The critical rheology of sheared frictional granular materials near jamming transition is numerically investigated. It is confirmed that there exists a true critical density which characterizes the onset of the yield stress and two fictitious critical densities which characterize the scaling laws of rheological properties. We find the existence of a hysteresis loop between two of the critical densities for each friction coefficient. It is noteworthy that the critical scaling law for frictionless jamming transition seems to be still valid even for frictional jamming despite using fictitious critical density values.

We investigate two destabilization mechanisms for elastic polymer films and put them into a general framework: first, instabilities due to in-plane stress and, second, due to an externally applied electric field normal to the film’s free surface. As shown recently, polymer films are often stressed due to out-of-equilibrium fabrication processes such as, e.g., spin coating. Via an Asaro-Tiller-Grinfeld mechanism as known from solids, the system can decrease its energy by undulating its surface by surface diffusion of polymers and thereby relaxing stresses. On the other hand, application of an electric field is widely used experimentally to structure thin films; when the electric Maxwell surface stress overcomes surface tension and elastic restoring forces, the system undulates with a wavelength determined by the film thickness. We develop a theory taking into account both mechanisms simultaneously and discuss their interplay and the effects of the boundary conditions both at the substrate and at the free surface.

In this work, we will study how the effective geometry acquired by nematic molecules under thermal vibration contribute to the determination of the Leslie coefficients. To do this, we will divide this work in two sections. In the first section, we present the geometrical fundamentals of the so-called Hess-Baalss (HB) approach [D. Baalss and S. Hess, Phys. Rev. Lett. 57, 86 (1986)] where we show that its basic assumptions can be understood as a geometrical interpretation of de Gennes’ passage from the microscopic to the macroscopic order parameter. In the second section, we use an extended version of the HB approach [M. Simões, K. Yamaguti, and A. J. Palangana, Phys. Rev. E 80, 061701 (2009)] to obtain the geometrical contribution to each Leslie coefficient. Our results will be compared with experimental data, and we will show that the Miesowicz’s coefficients are connected as long as the ratio ${\alpha }_3/{\alpha }_4$ between these Leslie coefficients can be considered small.

We generalize the Eden model to take into account the screening effect, i.e., the end point grows much faster than the interior points do. Highly anisotropic clusters are obtained in our generalized Eden model. It is found that the length in the long direction scales differently than that in the short direction does as the number of sites increases.

The presence of a long-range correlation in the spatial distribution of a relevant word type, in spite of random occurrences of an irrelevant word type, is an important feature of human-written texts. We classify the correlation between the occurrences of words by nonextensive statistical mechanics for the word-ranking process. In particular, we look at the nonextensivity parameter as an alternative metric to measure the spatial correlation in the text, from which the words may be ranked in terms of this measure. Finally, we compare different methods for keyword extraction.

We present an analytical approach to determining the expected cascade size in a broad range of dynamical models on the class of random networks with arbitrary degree distribution and nonzero clustering introduced previously in [M. E. J. Newman, Phys. Rev. Lett. 103, 058701 (2009)]. A condition for the existence of global cascades is derived as well as a general criterion that determines whether increasing the level of clustering will increase, or decrease, the expected cascade size. Applications, examples of which are provided, include site percolation, bond percolation, and Watts’ threshold model; in all cases analytical results give excellent agreement with numerical simulations.

Scaling mobility patterns have been widely observed for animals. In this paper, we propose a deterministic walk model to understand the scaling mobility patterns, where walkers take the least-action walks on a lattice landscape and prey. Scaling laws in the displacement distribution emerge when the amount of prey resource approaches the critical point. Around the critical point, our model generates ordered collective movements of walkers with a quasiperiodic synchronization of walkers’ directions. These results indicate that the coevolution of walkers’ least-action behavior and the landscape could be a potential origin of not only the individual scaling mobility patterns but also the flocks of animals. Our findings provide a bridge to connect the individual scaling mobility patterns and the ordered collective movements.

We use the maximally permutation-symmetric set of three-body coordinates that consist of the “hyper-radius” $R=\sqrt{{\rho }^2+{\lambda }^2}$, the “rescaled area of the triangle” $\frac{\sqrt{3}}{2R^2}|\mathit{\rho }\times \mathit{\lambda }|$), and the (braiding) hyperangle $\varphi =\arctan (\frac{2\rho ·\lambda }{{\lambda }^2-{\rho }^2})$ to analyze the “figure-eight” choreographic three-body motion discovered by Moore [Phys. Rev. Lett. 70, 3675 (1993)] in the Newtonian three-body problem. Here $\mathit{\rho },\mathit{\lambda }$ are the two Jacobi relative coordinate vectors. We show that the periodicity of this motion is closely related to the braiding hyperangle $\varphi$. We construct an approximate integral of motion $\stackrel{̲}{G}$ that together with the hyperangle $\varphi$ forms the action-angle pair of variables for this problem and show that it is the underlying cause of figure-eight motion’s stability. We construct figure-eight orbits in two other attractive permutation-symmetric three-body potentials. We compare the figure-eight orbits in these three potentials and discuss their generic features, as well as their differences. We apply these variables to two new periodic, but nonchoreographic, orbits: One has a continuously rising $\varphi$ in time $t$, just like the figure-eight motion, but with a different, more complex, periodicity, whereas the other one has an oscillating $\varphi (t)$ temporal behavior.

A two-dimensional lattice Boltzmann model with 19 discrete velocities for compressible fluids is proposed. The fifth-order weighted essentially nonoscillatory (5th-WENO) finite difference scheme is employed to calculate the convection term of the lattice Boltzmann equation. The validity of the model is verified by comparing simulation results of the Sod shock tube with its corresponding analytical solutions [G. A. Sod, J. Comput. Phys. 27, 1 (1978).]. The velocity and density gradient effects on the Kelvin-Helmholtz instability (KHI) are investigated using the proposed model. Sharp density contours are obtained in our simulations. It is found that the linear growth rate $\gamma$ for the KHI decreases by increasing the width of velocity transition layer $D_v$ but increases by increasing the width of density transition layer $D_{\rho }$. After the initial transient period and before the vortex has been well formed, the linear growth rates ${\gamma }_v$ and ${\gamma }_{\rho }$, vary with $D_v$ and $D_{\rho }$ approximately in the following way, $\ln {\gamma }_v=a-{\mathit{bD}}_v$ and ${\gamma }_{\rho }=c+e\ln D_{\rho }(D_{\rho }<D_{\rho }^E)$, where $a$, $b$, $c$, and $e$ are fitting parameters and $D_{\rho }^E$ is the effective interaction width of the density transition layer. When $D_{\rho }>D_{\rho }^E$ the linear growth rate ${\gamma }_{\rho }$ does not vary significantly any more. One can use the hybrid effects of velocity and density transition layers to stabilize the KHI. Our numerical simulation results are in general agreement with the analytical results [L. F. Wang et al., Phys. Plasma 17, 042103 (2010)].

Population dynamics in systems composed of cyclically competing species has been of increasing interest recently. Here we investigate a system with four or more species. Using mean field theory, we study in detail the trajectories in configuration space of the population fractions. We discover a variety of orbits, shaped like saddles, spirals, and straight lines. Many of their properties are found explicitly. Most remarkably, we identify a collective variable that evolves simply as an exponential: $\mathcal{Q}\propto e^{\lambda t}$, where $\lambda$ is a function of the reaction rates. It provides information on the state of the system for late times (as well as for $t\to -\infty$). We discuss implications of these results for the evolution of a finite, stochastic system. A generalization to an arbitrary number of cyclically competing species yields valuable insights into universal properties of such systems.

We consider the occurrence of record-breaking events in random walks with asymmetric jump distributions. The statistics of records in symmetric random walks was previously analyzed by Majumdar and Ziff [Phys. Rev. Lett. 101, 050601 (2008)] and is well understood. Unlike the case of symmetric jump distributions, in the asymmetric case the statistics of records depends on the choice of the jump distribution. We compute the record rate $P_n(c)$, defined as the probability for the $n$th value to be larger than all previous values, for a Gaussian jump distribution with standard deviation $\sigma$ that is shifted by a constant drift $c$. For small drift, in the sense of $c/\sigma \ll n^{-1/2}$, the correction to $P_n(c)$ grows proportional to arctan$(\sqrt{n})$ and saturates at the value $\frac{c}{\sqrt{2}\sigma }$. For large $n$ the record rate approaches a constant, which is approximately given by $1-(\sigma /\sqrt{2\pi }c)\text{exp}(-c^2/2{\sigma }^2)$ for $c/\sigma \gg 1$. These asymptotic results carry over to other continuous jump distributions with finite variance. As an application, we compare our analytical results to the record statistics of 366 daily stock prices from the Standard & Poor's 500 index. The biased random walk accounts quantitatively for the increase in the number of upper records due to the overall trend in the stock prices, and after detrending the number of upper records is in good agreement with the symmetric random walk. However the number of lower records in the detrended data is significantly reduced by a mechanism that remains to be identified.

Vitamin-A acetate is one of the most versatile vitamins. It is applied in medicine because of its antioxidative properties, in tumor therapy because of its cytostatic activity, and in cosmetics because of its nutritional additives. Herein, using broadband dielectric spectroscopy, the molecular dynamics of supercooled and glassy vitamin-A acetate was investigated. It was shown that dielectric measurements carried out at ambient and elevated pressures reveal a number of relaxation processes associated with different types of molecular motions: α, δ, and ν processes—observed above the glass transition temperature and the next two modes: β and γ identified in the glassy state. The occurrence of the δ mode in the dielectric spectrum may imply the existence of nanoscale domains with nematic order. This hypothesis is further checked by atomic force microscopy measurements. Finally, we have determined the value of the glass transition temperature ($T_{\mathrm{g}}$) as well as the steepness index ($m_{\mathrm{P}}$) at various $T$-$P$ conditions.

Traditionally, the main role of cell-to-cell communication was thought of as synchronizing a population of cells, thereby coordinating cellular behavior. Here we show that cell density, which quantifies cellular communication, can induce multistability and multirhythmicity in a synthetic multicellular system, where individual oscillators are a combination of repressillator and hysteresis-based oscillators and are coupled through a quorum-sensing mechanism. Specifically, for moderately small cell densities, the coupled system can exhibit multistability including stable homogenous and inhomogeneous steady states. For moderately large cell densities, it has the potential to generate multirhythmicity including multimode oscillations such as an in-phase periodic solution, antiphase periodic solution, asymmetric periodic solution, mixed-mode oscillations, coexistence of periodic orbits of several different modes, and bursting oscillations such as periodic bursting, torus quasiperiodic bursting, and chaotic bursting. Such versatility of cell-to-cell communication would be beneficial for cells or organisms to live in diversely changeable environments.

We perform simulations to investigate how the energy carried by a molecule transfers to others in an equilibrium gas model. For this purpose we consider a microcanonical ensemble of equilibrium gas systems; each of them contains a tagged molecule located at the same position initially. The ensuing transfer process of the energy initially carried by the tagged molecule is then exposed in terms of the ensemble-averaged energy density distribution. In both a two- and a three-dimensional gas model with Lennard-Jones interactions at room temperature, it is found that the energy carried by a molecule propagates in the gas ballistically, in clear contrast with the Gaussian diffusion widely assumed in previous studies. A possible scheme of experimental study of this issue is also proposed.

The ability to find good solutions to the traveling salesman problem can benefit some biological organisms. Bacterial infection would, for instance, be eradicated most promptly if cells of the immune system minimized the total distance they traveled when moving between bacteria. Similarly, foragers would maximize their net energy gain if the distance that they traveled between multiple dispersed prey items was minimized. The traveling salesman problem is one of the most intensively studied problems in combinatorial optimization. There are no efficient algorithms for even solving the problem approximately (within a guaranteed constant factor from the optimum) because the problem is nondeterministic polynomial time complete. The best approximate algorithms can typically find solutions within 1%–2% of the optimal, but these are computationally intensive and can not be implemented by biological organisms. Biological organisms could, in principle, implement the less efficient greedy nearest-neighbor algorithm, i.e., always move to the nearest surviving target. Implementation of this strategy does, however, require quite sophisticated cognitive abilities and prior knowledge of the target locations. Here, with the aid of numerical simulations, it is shown that biological organisms can simply use chemotaxis to solve, or at worst provide good solutions (comparable to those found by the greedy algorithm) to, the traveling salesman problem when the targets are sources of a chemoattractant and are modest in number ($n$ < 10). This applies to neutrophils and macrophages in microbial defense and to some predators.

Coupled systems can exhibit an unusual kind of multistability, namely, the coexistence of infinitely many attractors for a given set of parameters. This extreme multistability is demonstrated to occur in coupled chemical model systems with various types of coupling. We show that the appearance of extreme multistability is associated with the emergence of a conserved quantity in the long-term limit. This conserved quantity leads to a “slicing” of the state space into manifolds corresponding to the value of the conserved quantity. The state space “slices” develop as $t\to \infty$ and there exists at least one attractor in each of them. We discuss the dependence of extreme multistability on the coupling and on the mismatch of parameters of the coupled systems.

Transition routes of propagating pulses in the Gray-Scott model from oscillatory to chaotic motion are investigated by numerical studies. Global bifurcation of the Gray-Scott model gives us information about the onset mechanism of transient dynamics, such as the splitting and extinction of pulses. However, the instability mechanism of oscillatory pulses has not been clarified, even numerically. Global bifurcation analysis of time periodic oscillatory traveling pulses, called traveling breathers, enables us to find chaotic motions of oscillatory pulse solutions. Two types of transitions to chaos, namely, period-doubling sequences and breakdown of quasiperiodic solutions, are found near the bifurcation points of traveling breathers.

We consider the robustness of multilayer networks composed of active and inactive oscillators from the viewpoint of interlayer coupling effects through the aging transition [H. Daido and K. Nakanishi, Phys. Rev. Lett. 93, 104101 (2004)]. We show in detail that two-layer networks increase or decrease their robustness depending on interlayer coupling schemes compared with single-layer networks. In addition, we find that an increase of mismatches of oscillator types (active or inactive) among interlayer-connected oscillators reduces the robustness of the networks with mean-field, chain, and diffusive interlayer couplings in two-layer networks. Moreover, we discuss the robustness of networks with more than two layers.

The decay of a passive scalar in a three-dimensional chaotic flow is studied using high-resolution numerical simulations. The (volume-preserving) flow considered is a three-dimensional extension of the randomized alternating sine flow employed extensively in studies of mixing in two dimensions. It is used to show that theoretical predictions for two-dimensional flows with small diffusivity carry over to three dimensions even though the stretching properties differ significantly. The variance decay rate, scalar field structure, and time evolution of statistical moments confirm that there are two distinct regimes of scalar decay: a locally controlled regime, which applies when the domain size is comparable to the characteristic length scale of the velocity field, and a globally controlled regime, which applies when the domain is larger. Asymptotic predictions for the variance decay rate in both regimes show excellent agreement with the numerical results. Consideration of both the forward flow and its time reverse makes it possible to compare the scalar evolution in flows with one or two expanding directions; simulations confirm the theoretical prediction that the decay rate of the scalar is the same in both flows, despite the very different scalar field structures.

Nanochannel ion transport is known to be governed by surface charge at low ionic concentrations. In this paper, we show that this surface charge is typically dominated by hydronium ions arising from dissolution of ambient atmospheric carbon dioxide. Taking the hydronium ions into account, we model the nanochannel conductance at low salt concentrations and identify a conductance minimum before saturation at a value independent of salt concentration in the dilute limit. Via the Poisson–Boltzmann equation, our model self-consistently couples chemical-equilibrium dissociation models of the silica wall and of the electrolyte bulk, parametrized by the dissociation reaction constants. Experimental data with aqueous KCl solutions in 165-nm-high silica nanochannels are described well by our model, both with and without extra hydronium from added HCl.