The neoclassical model of $\text{Sm-}C$ (and $\text{Sm-}{C}^{\ast }$) elastomers developed by Warner and Adams predicts a class of “soft” (zero energy) deformations. We find and describe the full set of stripe domains—laminate structures in which the laminates alternate between two different deformations—that can form between pairs of these soft deformations. All the stripe domains fall into two classes, one in which the smectic layers are not bent at the interfaces, but for which—in the $\text{Sm-}{C}^{\ast }$ case—the interfaces are charged, and one in which the smectic layers are bent but the interfaces are never charged. Striped deformations significantly enhance the softness of the macroscopic elastic response.

Brain “rest” is defined—more or less unsuccessfully—as the state in which there is no explicit brain input or output. This work focuses on the question of whether such state can be comparable to any known dynamical state. For that purpose, correlation networks from human brain functional magnetic resonance imaging are contrasted with correlation networks extracted from numerical simulations of the Ising model in two dimensions at different temperatures. For the critical temperature $T_c$, striking similarities appear in the most relevant statistical properties, making the two networks indistinguishable from each other. These results are interpreted here as lending support to the conjecture that the dynamics of the functioning brain is near a critical point.

In this Rapid Communication we present an analytic study of sampled networks in the case of some important shortest-path sampling models. We present analytic formulas for the probability of edge discovery in the case of an evolving and a static network model. We also show that the number of discovered edges in a finite network scales much more slowly than predicted by earlier mean-field models. Finally, we calculate the degree distribution of sampled networks and we demonstrate that they are analogous to a destroyed network obtained by randomly removing edges from the original network.

The problem of community detection is relevant in many disciplines of science and modularity optimization is the widely accepted method for this purpose. It has recently been shown that this approach presents a resolution limit by which it is not possible to detect communities with sizes smaller than a threshold, which depends on the network size. Moreover, it might happen that the communities resulting from such an approach do not satisfy the usual qualitative definition of commune; i.e., nodes in a commune are more connected among themselves than to nodes outside the commune. In this paper we present a different method for community detection in complex networks. We define merit factors based on the weak and strong community definitions formulated by Radicchi et al. [Proc. Natl. Acad. Sci. U.S.A. 101, 2658 (2004)] and we show that these local definitions avoid the resolution limit problem found in the modularity optimization approach.

We present an exact solution of percolation in a generalized class of Watts-Strogatz graphs defined on a one-dimensional underlying lattice. We find a nonclassical critical point in the limit of the number of long-range bonds in the system going to zero, with a discontinuity in the percolation probability and a divergence in the mean finite-cluster size. We show that the critical behavior falls into one of three regimes depending on the proportion of occupied long-range to unoccupied nearest-neighbor bonds, with each regime being characterized by different critical exponents. The three regimes can be united by a single scaling function around the critical point. These results can be used to identify the number of long-range links necessary to secure connectivity in a communication or transportation chain. As an example, we can resolve the communication problem in a game of “telephone.”

In this paper, we develop a macroscopic model for pedestrian flow using the dynamic continuum modeling approach. We consider a two-dimensional walking facility that is represented as a continuum within which pedestrians can move freely in any direction. A pedestrian chooses a route based on his or her memory of the shortest path to the desired destination when the facility is empty and, at the same time, tries to avoid high densities. In this model, pedestrian flow is governed by a two-dimensional conservation law, and a general speed-flow-density relationship is considered. The model equation is solved numerically using the discontinuous Galerkin method, and a numerical example is employed to demonstrate both the model and the effectiveness of the numerical method.

Turbulent diffusion of a passive scalar with a large-Schmidt number $\left(\text{Sc}⪢1\right)$ is considered in the viscous sublayer of a turbulent channel flow. Close to the wall, the corresponding eddy diffusivity coefficient is expanded as a power series in terms of the viscous distance to the wall $y$. The coefficients of the series depend on the Schmidt number and the analysis of recent numerical results allows to conclude that in the close vicinity of the wall $\left(y⪡{\text{Sc}}^{-1/3}\right)$, the $y^3$ term is the dominant term; whereas, at distances relatively large from the wall $\left({\text{Sc}}^{-1/3}⪡y⪡1\right)$, the $y^4$ term becomes dominant. Accordingly, in this region the turbulent Schmidt number is not constant but follows a hyperbolic law in terms of the distance to the wall that matches the values taken in the vicinity of the wall, on the order of ${\text{Sc}}^{-1/3}$, with the values of order unity in the rest of the viscous layer. The implications of this behavior on the surface-transfer coefficient are analyzed.

We study low-temperature properties of the $XY$ spin model on a negatively curved surface. Geometric curvature of the surface gives rise to frustration in local spin configuration, which results in the formation of high-energy spin clusters scattered over the system. Asymptotic behavior of the spin-glass susceptibility suggests a zero-temperature glass transition, which is attributed to multiple optimal configurations of spin clusters due to nonzero surface curvature of the system. It implies that a constant ferromagnetic spin interaction on a regular lattice can exhibit glasslike behavior without possessing any disorder if the lattice is put on top of a negatively curved space such as a hyperbolic surface.

Using Feynman-Kac and Cameron-Martin-Girsanov formulas, we find a generalized integral fluctuation theorem (GIFT) for general diffusion processes by constructing a time-invariable integral. The existing integral fluctuation theorems can be derived as its specific cases. We interpret the origin of the GIFT in terms of time reversal of stochastic systems.

We investigate the macroscopic properties of frictionless nonconvex particles using molecular dynamics. The calculations are based on a simple and efficient method to simulate complex-shaped interacting bodies. The particle shape is represented by Minkowski operators. A multicontact time-continuous interaction between bodies is derived using simple concepts of computational geometry. Three-dimensional simulations of hopper flow show that the nonconvexity of the particles strongly affects the jamming on granular flow. Also the model allows the representation of complex bodies with rough surfaces as in friction studies and the reproduction of a wide range of friction and dilatancy angles as in true triaxial tests.

We study a system of $N$ nonintersecting $(1+1)$-dimensional fluctuating elastic interfaces (“vicious bridges”) at thermal equilibrium, each subject to periodic boundary condition in the longitudinal direction and in presence of a substrate that induces an external confining potential for each interface. We show that, for a large sytem and with an appropriate choice of the external confining potential, the joint distribution of the heights of the $N$ nonintersecting interfaces at a fixed point on the substrate can be mapped to the joint distribution of the eigenvalues of a Wishart matrix of size $N$ with complex entries (Dyson index $\beta =2$), thus providing a physical realization of the Wishart matrix. Exploiting this analogy to random matrix, we calculate analytically (i) the average density of states of the interfaces, (ii) the height distribution of the uppermost and lowermost interfaces (extrema), and (iii) the asymptotic (large-$N$) distribution of the center of mass of the interfaces. In the last case, we show that the probability density of the center of mass has an essential singularity around its peak, which is shown to be a direct consequence of a phase transition in an associated Coulomb gas problem.

We study a percolation problem based on critical loop configurations of the $\text{O}\left(n\right)$ loop model on the honeycomb lattice. We define dual clusters as groups of sites on the dual triangular lattice that are not separated by a loop, and investigate the bond-percolation properties of these dual clusters. The universal properties at the percolation threshold are argued to match those of Kasteleyn-Fortuin random clusters in the critical Potts model. This relation is checked numerically by means of cluster simulations of several $\text{O}\left(n\right)$ models in the range $1\le n\le 2$. The simulation results include the percolation threshold for several values of $n$, as well as the universal exponents associated with bond dilution and the size distribution of the diluted clusters at the percolation threshold. Our numerical results for the exponents are in agreement with existing Coulomb-gas results for the random-cluster model, which confirms the relation between both models. We discuss the renormalization flow of the bond-dilution parameter $p$ as a function of $n$, and provide an expression that accurately describes a line of unstable fixed points as a function of $n$, corresponding with the percolation threshold. Furthermore, the renormalization scenario indicates the existence, in a $p$ versus $n$ diagram, of another line of fixed points at $p=1$, which is stable with respect to $p$.

An extensive study of the one-dimensional two-segment Frenkel-Kontorova (FK) model reveals a transition from the counterintuitive existence to the ordinary nonexistence of a negative-differential-thermal-resistance (NDTR) regime, when the system size or the intersegment coupling constant increases to a critical value. A “phase” diagram which depicts the relevant conditions for the exhibition of NDTR was obtained. In the existence of a NDTR regime, the link at the segment interface is weak and therefore the corresponding exhibition of NDTR can be explained in terms of effective phonon-band shifts. In the case where such a regime does not exist, the theory of phonon-band mismatch is not applicable due to sufficiently strong coupling between the FK segments. The findings suggest that the behavior of a thermal transistor will depend critically on the properties of the interface and the system size.

For a variety of quenched random spin systems on an Apollonian network, including ferromagnetic and antiferromagnetic bond percolation and the Ising spin glass, we find the persistence of ordered phases up to infinite temperature over the entire range of disorder. We develop a renormalization-group technique that yields highly detailed information, including the exact distributions of local magnetizations and local spin-glass order parameters, which turn out to exhibit, as function of temperature, complex and distinctive tulip patterns.

To put it in the framework of information processing, stochastic resonance (SR) is a phenomenon in which the transfer of information from input to output signals can be significantly increased by noise with appropriate (nonzero) intensity. The minimum requirements for SR are generally input signals, nonlinearity, and noise, in addition to a quantifier to measure the efficiency of information transfer. We study a simple threshold system and propose an adaptation mechanism for system parameters, such as a threshold and noise intensity (i.e., temperature), which are held fixed in a normal SR setting. Our emphasis is put on parameter dynamics induced by this adaptation, which we call self-tuning (ST), and on how this dynamics modifies or changes the SR picture with respect to information processing efficiency. As a measure for performance of the threshold system we take mutual information and the signal-to-noise ratio. These quantities are calculated by an analytical method and by a simulational one. ST of temperature results in oscillatory time variation in temperature with its average located around the temperature at which performance is maximized in the SR setting. ST of a threshold turns out to improve performance in the weak noise region.

We study the four-wave kinetic equation of weak turbulence linearized around the Rayleigh-Jeans spectrum when the collision integral is associated with short-range interactions between nonrelativistic bosonic quasiparticles. The technique used for the analysis of the stability is based on the properties of the Mellin transform of the kernel in the integral equation. We find that any perturbation of the Rayleigh-Jeans distribution evolves toward low-momentum scales in such a form that when $t\to \infty$, all the particles occupy a sphere of radius arbitrary small.

Using a microscopic theory based on excluded-volume interactions, we analyze the structure and thermodynamic stability of configurations in a two-dimensional liquid crystal confined into a (small) circular nanocavity. Weak homeotropic anchoring conditions are considered, and topological defects of total charge $k=+1$ are discussed. It is found that, for small cavity radii, the cavity is free of defects at the expense of surface free energy not being optimized. For larger cavities, a configuration with two repulsive $k=+1/2$-charge point defects is always stable. The two configurations are equally stable thermodynamically (structural or Frederiks transition) on a curve in the chemical potential-cavity radius plane. This curve ends for chemical potential and cavity radius below some critical values. Elastic-theory arguments are used to explain the stability of the defected structure compared with the one free of defects. Our results indicate that the two-defect structure is always more stable than the one with a single point defect of charge $k=+1$ at the cavity center, which, in agreement with computer simulation, is never found to be stable. Finally, the relation with the bulk behavior of the fluid is discussed.

Birdsong is a complex phenomenon, generated by a nonlinear vocal device capable of displaying complex solutions even under simple physiological motor commands. Among the peripheral physical mechanisms responsible for the generation of complex sounds in songbirds, the understanding of the dynamics emerging from the interaction between the sound source and the upper vocal tract remains most elusive. In this work we study a highly dissipative limit of a simple sound source model interacting with a tract, mathematically described in terms of a delay differential equation. We explore the system numerically and, by means of reducing the problem to a phase equation, we are capable of studying its periodic solutions. Close in parameter space to the point where the resonances of the tract match the frequencies of the uncoupled source solutions, we find coexistence of periodic limit cycles. This hysteresis phenomenon allows us to interpret recently reported features found in the vocalization of some songbirds, in particular, “frequency jumps.”

Suppression of spiral and turbulence in inhomogeneous media due to local heterogeneity with higher excitability is investigated numerically. When the inhomogeneity is small, control tactics by boundary periodic forcing (BPF) is effective against the existing spiral and turbulence. When the inhomogeneity of excitability is large, a rotating electric field (REF) is utilized to “smooth” regional heterogeneity based on driven synchronization. Consequently, a control approach combining BPF with REF is proposed to suppress the spiral and turbulence. The underlying mechanism of successful suppression is discussed in terms of dispersion relation.

In practical problems, the observability of a system not only depends on the choice of observable(s) but also on the space which is reconstructed. In fact starting from a given set of observables, the reconstructed space is not unique, since the dimension can be varied and, in the case of multivariate measurement functions, there are various ways to combine the measured observables. Using a graphical approach recently introduced, we analytically compute symbolic observability coefficients which allow to choose from the system equations the best observable, in the case of scalar reconstructions, and the best way to combine the observables in the case of multivariate reconstructions. It is shown how the proposed coefficients are also helpful for analysis in higher dimension.