We study the collective dynamics of elongated swimmers in a very thin fluid layer by devising long filamentous nontumbling bacteria. The strong confinement induces weak nematic alignment upon collision, which, for large enough density of cells, gives rise to global nematic order. This homogeneous but fluctuating phase, observed on the largest experimentally accessible scale of millimeters, exhibits the properties predicted by standard models for flocking, such as the Vicsek-style model of polar particles with nematic alignment: true long-range nematic order and nontrivial giant number fluctuations.

We investigate the time-averaged square displacement (TASD) of continuous-time random walks with respect to the number of steps $N$ which the random walker performed during the data acquisition time $T$. We prove that in each realization the TASD grows asymptotically linear in the lag time $\tau$ and in $N$, provided the steps cannot accumulate in small intervals. Consequently, the fluctuations of the latter are dominated by the fluctuations of $N$, and fluctuations of the walker's thermal history are irrelevant. Furthermore, we show that the relative scatter decays as $1/\sqrt{N}$, which suppresses all nonlinear features in a plot of the TASD against the lag time. Parts of our arguments also hold for continuous-time random walks with correlated steps or with correlated waiting times.

We have studied the phase transition of the contact process near a multiple junction of $M$ semi-infinite chains by Monte Carlo simulations. As opposed to the continuous transitions of the translationally invariant $\left(M=2\right)$ and semi-infinite $\left(M=1\right)$ system, the local order parameter is found to be discontinuous for $M>2$. Furthermore, the temporal correlation length diverges algebraically as the critical point is approached, but with different exponents on the two sides of the transition. In the active phase, the estimate is compatible with the bulk value, while in the inactive phase it exceeds the bulk value and increases with $M$. The unusual local critical behavior is explained by a scaling theory with an irrelevant variable, which becomes dangerous in the inactive phase. Quenched spatial disorder is found to make the transition continuous in agreement with earlier renormalization group results.

Interactions in nature can be described by their coupling strength, direction of coupling, and coupling function. The coupling strength and directionality are relatively well understood and studied, at least for two interacting systems; however, there can be a complexity in the interactions uniquely dependent on the coupling functions. Such a special case is studied here: synchronization transition occurs only due to the time variability of the coupling functions, while the net coupling strength is constant throughout the observation time. To motivate the investigation, an example is used to present an analysis of cross-frequency coupling functions between delta and alpha brain waves extracted from the electroencephalography recording of a healthy human subject in a free-running resting state. The results indicate that time-varying coupling functions are a reality for biological interactions. A model of phase oscillators is used to demonstrate and detect the synchronization transition caused by the varying coupling functions during an invariant coupling strength. The ability to detect this phenomenon is discussed with the method of dynamical Bayesian inference, which was able to infer the time-varying coupling functions. The form of the coupling function acts as an additional dimension for the interactions, and it should be taken into account when detecting biological or other interactions from data.

We study the phase behavior of a system of charged colloidal particles that are electrostatically bound to an almost flat interface between two fluids. We show that, despite the fact that our experimental system consists of only ${10}^3–{10}^4$ particles, the phase behavior is consistent with the theory of melting due to Kosterlitz, Thouless, Halperin, Nelson, and Young. Using spatial and temporal correlations of the bond-orientational order parameter, we classify our samples into solid, isotropic fluid, and hexatic phases. We demonstrate that the topological defect structure we observe in each phase corresponds to the predictions of Kosterlitz-Thouless-Halperin-Nelson-Young theory. By measuring the dynamic Lindemann parameter ${\gamma }_L\left(\tau \right)$ and the non-Gaussian parameter ${\alpha }_2\left(\tau \right)$ of the displacements of the particles relative to their neighbors, we show that each of the phases displays distinctive dynamical behavior.

The Nelson-Peliti formulation of the elasticity theory of isolated fluid membranes with orientational order emphasizes the interplay between geometry, topology, and thermal fluctuations. Fluid layers of lamellar liquid crystals such as smectic-$C$, hexatic smectics, and smectic-$C^{*}$ are endowed with in-plane orientational order. We extend the Nelson-Peliti formulation so as to bring these smectics within its ambit. Using the elasticity theory of smectics-$C^{*}$, we show that positive and negative dispirations (topological defects in Smectic-$C^{*}$ liquid crystals) with strengths of equal magnitude have disparate energies—a result that is amenable to experimental tests.

A family of what can be so-called Maxwell times which arises in the context of higher-order generalized hydrodynamics (HOGH; also called mesoscopic hydrothermodynamics) is evidenced. This is done in the framework of a HOGH built within a statistical formalism in terms of a nonequilibrium statistical ensemble formalism. It consists in a description in terms of the densities of particles and energy and their fluxes of all orders, with the motion described by a set of coupled nonlinear integro-differential equations involving them. These Maxwell times have a fundamental role in determining the type of hydrodynamic motion that the system would display in the given conditions and constraints. They determine a Maxwell viscous force not present in the usual hydrodynamic equations, for example, in Navier-Stokes equation.

We describe a general method to model multicomponent ordered crystals using the phase-field-crystal (PFC) formalism. As a test case, a generic B2 compound is investigated. We are able to produce a line of either first-order or second-order order-disorder phase transitions, features that have not been incorporated in existing PFC approaches. Further, it is found that the only elastic constant for B2 that depends on ordering is $C_{11}$. This B2 model is then used to study antiphase boundaries (APBs). The APBs are shown to reproduce classical mean-field results. Dynamical simulations of ordering across small-angle grain boundaries predict that dislocation cores pin the evolution of APBs.

We consider a modified Nagel-Schreckenberg (NS) model in which drivers do not decelerate if their speed is smaller than the headway (number of empty sites to the car ahead). (In the original NS model, such a reduction in speed occurs with probability $p$, independent of the headway, as long as the current speed is greater than zero.) In the modified model the free-flow state (with all vehicles traveling at the maximum speed, $v_{max}$) is absorbing for densities $\rho$ smaller than a critical value ${\rho }_c=1/(v_{max}+2)$. The phase diagram in the $\rho -p$ plane is reentrant: for densities in the range ${\rho }_{c,<}<\rho <{\rho }_c$, both small and large values of $p$ favor free flow, while for intermediate values, a nonzero fraction of vehicles have speeds $<v_{max}$. In addition to representing a more realistic description of driving behavior, this change leads to a better understanding of the phase transition in the original model. Our results suggest an unexpected connection between traffic models and stochastic sandpiles.

Gradient-driven diffusion in crowded, multicomponent mixtures is a topic of high interest because of its role in biological processes such as transport in cell membranes. In partially phase-separated solutions, gradient-driven diffusion affects microstructure, which in turn affects diffusivity; a key question is how this complex coupling controls both transport and pattern formation. To examine these mechanisms, we study a two-dimensional multicomponent lattice gas model, where “tracer” molecules diffuse between a source and a sink separated by a solution of sticky “crowder” molecules that cluster to form dynamically evolving obstacles. In the high-temperature limit, crowders and tracers are miscible, and transport may be predicted analytically. At intermediate temperatures, crowders phase separate into clusters that drift toward the tracer sink. As a result, steady-state tracer diffusivity depends nonmonotonically on both temperature and crowder density, and we observe a variety of complex microstructures. In the low-temperature limit, crowders rapidly aggregate to form obstacles that are kinetically arrested; if crowder density is near the percolation threshold, resulting tracer diffusivity shows scaling behavior with the same scaling exponent as the random resistor network model. Though highly idealized, this simple model reveals fundamental mechanisms governing coupled gradient-driven diffusion, phase separation, and microstructural evolution in crowded mixtures.

We investigate the quantum synchronization phenomenon of the complex network constituted by coupled optomechanical systems and prove that the unknown identical quantum states can be shared or distributed in the quantum network even though the topology is varying. Considering a channel constructed by quantum correlation, we show that quantum synchronization can sustain and maintain high levels in Markovian dissipation for a long time. We also analyze the state-sharing process between two typical complex networks, and the results predict that linked nodes can be directly synchronized, but the whole network will be synchronized only if some specific synchronization conditions are satisfied. Furthermore, we give the synchronization conditions analytically through analyzing network dynamics. This proposal paves the way for studying multi-interaction synchronization and achieving effective quantum information processing in a complex network.

We explore the nonequilibrium dissipative dynamics of a system of identical charged particles trapped on a closed helix. The particles are subject to an external force accelerating them along the underlying structure. The effective interactions between the charges induce a coupling of the center of mass to the relative motion which in turn gives rise to a pinned-to-sliding transition with increasing magnitude of the external force. In the sliding regime we observe an Ohmic behavior signified by a constant mobility. Within the same regime a structural transition of the helical particle chain takes place with increasing the helix radius leading to a global change of the crystalline arrangement. The resulting crystal is characterized by the existence of multiple defects whose number increases with the helix radius.

We consider the evolution of the packing of disks (representing the position of buds) that are introduced at the top of a surface which has the form of a growing stem. They migrate downwards, while conforming to three principles, applied locally: dense packing, homogeneity, and continuity. We show that spiral structures characterized by the widely observed Fibonacci sequence (1, 1, 2, 3, 5, 8, 13, ...), as well as related structures, occur naturally under such rules. Typical results are presented in an animation.

We present a study of the spreading of liquid droplets on a solid substrate at very small scales. We focus on the regime where effective wetting energy (binding potential) and surface tension effects significantly influence steady and spreading droplets. In particular, we focus on strong packing and layering effects in the liquid near the substrate due to underlying density oscillations in the fluid caused by attractive substrate-liquid interactions. We show that such phenomena can be described by a thin-film (or long-wave or lubrication) model including an oscillatory Derjaguin (or disjoining or conjoining) pressure and explore the effects it has on steady droplet shapes and the spreading dynamics of droplets on both an adsorption (or precursor) layer and completely dry substrates. At the molecular scale, commonly used two-term binding potentials with a single preferred minimum controlling the adsorption layer height are inadequate to capture the rich behavior caused by the near-wall layered molecular packing. The adsorption layer is often submonolayer in thickness, i.e., the dynamics along the layer consists of single-particle hopping, leading to a diffusive dynamics, rather than the collective hydrodynamic motion implicit in standard thin-film models. We therefore modify the model in such a way that for thicker films the standard hydrodynamic theory is realized, but for very thin layers a diffusion equation is recovered.

Electromagnetic instability is investigated in homogeneous plasmas heated by a laser wave in the range $\alpha =v_0^2/v_t^2\le 2$, where $v_0$ is the electron quiver velocity and $v_t$ is the thermal velocity. The anisotropic electron distribution function that drives unstable quasistatic electromagnetic modes is calculated numerically with the Vlasov-Landau equation in the high ion charge number approximation. A dispersion relation of electromagnetic waves which accounts for further nonlinear terms on $v_0^2$ from previous results is derived. In typical simulation with ion charge number $Z=13$, a temperature $T=5\mathrm{keV}$, a density $n=9.8\times {10}^{20}\mathrm{c}{\mathrm{m}}^{-3}$, and a laser wavelength ${\lambda }_{\mathrm{laser}}=1.06\mu \mathrm{m}$, growth rates larger than ${10}^{12}{\mathrm{s}}^{-1}$ in the quasicollisionless wave-number range were found for $\alpha \ge 1$. In the same physical conditions and in the mildly collisional range a growth rate about ${10}^{11}{\mathrm{s}}^{-1}$ was also obtained. The extent of the growth wave-number region increases significantly with increasing $\alpha$.

We have found that the minimum energy configuration of $N=395$ charges confined in a disk and interacting via the Coulomb potential, reported by Cerkaski et al. [Phys. Rev. E 91, 032312 (2015)], is not a global minimum of the total electrostatic energy. We have identified a large number of configurations with lower energy, where defects are present close to the center of the disk; thus, the formation of a hexagonal core and valence circular rings for the centered configurations, predicted by the model of the above-mentioned reference, is not supported by numerical evidence, and the configurations obtained with this model cannot be used as a guide for the numerical calculations, as claimed by the authors.

We demonstrate that our model [Phys. Rev. E 91, 032312 (2015)] serves as a useful tool to trace the evolution of equilibrium configurations of one-component charged particles confined in a disk. Our approach reduces significantly the computational effort in minimizing the energy of equilibrium configurations, and it demonstrates a remarkable agreement with the values provided by molecular-dynamics calculations. We show that the Comment misrepresents our paper and fails to provide plausible arguments against the formation hexagonal structure for $n\ge 200$ in molecular-dynamics calculations.

By studying numerically the phase-ordering kinetics of a two-dimensional ferromagnetic Ising model with quenched disorder (either random bonds or random fields) we show that a critical percolation structure forms at an early stage. This structure is then rendered more and more compact by the ensuing coarsening process. Our results are compared to the nondisordered case, where a similar phenomenon is observed, and they are interpreted within a dynamical scaling framework.

According to the van der Waals picture, attractive and repulsive forces play distinct roles in the structure of simple fluids. Here, we examine their roles in dynamics; specifically, in the degree of deterministic chaos using the Kolmogorov-Sinai (KS) entropy rate and the spectra of Lyapunov exponents. With computer simulations of three-dimensional Lennard-Jones and Weeks-Chandler-Andersen fluids, we find repulsive forces dictate these dynamical properties, with attractive forces reducing the KS entropy at a given thermodynamic state. Regardless of interparticle forces, the maximal Lyapunov exponent is intensive for systems ranging from 200 to 2000 particles. Our finite-size scaling analysis also shows that the KS entropy is both extensive (a linear function of system-size) and additive. Both temperature and density control the “dynamical chemical potential,” the rate of linear growth of the KS entropy with system size. At fixed system-size, both the KS entropy and the largest exponent exhibit a maximum as a function of density. We attribute the maxima to the competition between two effects: as particles are forced to be in closer proximity, there is an enhancement from the sharp curvature of the repulsive potential and a suppression from the diminishing free volume and particle mobility. The extensivity and additivity of the KS entropy and the intensivity of the largest Lyapunov exponent, however, hold over a range of temperatures and densities across the liquid and liquid-vapor coexistence regimes.

In this paper we point out that the generalized statistics of Tsallis-Havrda-Charvát can be conveniently used as a conceptual framework for statistical treatment of random chains. In particular, we use the path-integral approach to show that the ensuing partition function can be identified with the partition function of a fluctuating oriented random loop of arbitrary length and shape in a background scalar potential. To put some meat on the bare bones, we illustrate this with two statistical systems: Schultz-Zimm polymer and relativistic particle. Further salient issues such as the projective special linear group $\mathrm{PSL}(2,\mathbb{R})$ transformation properties of Tsallis' inverse-temperature parameter and a grand-canonical ensemble of fluctuating random loops related to the Tsallis-Havrda-Charvát statistics are also briefly discussed.