As a model for cell-to-cell communication in biological tissues, we construct repressor lattices by repeating a regulatory three-node motif on a hexagonal structure. Local interactions can be unidirectional, where a node either represses or activates a neighbor that does not communicate backwards. Alternatively, they can be bidirectional where two neighboring nodes communicate with each other. In the unidirectional case, we perform stability analyses for the transitions from stationary to oscillating states in lattices with different regulatory units. In the bidirectional case, we investigate transitions from oscillating states to ordered patterns generated by local switches. Finally, we show how such stable patterns in two-dimensional lattices can be generalized to three-dimensional systems.

An approach based on effective field theory (EFT) is discussed and applied to the problem of surface-mediated interactions between rigid inclusions of circular footprint on a membrane. Instead of explicitly constraining the surface fluctuations in accord with the boundary conditions around the inclusions, the EFT formalism rewrites the theory; the Hamiltonian of a freely fluctuating surface is augmented by pointwise localized terms that capture the same constraints. This allows one to compute the interaction free energy as an asymptotic expansion in inverse separations in a systematic, efficient, and transparent way. Both entropic (fluctuation-induced, Casimir-like) and curvature-elastic (ground-state) forces are considered. Our findings include higher-order corrections to known asymptotic results, on both the pair and the multibody levels. We also show that the few previous attempts in the literature at predicting subleading orders missed some terms due to an uncontrolled point-particle approximation.

Clathrin-mediated endocytosis is a complex process through which eukaryotic cells internalize nutrients, antigens, growth factors, pathogens, etc. The process occurs via the formation of invaginations on the cell membrane, called clathrin-coated pits (CCPs). Over the years, much has been learned about the mechanism of CCP assembly, but a complete understanding of the assembly process still remains elusive. In recent years, using fluorescence microscopy, studies have been done to determine the statistical properties of CCP formation. In this paper, using a recently proposed coarse-grained, stochastic model of CCP assembly [Banerjee, Berezhkovskii, and Nossal, Biophys. J. 102, 2725 (2012)], we suggest new ways of analyzing such experimental data. To be more specific, we derive analytical expressions for the distribution of maximum size of abortive CCPs, and the probability density of their lifetimes. Our results show how these functions depend on the kinetic and energetic parameters characterizing the assembly process, and therefore could be useful in extracting information about the mechanism of CCP assembly from experimental data. We find excellent agreement between our analytical results and those obtained from kinetic Monte Carlo simulations of the assembly process.

A collective-risk social dilemma implies that personal endowments will be lost if contributions to the common pool within a group are too small. Failure to reach the collective target thus has dire consequences for all group members, independently of their strategies. Wanting to move away from unfavorable locations is therefore anything but surprising. Inspired by these observations, we here propose and study a collective-risk social dilemma where players are allowed to move if the collective failure becomes too probable. More precisely, this so-called risk-driven migration is launched depending on the difference between the actual contributions and the declared target. Mobility therefore becomes an inherent property that is utilized in an entirely self-organizing manner. We show that under these assumptions cooperation is promoted much more effectively than under the action of manually determined migration rates. For the latter, we in fact identify parameter regions where the evolution of cooperation is greatly inhibited. Moreover, we find unexpected spatial patterns where cooperators that do not form compact clusters outperform those that do, and where defectors are able to utilize strikingly different ways of invasion. The presented results support the recently revealed importance of percolation for the successful evolution of public cooperation, while at the same time revealing surprisingly simple methods of self-organization towards socially desirable states.

In fluids and plasmas with zonal flow reversed shear, a peculiar kind of transport barrier appears in the shearless region, one that is associated with a proper route of transition to chaos. These barriers have been identified in symplectic nontwist maps that model such zonal flows. We use the so-called standard nontwist map, a paradigmatic example of nontwist systems, to analyze the parameter dependence of the transport through a broken shearless barrier. On varying a proper control parameter, we identify the onset of structures with high stickiness that give rise to an effective barrier near the broken shearless curve. Moreover, we show how these stickiness structures, and the concomitant transport reduction in the shearless region, are determined by a homoclinic tangle of the remaining dominant twin island chains. We use the finite-time rotation number, a recently proposed diagnostic, to identify transport barriers that separate different regions of stickiness. The identified barriers are comparable to those obtained by using finite-time Lyapunov exponents.

Self-propelled microorganisms, such as unicellular algae or bacteria, swim along their director relative to the fluid velocity. Under a steady shear flow the director rotates in close orbit, a periodic structure that is preserved under an oscillatory shear flow. If the shear flow is subjected to small fluctuations produced by small irregularities in the microchannel or by other swimmers nearby, the director dynamics becomes stochastic. Numerical integration of the swimmer motion shows that there is stochastic resonance: The displacement in the vorticity direction is maximized for a finite noise intensity. This transverse displacement resonance is observed when the displacement is coarse grained over several periods, although the director is preferentially oriented along the flow. The resonant noise intensity is proportional to the oscillation frequency and independent of the shear rate. The enhanced displacement can have effects on the transverse diffusion of swimmers and the rheology of the suspension.

In this work we use a multiscale framework to calculate the fluidization threshold of three-dimensional cohesive granulates under shear forces exerted by a creeping flow. A continuum model of flow through porous media provides an analytical expression for the average drag force on a single grain. The balance equation for the forces and a force propagation model are then used to investigate the effects of porosity and packing structure on the stability of the pile. We obtain a closed-form expression for the instability threshold of a regular packing of monodisperse frictionless cohesive spherical grains in a planar fracture. Our result quantifies the compound effect of structural (packing orientation and porosity) and dynamical properties of the system on its stability.

We consider concentration dependence of rheological properties of associative telechelic polymer solutions. Experimental results for model telechelic polymer solutions show rather strong concentration dependence of rheological properties. For solutions with relatively high concentrations, linear viscoelasticity deviates from the single Maxwell behavior. The concentration dependence of characteristic relaxation time and moduli is different in high- and low-concentration cases. These results suggest that there are two different concentration regimes. We expect that densely connected (well percolated) networks are formed in high-concentration solutions, whereas sparsely connected (weakly percolated) networks are formed in low-concentration solutions. We propose single chain type transient network models to explain experimental results. Our models incorporate the spatial correlation effect of micellar cores and average number of elastically active chains per micellar core (the network functionality). Our models can reproduce nonsingle Maxwellian relaxation and nonlinear rheological behavior such as the shear thickening and thinning. They are qualitatively consistent with experimental results. In our models, the linear rheological behavior is mainly attributable to the difference of network structures (functionalities). The nonlinear rheological behavior is attributable to the nonlinear flow rate dependence of the spatial correlation of micellar core positions.

Some phase space transport properties for a conservative bouncer model are studied. The dynamics of the model is described by using a two-dimensional measure preserving mapping for the variables' velocity and time. The system is characterized by a control parameter $\epsilon$ and experiences a transition from integrable ($\epsilon =0$) to nonintegrable ($\epsilon \ne 0$). For small values of $\epsilon$, the phase space shows a mixed structure where periodic islands, chaotic seas, and invariant tori coexist. As the parameter $\epsilon$ increases and reaches a critical value ${\epsilon }_c$, all invariant tori are destroyed and the chaotic sea spreads over the phase space, leading the particle to diffuse in velocity and experience Fermi acceleration (unlimited energy growth). During the dynamics the particle can be temporarily trapped near periodic and stable regions. We use the finite time Lyapunov exponent to visualize this effect. The survival probability was used to obtain some of the transport properties in the phase space. For large $\epsilon$, the survival probability decays exponentially when it turns into a slower decay as the control parameter $\epsilon$ is reduced. The slower decay is related to trapping dynamics, slowing the Fermi Acceleration, i.e., unbounded growth of the velocity.

A small-world (SW) network of similar phase oscillators, interacting according to the Kuramoto model, is studied numerically. It is shown that deterministic Kuramoto dynamics on SW networks has various stable stationary states. This can be attributed to the so-called defect patterns in an SW network, which it inherits from deformation of helical patterns in its regular parent. Turning on an uncorrelated random force causes vanishing of the defect patterns, hence increasing the synchronization among oscillators for moderate noise intensities. This phenomenon, called stochastic synchronization, is generally observed in some natural networks such as the brain neural network.

Scroll waves are three-dimensional excitation vortices rotating around one-dimensional phase singularities called filaments. In experiments with a chemical reaction-diffusion system and in numerical simulations, we study the pinning of closed filament loops to inert cylindrical heterogeneities. We show that the filament wraps itself around the heterogeneity and thus avoids contraction and annihilation. This entwining steadily increases the total length of the pinned filament and reshapes the entire rotation backbone of the vortex. Self-pinning is fastest for thin cylinders with radii not much larger than the core of the unpinned rotor. The process ends when the filament is attached to the entire length of the cylinder. The possible importance of self-pinning in cardiac systems is discussed.

Ocean waves are complex and often turbulent. While most ocean-wave interactions are essentially linear, sometimes two or more waves interact in a nonlinear way. For example, two or more waves can interact and yield waves that are much taller than the sum of the original wave heights. Most of these shallow-water nonlinear interactions look like an X or a Y or two connected Ys; at other times, several lines appear on each side of the interaction region. It was thought that such nonlinear interactions are rare events: they are not. Here we report that such nonlinear interactions occur every day, close to low tide, on two flat beaches that are about 2000 km apart. These interactions are closely related to the analytic, soliton solutions of a widely studied multidimensional nonlinear wave equation. On a much larger scale, tsunami waves can merge in similar ways.

We have performed experimental and theoretical investigation of the formation and behavior of Coulomb clusters of charged diamagnetic particles in a cusp magnetic trap under microgravity conditions aboard the International Space Station. Graphite particles of 100–400 μm in size were used in experiments due to the highest specific magnetic susceptibility. We have observed the formation of clusters in the shape of an oblate ellipsoid of revolution and their oscillations after dynamical action by changing the magnetic field. Observing the excitation and damping of oscillations we have made some estimations. Molecular dynamics simulations of the observed processes have been made. Their results are in reasonable agreement with experiments. Some differences are evidently due to some unaccounted-for reasons.

We report new types of matter rogue waves of a spinor (three-component) model of the Bose-Einstein condensate governed by a system of three nonlinearly coupled Gross-Pitaevskii equations. The exact first-order rational solutions containing one free parameter are obtained by means of a Darboux transformation for the integrable system where the mean-field interaction is attractive and the spin-exchange interaction is ferromagnetic. For different choices of the parameter, there exists a variety of different shaped solutions including two peaks in bright rogue waves and four dips in dark rogue waves. Furthermore, by utilizing the relation between the three-component and the one-component versions of the nonlinear Schrödinger equation, we can devise higher-order rational solutions, in which three components have different shapes. In addition, it is noteworthy that dark rogue wave features disappear in the third-order rational solution.

We report Monte Carlo simulations that show a closed-loop liquid-vapor equilibrium in a pure substance. This finding has been achieved on a two-dimensional lattice model for patchy particles that can form network fluids. We have considered related models with a slightly different patch distribution in order to understand the features of the distribution of patches on the surface of the particles that make possible the presence of the closed-loop liquid-vapor equilibrium, and its relation to the phase diagram containing so-called empty liquids. Finally we discuss the likelihood of finding the closed-loop liquid-vapor equilibria on related models for three-dimensional models of patchy particles in the continuum, and speculate on the possible relationship between the mechanism behind the closed-loop liquid-vapor equilibrium of our simple lattice model and the salt-induced reentrant condensation found in complex systems.

The anomalous mesoscopic transport in supercooled liquids was investigated using three-dimensional molecular dynamics simulation. We show that the dynamic correlation length, $\xi$, can be identified as a crossover length between the microscopic and macroscopic transports. We also find that in highly supercooled states, where a clear stress plateau is observed in the stress autocorrelation, cooperative transport, in both the (longitudinal) density diffusion and the (transverse) viscous relaxation, can be characterized by the single length scale, $\xi$. The present identification of the dynamic correlation length has an advantage over other characterization methods in that it directly interprets the anomalous hydrodynamic transport in terms of the growing length scale. In the context of the present study, we provide a simple explanation for the long-standing problem of the breakdown of the Stokes-Einstein relation.

Having reached the quantum and thermodynamic limits of detection, atomic force microscopy (AFM) experiments are routinely being performed at the fundamental limit of signal to noise. A critical understanding of the statistical properties of noise leads to more accurate interpretation of data, optimization of experimental protocols, advancements in instrumentation, and new measurement techniques. Furthermore, accurate simulation of cantilever dynamics requires knowledge of stochastic behavior of the system, as stochastic noise may exceed the deterministic signals of interest, and even dominate the outcome of an experiment. In this article, the power spectral density (PSD), used to quantify stationary stochastic processes, is introduced in the context of a thorough noise analysis of the light source used to detect cantilever deflections. The statistical properties of PSDs are then outlined for various stationary, nonstationary, and deterministic noise sources in the context of AFM experiments. Following these developments, a method for integrating PSDs to provide an accurate standard deviation of linear measurements is described. Lastly, a method for simulating stochastic Gaussian noise from any arbitrary power spectral density is presented. The result demonstrates that mechanical vibrations of the AFM can cause a logarithmic velocity dependence of friction and induce multiple slip events in the atomic stick-slip process, as well as predicts an artifactual temperature dependence of friction measured by AFM.

We present a master equation approach to the narrow escape time (NET) problem, i.e., the time needed for a particle contained in a confining domain with a single narrow opening to exit the domain for the first time. We introduce a finite transition probability, $\nu$, at the narrow escape window, allowing the study of the imperfect trapping case. Ranging from 0 to $\infty$, $\nu$ allowed the study of both extremes of the trapping process: that of a highly deficient capture and situations where escape is certain (“perfect trapping” case). We have obtained analytic results for the basic quantity studied in the NET problem, the mean escape time, and we have studied its dependence in terms of the transition (desorption) probability over (from) the surface boundary, the confining domain dimensions, and the finite transition probability at the escape window. Particularly we show that the existence of a global minimum in the NET depends on the “imperfection” of the trapping process. In addition to our analytical approach, we have implemented Monte Carlo simulations, finding excellent agreement between the theoretical results and simulations.

We employ the macroscopic fluctuation theory to study fluctuations of integrated current in one-dimensional lattice gases with a steplike initial density profile. We analytically determine the variance of the current fluctuations for a class of diffusive processes with a density-independent diffusion coefficient. Our calculations rely on a perturbation theory around the noiseless hydrodynamic solution. We consider both quenched and annealed types of averaging (the initial condition is allowed to fluctuate in the latter situation). The general results for the variance are specialized to a few interesting models including the symmetric exclusion process and the Kipnis-Marchioro-Presutti model [Kipnis, Marchioro, and Presutti, J. Stat. Phys. 27, 65 (1982)]. We also probe large deviations of the current for the symmetric exclusion process. This is done by numerically solving the governing equations of the macroscopic fluctuation theory using an efficient iteration algorithm.

Partial differential equation models are ubiquitous in studies of motile cell populations, giving a phenomenological description of events which can be analyzed and simulated using a wide range of existing tools. However, these models are seldom derived from individual cell behaviors and so it is difficult to accurately include biological hypotheses on this spatial scale. Moreover, studies which do attempt to link individual- and population-level behavior generally employ lattice-based frameworks in which the artifacts of lattice choice at the population level are unclear. In this work we derive limiting population-level descriptions of a motile cell population from an off-lattice, individual-based model (IBM) and investigate the effects of volume exclusion on the population-level dynamics. While motility with excluded volume in on-lattice IBMs can be accurately described by Fickian diffusion, we demonstrate that this is not the case off lattice. We show that the balance between two key parameters in the IBM (the distance moved in one step and the radius of an individual) determines whether volume exclusion results in enhanced or slowed diffusion. The magnitude of this effect is shown to increase with the number of cells and the rate of their movement. The method we describe is extendable to higher-dimensional and more complex systems and thereby provides a framework for deriving biologically realistic, continuum descriptions of motile populations.