Ellipsoidal micron-sized colloidal particles can oscillate spontaneously when trapped in a focused laser beam. If two oscillating particles are held in proximity their oscillations synchronize through hydrodynamic interactions. The degree of synchronization depends on the distance between the oscillators and on their orientation. Due to the anisotropic nature of hydrodynamic coupling the synchronization is strongest when particles are arranged along the direction of oscillations. Similar behavior is observed for many oscillating particles arranged in a row. Experimental observations are well reproduced with a model that uses a phenomenological description of the optical force and hydrodynamic interactions. Our results show that oscillating ellipsoidal particles can serve as a model system for studying hydrodynamic synchronization between biological cilia.

We present a model of soft active particles that leads to a rich array of collective behavior found also in dense biological swarms of bacteria and other unicellular organisms. Our model uses only local interactions, such as Vicsek-type nearest-neighbor alignment, short-range repulsion, and a local boundary term. Changing the relative strength of these interactions leads to migrating swarms, rotating swarms, and jammed swarms, as well as swarms that exhibit run-and-tumble motion, alternating between migration and either rotating or jammed states. Interestingly, although a migrating swarm moves slower than an individual particle, the diffusion constant can be up to three orders of magnitude larger, suggesting that collective motion can be highly advantageous, for example, when searching for food.

Irregular firing of neurons can be modeled as a stochastic process. Here we study the perfect integrate-and-fire neuron driven by dichotomous noise, a Markovian process that jumps between two states (i.e., possesses a non-Gaussian statistics) and exhibits nonvanishing temporal correlations (i.e., represents a colored noise). Specifically, we consider asymmetric dichotomous noise with two different transition rates. Using a first-passage-time formulation, we derive exact expressions for the probability density and the serial correlation coefficient of the interspike interval (time interval between two subsequent neural action potentials) and the power spectrum of the spike train. Furthermore, we extend the model by including additional Gaussian white noise, and we give approximations for the interspike interval (ISI) statistics in this case. Numerical simulations are used to validate the exact analytical results for pure dichotomous noise, and to test the approximations of the ISI statistics when Gaussian white noise is included. The results may help to understand how correlations and asymmetry of noise and signals in nerve cells shape neuronal firing statistics.

We outline a framework for describing photoactivated biological reactions as generalized quantum measurements of external fields, for which the biological system takes on the role of a quantum meter. By using general arguments regarding the Hamiltonian that describes the measurement interaction, we identify the cases where it is essential for a complex chemical or biological system to exhibit nonequilibrium quantum coherent dynamics in order to achieve the requisite functionality. We illustrate the analysis by considering measurement of the solar radiation field in photosynthesis and measurement of the earth's magnetic field in avian magnetoreception.

In type II superconductors, the dynamics of superconducting vortices determine their transport properties. In the Ginzburg-Landau theory, vortices correspond to topological defects in the complex order parameter. Extracting their precise positions and motion from discretized numerical simulation data is an important, but challenging, task. In the past, vortices have mostly been detected by analyzing the magnitude of the complex scalar field representing the order parameter and visualized by corresponding contour plots and isosurfaces. However, these methods, primarily used for small-scale simulations, blur the fine details of the vortices, scale poorly to large-scale simulations, and do not easily enable isolating and tracking individual vortices. Here we present a method for exactly finding the vortex core lines from a complex order parameter field. With this method, vortices can be easily described at a resolution even finer than the mesh itself. The precise determination of the vortex cores allows the interplay of the vortices inside a model superconductor to be visualized in higher resolution than has previously been possible. By representing the field as the set of vortices, this method also massively reduces the data footprint of the simulations and provides the data structures for further analysis and feature tracking.

We present an experimental study of a flock passing through a narrow door. Video monitoring of daily routines in a farm has enabled us to collect a sizable amount of data. By measuring the time lapse between the passage of consecutive animals, some features of the flow regime can be assessed. A quantitative definition of clogging is demonstrated based on the passage time statistics. These display broad tails, which can be fitted by power laws with a relatively large exponent. On the other hand, the distribution of burst sizes robustly evidences exponential behavior. Finally, borrowing concepts from granular physics and statistical mechanics, we evaluate the effect of increasing the door size and the performance of an obstacle placed in front of it. The success of these techniques opens new possibilities regarding their eventual extension to the management of human crowds.

Particle degradation and fracture play an important role in natural granular flows and in many applications of granular materials. We analyze the fracture properties of two-dimensional disklike particles modeled as aggregates of rigid cells bonded along their sides by a cohesive Mohr-Coulomb law and simulated by the contact dynamics method. We show that the compressive strength scales with tensile strength between cells but depends also on the friction coefficient and a parameter describing cell shape distribution. The statistical scatter of compressive strength is well described by the Weibull distribution function with a shape parameter varying from 6 to 10 depending on cell shape distribution. We show that this distribution may be understood in terms of percolating critical intercellular contacts. We propose a random-walk model of critical contacts that leads to particle size dependence of the compressive strength in good agreement with our simulation data.

We examine the shape change of a thin disk with an inserted wedge of material when it is pushed against a plane, using analytical, numerical, and experimental methods. Such sheets occur in packaging, surgery, and nanotechnology. We approximate the sheet as having vanishing strain, so that it takes a conical form in which straight generators converge to a disclination singularity. Then, its shape is that which minimizes elastic bending energy alone. Real sheets are expected to approach this limiting shape as their thickness approaches zero. The planar constraint forces a sector of the sheet to buckle into the third dimension. We find that the unbuckled sector is precisely semicircular, independent of the angle $\delta$ of the inserted wedge. We generalize the analysis to include conical as well as planar constraints and thereby establish a law of corresponding states for shallow cones of slope $\epsilon$ and thin wedges. In this regime, the single parameter $\delta /{\epsilon }^2$ determines the shape. We discuss the singular limit in which the cone becomes a plane, and the unexpected slow convergence to the semicircular buckling observed in real sheets.

It is an important and interesting problem to elucidate how the degree of phase order in a large population of coupled oscillators responds to a synchronizing periodic force from the outside. Here this problem is studied analytically as well as numerically by introducing the concept of susceptibility for globally coupled phase oscillators with either nonrandom or random interactions. It is shown that the susceptibility diverges at the critical point in the nonrandom case with Widom's equality satisfied, while it exhibits a cusp in the most random case.

We experimentally study the critical properties of the nonequilibrium solid-liquid–like transition that takes place in vibrated granular matter. The critical dynamics is characterized by the coupling of the density field with the bond-orientational order parameter $Q_4$, which measures the degree of local crystallization. Two setups are compared, which present the transition at different critical accelerations as a result of modifying the energy dissipation parameters. In both setups five independent critical exponents are measured, associated to different properties of $Q_4$: the correlation length, relaxation time, vanishing wavenumber limit (static susceptibility), the hydrodynamic regime of the pair correlation function, and the amplitude of the order parameter. The respective critical exponents agree in both setups and are given by ${\nu }_{\perp }=1,{\nu }_{\parallel }=2,\gamma =1,\eta \approx 0.6-0.67$, and $\beta =1/2$, whereas the dynamical critical exponent is $z={\nu }_{\parallel }/{\nu }_{\perp }=2$. The agreement on five exponents is an exigent test for the universality of the transition. Thus, while dissipation is strictly necessary to form the crystal, the path the system undergoes toward the phase separation is part of a well-defined universality class. In fact, the local order shows critical properties while density does not. Being the later conserved, the appropriate model that couples both is model C in the Hohenberg and Halperin classification. The measured exponents are in accord with the nonequilibrium extension to model C if we assume that $\alpha$, the exponent associated in equilibrium to the specific heat divergence but with no counterpart in this nonequilibrium experiment, vanishes.

We use large scale computer simulations and finite-size scaling analysis to study the shear rheology of dense three-dimensional suspensions of frictionless non-Brownian particles in the vicinity of the jamming transition. We perform simulations of soft repulsive particles at constant shear rate, constant pressure, and finite system size and carefully study the asymptotic limits of large system sizes and infinitely hard particle repulsion. We first focus on the asymptotic behavior of the shear viscosity in the hard particle limit. By measuring the viscosity increase over about 5 orders of magnitude, we are able to confirm its asymptotic power law divergence close to the jamming transition. However, a precise determination of the critical density and critical exponent is difficult due to the “multiscaling” behavior of the viscosity. Additionally, finite-size scaling analysis suggests that this divergence is accompanied by a growing correlation length scale, which also diverges algebraically. Finally, we study the effect of particle softness and propose a natural extension of the standard granular rheology, which we test against our simulation data. Close to the jamming transition, this “soft granular rheology” offers a detailed description of the nonlinear rheology of soft particles, which differs from earlier empirical scaling forms.

A central challenge for organisms during development is determining a means to efficiently export toxic molecules from inside the developing embryo. For aquatic microorganisms, the strategies employed should be robust with respect to the variable ocean environment and limit the chances that exported toxins are reabsorbed. As a result, the problem of toxin export is closely related to the physics of mass transport in a fluid. In this paper, we consider a model first-passage problem for the uptake of exported toxins by a spherical embryo. By considering how macroscale fluid turbulence manifests itself on the microscale of the embryo, we determine that fluid flow enhances the effectiveness of toxin export as compared to the case of diffusion-limited transport. In the regime of a large Péclet number, a perturbative solution of the advection-diffusion equation reveals that a concentration boundary layer forms at the surface of the embryo. The model results suggest a functional role for cell surface roughness in the export process, with the thickness of the concentration boundary layer setting the length scale for cell membrane protrusions known as microvilli. We highlight connections between the model results and experiments on the development of sea urchin embryos.

The vast majority of parallel scientific applications distributes computation among processes that are in a busy state when computing and in an idle state when waiting for information from other processes. We identify the propagation of idle waves through processes in scientific applications with a local information exchange between the two processes. Idle waves are nondispersive and have a phase velocity inversely proportional to the average busy time. The physical mechanism enabling the propagation of idle waves is the local synchronization between two processes due to remote data dependency. This study provides a description of the large number of processes in parallel scientific applications as a continuous medium. This work also is a step towards an understanding of how localized idle periods can affect remote processes, leading to the degradation of global performance in parallel scientific applications.

Empirical evidence shows that the rate of irregular usage of English verbs exhibits discontinuity as a function of their frequency: the most frequent verbs tend to be totally irregular. We aim to qualitatively understand the origin of this feature by studying simple agent-based models of language dynamics, where each agent adopts an inflectional state for a verb and may change it upon interaction with other agents. At the same time, agents are replaced at some rate by new agents adopting the regular form. In models with only two inflectional states (regular and irregular), we observe that either all verbs regularize irrespective of their frequency, or a continuous transition occurs between a low-frequency state, where the lemma becomes fully regular, and a high-frequency one, where both forms coexist. Introducing a third (mixed) state, wherein agents may use either form, we find that a third, qualitatively different behavior may emerge, namely, a discontinuous transition in frequency. We introduce and solve analytically a very general class of three-state models that allows us to fully understand these behaviors in a unified framework. Realistic sets of interaction rules, including the well-known naming game (NG) model, result in a discontinuous transition, in agreement with recent empirical findings. We also point out that the distinction between speaker and hearer in the interaction has no effect on the collective behavior. The results for the general three-state model, although discussed in terms of language dynamics, are widely applicable.

Hyperuniformity characterizes a state of matter for which (scaled) density fluctuations diminish towards zero at the largest length scales. However, the task of determining whether or not an image of an experimental system is hyperuniform is experimentally challenging due to finite-resolution, noise, and sample-size effects that influence characterization measurements. Here we explore these issues, employing video optical microscopy to study hyperuniformity phenomena in disordered two-dimensional jammed packings of soft spheres. Using a combination of experiment and simulation we characterize the possible adverse effects of particle polydispersity, image noise, and finite-size effects on the assignment of hyperuniformity, and we develop a methodology that permits improved diagnosis of hyperuniformity from real-space measurements. The key to this improvement is a simple packing reconstruction algorithm that incorporates particle polydispersity to minimize the free volume. In addition, simulations show that hyperuniformity in finite-sized samples can be ascertained more accurately in direct space than in reciprocal space. Finally, our experimental colloidal packings of soft polymeric spheres are shown to be effectively hyperuniform.

Vacancies represent an important class of crystallographic defects, and their behaviors can be strongly coupled with relevant material properties. In this work, we study the dynamics of generic $n$-point vacancies in two-dimensional Lennard-Jones crystals in several thermodynamic states. Simulations reveal the spectrum of distinct, size-dependent vacancy dynamics, including the nonmonotonously varying diffusive mobilities of one-, two- and three-point vacancies, and several healing routines of linear vacancies. Specifically, we numerically observe significantly faster diffusion of the two-point vacancy that can be attributed to its rotational degree of freedom. The high mobility of the two-point vacancies opens the possibility of doping two-point vacancies into atomic materials to enhance atomic migration. The rich physics of vacancies revealed in this study may have implications in the engineering of defects in extensive crystalline materials for desired properties.

A bouncing droplet, self-propelled by its interaction with the waves it generates, forms a classical wave-particle association called a “walker.” Previous works have demonstrated that the dynamics of a single walker is driven by its global surface wave field that retains information on its past trajectory. Here we investigate the energy stored in this wave field for two coupled walkers and how it conveys an interaction between them. For this purpose, we characterize experimentally the “promenade modes” where two walkers are bound and propagate together. Their possible binding distances take discrete values, and the velocity of the pair depends on their mutual binding. The mean parallel motion can be either rectilinear or oscillating. The experimental results are recovered analytically with a simple theoretical framework. A relation between the kinetic energy of the droplets and the total energy of the standing waves is established.

This paper investigates how economic shocks propagate and amplify through the input-output network connecting industrial sectors in developed economies. We study alternative models of diffusion on networks and we calibrate them using input-output data on real-world inter-sectoral dependencies for several European countries before the Great Depression. We show that the impact of economic shocks strongly depends on the nature of the shock and country size. Shocks that impact on final demand without changing production and the technological relationships between sectors have on average a large but very homogeneous impact on the economy. Conversely, when shocks change also the magnitudes of input-output across-sector interdependencies (and possibly sector production), the economy is subject to predominantly large but more heterogeneous avalanche sizes. In this case, we also find that (i) the more a sector is globally central in the country network, the larger its impact; (ii) the largest European countries, such as those constituting the core of the European Union's economy, typically experience the largest avalanches, signaling their intrinsic higher vulnerability to economic shocks.

We theoretically find the effect of confinement and thermal fluctuations on the diffusivity of a spherical active swimmer moving inside a two-dimensional narrow cavity of general shape. The explicit formulas for the effective diffusion coefficient of a swimmer moving inside two particular cavities are presented. We also compare our analytical results with Brownian dynamics simulations and we obtain excellent agreement.

In this study we investigate the effect of geometrical or thermal discontinuities on the growth of water droplets condensing on a cooled substrate. Edges, corners, and cooled and noncooled boundaries can have a strong effect on the vapor concentration profile and mass diffusion around the drops. In comparison to growth in a pattern where droplets have to compete to catch vapor, which results in a linear water concentration profile directed perpendicularly to the substrate, droplets near discontinuities can get more vapor (outer edges, corners), resulting in faster growth or less vapor (inner edges), giving lower growth. When the cooling heat flux limits growth instead of mass diffusion (substrate with low thermal conductivity, strong heat exchange with air), edge effects can be canceled. In certain cases, growth enhancement can reach nearly 500% on edges or corners.