We conduct a numerical study on the dynamic behavior of a buoyancy-induced turbulent fire from the viewpoints of symbolic dynamics, complex networks, and statistical complexity. Here, we consider two classes of entropies: the permutation entropy and network entropy in $\epsilon$-recurrence networks, both of which evaluate the degree of randomness in the underlying dynamics. These entropies enable us to capture the significant changes in the dynamic behavior of flow velocity fluctuations. The possible presence of two important dynamics, low-dimensional deterministic chaos in the near field dominated by the motion of large-scale vortices and high-dimensional chaos in the far field forming a well-developed turbulent plume, is clearly identified by the multiscale complexity-entropy causality plane.

Small-angle orientation fluctuations in ordered stripe-forming systems free of topological defects can exhibit aging and anisotropic growth of two length scales. In infinitely extended systems, the stripe orientation field develops a dominant modulation length ${\lambda }_{\parallel }^{*}\left(t\right)$ in the direction parallel to the stripes, which increases with time $t$ as ${\lambda }_{\parallel }^{*}\left(t\right)\sim t^{1/4}$. Simultaneously, the orientation correlation length ${\xi }_{\perp }\left(t\right)$ in the direction perpendicular to the stripes increases as ${\xi }_{\perp }\left(t\right)\sim t^{1/2}$ [Riesch et al., Interface Focus 7, 20160146 (2017)]. Here we show that finite systems of size $L_{\perp }\times L_{\parallel }$ with periodic boundary conditions reach equilibrium when the dominant modulation length ${\lambda }_{\parallel }^{*}\left(t\right)$ reaches the system size $L_{\parallel }$ in the stripe direction. The equilibration time ${\tau }_{\mathrm{eq}}^{\parallel }$ is solely determined by $L_{\parallel }$, with ${\tau }_{\mathrm{eq}}^{\parallel }\sim L_{\parallel }^4$. In systems with $L_{\perp }<L_{\parallel }^2/2\pi {\lambda }_{\mathrm{p}}$, where ${\lambda }_{\mathrm{p}}$ is the undulation penetration length, the initial aging and coarsening dynamics changes at the crossover time ${\tau }_{\mathrm{C}}^{\perp }\sim L_{\perp }^2$ to an aging and coarsening dynamics described by the one-dimensional Mullins-Herring equation, before reaching equilibrium at ${\tau }_{\parallel }^{\mathrm{eq}}$. Our work reveals the two pathways to equilibrium in stripe phases with periodic boundary conditions, the finite-size scaling behavior of equilibrium orientation fluctuations, and the characteristic exponents associated with the influence of a finite system size.

The adaptive voter model has been widely studied as a conceptual model for opinion formation processes on time-evolving social networks. Past studies on the effect of zealots, i.e., nodes aiming to spread their fixed opinion throughout the system, only considered the voter model on a static network. Here we extend the study of zealotry to the case of an adaptive network topology co-evolving with the state of the nodes and investigate opinion spreading induced by zealots depending on their initial density and connectedness. Numerical simulations reveal that below the fragmentation threshold a low density of zealots is sufficient to spread their opinion to the whole network. Beyond the transition point, zealots must exhibit an increased degree as compared to ordinary nodes for an efficient spreading of their opinion. We verify the numerical findings using a mean-field approximation of the model yielding a low-dimensional set of coupled ordinary differential equations. Our results imply that the spreading of the zealots' opinion in the adaptive voter model is strongly dependent on the link rewiring probability and the average degree of normal nodes in comparison with that of the zealots. In order to avoid a complete dominance of the zealots' opinion, there are two possible strategies for the remaining nodes: adjusting the probability of rewiring and/or the number of connections with other nodes, respectively.

The positions along DNA molecules of nucleosomes, the most abundant DNA-protein complexes in cells, are influenced by the sequence-dependent DNA mechanics and geometry. This leads to the “nucleosome positioning code”, a preference of nucleosomes for certain sequence motives. Here we introduce a simplified model of the nucleosome where a coarse-grained DNA molecule is frozen into an idealized superhelical shape. We calculate the exact sequence preferences of our nucleosome model and find it to reproduce qualitatively all the main features known to influence nucleosome positions. Moreover, using well-controlled approximations to this model allows us to come to a detailed understanding of the physics behind the sequence preferences of nucleosomes.

We perform a series of Monte Carlo simulations on an interface between a liquid crystal (LC) material in isotropic phase in its bulk and a surfactant membrane. These two objects are simulated using coarse-grained molecular models. We estimate physical properties of the membrane such as the interfacial tension and the bending rigidity, focusing on the anchoring effects of the membrane on the LC. According to our simulation results, when the strength of the homeotropic anchoring denoted by the anchoring parameter $\xi$ is increased, the interfacial tension decreases and the bending rigidity first increases in $\xi <{\xi }_{\mathrm{m}}$, and it then decreases in ${\xi }_{\mathrm{m}}<\xi$. We explain these results by constructing a continuum field model based on the two order parameters: directional order of LC and the membrane shape. These order parameters are mutually interacting through the anchoring effect, the fluctuation coupling between the LC and the membrane, and the effect of the nematic layer.

An optical vortex is a light wave with a twisting wavefront around its propagation axis and null intensity in the beam center. Its unique spatial structure of field lends itself to a broad range of applications, including optical communication, quantum information, superresolution microscopy, and multidimensional manipulation of particles. However, accessible intensity of optical vortices have been limited to material ionization threshold. This limitation might be removed by using the plasma medium. Here we propose the design of suitably magnetized plasmas which, functioning as a $q$-plate, leads to a direct conversion from a high-intensity Gaussian beam into a twisted beam. A circularly polarized laser beam in the plasma accumulates an azimuthal-angle-dependent phase shift and hence forms a twisting wavefront. Our three-dimensional particle-in-cell simulations demonstrate extremely high-power conversion efficiency. The plasma $q$-plate can work in a large range of frequencies spanning from terahertz to the optical domain.

Transport properties of two-dimensional (2D) strongly coupled dusty plasmas have been investigated in detail, but never for viscosity with a strong perpendicular magnetic field; here, we examine this scenario using Langevin dynamics simulations of 2D liquids with a binary Yukawa interparticle interaction. The shear viscosity $\eta$ of 2D liquid dusty plasma is estimated from the simulation data using the Green-Kubo relation, which is the integration of the shear stress autocorrelation function. It is found that, when a perpendicular magnetic field is applied, the shear viscosity of 2D liquid dusty plasma is modified substantially. When the magnetic field is increased, its viscosity increases at low temperatures, while at high temperatures its viscosity diminishes. It is determined that these different variational trends of $\eta$ arise from the different behaviors of the kinetic and potential parts of the shear stress under external magnetic fields.

We study the nonlinear wave modulation of Langmuir waves (LWs) in a fully degenerate plasma. Using the Wigner–Moyal equation coupled to the Poisson equation and the multiple scale expansion technique, a modified nonlocal nonlinear Schrödinger (NLS) equation is derived which governs the evolution of LW envelopes in degenerate plasmas. The nonlocal nonlinearity in the NLS equation appears due to the group velocity and multiplasmon resonances, i.e., resonances induced by the simultaneous particle absorption of multiple wave quanta. We focus on the regime where the resonant velocity of electrons is larger than the Fermi velocity and thereby the linear Landau damping is forbidden. As a result, the nonlinear wave-particle resonances due to the group velocity and multiplasmon processes are the dominant mechanisms for wave–particle interaction. It is found that in contrast to classical or semiclassical plasmas, the group velocity resonance does not necessarily give rise the wave damping in the strong quantum regime where $\hslash k\sim m{v}_F$ with $\hslash$ denoting the reduced Planck's constant, $m$ the electron mass, and $v_F$ the Fermi velocity; however, the three-plasmon process plays a dominant role in the nonlinear Landau damping of wave envelopes. In this regime, the decay rate of the wave amplitude is also found to be higher compared to that in the modest quantum regime where the multiplasmon effects are forbidden.

Laboratory plasmas inherently exhibit temperature and density gradients leading to complex investigations. We show that plasmas generated by laser ablation can constitute a robust exception to this. Supported by emission features not observed with other sources, we achieve plasmas of various compositions which are both uniform and in local thermodynamic equilibrium. These properties characterize an ideal radiation source opening multiple perspectives in plasma spectroscopy. The finding also constitutes a breakthrough in the analytical field as fast analyses of complex materials become possible.

We present the stochastic thermodynamic analysis of a time-periodic single-particle pump, including explicit results for flux, thermodynamic force, entropy production, work, heat, and efficiency. These results are valid far from equilibrium. The deviations from the linear (Onsager) regime are discussed.

Uphill currents are observed when mass diffuses in the direction of the density gradient. We study this phenomenon in stationary conditions in the framework of locally perturbed one-dimensional zero range processes (ZRPs). We show that the onset of currents flowing from the reservoir with smaller density to the one with larger density can be caused by a local asymmetry in the hopping rates on a single site at the center of the lattice. For fixed injection rates at the boundaries, we prove that a suitable tuning of the asymmetry in the bulk may induce uphill diffusion at arbitrarily large, finite volumes. We also deduce heuristically the hydrodynamic behavior of the model and connect the local asymmetry characterizing the ZRP dynamics to a matching condition relevant for the macroscopic problem.

Directionality indices can be used as an indicator of the asymmetry in coupling between systems and have found particular application in relation to neurological systems. The directionality index between two systems is a function of measures of information transfer in both directions. Here we illustrate that before inferring the directionality of coupling it is first necessary to consider the use of appropriate tests of significance. We propose a surrogate corrected directionality index which incorporates such testing. We also highlight the differences between testing the significance of the directionality index itself versus testing the individual measures of information transfer in each direction. To validate the approach we compared two different methods of estimating coupling, both of which have previously been used to estimate directionality indices. These were the modeling-based evolution map approach and a conditional mutual information (CMI) method for calculating dynamic information rates. For the CMI-based approach we also compared two different methods for estimating the CMI, an equiquantization-based estimator and a $k$-nearest neighbors estimator.

In most realistic models for quantum chaotic systems, the Hamiltonian matrices in unperturbed bases have a sparse structure. We study correlations in eigenfunctions of such systems and derive explicit expressions for some of the correlation functions with respect to energy. The analytical results are tested in several models by numerical simulations. Some applications are discussed for a relation between transition probabilities and for expectation values of some local observables.

We propose an approximation framework that unifies and generalizes a number of existing mean-field approximation methods for the susceptible-infected-susceptible (SIS) epidemic model on complex networks. We derive the framework, which we call the unified mean-field framework (UMFF), as a set of approximations of the exact Markovian SIS equations. Our main novelty is that we describe the mean-field approximations from the perspective of the isoperimetric problem, which results in bounds on the UMFF approximation error. These new bounds provide insight in the accuracy of existing mean-field methods, such as the N-intertwined mean-field approximation and heterogeneous mean-field method, which are contained by UMFF. Additionally, the isoperimetric inequality relates the UMFF approximation accuracy to the regularity notions of Szemerédi's regularity lemma.

The ability of a simple coarse-grained finite-extensible nonlinear elastic (FENE) Lennard-Jones (LJ) polymer model to be crystallized is investigated by molecular dynamics simulations. The optimal FENE Lennard-Jones parameter combinations (ratio between FENE and LJ equilibrium distances) and the optimal lattice parameters are calculated for five different perfect crystallite structures: simple tetragonal, body-centered tetragonal, body-centered orthorhombic, hexagonal primitive, and hexagonal close packed. It was found that the most energetically favorable structure is the body-centered orthorhombic. Starting with an equilibrated polymer liquid and with the optimal parameters found for the body-centered orthorhombic, an isothermal treatment led to the formation of large lamellar crystallites with a typical chain topology: folded, loop, and tie chains, and with a crystallinity of about 60%–70%, similar to real semicrystalline polymers. This simple coarse-grained Lennard-Jones model provides a qualitative tool to study semicrystalline microstructures for polymers.

We analyze a minimal model for a rigid spherical microswimmer and explore the consequences of its extended surface on the interplay between its self-propulsion and flow properties. The model is the first order representation of microswimmers, such as bacteria and algae, with rigid bodies and flexible propelling appendages. The flow field of such a microswimmer at finite distances significantly differs from that of a point-force (Stokeslet) dipole. For a suspension of microswimmers, we derive the grand mobility matrix that connects the motion of an individual swimmer to the active and passive forces and torques acting on all the swimmers. Our investigation of the mobility tensors reveals that hydrodynamic interactions among rigid-bodied microswimmers differ considerably from those among the corresponding point-force dipoles. Our results are relevant for the study of collective behavior of hydrodynamically interacting microswimmers by means of Stokesian dynamics simulations at moderate concentrations.

The effects of particle-size polydispersity on the magnetostatic properties of concentrated ferrofluids are studied using theory and computer simulation. The second-order modified mean-field (MMF2) theory of Ivanov and Kuznetsova [Phys. Rev. E 64, 041405 (2001)] has been extended by calculating additional terms of higher order in the dipolar coupling constant in the expansions of the initial magnetic susceptibility and the magnetization curve. The theoretical predictions have been tested rigorously against results from Monte Carlo simulations of model monodisperse, bidisperse, and highly polydisperse ferrofluids. Comparisons have been made between systems with the same Langevin susceptibility and the same saturation magnetization. In all cases, the new theoretical magnetization curve shows better agreement with simulation data than does the MMF2 theory. As for the initial susceptibility, MMF2 theory is most accurate for the monodisperse model, while the new theory works best for polydisperse systems with a significant proportion of large particles. These results are important for the analysis and characterization of recently synthesized polydisperse ferrofluids with record-breaking values of the initial magnetic susceptibility.

Micro-organisms usually can swim in their liquid environment by flagellar or ciliary beating. In this numerical work, we analyze the influence of flagellar beating on the orbits of a swimming cell in a shear flow. We also calculate the effect of the flagellar beating on the rheology of a dilute suspension of microswimmers. A three-dimensional model is proposed for Chlamydomonas Reinhardtii swimming with a breaststroke-like beating of two anterior flagella modeled by two counter-rotating fore beads. The active swimmer model reveals unusual angular orbits in a linear shear flow. Namely, the swimmer sustains orientations transiently across the flow. Such behavior is a result of the interplay between shear flow and the swimmer's periodic beating motion of flagella, which exert internal torques on the cell body. This peculiar behavior has some significant consequences on the rheological properties of the suspension. We calculate Einstein's viscosity of the suspension composed of such isolated modeled microswimmers (dilute case) in a shear flow. We use numerical simulations based on a Rotne-Prager-like approximation for hydrodynamic interaction between simplified flagella and the cell body. The results show an increased intrinsic viscosity for active swimmer suspensions in comparison to nonactive ones as well as a shear thinning behavior in accordance with previous experimental measurements [Phys. Rev. Lett. 104, 098102 (2010)].

The mesoscale structure of aeolian sand transport determines a variety of natural phenomena studied in planetary and Earth science. We analyze it theoretically beyond the mean-field level, based on the grain-scale transport kinetics and splash statistics. A coarse-grained analytical model is proposed and verified by numerical simulations resolving individual grain trajectories. The predicted height-resolved sand flux and other important characteristics of the aeolian transport layer agree remarkably well with a comprehensive compilation of field and wind-tunnel data, suggesting that the model robustly captures the essential mesoscale physics. By comparing the predicted saturation length with field data for the minimum sand-dune size, we elucidate the importance of intermittent turbulent wind fluctuations for field measurements and reconcile conflicting previous models for this most enigmatic emergent aeolian scale.