We investigate the cooperative dynamics of an ensemble of $N$ microtubules growing against an elastic barrier. Microtubules undergo so-called catastrophes, which are abrupt stochastic transitions from a growing to a shrinking state, and rescues, which are transitions back to the growing state. Microtubules can exert pushing or polymerization forces on an obstacle, such as an elastic barrier, if the growing end is in contact with the obstacle. We use dynamical mean-field theory and stochastic simulations to analyze a model where each microtubule undergoes catastrophes and rescues and where microtubules interact by force sharing. For zero rescue rate, cooperative growth terminates in a collective catastrophe. The maximal polymerization force before catastrophes grows linearly with $N$ for small $N$ or a stiff elastic barrier, in agreement with available experimental results, whereas it crosses over to a logarithmic dependence for larger $N$ or a soft elastic barrier. For a nonzero rescue rate and a soft elastic barrier, the dynamics becomes oscillatory with both collective catastrophe and rescue events, which are part of a robust limit cycle. Both the average and maximal polymerization forces then grow linearly with $N$, and we investigate their dependence on tubulin on-rates and rescue rates, which can be involved in cellular regulation mechanisms. We further investigate the robustness of the collective catastrophe and rescue oscillations with respect to different catastrophe models.

We study a neural network model of interacting stochastic discrete two-state cellular automata on a regular lattice. The system is externally tuned to a critical point which varies with the degree of stochasticity (or the effective temperature). There are avalanches of neuronal activity, namely, spatially and temporally contiguous sites of activity; a detailed numerical study of these activity avalanches is presented, and single, joint, and marginal probability distributions are computed. At the critical point, we find that the scaling exponents for the variables are in good agreement with a mean-field theory.

The free-energy calculation is usually limited to close to equilibrium perturbation regimes because faster perturbations introduce a bias into the estimate. The Jarzynski equality offers a solution to this problem by directly connecting the free-energy difference and the external work, regardless how far from equilibrium that work may be. However, a limited sampling coupled to the fast perturbation introduces a slowly converging bias into the Jarzynski free-energy estimate also. In this paper we present two perturbation protocols devised with the intention to overcome the convergence issues of the Jarzynski-based potential of mean force estimation in the single-molecule, constant velocity manipulation experiments. The protocols are designed to improve the convergence issues by increasing the variation of the external work through the modulation of the spring used to pull a molecule. Of the two methods, the one which continuously changes the amplitude of the spring stiffness offers an excellent reconstruction and requires less than one tenth of the samples required by the normal, constant spring pulling to produce the same quality of the reconstruction.

This brief report supplements and refines previous publications [Korobov, Phys. Rev. B 76, 085430 (2007); Korobov, Phys. Rev. E 79, 031607 (2009); Korobov, Phys. Rev. E 84, 021602 (2011)] to show that the scaling properties of the area distribution functions and kinetic curves actually hold for dense plane discrete Poisson-Voronoi tessellations. The previously noted apparent violations are due to the involved structures of boundaries of random domains.

We show the existence of a twisted electrostatic ion-cyclotron (ESIC) wave carrying orbital angular momentum (OAM) in a magnetized dusty plasma. For our purposes, we derive a 3D wave equation for the coupled ESIC and dust ion-acoustic (DIA) waves from the hydrodynamic equations that are composed of the continuity and momentum equations, together with Poisson's equation. The 3D wave equation reveals the formation of a braided or twisted ESIC wave structure carrying OAM. The braided or twisted ESIC wave structure can trap and transport plasma particles in magnetoplasmas, such as those in Saturn's F-ring and in the forthcoming magnetized dusty plasma experiments.

We investigate extinction dynamics in the paradigmatic model of two competing species $A$ and $B$ that reproduce ($A\to 2A$, $B\to 2B$), self-regulate by annihilation ($2A\to 0$, $2B\to 0$), and compete ($A+B\to A$, $A+B\to B$). For a finite system that is in the well-mixed limit, a quasistationary state arises which describes coexistence of the two species. Because of discrete noise, both species eventually become extinct in time that is exponentially long in the quasistationary population size. For a sizable range of asymmetries in the growth and competition rates, the paradoxical situation arises in which the numerically disadvantaged species according to the deterministic rate equations survives much longer.

Critical dynamics in various glass models, including those described by mode-coupling theory, is described by scale-invariant dynamical equations with a single nonuniversal quantity, i.e., the so-called parameter exponent that determines all the dynamical critical exponents. We show that these equations follow from the structure of the static replicated Gibbs free energy near the critical point. In particular, the exponent parameter is given by the ratio between two cubic proper vertexes that can be expressed as six-point cumulants measured in a purely static framework.

Monodisperse nanosuspension droplets, placed on a flat surface, evaporated following the stick-slip motion of the three-phase contact line. Unexpectedly, a disordered region formed at the exterior edge of a closely packed nanocolloidal crystalline structure during the “stick” period. In order to assess the role of particle velocity on particle structuring, we did experiments in a reduced pressure environment which allowed the enhancement of particle velocity. These experiments revealed the promotion of hexagonal packing at the very edge of the crystallite with increasing velocity. Quantification of particle velocity and comparison with measured deposit shape for each case allowed us to provide a tentative description of the underlying mechanisms that govern particle deposition of nanoparticles at the triple line of an evaporating droplet. Behavior is governed by an interplay between the fluid, and hence particle, flow velocity (main ordering parameter) and wedge constraints, and consequently disjoining pressure (main disordering parameter). Furthermore, the formation of a second disordered particle region at the interior edge of the deposit (towards bulk fluid) was found and attributed to the rapid motion of the triple line during the “slip” regime. Additionally, the magnitude of the pinning forces acting on the triple line of the same drops was calculated. These findings provide further insight into the mechanisms of the phenomenon and could facilitate its exploitation in various nanotechnological applications.

The mobility of tagged particles in a microrheological setup has been investigated via molecular dynamics simulations of a three-dimensional Lennard-Jones binary mixture. After coupling a small number of particles to a constant external driving force, the drift velocity and other observables of the dragged probe particles are reported in the linear and nonlinear response regime. In the nonlinear regime significant crowding effects are observed, thereby creating stringlike structures. Formation of the strings further enhances the nonlinear effects. A systematic study of these effects' dependence on temperature and total number of driven probe atoms is presented.

We study the dependence on the packing fraction of the pair-correlation function $g\left(r\right)$ and particle mobility in a dense three-dimensional packing of soft colloids made of poly N-isopropyl acrylamide (pNIPAM), a thermosensitive gel. We find that $g\left(r\right)$ for our samples is qualitatively like that of a liquid at all packing fractions. There is a peak in $g_1$, the height of the first peak of $g\left(r\right)$, as a function of the packing fraction. This peak is identified as a vestige, which remains at finite temperature, of the divergence found at the jamming transition in simulations of soft frictionless spheres at zero temperature. As the density is increased, the particle dynamics slow down and near the packing fraction where there is a peak in $g_1$ the particles become arrested on the time scale of the experiment.

Effects of scale coupling between mesoscopic slowly varying envelopes of liquid-solid profile and the underlying microscopic crystalline structure are studied in the phase-field-crystal (PFC) model. Such scale coupling leads to nonadiabatic corrections to the PFC amplitude equations, the effect of which increases strongly with decreasing system temperature below the melting point. This nonadiabatic amplitude representation is further coarse-grained for the derivation of effective sharp-interface equations of motion in the limit of small but finite interface thickness. We identify a generalized form of the Gibbs-Thomson relation with the incorporation of coupling and pinning effects of the crystalline lattice structure. This generalized interface equation can be reduced to the form of a driven sine-Gordon equation with Kardar-Parisi-Zhang (KPZ) nonlinearity, and can be combined with two other dynamic equations in the sharp interface limit obeying the conservation condition of atomic number density in a liquid-solid system. A sample application to the study of crystal layer growth is given, and the corresponding analytic solutions showing lattice pinning and depinning effects and two distinct modes of continuous vs nucleated growth are presented. We also identify the universal scaling behaviors governing the properties of pinning strength, surface tension, interface kinetic coefficient, and activation energy of atomic layer growth, which accommodate all range of liquid-solid interface thicknesses and different material elastic moduli.

The phenomenological antitrapping phase-field model has attained much success in describing alloy solidification. The heuristically introduced antitrapping current enables removing artificial effects due to the use of large interfacial width. Nevertheless, such a model is not thermodynamically consistent and has not been fitted into a variational framework. Here we present two approaches to develop a variational phase-field model to describe patten formation in alloys. Following the principles of linear irreversible thermodynamics we build in the cross-coupling between the phase transition rate and solute diffusion current. Our formulation not only naturally incorporates the antitrapping current but also predicts the conjugated mesoscopic solute drag effect. A more general form of the antitrapping current is obtained by thin-interface analysis. Benchmark simulations on isothermal dendrite growth are carried out to show the capability of our model to quantitatively characterize the interface evolution and solute profile even with a large interface width used. Importantly, our theory also provides general insights on how to obtain the genuine dynamic coupling between nonconserved and conserved order parameters. This leads to a thermodynamically consistent generalization of the celebrated model C proposed by Hohenberg and Halperin [Rev. Mod. Phys. 49, 435 (1977)].

The two-dimensional diffusion of isolated molecular tracers at the water–$n$-alkane interface was studied with fluorescence correlation spectroscopy. The interfacial diffusion coefficients of larger tracers with a hydrodynamic radius of 4.0 nm agreed well with the values calculated from the macroscopic viscosities of the two bulk phases. However, for small molecule tracers with hydrodynamic radii of only 1.0 and 0.6 nm, notable deviations were observed, indicating the existence of an interfacial region with reduced effective viscosity and increased mobility.

Integrins are essential receptors for the development and functioning of multicellular organisms because they mediate cell adhesion and migration, and regulate cell proliferation and apoptosis. In response to cues in the extracellular matrix, they are observed to organize into many clusters. The number and size of such clusters are observed to vary according to the concentration of and affinity for the extracellular ligand. The realization of a cluster point pattern is governed by a doubly stochastic process, controlling the number of clusters and the number of points per cluster. We construct entropy measures for the separation of two doubly stochastic processes and demonstrate how the self-organization of integrins in multiple clusters contributes to the accuracy in sensing the extracellular environment.

We analyze the out-of-equilibrium behavior of exclusion processes where agents interact with their nearest neighbors, and we study the short-range correlations which develop because of the exclusion and other contact interactions. The form of interactions we focus on, including adhesion and contact-preserving interactions, is especially relevant for migration processes of living cells. We show the local agent density and nearest-neighbor two-point correlations resulting from simulations on two-dimensional lattices in the transient regime where agents invade an initially empty space from a source and in the stationary regime between a source and a sink. We compare the results of simulations with the corresponding quantities derived from the master equation of the exclusion processes, and in both cases, we show that, during the invasion of space by agents, a wave of correlations travels with velocity $v\left(t\right)\sim t^{-1/2}$. The relative placement of this wave to the agent density front and the time dependence of its height may be used to discriminate between different forms of contact interactions or to quantitatively estimate the intensity of interactions. We discuss, in the stationary density profile between a full and an empty reservoir of agents, the presence of a discontinuity close to the empty reservoir. Then we develop a method for deriving approximate hydrodynamic limits of the processes. From the resulting systems of partial differential equations, we recover the self-similar behavior of the agent density and correlations during space invasion.

We employ a recently developed model that allows the study of two-dimensional brittle crack propagation under fixed grip boundary conditions. The crack development highlights the importance of voids which appear ahead of the crack as observed in experiments on the nanoscale. The appearance of these voids is responsible for roughening the crack path on small scales, in agreement with theoretical expectations. With increasing speed of propagation one observes the branching instabilities that were reported in experiments. The simulations allow understanding the phenomena by analyzing the elastic stress field that accompanies the crack dynamics.

Large crowds evacuating through narrow bottlenecks may create clogging and jams that slow down the egress flow. Especially if people try to push towards the exit, the so-called faster-is-slower effect may occur. We propose a spatial game to model the interaction of agents in such situations. Each agent has two possible modes of play that lead to either patient or impatient behavior. The payoffs of the game are derived from simple assumptions and correspond to a hawk-dove game, where the game parameters depend on the agent's location in the crowd and on external conditions. Equilibrium configurations are computed with a myopic best-response rule and studied in both a continuous space and a discrete lattice. We apply the game model to a continuous-time egress simulation, where the patient and impatient agents are given different individual parameter values, which are updated according to the local conditions in the crowd. The model shows how threatening conditions can increase the proportion of impatient agents, which leads to clogging and reduced flows through bottlenecks, even when smooth flows would be possible.

Dynamic behaviors of fronts connecting standing waves, such as the locking phenomenon, pinning-depinning transitions, propagation, and front interactions, are studied. Two systems are considered, a vertically driven pendulum chain and a generalized ${\varphi }^4$ model. Both models exhibit in an appropriate region of parameters bistability between standing waves. In the driven pendulum chain, using a Galerkin expansion we characterize the region of bistability between subharmonic waves for the upright and the upside-down pendulum states. We derive analytically the front dynamics in the generalized ${\varphi }^4$ model, showing regions where fronts are oscillatory or propagative. We also characterize the mechanism of the pinning-depinning transition of fronts between standing waves. Using front interactions we predict the emergence of dissipative localized waves supported on a standing wave and characterize their corresponding homoclinic snaking bifurcation diagrams. All these analytical predictions are confirmed by numerical simulations with quite good agreement.

We investigate the external synchronization of the oscillating pulse edges developed in a transmission line periodically loaded with tunnel diodes (TDs), termed a TD line. It is observed that the pulse edge oscillates on a TD line when supplied by an appropriate voltage at the end of the line. We discuss how the pulse edge oscillates on a TD line and the properties of the external synchronization of the edge oscillation driven by a sinusoidal perturbation. By applying a phase-reduction scheme to the transmission equation of a TD line, we obtain the phase sensitivity, which satisfactory explains the measured spatial dependence of the locking range on the frequency. Moreover, we successfully detect the spatiotemporal behaviors of the edge oscillation by establishing synchronization with the sampling trigger of an oscilloscope.

Gravitational instability occurs at the interface of two solutions when a higher-density solution (HDS) is placed on the surface of a lower-density solution (LDS). As the HDS sinks, a cell pattern forms on the surface. We investigate the size distribution of the cells in this pattern. We show that the cumulative size distribution obeys a power law with a power index that is independent of time as long as it is possible to neglect the interactions among the cells. To understand the power law mechanism, a simple model excluding the interactions is proposed, and we demonstrate that this simple model provides the power law measured in experiments. Our results indicate that independent cell generation and growth are key factors to understand the feature of the cell pattern.