exhibit a hydrodynamic instability leading to collective motion known as active turbulence, a phenomenon which is absent for pullers. In this Letter, we describe the collective dynamics of a binary pusher–puller mixture using kinetic theory and large-scale particle-resolved simulations. We derive and verify an instability criterion, showing that the critical density for active turbulence moves to higher values as the fraction $\chi$ of pullers is increased and disappears for $\chi \ge 0.5$. We then show analytically and numerically that the two-point hydrodynamic correlations of the $1:1$ mixture are equal to those of a suspension of noninteracting swimmers. Strikingly, our numerical analysis furthermore shows that the full probability distribution of the fluid velocity fluctuations collapses onto the one of a noninteracting system at the same density, where swimmer-swimmer correlations are strictly absent. Our results thus indicate that the fluid velocity fluctuations in $1:1$ pusher-puller mixtures are exactly equal to those of the corresponding noninteracting suspension at any density, a surprising cancellation with no counterpart in equilibrium long-range interacting systems.

Motivated by the mechanics of dynamin-mediated membrane tube fission, we analyze the stability of fluid membrane tubes subjected to shear flow in azimuthal direction. We find a novel helical instability driven by the membrane shear flow which results in a nonequilibrium steady state for the tube fluctuations. This instability has its onset at shear rates that may be physiologically accessible under the action of dynamin and could also be probed using in vitro experiments on membrane nanotubes, e.g., using magnetic tweezers. We discuss how such an instability may play a role in the mechanism for dynamin-mediated membrane tube fission.

We demonstrate that an achiral stretching force transforms disk-shaped colloidal membranes composed of chiral rods into twisted ribbons with handedness opposite the preferred twist of the rods. Using an experimental technique that enforces torque-free boundary conditions we simultaneously measure the force-extension curve and the ribbon shape. An effective theory that accounts for the membrane bending energy and uses geometric properties of the edge to model the internal liquid crystalline degrees of freedom explains both the measured force-extension curve and the force-induced twisted shape.

We present a fundamental classification of forces relevant in nonequilibrium structure formation under collective flow in Brownian many-body systems. The internal one-body force field is systematically split into contributions relevant for the spatial structure and for the coupled motion. We demonstrate that both contributions can be obtained straightforwardly in computer simulations and present a power functional theory that describes all types of forces quantitatively. Our conclusions and methods are relevant for flow in inertial systems, such as molecular liquids and granular media.

When a volatile droplet is deposited on a floating swellable sheet, it becomes asymmetric, lobed and mobile. We describe and quantify this phenomena that involves nonequilibrium swelling, evaporation and motion, working together to realize a self-excitable spatially extended oscillator. Solvent penetration causes the film to swell locally and eventually buckle, changing its shape and the drop responds by moving. Simultaneously, solvent evaporation from the swollen film causes it to regain its shape once the droplet has moved away. The process repeats and leads to complex pulsatile spinning and/or sliding movements. We use a one-dimensional experiment to highlight the slow swelling of and evaporation from the film and the fast motion of the drop, a characteristic of excitable systems. Finally, we provide a phase diagram for droplet excitability as a function of drop size and film thickness and scaling laws for the motion of the droplet.

Under favorable conditions, microscopic phytoplankton cells dwelling in the oceans can divide rapidly and reach high concentrations, forming blooms that span kilometers and last for weeks. When blooms collapse, dead cells settle and aggregate into “marine snow” particles, resulting in a large and climatically important vertical flux of carbon from the ocean surface to its depth, a process known as the “biological pump.” To date, the formation of marine snow has been modeled as coagulation between spherical particles driven by gravitational settling and turbulent mixing, characterized by coagulation dynamics that converge onto time-independent concentrations of aggregates. However, many phytoplankton species are elongated and how their rodlike shape affects the aggregation process has remained unknown. Here, we study marine snow formation in a quiescent fluid assuming the constituent particles are elongated and form bundles upon encounter. We derive the collision kernel between dissimilar rods settling under gravity and discover that the most frequent collisions occur between the thinnest and thickest bundles, rather than between bundles of similar size. As a consequence, in the full coagulation model that combines exponential growth with settling, the thin-thick coupling can lead to statistically stationary states where the concentrations of aggregates of different size oscillate in time, exhibiting periodic bursts. The bursts are predicted to occur on the scale of a week and eventually lead to broadening of aggregate size spectra and may thus be highly relevant for plankton dynamics and the carbon cycle in the ocean.

Particle-based simulations of discontinuous shear thickening (DST) and shear jamming (SJ) suspensions are used to study the role of stress-activated constraints, with an emphasis on resistance to gearlike rolling. Rolling friction decreases the volume fraction required for DST and SJ, in quantitative agreement with real-life suspensions with adhesive surface chemistries and “rough” particle shapes. It sets a distinct structure of the frictional force network compared to only sliding friction, and from a dynamical perspective leads to an increase in the velocity correlation length, in part responsible for the increased viscosity. The physics of rolling friction is thus a key element in achieving a comprehensive understanding of strongly shear-thickening materials.

We analyze the surface tension exerted at the interface between an active fluid and a solid boundary in terms of tangential forces. Focusing on active systems known to possess an equation of state for the pressure, we show that interfacial forces are of a more complex nature. Using a number of macroscopic setups, we show that the surface tension is a combination of an equation-of-state abiding part and of setup-dependent contributions. The latter arise from generic setup-dependent steady currents which “dress” the measurement of the “bare” surface tension. The former shares interesting properties with its equilibrium counterpart, and can be used to generalize the Young-Laplace law to active systems. Finally, we show how a suitably designed probe can directly access this bare surface tension, which can also be computed using a generalized virial formula.

We introduce two generalizations of core percolation in graphs to hypergraphs, related to the minimum hyperedge cover problem and the minimum vertex cover problem on hypergraphs, respectively. We offer analytical solutions of these two core percolations for uncorrelated random hypergraphs whose vertex degree and hyperedge cardinality distributions are arbitrary but have nondiverging moments. We find that for several real-world hypergraphs their two cores tend to be much smaller than those of their null models, suggesting that covering problems in those real-world hypergraphs can actually be solved in polynomial time.

In the Nernst-Planck equations in two or more dimensions, a non-Faradaic solenoidal current can arise as a consequence of connecting patches with different liquid junction potentials. Whereas this current vanishes for binary electrolytes or in one-dimensional problems, it is in general nonvanishing, for example, in crossed salt gradients. For a suspended colloidal particle, chemiphoresis in the concentration gradients is generally vectorially misaligned with electrophoresis in the electrostatic potential gradient, and there is a nonlocal contribution to the latter deriving from the Ohmic electric field associated with the current; in a case study this contributes up to 20%–30% of the total effect.

Integrating sensory inputs with prior beliefs from past experiences in unsupervised learning is a common and fundamental characteristic of brain or artificial neural computation. However, a quantitative role of prior knowledge in unsupervised learning remains unclear, prohibiting a scientific understanding of unsupervised learning. Here, we propose a statistical physics model of unsupervised learning with prior knowledge, revealing that the sensory inputs drive a series of continuous phase transitions related to spontaneous intrinsic-symmetry breaking. The intrinsic symmetry includes both reverse symmetry and permutation symmetry, commonly observed in most artificial neural networks. Compared to the prior-free scenario, the prior reduces more strongly the minimal data size triggering the reverse-symmetry breaking transition, and moreover, the prior merges, rather than separates, permutation-symmetry breaking phases. We claim that the prior can be learned from data samples, which in physics corresponds to a two-parameter Nishimori constraint. This Letter thus reveals mechanisms about the influence of the prior on unsupervised learning.

Microscopic symmetries impose strong constraints on the elasticity of a crystalline solid. In addition to the usual spatial symmetries captured by the tensorial character of the elastic tensor, hidden nonspatial symmetries can occur microscopically in special classes of mechanical structures. Examples of such nonspatial symmetries occur in families of mechanical metamaterials where a duality transformation relates pairs of different configurations. We show on general grounds how the existence of nonspatial symmetries further constrains the elastic tensor, reducing the number of independent moduli. In systems exhibiting a duality transformation, the resulting constraints on the number of moduli are particularly stringent at the self-dual point but persist even away from it, in a way reminiscent of critical phenomena.