The discontinuous shear thickening (DST) of dense suspensions is a remarkable phenomenon in which the viscosity can increase by several orders of magnitude at a critical shear rate. It has the appearance of a first-order phase transition between two hypothetical “states” that we have recently identified as Stokes flows with lubricated or frictional contacts, respectively. Here we extend the analogy further by means of stress-controlled simulations and show the existence of a nonmonotonic steady-state flow curve analogous to a nonmonotonic equation of state. While we associate DST with an $\mathsf{S}$-shaped flow curve, at volume fractions above the shear jamming transition the frictional state loses flowability and the flow curve reduces to an arch, permitting the system to flow only at small stresses. Whereas a thermodynamic transition leads to phase separation in the coexistence region, we observe a uniform shear flow all along the thickening transition. A stability analysis suggests that uniform shear may be mechanically stable for the small Reynolds numbers and system sizes in a rheometer.

We present numerical studies of first-order and continuous filling transitions in wedges of arbitrary opening angle $\psi$, using a microscopic fundamental measure density functional model with short-ranged fluid-fluid forces and long-ranged wall-fluid forces. In this system the wetting transition characteristic of the planar wall-fluid interface is always first order regardless of the strength of the wall-fluid potential ${\varepsilon }_w$. In the wedge geometry, however, the order of the filling transition depends not only on ${\varepsilon }_w$ but also on the opening angle $\psi$. In particular we show that even if the wetting transition is strongly first order the filling transition is continuous for sufficient acute wedges. We show further that the change in the order of the transition occurs via a tricritical point as opposed to a critical end point. These results extend previous effective Hamiltonian predictions which were limited only to shallow wedges.

We investigate the emergence of chiral meso-structures in one-dimensional fluids consisting of stacked discotic particles and demonstrate that helical undulations are generated spontaneously from internal elastic stresses. The stability of these helical conformations arises from an interplay between long-ranged soft repulsions and nanopore confinement which is naturally present in columnar liquid crystals. Using a simple mean-field theory based on microscopic considerations we identify generic scaling expressions for the typical buckling radius and helical pitch as a function of the density and interaction potential of the constituent particles.

We explore the dynamics of topological point defects on surfaces of magnetically responsive colloidal microspheres in a uniformly aligned nematic liquid crystal host. We show that pinning of the liquid crystal director to a particle surface with random nanostructured morphology results in unexpected translational dynamics of both particles and topological point defects on their surfaces when subjected to rotating magnetic fields. We characterize and quantify the “stick-slip” motion of defects as a function of field rotation rates as well as temperature, demonstrating the roles played by the competition of elastic forces, surface anchoring, and magnetic torques on the sphere as well as random-surface-mediated pinning of the easy axis of the nematic director on colloidal microspheres. We analyze our findings through their comparison to similar dynamic processes in other branches of science.

Several independent observations have suggested that the catastrophe transition in microtubules is not a first-order process, as is usually assumed. Recent in vitro observations by Gardner et al. [M. K. Gardner et al., Cell 147, 1092 (2011)] showed that microtubule catastrophe takes place via multiple steps and the frequency increases with the age of the filament. Here we investigate, via numerical simulations and mathematical calculations, some of the consequences of the age dependence of catastrophe on the dynamics of microtubules as a function of the aging rate, for two different models of aging: exponential growth, but saturating asymptotically, and purely linear growth. The boundary demarcating the steady-state and non-steady-state regimes in the dynamics is derived analytically in both cases. Numerical simulations, supported by analytical calculations in the linear model, show that aging leads to nonexponential length distributions in steady state. More importantly, oscillations ensue in microtubule length and velocity. The regularity of oscillations, as characterized by the negative dip in the autocorrelation function, is reduced by increasing the frequency of rescue events. Our study shows that the age dependence of catastrophe could function as an intrinsic mechanism to generate oscillatory dynamics in a microtubule population, distinct from hitherto identified ones.

Repeated game theory has been one of the most prevailing tools for understanding long-running relationships, which are the foundation in building human society. Recent works have revealed a new set of “zero-determinant” (ZD) strategies, which is an important advance in repeated games. A ZD strategy player can exert unilateral control on two players' payoffs. In particular, he can deterministically set the opponent's payoff or enforce an unfair linear relationship between the players' payoffs, thereby always seizing an advantageous share of payoffs. One of the limitations of the original ZD strategy, however, is that it does not capture the notion of robustness when the game is subjected to stochastic errors. In this paper, we propose a general model of ZD strategies for noisy repeated games and find that ZD strategies have high robustness against errors. We further derive the pinning strategy under noise, by which the ZD strategy player coercively sets the opponent's expected payoff to his desired level, although his payoff control ability declines with the increase of noise strength. Due to the uncertainty caused by noise, the ZD strategy player cannot ensure his payoff to be permanently higher than the opponent's, which implies dominant extortions do not exist even under low noise. While we show that the ZD strategy player can still establish a novel kind of extortions, named contingent extortions, where any increase of his own payoff always exceeds that of the opponent's by a fixed percentage, and the conditions under which the contingent extortions can be realized are more stringent as the noise becomes stronger.

In this paper we analyze the second-order Kuramoto model in the presence of a positive correlation between the heterogeneity of the connections and the natural frequencies in scale-free networks. We numerically show that discontinuous transitions emerge not just in disassortative but also in strongly assortative networks, in contrast with the first-order model. We also find that the effect of assortativity on network synchronization can be compensated by adjusting the phase damping. Our results show that it is possible to control collective behavior of damped Kuramoto oscillators by tuning the network structure or by adjusting the dissipation related to the phases' movement.

We study the synchronization of a stochastically driven, current-based, integrate-and-fire neuronal model on a preferential-attachment network with scale-free characteristics and high clustering. The synchrony is induced by cascading total firing events where every neuron in the network fires at the same instant of time. We show that in the regime where the system remains in this highly synchronous state, the firing rate of the network is completely independent of the synaptic coupling, and depends solely on the external drive. On the other hand, the ability for the network to maintain synchrony depends on a balance between the fluctuations of the external input and the synaptic coupling strength. In order to accurately predict the probability of repeated cascading total firing events, we go beyond mean-field and treelike approximations and conduct a detailed second-order calculation taking into account local clustering. Our explicit analytical results are shown to give excellent agreement with direct numerical simulations for the particular preferential-attachment network model investigated.

We analyze the replicator-mutator equations for the rock-paper-scissors game. Various graph-theoretic patterns of mutation are considered, ranging from a single unidirectional mutation pathway between two of the species, to global bidirectional mutation among all the species. Our main result is that the coexistence state, in which all three species exist in equilibrium, can be destabilized by arbitrarily small mutation rates. After it loses stability, the coexistence state gives birth to a stable limit cycle solution created in a supercritical Hopf bifurcation. This attracting periodic solution exists for all the mutation patterns considered, and persists arbitrarily close to the limit of zero mutation rate and a zero-sum game.

We consider the regime of fully developed isotropic and homogeneous turbulence of the Navier-Stokes equation with a stochastic forcing. We present two gauge symmetries of the corresponding Navier-Stokes field theory and derive the associated general Ward identities. Furthermore, by introducing a local source bilinear in the velocity field, we show that these symmetries entail an infinite set of exact and local relations between correlation functions. They include in particular the Kármán-Howarth relation and another exact relation for a pressure-velocity correlation function recently derived in G. Falkovich, I. Fouxon, and Y. Oz [J. Fluid Mech. 644, 465 (2010)] that we further generalize.

We present numerical simulations of the different two-dimensional flow regimes generated by a constant spatially periodic forcing balanced by viscous dissipation and large-scale drag with a dimensionless damping rate $1/\mathrm{Rh}$. The linear response to the forcing is a $6\times 6$ square array of counterrotating vortices, which is stable when the Reynolds number $\mathrm{Re}$ or $\mathrm{Rh}$ are small. After identifying the sequence of bifurcations that lead to a spatially and temporally chaotic regime of the flow when $\mathrm{Re}$ and $\mathrm{Rh}$ are increased, we study the transitions between the different turbulent regimes observed for large $\mathrm{Re}$ by varying $\mathrm{Rh}$. A large-scale circulation at the box size (the condensate state) is the dominant mode in the limit of vanishing large-scale drag $(\mathrm{Rh}$ large). When $\mathrm{Rh}$ is decreased, the condensate becomes unstable and a regime with random reversals between two large-scale circulations of opposite signs is generated. It involves a bimodal probability density function of the large-scale velocity that continuously bifurcates to a Gaussian distribution when $\mathrm{Rh}$ is decreased further.

The present work discusses the implications of wall wettability and inclination of the surface on droplet dynamics. In this work, mesoscopic illustration of droplet dynamics in a duct with different inclination angles, based on the two-phase lattice Boltzmann model, is reported. Temporal evolution of wetted length, wetted area, and maximum height of the droplet for surfaces with different inclination angles and wettabilities is furnished in detail in order to elucidate the droplet displacement dynamics. It has been observed that the effect of inclination of the surface on droplet dynamics is more pronounced on a hydrophobic surface as compared to a hydrophilic surface. The time evolution of height and contact line motion of the droplet shows that higher angle of inclination of substrate affects the dynamics strongly irrespective of wettability.

Permeability of porous materials is an important characteristic which is extensively used in various engineering disciplines. There are a number of issues that influence the permeability coefficient among which the porosity, size of particles, pore shape, tortuosity, and particle size distribution are of great importance. In this paper a C++ GPU code based on three-dimensional lattice Boltzmann method (LBM) has been developed and used for investigating the effects of the above mentioned factors on the permeability coefficient of granular materials. Multirelaxation time collision scheme of the LBM equations is used in the simulator, which is capable of modeling the exact position of the fluid-solid interface leading to viscosity-independent permeabilities and better computational stability due to separation of the relaxations of various kinetic models. GPU-CPU parallel processing has been employed to reduce the computational time associated with three-dimensional simulations. Soil samples have been prepared using the discrete element method. The obtained results have demonstrated the importance of employing the concept of effective porosity instead of total porosity in permeability relationships. The results also show that a threshold porosity exists below which the connectivity of the pores vanishes and the permeability of the soils reduces drastically.

Modeling physical data with linear discrete-time series, namely, the autoregressive fractionally integrated moving average (ARFIMA) model, is a technique that has attracted attention in recent years. However, this model is used mainly as a statistical tool only, with weak emphasis on the physical background of the model. The main reason for this lack of attention is that the ARFIMA model describes discrete-time measurements, whereas physical models are formulated using continuous-time parameters. In order to eliminate this discrepancy, we show that time series of this type can be regarded as sampled trajectories of the coordinates governed by a system of linear stochastic differential equations with constant coefficients. The observed correspondence provides formulas linking ARFIMA parameters and the coefficients of the underlying physical stochastic system, thus providing a bridge between continuous-time linear dynamical systems and ARFIMA models.

Macroscopic systems with dissipation and time-modulated injection of energy, parametrically driven systems, can self-organize into localized states and/or patterns. We investigate a pulse that travels over a one-dimensional pattern in parametrically driven systems. Based on a minimal prototype model, we show that the pulses emerge through a subcritical Andronov-Hopf bifurcation of the underlying pattern. We describe a simple physical system, a magnetic wire forced with a transverse oscillatory magnetic field, which displays these traveling pulses.

We investigate the critical behavior of three-dimensional antiferromagnetic ${\text{CP}}^{N-1}$ $\left({\text{ACP}}^{N-1}\right)$ models in cubic lattices, which are characterized by a global $\text{U}\left(N\right)$ symmetry and a local U(1) gauge symmetry. Assuming that critical fluctuations are associated with a staggered gauge-invariant (Hermitian traceless matrix) order parameter, we determine the corresponding Landau-Ginzburg-Wilson (LGW) model. For $N=3$ this mapping allows us to conclude that the three-component ${\text{ACP}}^2$ model undergoes a continuous transition that belongs to the O(8) vector universality class, with an effective enlargement of the symmetry at the critical point. This prediction is confirmed by numerical analyses of the finite-size scaling behaviors of the ${\text{ACP}}^2$ and the O(8) vector models, which show the same universal features at their transitions. We also present a renormalization-group (RG) analysis of the LGW theories for $N\ge 4$. We compute perturbative series in two different renormalization schemes and analyze the corresponding RG flow. We do not find stable fixed points that can be associated with continuous transitions.

We explore fluctuation relations in a periodically driven micromechanical torsional oscillator. In the linear regime where the modulation is weak, we verify that the ratio of the work variance to the mean work is constant, consistent with conventional fluctuation theorems. We then increase the amplitude of the periodic drive so that the response becomes nonlinear and two nonequilibrium oscillation states coexist. Due to interstate transitions, the work variance exhibits a peak at the driving frequency at which the occupation of the two states is equal. Moreover, the work fluctuations depend exponentially on the inverse noise intensity. Our data are consistent with recent theories on systems driven into bistability that predict generic behaviors different from conventional fluctuation theorems.

The glass transition of mesoscopic charged particles in two-dimensional confinement is studied by mode-coupling theory. We consider two types of effective interactions between the particles, corresponding to two different models for the distribution of surrounding ions that are integrated out in coarse-grained descriptions. In the first model, a planar monolayer of charged particles is immersed in an unbounded isotropic bath of ions, giving rise to an isotropically screened Debye-Hückel (Yukawa)-type effective interaction. The second, experimentally more relevant system is a monolayer of negatively charged particles that levitate atop a flat horizontal electrode, as frequently encountered in laboratory experiments with complex (dusty) plasmas. A steady plasma current toward the electrode gives rise to an anisotropic effective interaction potential between the particles, with an algebraically long-ranged in-plane decay. In a comprehensive parameter scan that covers the typical range of experimentally accessible plasma conditions, we calculate and compare the mode-coupling predictions for the glass transition in both kinds of systems.

We model long-range correlations of nucleotides in the human DNA sequence using the long-range one-dimensional (1D) Ising model. We show that, for distances between ${10}^3$ and ${10}^6$ bp, the correlations show a universal behavior and may be described by the non-mean-field limit of the long-range 1D Ising model. This allows us to make some testable hypothesis on the nature of the interaction between distant portions of the DNA chain which led to the DNA structure that we observe today in higher eukaryotes.