Water striders enjoy an intriguing ability to stand and walk freely on water surfaces, which is mainly attributed to the superior water repellency of their slender legs. In previous theoretical analyses, the legs are usually treated as rigid beams and the results show that a tremendously deep dimple and a large supporting force can be achieved when the leg descends into water. In this paper, the effect of the flexibility of water strider legs on their water-repellent ability is investigated, both theoretically and experimentally. We analyze a hydrophobic and flexible leg pressing obliquely on water. The leg may undergo a large deformation and assume different geometric configurations. It is shown that the flexible leg can float easily on a water surface, inducing only a shallow water puddle and a moderate supporting force as observed in real water striders. When the long leg is sufficiently compliant, the water surface will never be pierced and the leg will never sink. The findings are experimentally testified by using flexible fibers to represent water strider legs pressing on water.

High-pressure in situ x-ray diffraction and specific-volume measurements on isotactic poly(4-methyl-1-pentene) melt have uncovered abrupt changes in the pressure dependence of microscopic structure as well as that of macroscopic density. The first sharp diffraction peak of the polymer melt, which is related to the intermediate-range order and is explained as resulting from the correlations between main chains, is suppressed at pressures less than 1 kbar. These changes in intermediate-range order show similarities to those seen in liquid-liquid or amorphous-amorphous transitions in simpler small molecule based systems, suggesting that this kind of phenomenon may occur in a wide range of materials.

This paper studies the rheology of weakly entangled polymer melts and films in the glassy domain and near the rubbery domain using two different methods: molecular dynamics (MD) and finite element (FE) simulations. In a first step, the uniaxial mechanical behavior of a bulk polymer sample is studied by means of particle-based MD simulations. The results are in good agreement with experimental data, and mechanical properties may be computed from the simulations. This uniaxial mechanical behavior is then implemented in FE simulations using an elasto-viscoelasto-viscoplastic constitutive law in a continuum mechanics (CM) approach. In a second step, the mechanical response of a polymer film during an indentation test is modeled with the MD method and with the FE simulations using the same constitutive law. Good agreement is found between the MD and CM results. This work provides evidence in favor of using MD simulations to investigate the local physics of contact mechanics, since the volume elements studied are representative and thus contain enough information about the microstructure of the polymer model, while surface phenomena (adhesion and surface tension) are naturally included in the MD approach.

In this paper, we investigate computationally the oscillatory tank-treading motion of healthy swollen human erythrocytes (owing to lower than physiological plasma osmolarity) in shear flows with capillary number $\mathrm{Ca}=O\left(1\right)$ and small to moderate viscosity ratios $0.01\le \lambda \le 2.75$. Swollen cells show similar shear flow dynamics with normal cells but with significantly higher inclination and tank-treading speed owing to the higher cell thickness. For a given viscosity ratio, as the flow rate increases, the steady-state erythrocyte length $L$ (in the shear plane) increases logarithmically while its depth $W$ (normal to the shear plane) decreases logarithmically; increase of the viscosity ratio results in lower cell deformation. The erythrocyte width $S$, which exists in the shear plane, is practically invariant in time, flow rate, and viscosity ratio and corresponds to a real cell thickness of about $2.5\mu \mathrm{m}$ at physiological osmolarity ($300\mathrm{mO}$) and $3.4\mu \mathrm{m}$ at an osmolarity of 217 mO. The erythrocyte inclination decreases as the flow rate increases or as the surrounding fluid viscosity decreases, owing to the increased inner rotational flow which tends to align the cell toward the flow direction. The ektacytometry deformation of swollen cells increases logarithmically with the shear stress but with a slower slope than that for normal cells owing mainly to the higher orientation of the more swollen cells. As the cell swelling increases, the tank-treading period decreases owing to the higher thickness of the actual cell which overcomes the opposite action of the reduced shape-memory effects (i.e., the more spherical-like erythrocyte's reference shape of shearing resistance). The local area incompressibility tensions from the lipid bilayer increase with the cell swelling and cause a higher cytoskeleton prestress; this increased prestress results in smaller, but still measurable, local area changes on the spectrin skeleton of the more swollen erythrocytes. Our work provides insight on the effects of clinical syndromes and biophysical processes associated with lowered plasma osmolarity (and thus higher cell swelling) such as inappropriate antidiuretic hormone secretion and diuretic therapy.

Pattern formation in microbial colonies of competing strains under purely space-limited population growth has recently attracted considerable research interest. We show that the reproduction time statistics of individuals has a significant impact on the sectoring patterns. Generalizing the standard Eden growth model, we introduce a simple one-parameter family of reproduction time distributions indexed by the variation coefficient $\delta \in [0,1]$, which includes deterministic ($\delta =0$) and memory-less exponential distribution ($\delta =1$) as extreme cases. We present convincing numerical evidence and heuristic arguments that the generalized model is still in the Kardar-Parisi-Zhang (KPZ) universality class, and the changes in patterns are due to changing prefactors in the scaling relations, which we are able to predict quantitatively. With the example of Saccharomyces cerevisiae, we show that our approach using the variation coefficient also works for more realistic reproduction time distributions.

We formulate the solution counting problem within the framework of the inverse Ising problem and use fast belief propagation equations to estimate the entropy whose value provides an estimate of the true one. We test this idea on both diluted models [random 2-SAT (2-satisfiability) and 3-SAT problems] and a fully connected model (binary perceptron), and show that when the constraint density is small, this estimate can be very close to the true value. The information stored by the salamander retina under the natural movie stimuli can also be estimated, and our result is consistent with that obtained by the Monte Carlo method. Of particular significance is that the sizes of other metastable states for this real neuronal network are predicted.

The identification of modules in complex networks is important for the understanding of systems. Here, we propose an ensemble clustering method incorporating node groupings in various sizes and the sequential removal of weak ties between nodes which are rarely grouped together. This method successfully detects modules in various networks, such as hierarchical random networks and the American college football network, with known modular structures. Some of the results are compared with those obtained by modularity optimization and $K$-means clustering.

Collective motion of bird flocks can be explained via the hypothesis of many wrongs and/or a structured leadership mechanism. In pigeons, previous studies have shown that there is a well-defined hierarchical structure and certain specific individuals occupy more dominant positions, suggesting that leadership by the few individuals drives the behavior of the collective. Conversely, by analyzing the same datasets, we uncover a more egalitarian mechanism. We show that both reciprocal relationships and a stratified hierarchical leadership are important and necessary in the collective movements of pigeon flocks. Rather than birds adopting either exclusive averaging or leadership strategies, our experimental results show that it is an integrated combination of both compromise and leadership which drives the group's movement decisions.

We study instabilities and pattern formation in reaction-diffusion layers that are diffusively coupled. For two-layer systems of identical two-component reactions, we analyze the stability of homogeneous steady states by exploiting the block symmetric structure of the linear problem. There are eight possible primary bifurcation scenarios, including a Turing-Turing bifurcation that involves two disparate length scales whose ratio may be tuned via the interlayer coupling. For systems of $n$-component layers and nonidentical layers, the linear problem's block form allows approximate decomposition into lower-dimensional linear problems if the coupling is sufficiently weak. As an example, we apply these results to a two-layer Brusselator system. The competing length scales engineered within the linear problem are readily apparent in numerical simulations of the full system. Selecting a $\sqrt{2}$:1 length-scale ratio produces an unusual steady square pattern.

We introduce an optimal phase description of chaotic oscillations by generalizing the concept of isochrones. On chaotic attractors possessing a general phase description, we define the optimal isophases as Poincaré surfaces showing return times as constant as possible. The dynamics of the resultant optimal phase is maximally decoupled from the amplitude dynamics and provides a proper description of the phase response of chaotic oscillations. The method is illustrated with the Rössler and Lorenz systems.

The probability densities of the mean recurrence time, which is the average time needed for a system to recur to a previously visited neighborhood, are investigated in various dynamical regimes and are found to be in agreement with those of the finite-time Lyapunov exponents. The important advantages of the former ones are that they are easy to estimate and that comparable short time series are sufficient. Asymmetric distributions with exponential tails are observed for intermittency and crisis-induced intermittency, while for typical chaos, the distribution has a Gaussian shape. Further, the shape of the distribution distinguishes intermittent strange nonchaotic attractors from those appearing through fractalization and tori collision mechanisms. Furthermore, statistics performed on the peaks in the frequency distribution of recurrence times unveil scaling behavior in agreement with that obtained from the spectral distribution function defined as the number of peaks in the Fourier spectrum greater than a predefined value. The results of the present recurrence statistics are of relevance in classifying different dynamics and providing important insights into the dynamics of a system when only one realization of this system is available. The practical use of this approach for experimental data is shown on experimental electrochemical time series.

We investigate the phenomenon of noise-enhanced phase synchronization (PS) in coupled time-delay systems, which usually exhibit non-phase-coherent attractors with complex topological properties. As a delay system is essentially an infinite dimensional in nature with multiple characteristic time scales, it is interesting and crucial to understand the interplay of noise and the time scales in achieving PS. In unidirectionally coupled systems, the response system adjust all its time scales to that of the drive, whereas both subsystems adjust their rhythms to a single (main time scale of the uncoupled system) time scale in bidirectionally coupled systems. We find similar effects for both a common and an independent additive Gaussian noise.

The unsteady relativistic shock-wave diffraction patterns generated by a relativistic blast wave impinging on a circular cylinder and a sphere are numerically simulated using some high-resolution relativistic kinetic beam schemes in a general coordinate system for solving the relativistic Euler equations of gas dynamics. The diffraction patterns are followed through about 6 radii of travel of the incident shock past the body. The complete diffraction patterns, including regular reflection, transition from regular to Mach reflection, slip lines, and the complex shock-on-shock interaction at the wake region resulting from the Mach shocks collision behind the body are reported in detail. Computational results of several incident shock Mach numbers covering the near ultrarelativistic limit are studied. Various contours of flow properties including the Lorentz factor and velocity streamline plots are also presented to add a better understanding of the complex diffraction phenomena. The three-dimensional relieving effects of the sphere cases are evident and can be quantitatively evaluated as compared with the corresponding cylinder cases.

In this study, effects of microstructure on the viscous permeability and Forchheimer coefficient of monodispersed fibers are investigated. The porous material is represented by a unit cell which is assumed to be repeated throughout the medium. Based on the orientation of the fibers in the space, fibrous media are divided into three categories: one-, two-, and three-directional (1D, 2D, and 3D) structures. Parallel and transverse flow through square arrangements of 1D fibers, simple 2D mats, and 3D simple cubic structures are solved numerically over a wide range of porosity (0.35 < $\varepsilon$ < 0.95) and Reynolds number (0.01 < $\mathrm{Re}$ < 200). The results are used to calculate the permeability and the inertial coefficient of the considered geometries. An experimental study is performed; the flow coefficients of three different ordered tube banks in the moderate range of Reynolds number (0.001 < Re < 15) are determined. The numerical results are successfully compared with the present and the existing experimental data in the literature. The results suggest that the permeability and Forchheimer coefficient are functions of porosity and fiber orientation. A comparison of the experimental and numerical results with the Ergun equation reveals that this equation is not suitable for highly porous materials. As such, accurate correlations are proposed for determining the Forchheimer coefficient in fibrous porous media.

In aerosol and dusty plasma systems, the behavior of suspended particles (grains) is often strongly influenced by collisions occurring between ions and particles, as well as between particles themselves. In determining the collision kernel or collision rate coefficient for such charged entities, complications arise in that the collision process can be completely described neither by continuum transport mechanics nor by free molecular (ballistic) mechanics; that is, collisions are transition regime processes. Further, both the thermal energy and the potential energy between colliding entities can strongly influence the collision rate and must be considered. Flux-matching theory, originally developed by Fuchs, is frequently applied for calculation of collision rate coefficients under these circumstances. However, recent work suggests that crucial assumptions in flux-matching theory are not appropriate to describe transition regime collisions in the presence of potential interactions. Here, we combine dimensional analysis and mean first passage time calculations to infer the collision kernel between dilute charged entities suspended in a light background gas at thermal equilibrium. The motion of colliding entities is described by a Langevin equation, and Coulombic interactions are considered. It is found that the dimensionless collision kernel for these conditions, $H$, is a function of the diffusive Knudsen number, Kn${}_{\mathrm{D}}$ (in contrast to the traditional Knudsen number), and the potential energy to thermal energy ratio, ${\Psi }_E$. For small and large Kn${}_{\mathrm{D}}$, it is found that the dimensionless collision kernels inferred from mean first passage time calculations collapse to the appropriate continuum and free molecular limiting forms, respectively. Further, for repulsive collisions (${\Psi }_E$ negative) or attractive collisions with ${\Psi }_E<0.5$, calculated results are in excellent agreement with flux-matching theory predictions, and the dimensionless collision kernel can be determined conveniently via use of the $H$(Kn${}_{\mathrm{D}}$) relationship found for hard-sphere collisions with modified definitions of $H$ and Kn${}_{\mathrm{D}}$ to account for potential energy. However, for ${\Psi }_E>0.5$, it is found that flux-matching theory predictions substantially underestimate the collision kernel. We find that the collision process in this regime is governed by the minimum of Kn${}_{\mathrm{D}}$ and Kn${}_{\Psi }$ (${\mathrm{Kn}}_{\Psi }=3{\mathrm{Kn}}_{\mathrm{D}}/2{\Psi }_E$), and based on calculations, propose a function H(Kn${}_{\mathrm{D}}$, Kn${}_{\Psi }$) for collision kernel evaluation. The situations for which ${\Psi }_E>0.5$ apply to singly charged nanoparticles and multiply charged submicrometer and supermicrometer particles, and are thus prevalent in both aerosol and dusty plasma environments.

We introduce a general model which augments the one-dimensional nonlinear Schrödinger (NLS) equation by nonlinear-diffraction terms competing with the linear diffraction. The new terms contain two irreducible parameters and admit a Hamiltonian representation in a form natural for optical media. The equation serves as a model for spatial solitons near the supercollimation point in nonlinear photonic crystals. In the framework of this model, a detailed analysis of the fundamental solitary waves is reported, including the variational approximation (VA), exact analytical results, and systematic numerical computations. The Vakhitov-Kolokolov (VK) criterion is used to precisely predict the stability border for the solitons, which is found in an exact analytical form, along with the largest total power (norm) that the waves may possess. Past a critical point, collapse effects are observed, caused by suitable perturbations. Interactions between two identical parallel solitary beams are explored by dint of direct numerical simulations. It is found that in-phase solitons merge into robust or collapsing pulsons, depending on the strength of the nonlinear diffraction.

In this paper, we construct a generalized Darboux transformation for the nonlinear Schrödinger equation. The associated $N$-fold Darboux transformation is given in terms of both a summation formula and determinants. As applications, we obtain compact representations for the $N$th-order rogue wave solutions of the focusing nonlinear Schrödinger equation and Hirota equation. In particular, the dynamics of the general third-order rogue wave is discussed and shown to exhibit interesting structures.

We study the behavior of particles having a finite electric permittivity and conductivity in a weakly conducting fluid under the action of the external electric field. We consider the case when the strength of the external electric field is above the threshold, and particles rotate due to the Quincke effect. We determine the magnitude of the dipole interaction of the Quincke rotating particles and the shift of frequency of the Quincke rotation caused by the dipole interaction between the particles. It is demonstrated that depending on the mutual orientation of the vectors of angular velocities of particles, vector-directed along the straight line between the centers of the particles and the external electric field strength vector, particles can attract or repel each other. In contrast to the case of nonrotating particles when the magnitude of the dipole interaction increases with the increase of the strength of the external electric field, the magnitude of the dipole interaction of the Quincke rotating particles either does not change or decreases with the increase of the strength of the external electric field depending on the strength of the external electric field and electrodynamic parameters of the particles.

A system's response to external periodic changes can provide crucial information about its dynamical properties. We investigate the synchronization transition, an archetypical example of a dynamic phase transition, in the framework of such a temporal response. The Kuramoto model under periodically switching interactions has the same type of phase transition as the original mean-field model. Furthermore, we see that the signature of the synchronization transition appears in the relative delay of the order parameter with respect to the phase of oscillating interactions as well. Specifically, the phase shift becomes significantly larger as the system gets closer to the phase transition, so that the order parameter at the minimum interaction density can even be larger than that at the maximum interaction density, counterintuitively. We argue that this phase-shift inversion is caused by the diverging relaxation time, in a similar way to the resonance near the critical point in the kinetic Ising model. Our result, based on exhaustive simulations on globally coupled systems as well as scale-free networks, shows that an oscillator system's phase transition can be manifested in the temporal response to the topological dynamics of the underlying connection structure.