We investigate the phase transitions of a nonlinear, parallel version of the Ising model, characterized by an antiferromagnetic linear coupling and ferromagnetic nonlinear one. This model arises in problems of opinion formation. The mean-field approximation shows chaotic oscillations, by changing the couplings or the connectivity. The spatial model shows bifurcations in the average magnetization, similar to that seen in the mean-field approximation, induced by the change of the topology, after rewiring short-range to long-range connection, as predicted by the small-world effect. These coherent periodic and chaotic oscillations of the magnetization reflect a certain degree of synchronization of the spins, induced by long-range couplings. Similar bifurcations may be induced in the randomly connected model by changing the couplings or the connectivity and also the dilution (degree of asynchronism) of the updating. We also examined the effects of inhomogeneity, mixing ferromagnetic and antiferromagnetic coupling, which induces an unexpected bifurcation diagram with a “bubbling” behavior, as also happens for dilution.

We study excitation and suppression of chimera states in an ensemble of nonlocally coupled oscillators arranged in a framework of multiplex network. We consider the homogeneous network (all identical oscillators) with different parametric cases and interlayer heterogeneity by introducing parameter mismatch between the layers. We show the feasibility to suppress chimera states in the multiplex network via moderate interlayer interaction between a layer exhibiting chimera state and other layers which are in a coherent or incoherent state. On the contrary, for larger interlayer coupling, we observe the emergence of identical chimera states in both layers which we call an interlayer chimera state. We map the spatiotemporal behavior in a wide range of parameters, varying interlayer coupling strength and phase lag in two and three multiplexing layers. We also prove the emergence of interlayer chimera states in a multiplex network via evaluation of a continuous model. Furthermore, we consider the two-layered network of Hindmarsh-Rose neurons and reveal that in such a system multiplex interaction between layers is capable of exciting not only the synchronous interlayer chimera state but also nonidentical chimera patterns.

This paper focuses on the dispersion properties and mechanism of the one-dimensional strongly nonlinear acoustic metamaterials (NAMMs) based on the homotopy method. The local bifurcation mechanism, which is different from conventional local resonance, is found. It is demonstrated that the local period-doubling bifurcation of multiple cells will induce chaotic bands in the NAMMs, which can significantly expand the bandwidth for wave suppression. The saddle-node bifurcation leads the system state jumping to the chaotic branch. Furthermore, the amplitude-dependent dispersion properties enable NAMMs to manipulate elastic waves externally. Study of broadband tunable abilities reveals that stronger nonlinearity (larger nonlinear coefficient or higher amplitude) presents a broader nonlinear band gap and larger transmission loss. Moreover, with less attached mass, a low frequency and broadband are achievable simultaneously. This research may provide useful approaches for elastic wave control.

Symbolic sequences have been extensively investigated in the past few years within the framework of statistical physics. Paradigmatic examples of such sequences are written texts, and deoxyribonucleic acid (DNA) and protein sequences. In these examples, the spatial distribution of a given symbol (a word, a DNA motif, an amino acid) is a key property usually related to the symbol importance in the sequence: The more uneven and far from random the symbol distribution, the higher the relevance of the symbol to the sequence. Thus, many techniques of analysis measure in some way the deviation of the symbol spatial distribution with respect to the random expectation. The problem is then to know the spatial distribution corresponding to randomness, which is typically considered to be either the geometric or the exponential distribution. However, these distributions are only valid for very large symbolic sequences and for many occurrences of the analyzed symbol. Here, we obtain analytically the exact, randomly expected spatial distribution valid for any sequence length and any symbol frequency, and we study its main properties. The knowledge of the distribution allows us to define a measure able to properly quantify the deviation from randomness of the symbol distribution, especially for short sequences and low symbol frequency. We apply the measure to the problem of keyword detection in written texts and to study amino acid clustering in protein sequences. In texts, we show how the results improve with respect to previous methods when short texts are analyzed. In proteins, which are typically short, we show how the measure quantifies unambiguously the amino acid clustering and characterize its spatial distribution.

Compressive sensing is an effective way to reconstruct the network structure. In this paper, we investigate the effect of the mixing patterns, measured by the assortative coefficient, on the performance of network reconstruction. First, we present a model to generate networks with different assortativity coefficients, then we reconstruct the network structure by using the compressive sensing method. The experimental results show that when the assortativity coefficient $r=0.2$, the accuracy of the network reconstruction reaches the maximum value, which suggests that the compressive sensing is more effective for uncovering the links of social networks. Moreover, the accuracy of the network reconstruction will be higher as the network size increases.

We report thickness-dependent glass transition temperature ($T_g$) and charge mobility in cross-linked thin films made of conjugated polymer poly(9,9-dioctylfluorene-co-$N$-(4-butylphenyl)diphenylamine) (TFB). Monotonic $T_g$ depressions with reducing film thickness in thermally and UV cross-linked TFB thin films supported on Si-SiOx substrates are observed through ellipsometry measurements, suggesting that a surface mobile layer with enhanced chain dynamics still exists in cross-linked TFB thin films, even with a high cross-linking percentage. Data fitting using a three-layer model shows that the $T_g$ in the interface, bulk and surface layer both increases with increasing cross-linking, while the thickness of the interface and surface layer increases and reduces, respectively. Cross-linking of TFB thin film generates traps that hinder charge transport and consequently reduce charge mobility. The charge mobility converges in thick (>140 nm) and thin (<40 nm) TFB films but shows strong thickness dependence in between, reducing from $4.0\times {10}^{-4}\mathrm{c}{\mathrm{m}}^2/\mathrm{V}\mathrm{s}$ in a 180-nm film to $0.1\times {10}^{-4}\mathrm{c}{\mathrm{m}}^2/\mathrm{V}\mathrm{s}$ in a 20-nm thin film.

Recently a theoretical scheme explaining the vorticity generation by surface waves in liquids was developed [Phys. Rev. Lett. 116, 054501 (2016)]. Here we study how a thin (monomolecular) film presented on the surface of liquid affects the generated vorticity. We demonstrate that the vorticity becomes parametrically larger than for the case of liquid with a free surface, and the parameter is the quality factor of surface waves up to numerical factor. We also discuss the PIV experimental scheme intended to observe the generated vorticity and find that Stokes drift influences the measured velocity field. Explicit expression for the vertical vorticity was obtained.

Ultrasonic near-field levitation allows for contactless support and transportation of an object over vibrating surface. We developed an accurate model predicting pressure distribution in the gap between the surface and levitating object. The formulation covers a wide range of the air flow regimes: from viscous squeezed flow dominating in small gap to acoustic wave propagation in larger gap. The paper explains derivation of the governing equations from the basic fluid dynamics. The nonreflective boundary conditions were developed to properly define air flow at the outlet. Comparing to direct computational fluid dynamics modeling our approach allows achieving good accuracy while keeping the computation cost low. Using the model we studied the levitation force as a function of gap distance. It was shown that there are three distinguished flow regimes: purely viscous, viscoacoustic, and acoustic. The regimes are defined by the balance of viscous and inertial forces. In the viscous regime the pressure in the gap is close to uniform while in the intermediate viscoacoustic and the acoustic regimes the pressure profile is wavy. The model was validated by a dedicated levitation experiment and compared to similar published results.

We numerically investigate the hydrodynamic interaction of swimming organisms at small to intermediate Reynolds number regimes, i.e., $\text{Re}\sim \mathrm{O}(0.1–100)$, where inertial effects are important. The hydrodynamic interaction of swimming organisms in this regime is significantly different from the Stokes regime for microorganisms, as well as the high Reynolds number flows for fish and birds, which involves strong flow separation and detached vortex structures. Using an archetypal swimmer model, called a “squirmer,” we find that the inertial effects change the contact time and dispersion dynamics of a pair of pusher swimmers, and trigger hydrodynamic attraction for two pullers. These results are potentially important in investigating predator-prey interactions, sexual reproduction, and the encounter rate of marine organisms such as copepods, ctenophora, and larvae.

Rotating fluid flows under two-dimensional homogeneous porous media conditions (or in a rotating Hele-Shaw cell) reveal the development of complex interfacial fingering patterns. These pattern-forming structures are characterized by the occurrence of finger competition events, finger pinch-off episodes, as well as by the production of satellite droplets. In this work, we use intensive numerical simulations to investigate how these fully nonlinear pattern growth phenomena are altered by the presence of permeability heterogeneities in the rotating porous medium. This is done by employing a diffuse-interface Darcy-Cahn-Hilliard description of the problem and considering a permeability field presenting a log-Gaussian distribution, characterized by a variance $s$ and a correlation length $l$. We study how the heterogeneity measures $s$ and $l$ couple to the governing hydrodynamic dimensionless parameters of the problem and introduce important changes on the pattern formation dynamics of the system.

In this work we investigate electron heating induced by intense laser interaction with micrometric flat solid foils in the context of laser-driven ion acceleration. We propose a simple law to predict the electron temperature in a wider range of laser parameters with respect to commonly used existing models. An extensive two-dimensional (2D) and 3D numerical campaign shows that electron heating is due to the combined actions of $\mathbf{j}\times \mathbf{B}$ and Brunel effect. Electron temperature can be well described with a simple function of pulse intensity and angle of incidence, with parameters dependent on pulse polarization. We then combine our model for the electron temperature with an existing model for laser-ion acceleration, using recent experimental results as a benchmark. We also discuss an exploratory attempt to model electron temperature for multilayered foam-attached targets, which have been proven recently to be an attractive target concept for laser-driven ion acceleration.

An integral operator is developed to describe nonlocal transport in a one-dimensional system bounded on both ends by material walls. The “jump” distributions associated with nonlocal transport are taken to be Lévy $\alpha$-stable distributions, which become naturally truncated by the bounding walls. The truncation process results in the operator containing a self-consistent, convective inward transport term (pinch). The properties of the integral operator as functions of the Lévy distribution parameter set $\left[\alpha ,\gamma \right]$ and the wall conductivity are presented. The integral operator continuously recovers the features of local transport when $\alpha =2$. The self-adjoint formulation allows for an accurate description of spatial variation in the Lévy parameters in the nonlocal system. Spatial variation in the Lévy parameters is shown to result in internally generated flows. Examples of cold-pulse propagation in nonlocal systems illustrate the capabilities of the methodology.

We explore the thermodynamic geometry of a simple system that models the bistable dynamics of nucleic acid hairpins in single molecule force-extension experiments. Near equilibrium, optimal (minimum-dissipation) driving protocols are governed by a generalized linear response friction coefficient. Our analysis demonstrates that the friction coefficient of the driving protocols is sharply peaked at the interface between metastable regions, which leads to minimum-dissipation protocols that drive rapidly within a metastable basin, but then linger longest at the interface, giving thermal fluctuations maximal time to kick the system over the barrier. Intuitively, the same principle applies generically in free energy estimation (both in steered molecular dynamics simulations and in single-molecule experiments), provides a design principle for the construction of thermodynamically efficient coupling between stochastic objects, and makes a prediction regarding the construction of evolved biomolecular motors.

In this study, a method of causality detection was designed to reveal coupling between dynamical systems represented by time series. The method is based on the predictions in reconstructed state spaces. The results of the proposed method were compared with outcomes of two other methods, the Granger VAR test of causality and the convergent cross-mapping. We used two types of test data. The first test example is a unidirectional connection of chaotic systems of Rössler and Lorenz type. The second one, the fishery model, is an example of two correlated observables without a causal relationship. The results showed that the proposed method of optimized mixed prediction was able to reveal the presence and the direction of coupling and distinguish causality from mere correlation as well.

We study the existence and stability of splay states in the coupled sine circle map lattice system using analytic and numerical techniques. The splay states are observed for very low values of the nonlinearity parameter, i.e., for maps which deviate very slightly from the shift map case. We also observe that depending on the parameters of the system the splay state bifurcates to a mixed or chimera splay state consisting of a mixture of splay and synchronized states, together with kinks in the phases of some of the maps and then to a stable globally synchronized state. We show that these pure states and the mixed states are all temporally chaotic for our systems, and we explore the stability of these states to perturbations. Our studies may provide pointers to the behavior of systems in diverse application contexts such as Josephson junction arrays and chemical oscillations.

We investigate the effect of self-propulsion on a mean-field order-disorder transition. Starting from a ${\phi }^4$ scalar field theory subject to an exponentially correlated noise, we exploit the unified colored-noise approximation to map the nonequilibrium active dynamics onto an effective equilibrium one. This allows us to follow the evolution of the second-order critical point as a function of the noise parameters: the correlation time $\tau$ and the noise strength $D$. Our results suggest that the universality class of the model remains unchanged. We also estimate the effect of Gaussian fluctuations on the mean-field approximation finding an Ornstein-Zernike-like expression for the static structure factor at long wavelengths. Finally, to assess the validity of our predictions, we compare the mean-field theoretical results with numerical simulations of active Lennard-Jones particles in two and three dimensions, finding good qualitative agreement at small $\tau$ values.

Hydrodynamic interactions play an important role in biological processes in cellular membranes, a large separation of length scales often allowing such membranes to be treated as continuous, two-dimensional (2D) fluids. We study experimentally and theoretically the hydrodynamic interaction of pairs of inclusions in two-dimensional, fluid smectic liquid crystal films suspended in air. Such smectic membranes are ideal systems for performing controlled experiments as they are mechanically stable, of highly uniform structure, and have well-defined, variable thickness, enabling experimental investigation of the crossover from 2D to 3D hydrodynamics. Our theoretical model generalizes the Levine-MacKintosh theory of point-force response functions and uses a boundary-element approach to calculate the mobility matrix for inclusions of finite extent. We describe in detail the theoretical and computational approach previously outlined in Z. Qi et al., Phys. Rev. Lett. 113, 128304 (2014) and extend the method to study the mutual mobilities of inclusions with asymmetric shapes. The model predicts well the observed mutual mobilities of pairs of circular inclusions in films and the self-mobility of a circular inclusion in the vicinity of a linear boundary.

In this study we investigate, both numerically and experimentally, the interplay between the intrinsic Darrieus-Landau (DL) or hydrodynamic instability of a premixed flame and the moderately turbulent flow field in which the flame propagates. The objective is threefold: to establish, unambiguously, through a suitably defined marker, the presence or absence of DL-induced effects on the turbulent flame, to quantify the DL effects on the flame propagation and morphology and, finally, to asses whether such effects are mitigated or suppressed as the turbulence intensity is increased. The numerical simulations are based on a deficient reactant model which lends itself to a wealth of results from asymptotic theory, such as the determination of stability limits. The skewness of the flame curvature probability density function is identified as an unambiguous morphological marker for the presence or absence of DL effects in a turbulent environment. In addition, the turbulent propagation speed is shown to exhibit a distinct dual behavior whereby it is noticeably enhanced in the presence of DL instability while it is unchanged otherwise. Furthermore, increasing the turbulence intensity is found to be mitigating with respect to DL-induced effects such as the mentioned dual behavior which disappears at higher intensities. Experimental propane and/or air Bunsen flames are also investigated, utilizing two distinct diameters, respectively, above and below the estimated DL cutoff wavelength. Curvature skewness is still clearly observed to act as a marker for DL instability while the turbulent propagation speed is concurrently enhanced in the presence of the instability.

We report experimental results and simulations showing efficient laser energy coupling into plasmas at conditions relevant to the magnetized liner inertial fusion (MagLIF) concept. In MagLIF, to limit convergence and increase the hydrodynamic stability of the implosion, the fuel must be efficiently preheated. To determine the efficiency and physics of preheating by a laser, an Ar plasma with $n_e/n_{crit}\sim 0.04$ is irradiated by a multi-ns, multi-kJ, 0.35-μm, phase-plate-smoothed laser at spot-averaged intensities ranging from $1.0\times {10}^{14}$ to $2.5\times {10}^{14}\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$ and pulse widths from 2 to 10 ns. Time-resolved x-ray images of the laser-heated plasma are compared to two-dimensional radiation-hydrodynamic simulations that show agreement with the propagating emission front, a comparison that constrains laser energy deposition to the plasma. The experiments show that long-pulse, modest-intensity $\left(I=1.5\times {10}^{14}\mathrm{W}/\mathrm{c}{\mathrm{m}}^2\right)$ beams can efficiently couple energy ($\sim 82\%$ of the incident energy) to MagLIF-relevant long-length (9.5 mm) underdense plasmas. The demonstrated heating efficiency is significantly higher than is thought to have been achieved in early integrated MagLIF experiments [A. B. Sefkow et al., Phys. Plasmas 21, 072711 (2014)].