The paper presents an algorithm to generate two-dimensional, saturated random sequential adsorption packings of identical, unoriented, anisotropic convex shapes. The method consists in tracking regions where the next shape can be added. The algorithm was tested on packings built of spherocylinders and ellipses of different width-to-height ratio. Obtained packing fractions at saturation agree with earlier predictions using an estimation of the saturated packing fraction based on the kinetics of packing growth, but they are much more accurate. Additionally, we discuss how to increase packing generation speed using parallel computations.

Driven diffusive systems may undergo phase transitions to sustain atypical values of the current. This leads in some cases to symmetry-broken space-time trajectories which enhance the probability of such fluctuations. Here, we shed light on both the macroscopic large deviation properties and the microscopic origin of such spontaneous symmetry breaking in the open weakly asymmetric exclusion process. By studying the joint fluctuations of the current and a collective order parameter, we uncover the full dynamical phase diagram for arbitrary boundary driving, which is reminiscent of a ${\mathbb{Z}}_2$ symmetry-breaking transition. The associated joint large deviation function becomes nonconvex below the critical point, where a Maxwell-like violation of the additivity principle is observed. At the microscopic level, the dynamical phase transition is linked to an emerging degeneracy of the ground state of the microscopic generator, from which the optimal trajectories in the symmetry-broken phase follow. In addition, we observe this symmetry-breaking phenomenon in extensive rare-event simulations, confirming our macroscopic and microscopic results.

The data generated by long-delayed dynamical systems can be organized in patterns by means of the so-called spatiotemporal representation, uncovering the role of multiple timescales as independent degrees of freedom. However, their identification as equivalent space and time variables does not lead to a correct dynamical rule. We introduce a framework for a proper description of the dynamics in the thermodynamic limit, providing a general avenue for the treatment of long-delayed systems in terms of partial differential equations. Such scheme is generic and does not rely on either the vicinity to bifurcations or on multiple-scale approaches. We discuss the validity of this method and consider the exemplary cases of long-delayed excitable, bistable, and Landau systems.

The driven diffusive system is a powerful tool to investigate properties of nonequilibrium state statistical physics, vehicle traffic, and biological transport systems. This paper presents a two-channel asymmetric exclusion process model, in which collective dynamics with interactions of particles between two lanes are considered. Computer simulation and mean-field analysis are carried out to calculate the flow rate under periodic boundary. On the whole, the results from the two-vertical-horizontal-cluster mean-field method are in good agreement with the simulation results. Two types of phases including double peaked and single peaked appear in the flow rate of the system. Based on investigating the coarsening process of the system, one can get a conjecture that the system is homogeneous when the critical density at which normalized residence distribution turns into nonmonotonous variability from monotonous decrease equals 0.5. These findings may be helpful to deeply understand the dynamic features of nonequilibrium state systems and traffic or transport systems.

We propose a macroscopic realization of planar Brownian motion by vertically vibrated disks. We perform a systematic statistical analysis of many random trajectories of individual disks. The distribution of increments is shown to be almost Gaussian, with slight deviations at large increments caused by interdisk collisions. The velocity autocorrelation function takes both positive and negative values at short lag times but rapidly vanishes. We compare the empirical and theoretical distributions of time-averaged mean-squared displacements and discuss distinctions between their mean and mode. These well-controlled experimental data can serve for validating various statistical tools developed for the analysis of single-particle trajectories in microbiology.

Spatially localized and temporally oscillating solutions, known as discrete breathers, have been experimentally and theoretically discovered in many physical systems. Here, we consider a lattice of coupled damped and driven Helmholtz-Duffing oscillators in which we found a spatial coexistence of oscillating solutions with different frequencies. Specifically, we demonstrate that stable period-doubled solutions coexist with solutions oscillating at the frequency of the driving force. Such solutions represent period-doubled breathers resulting from a stability overlap between subharmonic and harmonic solutions and exist up to a certain strength of the lattice coupling. Our findings suggest that this phenomenon can occur in any driven lattice where the nonlinearity admits bistability (or multi-stability) of subharmonic and harmonic solutions.

Chaotic scattering in open Hamiltonian systems is a topic of fundamental interest in physics, which has been mainly studied in the purely conservative case. However, the effect of weak perturbations in this kind of system has been an important focus of interest in the past decade. In a previous work, the authors studied the effects of a periodic forcing in the decay law of the survival probability, and they characterized the global properties of escape dynamics. In the present paper, we add two important issues in the effects of periodic forcing: the fractal dimension of the set of singularities in the scattering function and the unpredictability of the exit basins, which is estimated by using the concept of basin entropy. Both the fractal dimension and the basin entropy exhibit a resonant-like decrease as the forcing frequency increases. We provide a theoretical reasoning which could justify this decreasing in the fractality near the main resonant frequency that appears for $\omega \approx 1$. We attribute the decrease in the basin entropy to the reduction of the area occupied by the Kolmogorov-Arnold-Moser (KAM) islands and the basin boundaries when the frequency is close to the resonance. On the other hand, the decay rate of the exponential decay law shows a minimum value of the amplitude, $A_c$, which reflects the complete destruction of the KAM islands in the resonance. Finally, we have found the existence of Wada basins for a wide range of values of the frequency and the forcing amplitude. We expect that this work could be potentially useful in research fields related to chaotic Hamiltonian pumps and oscillations in chemical reactions and companion galaxies, among others.

With the increasing abundance of “digital footprints” left by human interactions in online environments, e.g., social media and app use, the ability to model complex human behavior has become increasingly possible. Many approaches have been proposed, however, most previous model frameworks are fairly restrictive. We introduce a new social modeling approach that enables the creation of models directly from data with minimal a priori restrictions on the model class. In particular, we infer the minimally complex, maximally predictive representation of an individual's behavior when viewed in isolation and as driven by a social input. We then apply this framework to a heterogeneous catalog of human behavior collected from 15 000 users on the microblogging platform Twitter. The models allow us to describe how a user processes their past behavior and their social inputs. Despite the diversity of observed user behavior, most models inferred fall into a small subclass of all possible finite-state processes. Thus, our work demonstrates that user behavior, while quite complex, belies simple underlying computational structures.

The functional patterns of the visual cortex observed in some mammals such as cats, primates, and humans has allowed us to understand basic principles of organization in the structure of the cortex. However, the observation of different kinds of functional arrangement in other animals such as mice, rats, rabbits, and squirrels, called salt and pepper patterns, raise questions about which of these principles can be transferred to the understanding of visual processing in general. In order to gain insight into these basic principles, in this work we propose a simple model for the formation of spatiotemporal patterns in the visual cortex. The model is based on coupled phase oscillators that interact through an evolving complex network that is embedded in a two-dimensional Euclidean space. In this way we are able to explore the relation between network structure and functional organization. We find that the model allows for the emergence of clustered synchronized states that are spatially segregated as some orientation maps, and also synchronized states that are spatially interspersed, resembling salt and pepper organizational maps.

Recently, the problem of classes of vulnerable vertices (represented by colors) in complex networks has been discussed, where all vertices with the same vulnerability are prone to fail together. Utilizing redundant paths each avoiding one vulnerability (color), a robust color-avoiding connectivity is possible. However, many infrastructure networks show the problem of vulnerable classes of edges instead of vertices. Here we formulate color-avoiding percolation for colored edges as well. Additionally, we allow for random failures of vertices or edges. The interplay of random failures and possible collective failures implies a rich phenomenology. An interesting form of critical behavior is found for networks with a power-law degree distribution independent of the number of colors, but still dependent on the existence of the colors and therefore different from standard percolation. Our percolation framework fills a gap between different multilayer network percolation scenarios.

Cell motion in response to external chemical cues (chemotaxis) is a fundamental step in many physiological and pathological phenomena. The ability of cells to move onto two-dimensional flat substrates requires the activation of numerous intracellular mechanical and chemical mechanisms to achieve cell polarization and dynamic assembly and reorganization of the actin network. In this work we aim to bridge the gap between the mathematical models focusing on the mechanics of cell motion and the one describing the final motion of the cell in response to the external chemical field. We thus develop a one-dimensional continuous model representing cell migration, taking into account the mechanical stress inside the cell, the intracellular signaling molecules triggered by external factors, such as an external chemical field, and the actin dynamics during polymerization and depolymerization. The proposed model is solved numerically to simulate cell behavior during biologically relevant conditions and to study different mechanisms of conversion of the external field onto the intracellular chemical messenger, here called the polymerizing factor. The model is able to reproduce the transitions from the nonmigrating to the migrating regime, possibly triggered by the external chemotactic gradient, which is amplified by the internal chemical dynamics. More complex migratory behaviors can be described, as well, by including intracellular regulatory pathways of the polymerizing factor. Thus, the proposed model, even though kept as simple as possible, provides an interesting insight onto possible mathematical laws defining cell migratory velocity inside external chemical field gradients.

We report our development of a simple and cost-effective method to amplify and probe the interactions of DNA with metal ions, which are important for various fundamental processes in living systems. This method is based on perturbing energy landscapes using mechanical energy stored in bent DNA molecules. In this proof-of-principle study, the mechanical-energy-based amplifiers were applied to examine the interactions between DNA and ${\mathrm{Mg}}^{2+}$ ions or ${\mathrm{Ag}}^{+}$ ions. We demonstrated that interactions between DNA and ${\mathrm{Mg}}^{2+}$ or ${\mathrm{Ag}}^{+}$ ions, which are not detectable using gel electrophoresis without amplification, can be easily measured using our molecular amplifiers. In addition, we showed that quantitative details about the DNA-metal interactions can be estimated using our method. Our method is simple, sensitive, and cost-effective. We expect that the developed method will be useful for various applications.

In a stochastic process, noise often modifies the picture offered by the mean-field dynamics. In particular, when there is an absorbing state, the noise erases a stable fixed point of the mean field equation from the stationary distribution and turns it into a transient peak. We make a quantitative analysis of this effect for a simple genetic regulatory network with positive feedback where the proteins become extinct in the presence of stochastic noise, contrary to the prediction of the deterministic rate equation that the protein number converges to a nonzero value. We show that the transient peak appears near the stable fixed point of the rate equation, and the extinction time diverges exponentially as the stochastic noise approaches zero. We also show how the baseline production from the inactive gene ameliorates the effect of the stochastic noise and interpret the opposite effects of the noise and the baseline production in terms of the position shift of the unstable fixed point. The order of magnitude estimates using biological parameters suggest that for a real gene regulatory network, the stochastic noise is sufficiently small so that not only is the extinction time much larger than biologically relevant timescales, but also the effect of the baseline production dominates over that of the stochastic noise, leading to protection from the catastrophic rare event of protein extinction.

The effect of quenched (frozen) orientational disorder on the collective motion of active particles is analyzed. We find that, as with annealed disorder (Langevin noise), active polar systems are far more robust against quenched disorder than their equilibrium counterparts. In particular, long-ranged order (i.e., the existence of a nonzero average velocity $\langle \mathbf{v}\rangle$) persists in the presence of quenched disorder even in spatial dimensions $d=3$, while it is destroyed even by arbitrarily weak disorder in $d\le 4$ in equilibrium systems. Furthermore, in $d=2$, quasi-long-ranged order (i.e., spatial velocity correlations that decay as a power law with distance) occurs when quenched disorder is present, in contrast to the short-ranged order that is all that can survive in equilibrium. These predictions are borne out by simulations in both two and three dimensions.

The physical properties of multicomponent anisotropic colloidal dispersions are still far from being fully understood. This is mainly due to the fact that dealing with nonspherical particles and highly directional interactions is, from both experimental and theoretical points of view, a complicated task. In fact, experiments are scarce, and we still lack of model colloidal dispersions that allow us to simultaneously simplify and capture the complexity of such systems. In this contribution, we report on an experimental study of the hydrodynamic correlations and the long-time dynamics in anisotropic colloidal mixtures. The latter are composed of monomers and dimers highly confined between two parallel walls. The diffusive behavior is studied from low to intermediate particle concentrations. As concentration increases, crowding plays a significant role on the translational and rotational diffusion coefficients of monomers and dimers at short and long times. Nevertheless, in the short-time regime, the ratio between the dimer diffusion coefficients, parallel and perpendicular to the main axis of the dimer, becomes independent on the composition and total packing fraction; it depends only on the two translational hydrodynamic friction coefficients of the dimer. At long times, the dimer mean-square displacements, both parallel and perpendicular, reach the same value; i.e., the long-time diffusion coefficients seem not to be sensitive to the particle anisotropy and the crowded environment at which the dimer diffuses. Interestingly, both dynamical scenarios are analogous to the reported case for an isolated ellipsoid of similar dimensions, even though the dimer experiences collisions and hydrodynamic interactions with monomers and other dimers. Our findings also point out that the two-dimensional hydrodynamic correlations, monomer-monomer and monomer-dimer, differ mainly at short distances due to the difference in the shape of both types of species. However, contrary to the case of particles in a three-dimensional unbounded fluid, such hydrodynamic correlations decay faster, exhibiting a dipole-like long-ranged behavior with a $r^{-2}$ dependence, similar to the results previously reported for a monodisperse quasi-two-dimensional colloidal dispersion. Our measurements are corroborated by means of molecular dynamics computer simulations that explicitly include the information of the host solvent.

Why do particles, suspended in a fluid and traveling in a channel, deposit onto walls? The question has far-reaching implications in different domains (filtering, syringeability, fouling, etc.). Close to a channel wall, particles are subject to a variety of effects, which control their trajectories: hydrodynamic forces, diffusion, van der Waals adhesion forces, and electrostatic forces. The existing theories and phenomenologies, due to their inherent limitations, and the numerical and experimental studies, due to their scarcity, did not allow thus far to establish a general description of the deposition process. By coupling microfluidic experiments, theory, and numerics, we succeed in establishing a general description of the phenomenon. We discover that the problem is particularly rich. We show the existence of three regimes: van der Waals, Debye, and diffusive, each including various subregimes. Within each main regime, particle deposition is dominated respectively by (attractive) van der Waals forces, (repulsive) electrostatic forces, or diffusion. We establish the scaling laws governing the collector efficiency, $S$, in each regime. The ensemble of the regimes and their transitions can be displayed in diagrams. We focus on the case $\frac{A}{kT}\sim 1$ (the case of most practical interest), in which the diagram involves two dimensionless numbers, $P$ (incorporating the Debye layer characteristics) and ${\xi }_L$ (a function of the flow speed, diffusion constant, and the geometry). In this case, the three main regimes organize around a cantilever beam, in which the vertical support is defined by the condition $P=4e^{-2}$, and the horizontal beam is located at ${\xi }_L=\frac{A}{kT}$, where $A, k$, and $T$ are the Hamaker constant, the Boltzmann constant, and the absolute temperature, respectively. The present work allows understanding of empirical observations thus far left unexplained and provides a paradigm enabling engineering of devices in a way that reduces or enhances particle deposition.

We propose a simple, practical, and versatile acoustic-driven swimmer, composed of two spherical bodies that may radiate the sound field, monochromatically, at monopole state (breathing mode of vibration) and are linked by a rigid rod. Considering the nonlinear acoustic effects, the net acoustic radiation force exerted on the device is analytically derived and it is shown that the resultant radiation force exerted on the swimmer may be nonzero. Two different configurations are considered: In the first, both spheres radiate, and in the second, one of the spheres is off. In both cases, the full manipulability conditions of swimmers are obtained and the effects of size factors, frequency of radiation, etc., are discussed. Assuming low Reynolds number swimming condition, the frequency-dependent swimming velocity is obtained via the so-called reflection method and the optimal radiating states are discussed. Finally, the challenge of random walk due to host medium fluctuations is discussed and it is shown that the Brownian noise is negligible. Our methodology will open a path toward self-propulsive controllable devices, which may play the role of carriers, machines, or mechanisms at small scales.

This article reports the dominant governing role played by the direction of electric and magnetic fields on the internal advection pattern and strength within salt solution pendent droplets. The literature shows that solutal advection drives circulation cells within salt based droplets, even in the absence of any external field. An experimental study is performed, where electric and magnetic fields are applied across pendent droplets of salt solutions and their internal flow dynamics is observed. Flow visualization and velocimetry (two-dimensional) reveals that the direction of the applied field governs the enhancement or reduction in circulation velocity and the directionality of circulation inside the droplet. Further, it is noted that while magnetic fields augment the circulation velocity (with respect to the solutal advection already present in salt solution droplets at zero field) the electric field leads to deterioration of the same. The concepts of electro- and magnetohydrodynamics of droplets are appealed to and a Stokesian stream function based mathematical model to deduce the field mediated velocities has been proposed. The roles of the governing Hartmann, Stuart, Reynolds, and Masuda numbers are revealed by the proposed model. The theoretical predictions are observed to be in agreement with the experimentally determined averaged spatiotemporal circulation velocities. The present findings may have strong implications in microscale and interfacial electro- and/or magnetohydrodynamics.

The energy distributions of tantalum ions produced in a nanosecond laser-heated plasma at $4\times {10}^{15}\mathrm{W}/{\mathrm{cm}}^2$ are experimentally and theoretically investigated. They are measured far from the target with an electrostatic spectrometer and charge collectors. Shadowgraphy and interferometry are used to characterize the plasma dynamics in the first nanoseconds of the plasma expansion for electron densities ranging from ${10}^{18}$ to ${10}^{20}{\mathrm{cm}}^{-3}$. The experimental data clearly show two components in the energy distributions which depend on the ion charge states. These components are discussed in light of fluid and kinetic descriptions of the expanding plasma. In particular, quantitative comparisons with calculations performed with three-dimensional hydrodynamic (Troll) and 1D3V particle-in cell-codes demonstrate that a double layer created at the plasma-vacuum interface plays a crucial role in the acceleration of the highest-charge-state ions at high energy.

We combine machine learning (ML) with Monte Carlo (MC) simulations to study the crystal nucleation process. Specifically, we use ML to infer the canonical partition function of the system over the range of densities and temperatures spanned during crystallization. We achieve this on the example of the Lennard-Jones system by training an artificial neural network using, as a reference dataset, equations of state for the Helmholtz free energy for the liquid and solid phases. The accuracy of the ML predictions is tested over a wide range of thermodynamic conditions, and results are shown to provide an accurate estimate for the canonical partition function, when compared to the results from flat-histogram simulations. Then, the ML predictions are used to calculate the entropy of the system during MC simulations in the isothermal-isobaric ensemble. This approach is shown to yield results in very good agreement with the experimental data for both the liquid and solid phases of argon. Finally, taking entropy as a reaction coordinate and using the umbrella sampling technique, we are able to determine the Gibbs free energy profile for the crystal nucleation process. In particular, we obtain a free energy barrier in very good agreement with the results from previous simulation studies. The approach developed here can be readily extended to molecular systems and complex fluids, and is especially promising for the study of entropy-driven processes.