We have previously explored cylindrical packings of disks and their relation to sphere packings. Here we extend the analytical treatment of disk packings, analyzing the rules for phyllotactic indices of related structures and the variation of the density for line-slip structures, close to the symmetric ones. We show that rhombic structures, which are of a lower density, are always unstable, i.e., can be increased in density by small perturbations.

Predicting the bulk material properties of active matter is challenging since these materials are far from equilibrium and standard statistical-mechanics approaches may fail. We report a computational study of the surface properties of a well known active matter system: aggregations of self-propelled particles that are coupled via an orientational interaction and that resemble bird flocks. By simulating the impact of these models flocks on an impermeable surface, we find that they fragment into subflocks with power-law mass distributions, similar to shattering brittle solids but not to splashing liquid drops. Thus, we find that despite the interparticle interactions, these model flocks do not possess an emergent surface tension.

Capillary forces are involved in a variety of natural phenomena, ranging from droplet breakup to the physics of clouds. The forces from surface tension can also be exploited in industrial applications provided the length scales involved are small enough. Recent experimental investigations showed how to take advantage of capillarity to fold planar structures into three-dimensional configurations by selectively melting polymeric hinges joining otherwise rigid shapes. In this paper we use theoretical calculations to quantify the role of geometry and fluid wetting on the final folded state. Considering folding in two and three dimensions, studying both hydrophilic and hydrophobic situations with possible contact-angle hysteresis, and addressing the shapes to be folded to be successively infinite, finite, curved, kinked, and elastic, we are able to derive an overview of the geometrical parameter space available for capillary folding.

Inert, spherical heterogeneities can pin three-dimensional scroll waves in the excitable Belousov-Zhabotinsky reaction. Three pinning sites cause initially circular rotation backbones to approach equilateral triangles. The resulting stationary shapes show convex deviations that increase with decreasing anchor radii. This dependence is interpreted as a transition between filament termination at large surfaces and true, local pinning of a continuous curve. The shapes of the filament segments are described by a hyperbolic cosine function which is predicted by kinematic theory that considers filament tension and rigidity. The latter value is measured as $(1.0\pm 0.7)\times {10}^{-6}$ cm${}^4$/s.

There are two modes by which clusters of aggregating particles can coalesce: The clusters can merge either (i) by the Ostwald ripening process, in which particles diffuse from one cluster to the other while the cluster centers remain stationary, or (ii) by means of a cluster translation mode, in which the clusters move toward each other and join. To understand in detail the interplay between these different modes, we study a model system of hard particles with an additional attraction between them. The particles diffuse along narrow channels with smooth or periodically corrugated walls, so that the system may be treated as one-dimensional. When the attraction between the particles is strong enough, they aggregate to form clusters. The channel potential influences whether clusters can move easily or not through the system and can prevent cluster motion. We use dynamical density functional theory to study the dynamics of the aggregation process, focusing in particular on the coalescence of two equal-sized clusters. As long as the particle hard-core diameter is nonzero, we find that the coalescence process can be halted by a sufficiently strong corrugation potential. The period of the potential determines the size of the final stable clusters. For the case of smooth channel walls, we demonstrate that there is a crossover in the dominance of the two different coarsening modes, which depends on the strength of the attraction between particles, the cluster sizes, and the separation distance between clusters.

The problem of optimal microscopic swimming in a noisy environment is analyzed. A simplified model in which propulsion is generated by the relative motion of three spheres connected by immaterial links has been considered. We show that an optimized noisy microswimmer requires less power for propulsion (on average) than an optimal noiseless counterpart migrating with identical mean velocity and swimming stroke amplitude. We also show that noise can be used to overcome some of the limitations of the scallop theorem and have a swimmer that is able to propel itself with control over just one degree of freedom.

The xylem vessels of trees constitute a model natural microfluidic system. In this work, we have studied the mechanism of air flow in the Populus xylem. The vessel microstructure was characterized by optical microscopy, transmission electronic microscopy (TEM), and atomic force microscopy (AFM) at different length scales. The xylem vessels have length $\approx 15$ cm and diameter $\approx 20\mu \mathrm{m}$. Flow from one vessel to the next occurs through $\sim {10}^2$ pits, which are grouped together at the ends of the vessels. The pits contain a thin, porous pit membrane with a thickness of 310 nm. We have measured the Young's moduli of the vessel wall and of the pits (both water-saturated and after drying) by specific nanoindentation and nanoflexion experiments with AFM. We found that both the dried and water-saturated pit membranes have Young's modulus around 0.4 MPa, in agreement with values obtained by micromolding of pits deformed by an applied pressure difference. Air injection experiments reveal that air flows through the xylem vessels when the differential pressure across a sample is larger than a critical value $\Delta P_c=1.8$ MPa. In order to model the air flow rate for $\Delta P⩾\Delta P_c$, we assumed the pit membrane to be a porous medium that is strained by the applied pressure difference. Water menisci in the pit pores play the role of capillary valves, which open at $\Delta P=\Delta P_c$. From the point of view of the plant physiology, this work presents a basic understanding of the physics of bordered pits.

We describe a general simulation scheme for assessing the thermodynamic consequences of neglecting many-body effects in coarse-grained models of complex fluids. The method exploits the fact that the asymptote of a simple-to-measure structural function provides direct estimates of virial coefficients. Comparing the virial coefficients of an atomistically detailed system with those of a coarse-grained version described by pair potentials, permits the role of many-body effects to be quantified. The approach is applied to two models: (i) a size-asymmetrical colloid-polymer mixture, and (ii) a solution of star polymers. In the latter case, coarse-graining to an effective fluid described by pair potentials is found to neglect important aspects of the true behavior.

We generalize a stochastic model of DNA replication to the case where replication-origin-initiation rates vary locally along the genome and with time. Using this generalized model, we address the inverse problem of inferring initiation rates from experimental data concerning replication in cell populations. Previous work based on curve fitting depended on arbitrarily chosen functional forms for the initiation rate, with free parameters that were constrained by the data. We introduce a nonparametric method of inference that is based on Gaussian process regression. The method replaces specific assumptions about the functional form of the initiation rate with more general prior expectations about the smoothness of variation of this rate, along the genome and in time. Using this inference method, we recover, with high precision, simulated replication schemes from noisy data that are typical of current experiments.

A key open question in the glass transition field is whether a finite temperature thermodynamic transition to the glass state exists or not. Recent simulations of coupled replicas in atomistic models have found signatures of a static transition as a function of replica coupling. This can be viewed as evidence of an associated thermodynamic glass transition in the uncoupled system. We demonstrate here that a different interpretation is possible. We consider the triangular plaquette model, an interacting spin system which displays (East model-like) glassy dynamics in the absence of any static transition. We show that when two replicas are coupled, there is a curve of equilibrium phase transitions, between phases of small and large overlap, in the temperature-coupling plane (located on the self-dual line of an exact temperature-coupling duality of the system) which ends at a critical point. Crucially, in the limit of vanishing coupling the finite temperature transition disappears, and the uncoupled system is in the disordered phase at all temperatures. We discuss an interpretation of atomistic simulations in light of this result.

How does one optimally determine the diffusion coefficient of a diffusing particle from a single-time-lapse recorded trajectory of the particle? We answer this question with an explicit, unbiased, and practically optimal covariance-based estimator (CVE). This estimator is regression-free and is far superior to commonly used methods based on measured mean squared displacements. In experimentally relevant parameter ranges, it also outperforms the analytically intractable and computationally more demanding maximum likelihood estimator (MLE). For the case of diffusion on a flexible and fluctuating substrate, the CVE is biased by substrate motion. However, given some long time series and a substrate under some tension, an extended MLE can separate particle diffusion on the substrate from substrate motion in the laboratory frame. This provides benchmarks that allow removal of bias caused by substrate fluctuations in CVE. The resulting unbiased CVE is optimal also for short time series on a fluctuating substrate. We have applied our estimators to human 8-oxoguanine DNA glycolase proteins diffusing on flow-stretched DNA, a fluctuating substrate, and found that diffusion coefficients are severely overestimated if substrate fluctuations are not accounted for.

Dense packings of nonoverlapping bodies in three-dimensional Euclidean space ${\mathbb{R}}^3$ are useful models of the structure of a variety of many-particle systems that arise in the physical and biological sciences. Here we investigate the packing behavior of congruent ring tori in ${\mathbb{R}}^3$, which are multiply connected nonconvex bodies of genus 1, as well as horn and spindle tori. Specifically, we analytically construct a family of dense periodic packings of unlinked tori guided by the organizing principles originally devised for simply connected solid bodies [Torquato and Jiao, Phys. Rev. E 86, 011102 (2012)]. We find that the horn tori as well as certain spindle and ring tori can achieve a packing density not only higher than that of spheres (i.e., $\pi /\sqrt{18}=0.7404...$) but also higher than the densest known ellipsoid packings (i.e., $0.7707...$). In addition, we study dense packings of clusters of pair-linked ring tori (i.e., Hopf links), which can possess much higher densities than corresponding packings consisting of unlinked tori.

We explore thermal fluctuations of thin planar membranes with a frozen spatially varying background metric and a shear modulus. We focus on a special class of $D$-dimensional “warped membranes” embedded in a $d$-dimensional space with $d\ge D+1$ and a preferred height profile characterized by quenched random Gaussian variables $\left\{h_{\alpha }\left(\mathbf{q}\right)\right\}$, $\alpha =D+1,...,d$, in Fourier space with zero mean and a power-law variance $\overline{h_{\alpha }\left({\mathbf{q}}_1\right)h_{\beta }\left({\mathbf{q}}_2\right)}\sim {\delta }_{\alpha ,\beta }{\delta }_{{\mathbf{q}}_1,-{\mathbf{q}}_2}{q}_1^{-d_h}$. The case $D=2$, $d=3$, with $d_h=4$ could be realized by flash-polymerizing lyotropic smectic liquid crystals. For $D<max\{4,d_h\}$ the elastic constants are nontrivially renormalized and become scale dependent. Via a self-consistent screening approximation we find that the renormalized bending rigidity increases for small wave vectors $\mathbf{q}$ as ${\kappa }_R\sim q^{-{\eta }_f}$, while the in-hyperplane elastic constants decrease according to ${\lambda }_R,{\mu }_R\sim q^{+{\eta }_u}$. The quenched background metric is relevant (irrelevant) for warped membranes characterized by exponent $d_h>4-{\eta }_f^{\left(F\right)}$ ($d_h<4-{\eta }_f^{\left(F\right)}$), where ${\eta }_f^{\left(F\right)}$ is the scaling exponent for tethered surfaces with a flat background metric, and the scaling exponents are related through ${\eta }_u+{\eta }_f=d_h-D$ (${\eta }_u+2{\eta }_f=4-D$).

Implications of the recently discovered effect of channeling of upstream extra particles for transport phenomena in a two-dimensional plasma crystal are discussed. Upstream particles levitated above the lattice layer and tended to move between the rows of lattice particles. An example of heat transport is considered, where upstream particles act as moving heat sources, which may lead to anomalous heat transport. The average channeling length observed was 15–20 interparticle distances. Other features of the channeling process are also reported.

The crystallization of organic semiconductor thin films from an amorphous phase often results in a broad range of microstructures and molecular arrangements that in turn critically impact the electronic properties of the film. Here we present a diffuse-interface model of thin film crystallization that accounts for out-of-plane tilting of the kinetically favored crystalline orientation as well as the simultaneous appearance of multiple polymorphs. By adjusting the relative thermodynamic stability of grains oriented with the fast-growing axis either parallel or perpendicular to the substrate, crystallization can be made to occur in the form of either commonly observed spherulites or more complex morphologies such as sectors and centers. Furthermore, tuning the relative kinetic coefficients and free energies of multiple polymorphs can result in a spherulite of one crystal structure embedded within a spherulite of another crystal structure. A parametric study of the effects of anisotropy, densification, time-varying treatments, and substrate patterning reveals a wide variety of morphologies that are possible in these thin films, driven by a combination of kinetic and thermodynamics effects.

We propose a regularized thin-fiber (string) model that overcomes past numerical limitations and allows determination of the steady fiber velocity and diameter of a semi-infinite Newtonian viscous fiber emerging from a nozzle rotating about an axis in the presence of centrifugal, inertial, and viscous forces of arbitrary magnitudes. The results are controlled by two dimensionless groups, namely, the Rossby number $\mathrm{Rb}$ expressing the ratio of inertial to centrifugal forces and the Reynolds number $\mathrm{Re}$, the ratio of inertial to viscous forces. We find that for $\mathrm{Rb}<0.5$ and $\mathrm{Re}<1$, regularization of the string-model equations is required to provide numerical stability, which we achieve. Solutions are thereby obtained in which viscosity reduces curvature in the fiber trajectory; these solutions asymptotically approach the inviscid solution at large distances along the spin line. Thus, long spin lines reach a diameter that is independent of viscosity, as long as the fiber is sufficiently long, a criterion that is made clear in the paper. At $\mathrm{Rb}>0.5$, regularization is not required, the curvature in fiber trajectory is increased by viscosity, and the solution at large distances along the spin line does not converge to the inviscid result. Regimes of behavior in the plane formed by $\mathrm{Re}$ and $\mathrm{Rb}$ are mapped out and example behavior is given for each regime.

A recently introduced active phase field crystal model describes the formation of ordered resting and traveling crystals in systems of self-propelled particles. Increasing the active drive, a resting crystal can be forced to perform collectively ordered migration as a single traveling object. We demonstrate here that these ordered migrating structures are linearly stable. In other words, during migration, the single-crystalline texture together with the globally ordered collective motion is preserved even on large length scales. Furthermore, we consider self-propelled particles on a substrate that are surrounded by a thin fluid film. We find that in this case the resulting hydrodynamic interactions can destabilize the order.

In a recent Letter, Yang et al. [Phys. Rev. Lett. 109, 258701 (2012)] introduced the concept of observability transitions: the percolationlike emergence of a macroscopic observable component in graphs in which the state of a fraction of the nodes, and of their first neighbors, is monitored. We show how their concept of depth-$L$ percolation—where the state of nodes up to a distance $L$ of monitored nodes is known—can be mapped onto multitype random graphs, and use this mapping to exactly solve the observability problem for arbitrary $L$. We then demonstrate a nontrivial coexistence of an observable and of a nonobservable extensive component. This coexistence suggests that monitoring a macroscopic portion of a graph does not prevent a macroscopic event to occur unbeknown to the observer. We also show that real complex systems behave quite differently with regard to observability depending on whether they are geographically constrained or not.

We introduce a simple potential to describe the dynamics of the relative motion of two pedestrians socially interacting in a walking group. We show that the proposed potential, based on basic empirical observations and theoretical considerations, can qualitatively describe the statistical properties of pedestrian behavior. In detail, we show that the two-dimensional probability distribution of the relative distance is determined by the proposed potential through a Boltzmann distribution. After calibrating the parameters of the model on the two-pedestrian group data, we apply the model to three-pedestrian groups, showing that it describes qualitatively and quantitatively well their behavior. In particular, the model predicts that three-pedestrian groups walk in a $\mathsf{V}$-shaped formation and provides accurate values for the position of the three pedestrians. Furthermore, the model correctly predicts the average walking velocity of three-person groups based on the velocity of two-person ones. Possible extensions to larger groups, along with alternative explanations of the social dynamics that may be implied by our model, are discussed at the end of the paper.