We study the Reynolds number scaling of the Kolmogorov-Sinai entropy and attractor dimension for three-dimensional homogeneous isotropic turbulence through the use of direct numerical simulation. To do so, we obtain Lyapunov spectra for a range of different Reynolds numbers by following the divergence of a large number of orthogonal fluid trajectories. We find that the attractor dimension grows with the Reynolds number as ${\mathrm{Re}}^{2.35}$ with this exponent being larger than predicted by either dimensional arguments or intermittency models. The distribution of Lyapunov exponents is found to be finite around $\lambda \approx 0$ contrary to a possible divergence suggested by Ruelle. The relevance of the Kolmogorov-Sinai entropy and Lyapunov spectra in comparing complex physical systems is discussed.

Molecular self-assembly is usually done at low supersaturation, leading to low rates of growth, in order to allow time for binding mistakes to anneal. However, such conditions can lead to prohibitively long assembly times where growth proceeds by the slow nucleation of successive layers. Here we use a lattice model of molecular self-assembly to show that growth in this regime can be sped up by impurities, which lower the free-energy cost of layer nucleation. Under certain conditions impurities behave almost as a catalyst in that they are present at high concentration at the surface of the assembling structure, but at low concentration in the bulk of the assembled structure. Extrapolation of our numerics using simple analytic arguments suggests that this mechanism can reduce growth times by orders of magnitude in parameter regimes applicable to molecular systems.

We study site percolation on lattices confined to a semi-infinite strip. For triangular and square lattices we find that the probability that a cluster touches the three sides of such a system at the percolation threshold has a continuous limit of 1/2 and argue that this limit is universal for planar systems. This value is also expected to hold for finite systems for any self-matching lattice. We attribute this result to the asymptotic symmetry of the separation lines between alternating spanning clusters of occupied and unoccupied sites formed on the original and matching lattice, respectively.

Cooperators increase the fitness of others at a cost to themselves. Thus cooperation should not be favored by natural selection in a well-mixed population. It challenges the evolutionists since cooperation is widespread. Information spreading has been revealed to play a key role in the emergence of cooperation. Individuals, however, are typically assumed to be passive in the information spreading. Here we assume that individuals self-recommend themselves to those that are about to have new neighbors. Individuals with higher tendencies of self-recommendation are likely to have more neighbors. In this way, individuals are active to spread the information. We analytically obtain a critical cost-to-benefit ratio, below which cooperation emerges. It reveals quantitatively how eloquent cooperators have to be compared with defectors to ensure that cooperation takes over the population. It also indicates that individuals need to be open enough to the self-recommendation to enhance cooperation level. In addition, the critical cost-to-benefit ratio represents the viscosity of the population, measuring how close cooperators are to each other. Our results highlight the role self-recommendation plays in cooperation.

Approaches for mapping time series to networks have become essential tools for dealing with the increasing challenges of characterizing data from complex systems. Among the different algorithms, the recently proposed ordinal networks stand out due to their simplicity and computational efficiency. However, applications of ordinal networks have been mainly focused on time series arising from nonlinear dynamical systems, while basic properties of ordinal networks related to simple stochastic processes remain poorly understood. Here, we investigate several properties of ordinal networks emerging from random time series, noisy periodic signals, fractional Brownian motion, and earthquake magnitude series. For ordinal networks of random series, we present an approach for building the exact form of the adjacency matrix, which in turn is useful for detecting nonrandom behavior in time series and the existence of missing transitions among ordinal patterns. We find that the average value of a local entropy, estimated from transition probabilities among neighboring nodes of ordinal networks, is more robust against noise addition than the standard permutation entropy. We show that ordinal networks can be used for estimating the Hurst exponent of time series with accuracy comparable with state-of-the-art methods. Finally, we argue that ordinal networks can detect sudden changes in Earth's seismic activity caused by large earthquakes.

We investigate the effects of long-range social interactions in flocking dynamics by studying the dynamics of a scalar model of collective motion embedded in a complex network representing a pattern of social interactions, as observed in several social species. In this scalar model we find a phenomenology analogous to that observed in the classic Vicsek model: In networks with low heterogeneity, a phase transition separates an ordered from a disordered phase. At high levels of heterogeneity, instead, the transition is suppressed, and the system is always ordered. This observation is backed up analytically by the solution of a modified scalar model within an heterogeneous mean-field approximation. Our work extends the understanding of the effects of social interactions in flocking dynamics and opens the path to the analytical study of more complex topologies of social ties.

To account for the possibility of an externally driven taxis in active systems, we develop a model of a guided active drift which relies on the presence of an external guiding field and a vectorial coupling between the mechanical degrees of freedom and a chemical reaction. To characterize the ability of guided active particles to carry cargo, we generalize the notion of Stokes efficiency extending it to the case of stall conditions. To show the generality of the proposed mechanism, we discuss guided electric circuits capable of turning fluctuations into a directed current without a source of voltage.

The impact of an initial random magnetic field on the temporal evolution of a two-dimensional incompressible turbulent shearless mixing layer is investigated using direct numerical simulation. Different intensities of the initial random magnetic field are imposed with uniform probability distribution on an identical flow field. The initial flow field condition is the turbulent shearless mixing layer with different kinetic energy ratio ($E_H/E_L=6.7$) and identical integral length scale. Simulations are carried out in a moderate magnetic Reynolds number, which causes a two-way interaction between the velocity and magnetic fields. In order to analyze the effect of the initial random magnetic field on the mixing characteristics, the intermittency inside the mixing layer and the mixing evolution parameters are investigated. It is found that with small initial magnetic field intensity, the intermittency in both large and small scales are larger than those values in hydrodynamic flow. However, increasing the intensity of the initial magnetic field reduces the intermittency in the mixing region to lower values compared to the hydrodynamic flow. The mixing layer growth rate and the mixing efficiency both show reduction by increasing the initial magnetic field intensity, which is attributed to the reduction of the averaged Reynolds number of both homogenous isotropic turbulent regions due to the suppressing effect of the Lorentz force on the velocity fields of these regions.

This paper considers the narrow escape problem of a Brownian particle within a two-dimensional domain with two escape windows and an internal circulation modeled by the flow within a Hill's vortex. To account for the spatially inhomogeneous flow within the domain, a Lagrangian study is undertaken using the complete equations of motion for a dense particle which is necessary to distinguish between the various regimes as the strength of the internal circulation is varied. For very low internal circulation the particle undergoes the conventional narrow escape problem, and agreement is good with the asymptotic expression. As the internal circulation is increased, regimes are identified with different scaling for the mean escape time. The potential application of this for drug delivery (were nanoparticles are encased in a microsphere) is discussed.

We introduce and study a family of cooperative exclusion processes whose microscopic dynamics is governed by selective kinetic constraints. They display, in sharp contrast to the simple symmetric exclusion process, density profiles that can be concave, convex, or both, depending on the density of boundary particle reservoirs. A mean-field analysis based on a diffusion equation with a density-dependent diffusion coefficient qualitatively reproduces this behavior, and suggests its occurrence in liquids with a diffusivity anomaly.

This work investigates a one-component one-dimensional Coulomb system in sticky wall confinement. Sticky wall is introduced as an alternative and intuitive depiction of charge regulation, the notion that a surface charge is not a fixed but a fluctuating quantity in dynamic equilibrium with its immediate environment. Emphasis is placed on intuitive derivation and expressions are obtained by observing that the partition function of a charge regulated system can be decomposed into a collection of independent equilibriums with different fixed surface charges. Adsorbed particles behave as ideal-gas particles in a one-dimensional box whose length corresponds to the parameter of stickiness. Among various scenarios considered are a single- and two-wall confinement as well as the case of sticky counterions capable of associating into pairs. Exact solutions provide a view of the role and behavior of surface charge fluctuations, which is an important step in the “beyond-mean-field” analysis. Consequently, the model serves as a simple paradigm of the mechanism that gives rise to the Kirkwood-Shumaker interactions detected in real systems.

We revisit the problem of the predominance of the “weakest” species in the context of Lotka-Volterra and May-Leonard formulations of a spatial stochastic rock-paper-scissors model in which one of the species has its predation probability reduced by $0<{\mathcal{P}}_w<1$. We show that, despite the different population dynamics and spatial patterns, these two formulations lead to qualitatively similar results for the late time values of the relative abundances of the three species (as a function of ${\mathcal{P}}_w$), as long as the simulation lattices are sufficiently large for coexistence to prevail—the “weakest” species generally having an advantage over the others (specially over its predator). However, for smaller simulation lattices, we find that the relatively large oscillations at the initial stages of simulations with random initial conditions may result in a significant dependence of the probability of species survival on the lattice size.

Investigated in this paper is a quasigeostrophic two-layer model for the wave packets in a marginally stable or unstable baroclinic shear flow. We find that the wave packets can be modulated by certain long waves, resulting in different behaviors from those in the existing literature. Via the bilinear method, we construct the modulated $N\mathrm{th}$-order ($N=1,2,...$) solitary waves, breathers, and rogue waves for the wave-packet equations. Based on the modulation effects of the long waves, the solitary waves are classified into three types, i.e., Type-I, Type-II, and Type-III solitary waves. Type-I solitary waves, without the modulations, are the bell shaped and propagate with constant velocities; Type-II solitary waves, with the weak modulations, are shape changing within a short time and subsequently return to the bell-shaped state; and Type-III solitary waves, with the strong modulations, show not only the variations of shapes but also the appearances, splits, combinations, and disappearances of certain bulges in the evolution. For the interaction between the two unmodulated solitary waves, two Type-I solitary waves can bring about the oscillations in the interaction zone when they possess different velocities, and bring into being the bound-state, oscillation-state, and bi-oscillation-state solitary waves when they possess the same velocity. For the two interactive modulated solitary waves, bound-state, oscillation-state, and bi-oscillation-state solitary waves with the short-time variations of shapes or appearances of bulges can occur. Due to the modulations of the long waves, breathers and rogue waves are distorted and stretched, mainly in two aspects: one is the evolution trajectories for the breathers; the other is the shape variations for each element of the breathers and rogue waves. Numbers of the peaks and valleys for the rogue waves are adjustable via the modulations. In addition, modulated breathers and rogue waves can degenerate into the M- or W-shaped or multipeak solitary waves under certain conditions.

Relaxation of internal stresses through a cascade of microscopic restructuring events is the hallmark of many materials, ranging from amorphous solids like glasses and gels to geological structures subjected to a persistent external load. By means of photon correlation imaging, a recently developed technique that blends the powers of scattering and imaging, we provide a spatially and temporally resolved survey of the restructuring and aging processes that spontaneously occur in physical gels originating from an arrested phase separation. We show that the temporal dynamics is characterized by an intermittent sequence of spatially localized “microquakes” that eventually lead to global rearrangements occurring at a rate that scales with the gel age. Notably, these dramatic upheavals of the gel structure are heralded by a progressive acceleration of the microscopic gel dynamics that originates from recognizable active spots and then spreads at a large but finite speed through the gel. Within the “slack” phase between two of these “macroquakes,” the fluctuations of the degree of temporal correlation obey a non-Gaussian statistics described by a generalized logistic distribution. The evidence we obtained bear consistent analogies with the stress relaxation processes taking place in earthquake sequences and with the intermittent restructuring of plastic crystals at the microscale.

We analyze reversibility of displacements and rotations of spherical grains in three-dimensional compression experiments. Using transparent acrylic beads with cylindrical holes and index matching techniques, we are not only capable of tracking displacements but also analyzing reversibility of rotations. We observe that for moderate compression amplitudes, up to one bead diameter, the translational displacements of the beads after each cycle become mostly reversible after an initial transient. By contrast, granular rotations are largely irreversible. We find a weak correlation between translational and rotational displacements, indicating that rotational reversibility depends on more subtle changes in contact distributions and contact forces between grains compared with displacement reversibility. Three-dimensional rotations in dense granular systems are particularly important, since frictional losses associated with rotations are the dominant mechanism for energy dissipation. As such our work provides a first step toward a thorough study of rotations and tangential forces to understand the granular dynamics in dense systems.

We analyze the packing properties of simulated three-dimensional polydisperse samples of spherical particles assembled by mechanical compaction with zero interparticle friction, leading to random close-packed configurations of the highest packing fraction. The particle size distributions are generated from the incomplete beta distribution with three parameters: A size span and two shape parameters that control the curvature of the distribution function. For each size distribution, the number of particles is determined by accounting for the statistical representativity of all particle size classes in terms of both the numbers and volumes of particles. Remarkably, the packing fraction increases, up to a small variability, with an effective size span, known as the coefficient of uniformity, that combines the three control parameters of the distribution. The local particle environments are characterized by the particle connectivities and anisotropies, which unveil the class of particles with four contact neighbors as the largest class with an increasing population as a function of size span, indicating the higher stability of particles trapped by four larger particles. As a result of increasing topological inhomogeneity of the packings, the force distributions get increasingly broader with increasing effective size span. Finally, we find that larger particles do not always carry stronger average stresses, in particular when the particle size distribution allows for a sufficiently large number of small particles.

We investigate the precession of electron spins during beam-driven plasma-wakefield acceleration based on density down-ramp injection by means of full three-dimensional (3D) particle-in-cell (PIC) simulations. A relativistic electron beam generated via, e.g., laser wakefield acceleration, serves as the driving source. It traverses the prepolarized gas target and accelerates polarized electrons via the excited wakefield. We derive the criteria for the driving beam parameters and the limitation on the injected beam flux to preserve a high degree of polarization for the accelerated electrons, which are confirmed by our 3D PIC simulations and single-particle modeling. The electron-beam driver is free of the prepulse issue associated with a laser driver, thus eliminating possible depolarization of the prepolarized gas due to ionization by the prepulse. These results provide guidance for future experiments towards generating a source of polarized electrons based on wakefield acceleration.

Cell migration in fibrous extracellular matrix (ECM) is crucial to many physiological and pathological processes such as tissue regeneration, immune response, and cancer progression. During migration, individual cells can generate active pulling forces via actomyosin contraction, which are transmitted to the ECM fibers through focal adhesion complexes, remodel the ECM, and eventually propagate to and can be sensed by other cells in the system. The microstructure and physical properties of the ECM can also significantly influence cell migration, e.g., via durotaxis and contact guidance. Here, we develop a computational model for two-dimensional cell migration regulated by cell-ECM micromechanical coupling. Our model explicitly takes into account a variety of cellular-level processes, including focal adhesion formation and disassembly, active traction force generation and cell locomotion due to actin filament contraction, transmission and propagation of tensile forces in the ECM, as well as the resulting ECM remodeling. We validate our model by accurately reproducing single-cell dynamics of MCF-10A breast cancer cells migrating on collagen gels and show that the durotaxis and contact guidance effects naturally arise as a consequence of the cell-ECM micromechanical interactions considered in the model. Moreover, our model predicts strongly correlated multicellular migration dynamics, which are resulted from the ECM-mediated mechanical coupling among the migrating cell and are subsequently verified in in vitro experiments using MCF-10A cells. Our computational model provides a robust tool to investigate emergent collective dynamics of multicellular systems in complex in vivo microenvironment and can be utilized to design in vitro microenvironments to guide collective behaviors and self-organization of cells.