We study numerically the development of chimera states in networks of nonlocally coupled oscillators whose limit cycles emerge from a Hopf bifurcation. This dynamical system is inspired from population dynamics and consists of three interacting species in cyclic reactions. The complexity of the dynamics arises from the presence of a limit cycle and four fixed points. When the bifurcation parameter increases away from the Hopf bifurcation the trajectory approaches the heteroclinic invariant manifolds of the fixed points producing spikes, followed by long resting periods. We observe chimera states in this spiking regime as a coexistence of coherence (synchronization) and incoherence (desynchronization) in a one-dimensional ring with nonlocal coupling and demonstrate that their multiplicity depends on both the system and the coupling parameters. We also show that hierarchical (fractal) coupling topologies induce traveling multichimera states. The speed of motion of the coherent and incoherent parts along the ring is computed through the Fourier spectra of the corresponding dynamics.

The responses of soft-mode turbulence, a kind of spatiotemporal chaos seen in electroconvection of a nematic liquid crystal, to alternating-current magnetic fields is investigated to uncover the dynamical properties of spatiotemporal chaos. The dynamical responses can be measured by an order parameter, $M_p\left(t\right)$, which indicates ordering in the convective roll pattern induced by the magnetic field. Determined by properties of the liquid crystal in a magnetic field, $M_p\left(t\right)$ oscillates in accordance with the square of the magnetic field. The relaxation time of the system was obtained by fitting the frequency dependence of the complex susceptibility for the pattern obtained from the oscillation of $M_p\left(t\right)$ to the Debye-type relaxation spectra. However, for the high-frequency regime, the susceptibility deviates from the spectra because slow and large fluctuations of $M_p\left(t\right)$ contribute to the oscillation. The properties of this type of fluctuation were investigated by introducing a dynamic ordering parameter defined as the period average of $M_p\left(t\right)$.

In this paper, a simple and constructive method is presented to find the generalized perturbation $(n,M)$-fold Darboux transformations (DTs) of the modified nonlinear Schrödinger (MNLS) equation in terms of fractional forms of determinants. In particular, we apply the generalized perturbation $(1,N-1)$-fold DTs to find its explicit multi-rogue-wave solutions. The wave structures of these rogue-wave solutions of the MNLS equation are discussed in detail for different parameters, which display abundant interesting wave structures, including the triangle and pentagon, etc., and may be useful to study the physical mechanism of multirogue waves in optics. The dynamical behaviors of these multi-rogue-wave solutions are illustrated using numerical simulations. The same Darboux matrix can also be used to investigate the Gerjikov-Ivanov equation such that its multi-rogue-wave solutions and their wave structures are also found. The method can also be extended to find multi-rogue-wave solutions of other nonlinear integrable equations.

A method to approximately close the dynamic cavity equations for synchronous reversible dynamics on a locally treelike topology is presented. The method builds on (a) a graph expansion to eliminate loops from the normalizations of each step in the dynamics and (b) an assumption that a set of auxilary probability distributions on histories of pairs of spins mainly have dependencies that are local in time. The closure is then effectuated by projecting these probability distributions on $n$-step Markov processes. The method is shown in detail on the level of ordinary Markov processes $\left(n=1\right)$ and outlined for higher-order approximations $\left(n>1\right)$. Numerical validations of the technique are provided for the reconstruction of the transient and equilibrium dynamics of the kinetic Ising model on a random graph with arbitrary connectivity symmetry.

We revisit the light or heat-induced changes in topography of initially flat sheets of a solid that elongate or contract along patterned in-plane director fields. For radial or azimuthal directors, negative Gaussian curvature is generated—so-called “anticones.” We show that azimuthal material displacements are required for the distorted state to be stretch free and bend minimizing. The resultant shapes are smooth and asterlike and can become reentrant in the azimuthal coordinate for large deformations. We show that care is needed when considering elastomers rather than glasses, although the former offer huge deformations.

We analyze the critical connectivity of systems of penetrable $d$-dimensional spheres having size distributions in terms of weighed random geometrical graphs, in which vertex coordinates correspond to random positions of the sphere centers, and edges are formed between any two overlapping spheres. Edge weights naturally arise from the different radii of two overlapping spheres. For the case in which the spheres have bounded size distributions, we show that clusters of connected spheres are treelike for $d\to \infty$ and they contain no closed loops. In this case, we find that the mean cluster size diverges at the percolation threshold density ${\eta }_c\to 2^{-d}$, independently of the particular size distribution. We also show that the mean number of overlaps for a particle at criticality $z_c$ is smaller than unity, while $z_c\to 1$ only for spheres with fixed radii. We explain these features by showing that in the large dimensionality limit, the critical connectivity is dominated by the spheres with the largest size. Assuming that closed loops can be neglected also for unbounded radii distributions, we find that the asymptotic critical threshold for systems of spheres with radii following a log-normal distribution is no longer universal, and that it can be smaller than $2^{-d}$ for $d\to \infty$.

Recent theoretical advances predict the existence, deep into the glass phase, of a novel phase transition, the so-called Gardner transition. This transition is associated with the emergence of a complex free energy landscape composed of many marginally stable sub-basins within a glass metabasin. In this study, we explore several methods to detect numerically the Gardner transition in a simple structural glass former, the infinite-range Mari-Kurchan model. The transition point is robustly located from three independent approaches: (i) the divergence of the characteristic relaxation time, (ii) the divergence of the caging susceptibility, and (iii) the abnormal tail in the probability distribution function of cage order parameters. We show that the numerical results are fully consistent with the theoretical expectation. The methods we propose may also be generalized to more realistic numerical models as well as to experimental systems.

Vesiculation of mature red blood cells (RBCs) contributes to removal of defective patches of the erythrocyte membrane. In blood disorders, which are related to defects in proteins of the RBC membrane, vesiculation of the plasma membrane is intensified. Several hypotheses have been proposed to explain RBC vesiculation but the exact underlying mechanisms and what determines the sizes of the vesicles are still not completely understood. In this work, we apply a two-component coarse-grained molecular dynamics RBC membrane model to study how RBC vesiculation is controlled by the membrane spontaneous curvature and by lateral compression of the membrane. Our simulation results show that the formation of small homogeneous vesicles with a diameter less than 40 nm can be attributed to a large spontaneous curvature of membrane domains. On the other hand, compression on the membrane can cause the formation of vesicles with heterogeneous composition and with sizes comparable with the size of the cytoskeleton corral. When spontaneous curvature and lateral compression are simultaneously considered, the compression on the membrane tends to facilitate formation of vesicles originating from curved membrane domains. We also simulate vesiculation of RBCs with membrane defects connected to hereditary elliptocytosis (HE) and to hereditary spherocytosis (HS). When the vertical connectivity between the lipid bilayer and the membrane skeleton is elevated, as in normal RBCs, multiple vesicles are shed from the compressed membrane with diameters similar to the cytoskeleton corral size. In HS RBCs, where the connectivity between the lipid bilayer and the cytoskeleton is reduced, larger-size vesicles are released under the same compression ratio as in normal RBCs. Lastly, we find that vesicles released from HE RBCs can contain cytoskeletal filaments due to fragmentation of the membrane skeleton while vesicles released from the HS RBCs are depleted of cytoskeletal filaments.

We define auto- and cross-correlation functions capable of capturing dynamical characteristics induced by local phase-space structures in a general dynamical system. These correlation functions are calculated in the standard map for a range of values of the nonlinearity parameter $k$. Using a model of noninteracting particles, each evolving according to the same standard map dynamics and located initially at specific phase-space regions, we show that for $0.6<k\le 1.2$ long-range cross correlations emerge. They occur as an ensemble property of particle trajectories by an appropriate choice of the phase-space cells used in the statistical averaging. In this region of $k$ values the single-particle phase space is either dominated by local chaos $(k\le k_c$ with $k_c\approx 0.97)$ or it is characterized by the transition from local to global chaos $\left(k_c<k\le 1.2\right)$. Introducing suitable symbolic dynamics we demonstrate that the emergence of long-range cross correlations can be attributed to the existence of an effective intermittent dynamics in specific regions of the phase space. Our findings support the recently established relation of intermittent dynamics and cross correlations [F. K. Diakonos, A. K. Karlis, and P. Schmelcher, Europhys. Lett. 105, 26004 (2014)] in simple one-dimensional intermittent maps, suggesting its validity also for two-dimensional Hamiltonian maps.

Ability to characterize the heat transfer in flowing gases is important for a wide range of applications involving micro- and nanoscale devices. Gas flows away from the continuum limit can be captured using the Boltzmann equation, whose analytical solution poses a formidable challenge. An efficient and accurate numerical simulation of the Boltzmann equation is thus highly desirable. In this article, the linearized Boltzmann Bhatnagar-Gross-Krook equation is used to develop a hierarchy of thermal lattice Boltzmann (LB) models based on half-space Gaussian-Hermite (GH) quadrature ranging from low to high algebraic precision, using double distribution functions. Simplified versions of the LB models in the continuum limit are also derived, and are shown to be consistent with existing thermal LB models for noncontinuum heat transfer reported in the literature. Accuracy of the proposed LB hierarchy is assessed by simulating thermal Couette flows for a wide range of Knudsen numbers. Effects of the underlying quadrature schemes (half-space GH vs full-space GH) and continuum-limit simplifications on computational accuracy are also elaborated. The numerical findings in this article provide direct evidence of improved computational capability of the proposed LB models for modeling noncontinuum flows and heat transfer at small length scales.

A polymer chain pinned in space exerts a fluctuating force on the pin point in thermal equilibrium. The average of such fluctuating force is well understood from statistical mechanics as an entropic force, but little is known about the underlying force distribution. Here, we introduce two phase space sampling methods that can produce the equilibrium distribution of instantaneous forces exerted by a terminally pinned polymer. In these methods, both the positions and momenta of mass points representing a freely jointed chain are perturbed in accordance with the spatial constraints and the Boltzmann distribution of total energy. The constraint force for each conformation and momentum is calculated using Lagrangian dynamics. Using terminally pinned chains in space and on a surface, we show that the force distribution is highly asymmetric with both tensile and compressive forces. Most importantly, the mean of the distribution, which is equal to the entropic force, is not the most probable force even for long chains. Our work provides insights into the mechanistic origin of entropic forces, and an efficient computational tool for unbiased sampling of the phase space of a constrained system.

A water cylinder deposited on a heated channel levitates on its own generated vapor film owing to the Leidenfrost effect. This experimental setup permits the study of the one-dimensional propagation of surface waves in a free-to-move liquid system. We report the observation of gravity-capillary waves under a dramatic reduction of gravity (up to a factor 30), leading to capillary waves at the centimeter scale. The generated nonlinear structures propagate without deformation and undergo mutual collisions and reflections at the boundaries of the domain. They are identified as Korteweg–de Vries solitons with negative amplitude and subsonic velocity. The typical width and amplitude-dependent velocities are in excellent agreement with theoretical predictions based on a generalized Korteweg–de Vries equation adapted to any substrate geometry. When multiple solitons are present, they interact and form a soliton turbulencelike spectrum.

The non-Markovian stochastic dynamics involving Lévy flights and a potential in the form of a harmonic and nonlinear oscillator is discussed. The subordination technique is applied and the memory effects, which are nonhomogeneous, are taken into account by a position-dependent subordinator. In the nonlinear case, the asymptotic stationary states are found. The relaxation pattern to the stationary state is derived for the quadratic potential: the density decays like a linear combination of the Mittag-Leffler functions. It is demonstrated that in the latter case the density distribution satisfies a fractional Fokker-Planck equation. The densities for the nonlinear oscillator reveal a complex picture, qualitatively dependent on the potential strength, and the relaxation pattern is exponential at large time.

We report a type of colloidal gel, induced by a minute incremental addition of mutually attractive small particles (size $\sim 12$ nm) to a suspension of highly charged large particles (size $\sim 500$ nm). The gel's morphological behavior does not follow the typical power-law scaling for fractal clusters. Its unique scaling behavior has two distinct power-law indices, based on particle volume fraction. We show the unique scaling behavior arises when nonfractal networks of large particles are bridged by small-particle clusters, which occurs between a lower and upper critical boundary of small particle volume fraction.

Using numerical simulations, we characterized the behavior of an elastic membrane immersed in an active fluid. Our findings reveal a nontrivial folding and re-expansion of the membrane that is controlled by the interplay of its resistance to bending and the self-propulsion strength of the active components in solution. We show how flexible membranes tend to collapse into multifolded states, whereas stiff membranes fluctuate between an extended configuration and a singly folded state. This study provides a simple example of how to exploit the random motion of active particles to perform mechanical work at the microscale.

Recent studies have shown that double-stranded DNA can collapse in the presence of a strong electric field. Here we provide an in-depth study of the collapse of DNA under weak confinement in microchannels as a function of buffer strength, driving frequency, applied electric-field strength, and molecule size. We find that the critical electric field at which DNA molecules collapse (tens of kV/m) is strongly dependent on driving frequency (100–800 Hz) and molecular size (20–160 kbp), and weakly dependent on the ionic strength (8–60 mM). We argue that an apparent stretching at very high electric fields is an artifact of the finite frame time of video microscopy.

Taking into account the fact that overload failures in real-world functional networks are usually caused by extreme values of temporally fluctuating loads that exceed the allowable range, we study the robustness of scale-free networks against cascading overload failures induced by fluctuating loads. In our model, loads are described by random walkers moving on a network and a node fails when the number of walkers on the node is beyond the node capacity. Our results obtained by using the generating function method show that scale-free networks are more robust against cascading overload failures than Erdős-Rényi random graphs with homogeneous degree distributions. This conclusion is contrary to that predicted by previous works, which neglect the effect of fluctuations of loads.

A method for the estimation of the Lyapunov exponent corresponding to enslaved phase dynamics from time series has been proposed. It is valid for both nonautonomous systems demonstrating periodic dynamics in the presence of noise and coupled chaotic oscillators and allows us to estimate precisely enough the value of this Lyapunov exponent in the supercritical region of the control parameters. The main results are illustrated with the help of the examples of the noised circle map, the nonautonomous Van der Pole oscillator in the presence of noise, and coupled chaotic Rössler systems.

Molecular dynamics results are reported for the thermodynamic properties of supercritical water using examples of both rigid $\left(\mathrm{TIP}4\mathrm{P}\text{/}2005\right)$ and flexible $\left(\mathrm{TIP}4\mathrm{P}\text{/}2005\mathrm{f}\right)$ transferable interaction potentials. Data are reported for pressure, isochoric and isobaric heat capacities, the thermal expansion coefficient, isothermal and adiabatic compressibilities, Joule-Thomson coefficient, speed of sound, self-diffusion coefficient, viscosities, and thermal conductivity. Many of these properties have unusual behavior in the supercritical phase such as maximum and minimum values. The effectiveness of bond flexibility on predicting these properties is determined by comparing the results to experimental data. The influence of the intermolecular potential on these properties is both variable and state point dependent. In the vicinity of the critical density, the rigid and flexible potentials yield very different values for the compressibilities, heat capacities, and thermal expansion coefficient, whereas the self-diffusion coefficient, viscosities, and thermal conductivities are much less potential dependent. Although the introduction of bond flexibility is a computationally expedient way to improve the accuracy of an intermolecular potential, it can be counterproductive in some cases and it is not an adequate replacement for incorporating the effects of polarization.

Granular systems present surprisingly complicated dynamics. In particular, nonlinear interactions and energy dissipation play important roles in these dynamics. Usually (but admittedly not always), constant coefficients of restitution are introduced phenomenologically to account for energy dissipation when grains collide. The collisions are assumed to be instantaneous and to conserve momentum. Here, we introduce the dissipation through a viscous (velocity-dependent) term in the equations of motion for two colliding grains. Using a first-order approximation, we solve the equations of motion in the low viscosity regime. This approach allows us to calculate the collision time, the final velocity of each grain, and a coefficient of restitution that depends on the relative velocity of the grains. We compare our analytic results with those obtained by numerical integration of the equations of motion and with exact ones obtained by other methods for some geometries.