We numerically study the distributions of global pressure that are found in ensembles of statically jammed and quasistatically sheared systems of bidisperse, frictionless disks at fixed packing fraction $\varphi$ in two dimensions. We use these distributions to address the question of how pressure increases as $\varphi$ increases above the jamming point ${\varphi }_J$, $p\sim |\varphi -{\varphi }_J{|}^y$. For statically jammed ensembles, our results are consistent with the exponent $y$ being simply related to the power law of the interparticle soft-core interaction. For sheared systems, however, the value of $y$ is consistent with a nontrivial value, as found previously in rheological simulations.

Dense non-Brownian suspension flows of hard particles display mystifying properties: As the jamming threshold is approached, the viscosity diverges, as well as a length scale that can be identified from velocity correlations. To unravel the microscopic mechanism governing dissipation and its connection to the observed correlation length, we develop an analogy between suspension flows and the rigidity transition occurring when floppy networks are pulled, a transition believed to be associated with the stress stiffening of certain gels. After deriving the critical properties near the rigidity transition, we show numerically that suspension flows lie close to it. We find that this proximity causes a decoupling between viscosity and the correlation length of velocities $\xi$, which scales as the length $l_c$ characterizing the response to a local perturbation, previously predicted to follow $l_c\sim 1/\sqrt{z_c-z}\sim p^{0.18}$, where $p$ is the dimensionless particle pressure, $z$ is the coordination of the contact network made by the particles, and $z_c$ is twice the spatial dimension. We confirm these predictions numerically and predict the existence of a larger length scale $l_r\sim \sqrt{p}$ with mild effects on velocity correlation and of a vanishing strain scale $\delta \gamma \sim 1/p$ that characterizes decorrelation in flow.

The chiral, heliconical (twist-bend) nematic ground state is reported in an achiral, rigid, bent-core mesogen (UD68). Similar to the nematic twist-bend ($N_{\mathrm{TB}}$) phase observed in bent molecular dimers, the $N_{\mathrm{TB}}$ phase of UD68 forms macroscopic, smecticlike focal-conic textures and exhibits nanoscale, periodic modulation with no associated modulation of the electron density, i.e., without a detectable lamellar x-ray reflection peak. The $N_{\mathrm{TB}}$ helical pitch is $p_{\mathrm{TB}}$∼14 nm. When an electric field is applied normal to the helix axis, a weak electroclinic effect is observed, revealing 50-μm-scale left- and right-handed domains in a chiral conglomerate.

We are interested in the chiral tilted smectic subphases, smectic-$C_{tilted}^{*}$, including commensurate structures as well as the incommensurate smectic-$C_{\alpha }^{*}$ one. The continuum theory defines two scalar order parameters $I$ and $J$, which can be coupled with an external electric field through a linear term $I\times E$ and a dielectric term $J\times E^2$. We have calculated the changes due to these terms in the phase diagrams in the $(\alpha ,\eta )$ plane, where $\alpha$ comes from the spontaneous twist and $\eta$ measures the strength of the biaxial order. The coupling with an external electric field induces the expansion of the areas with spontaneous polarization and the appearance of an electroazimuthal effect.

A small quantity of ${\text{BaTiO}}_3$ ferroelectric nanoparticles (FNP) was doped in a liquid crystal (LC), and the LC + FNP hybrid was found to exhibit a nonvolatile electromechanical memory effect in the isotropic phase. The permanent dipole moment of the FNPs causes the LC molecule to form short-range pseudonematic domains surrounding the FNPs. The FNP-induced short-range orders become more prominent in the isotropic phase when the global nematic order is absent. These short-range domains, being anisotropic in nature, interact with an external electric field, exhibiting a Fréedericksz-type transition. When the field is turned off, these domains stay oriented, showing a hysteresis effect due to the absence of any long-range order and restoring forces in the isotropic phase. The hysteresis graph for this memory effect shows a significant pretransitional behavior on approaching the nematic phase from the isotropic phase.

We study a simple model of how social behaviors, like trends and opinions, propagate in networks where individuals adopt the trend when they are informed by threshold $T$ neighbors who are adopters. Using a dynamic message-passing algorithm, we develop a tractable and computationally efficient method that provides complete time evolution of each individual's probability of adopting the trend or of the frequency of adopters and nonadopters in any arbitrary networks. We validate the method by comparing it with Monte Carlo-based agent simulation in real and synthetic networks and provide an exact analytic scheme for large random networks, where simulation results match well. Our approach is general enough to incorporate non-Markovian processes and to include heterogeneous thresholds and thus can be applied to explore rich sets of complex heterogeneous agent-based models.

The study of the response of complex dynamical social, biological, or technological networks to external perturbations has numerous applications. Random Boolean networks (RBNs) are commonly used as a simple generic model for certain dynamics of complex systems. Traditionally, RBNs are interconnected randomly and without considering any spatial extension and arrangement of the links and nodes. However, most real-world networks are spatially extended and arranged with regular, power-law, small-world, or other nonrandom connections. Here we explore the RBN network topology between extreme local connections, random small-world, and pure random networks, and study the damage spreading with small perturbations. We find that spatially local connections change the scaling of the Hamming distance at very low connectivities ($\overline{K}\ll 1$) and that the critical connectivity of stability $K_s$ changes compared to random networks. At higher $\overline{K}$, this scaling remains unchanged. We also show that the Hamming distance of spatially local networks scales with a power law as the system size $N$ increases, but with a different exponent for local and small-world networks. The scaling arguments for small-world networks are obtained with respect to the system sizes and strength of spatially local connections. We further investigate the wiring cost of the networks. From an engineering perspective, our new findings provide the key design trade-offs between damage spreading (robustness), the network's wiring cost, and the network's communication characteristics.

It is becoming more and more clear that complex networks present remarkable large fluctuations. These fluctuations may manifest differently according to the given model. In this paper we reconsider hidden-variable models which turn out to be more analytically treatable and for which we have recently shown clear evidence of non-self-averaging, the density of a motif being subject to possible uncontrollable fluctuations in the infinite-size limit. Here we provide full detailed calculations and we show that large fluctuations are only due to the node-hidden variables variability while, in ensembles where these are frozen, fluctuations are negligible in the thermodynamic limit and equal the fluctuations of classical random graphs. A special attention is paid to the choice of the cutoff: We show that in hidden-variable models, only a cutoff growing as $N^{\lambda }$ with $\lambda \ge 1$ can reproduce the scaling of a power-law degree distribution. In turn, it is this large cutoff that generates non-self-averaging.

We address the time decay of the Loschmidt echo, measuring the sensitivity of quantum dynamics to small Hamiltonian perturbations, in one-dimensional integrable systems. Using a semiclassical analysis, we show that the Loschmidt echo may exhibit a well-pronounced regime of exponential decay, similar to the one typically observed in quantum systems whose dynamics is chaotic in the classical limit. We derive an explicit formula for the exponential decay rate in terms of the spectral properties of the unperturbed and perturbed Hamilton operators and the initial state. In particular, we show that the decay rate, unlike in the case of the chaotic dynamics, is directly proportional to the strength of the Hamiltonian perturbation. Finally, we compare our analytical predictions against the results of a numerical computation of the Loschmidt echo for a quantum particle moving inside a one-dimensional box with Dirichlet-Robin boundary conditions, and find the two in good agreement.

We perform the stochastic analysis of a thermochemical system using a master equation which describes a chemical reaction and includes discrete and continuous temperature jumps. We study the time evolution of the system selecting the temperature of the thermostat as an easily tunable control parameter. Depending on the thermostat temperature, the system can be in an excitable, oscillatory, or stationary regime. Stochastic time series for the system temperature are generated and the distributions of interspike intervals are analyzed in the three dynamical regimes separated by a homoclinic bifurcation and a Hopf bifurcation. Different constructive roles of internal fluctuations are exhibited. A noise-induced transition is observed in the vicinity of the Hopf bifurcation. Coherence resonance and stochastic resonance are found in the oscillatory regime. In a range of thermostat temperatures, a nontrivial behavior of the highly nonlinear system is revealed by the existence of both a minimum and a maximum in the scaled standard deviation of interspike intervals as a function of particle number. This high sensitivity to system size illustrates that controlling dynamics in nanoreactors may remain a difficult task.

Network analysis was used to study the structure and time evolution of driven three-dimensional complex plasma clusters. The clusters were created by suspending micron-size particles in a glass box placed on top of the rf electrode in a capacitively coupled discharge. The particles were highly charged and manipulated by an external electric field that had a constant magnitude and uniformly rotated in the horizontal plane. Depending on the frequency of the applied electric field, the clusters rotated in the direction of the electric field or remained stationary. The positions of all particles were measured using stereoscopic digital in-line holography. The network analysis revealed the interplay between two competing symmetries in the cluster. The rotating cluster was shown to be more cylindrical than the nonrotating cluster. The emergence of vertical strings of particles was also confirmed.

The spatiotemporal evolution of the naturally occurring dust acoustic wave mode is experimentally investigated in a weakly coupled dc glow discharge dusty plasma system over a range of neutral gas pressures through the application of a time-resolved Hilbert Transform. Frequency clusters are observed over a range of neutral gas pressures, though their spatial distribution varies with neutral gas pressure. It is also observed that the wave frequency is observed to drop by $\sim 10$ Hz across these frequency clusters independent of the experimental parameters.

Modeling blood flow in larger vessels using lattice-Boltzmann methods comes with a challenging set of constraints: a complex geometry with walls and inlets and outlets at arbitrary orientations with respect to the lattice, intermediate Reynolds (Re) number, and unsteady flow. Simple bounce-back is one of the most commonly used, simplest, and most computationally efficient boundary conditions, but many others have been proposed. We implement three other methods applicable to complex geometries [Guo, Zheng, and Shi, Phys. Fluids 14, 2007 (2002); Bouzidi, Firdaouss, and Lallemand, Phys. Fluids 13, 3452 (2001); Junk and Yang, Phys. Rev. E 72, 066701 (2005)] in our open-source application hemelb. We use these to simulate Poiseuille and Womersley flows in a cylindrical pipe with an arbitrary orientation at physiologically relevant Re number (1–300) and Womersley (4–12) numbers and steady flow in a curved pipe at relevant Dean number (100–200) and compare the accuracy to analytical solutions. We find that both the Bouzidi-Firdaouss-Lallemand (BFL) and Guo-Zheng-Shi (GZS) methods give second-order convergence in space while simple bounce-back degrades to first order. The BFL method appears to perform better than GZS in unsteady flows and is significantly less computationally expensive. The Junk-Yang method shows poor stability at larger Re number and so cannot be recommended here. The choice of collision operator (lattice Bhatnagar-Gross-Krook vs multiple relaxation time) and velocity set (D3Q15 vs D3Q19 vs D3Q27) does not significantly affect the accuracy in the problems studied.

We define the violation fraction $\nu$ as the cumulative fraction of time that the entropy change is negative during single realizations of processes in phase space. This quantity depends on both the number of degrees of freedom $N$ and the duration of the time interval $\tau$. In the large-$\tau$ and large-$N$ limit we show that, for ergodic and microreversible systems, the mean value of $\nu$ scales as $\langle \nu (N,\tau )\rangle \sim {\left(\tau N^{\frac{1}{1+\alpha }}\right)}^{-1}$. The exponent $\alpha$ is positive and generally depends on the protocol for the external driving forces, being $\alpha =1$ for a constant drive. As an example, we study a nontrivial model where the fluctuations of the entropy production are non-Gaussian: an elastic line driven at a constant rate by an anharmonic trap. In this case we show that the scaling of $\langle \nu \rangle$ with $N$ and $\tau$ agrees with our result. Finally, we discuss how this scaling law may break down in the vicinity of a continuous phase transition.

Extortion strategies can dominate any opponent in an iterated prisoner's dilemma game. But if players are able to adopt the strategies performing better, extortion becomes widespread and evolutionary unstable. It may sometimes act as a catalyst for the evolution of cooperation, and it can also emerge in interactions between two populations, yet it is not the evolutionarily stable outcome. Here we revisit these results in the realm of spatial games. We find that pairwise imitation and birth-death dynamics return known evolutionary outcomes. Myopic best response strategy updating, on the other hand, reveals counterintuitive solutions. Defectors and extortioners coarsen spontaneously, which allows cooperators to prevail even at prohibitively high temptations to defect. Here extortion strategies play the role of a Trojan horse. They may emerge among defectors by chance, and once they do, cooperators become viable as well. These results are independent of the interaction topology, and they highlight the importance of coarsening, checkerboard ordering, and best response updating in evolutionary games.

The model of nonlocally coupled identical phase oscillators on complex networks is investigated. We find the existence of chimera states in which identical oscillators evolve into distinct coherent and incoherent groups. We find that the coherent group of chimera states always contains the same oscillators no matter what the initial conditions are. The properties of chimera states and their dependence on parameters are investigated on both scale-free networks and Erdös-Rényi networks.

The Gardner equation $u_t+au{u}_x+b{u}^2{u}_x+\mu u_{xxx}=0$ is a generic mathematical model for weakly nonlinear and weakly dispersive wave propagation when the effects of higher-order nonlinearity become significant. Using the so-called traveling wave ansatz $u(x,t)=\phi \left(\xi \right)$, $\xi =x-vt$ (where $v$ is the velocity of the wave) we convert the (1+1)-dimensional partial differential equation to a second-order ordinary differential equation in $\varphi$ with an arbitrary constant and treat the latter equation by the methods of the dynamical systems theory. With some special attention on the equilibrium points of the equation, we derive an analytical constraint for admissible values of the parameters $a$, $b$, and $\mu$. From the Hamiltonian form of the system we confirm that, in addition to the usual bright soliton solution, the equation can be used to generate three different varieties of internal waves of which one is a dark soliton recently observed in water [A. Chabchoub et al., Phys. Rev. Lett. 110, 124101 (2013)].