A rich variety of responsive behavior occurs in complex structured fluids due to their lower symmetries. On the other hand, fluid disorder tends to increase the symmetry of liquid crystal mesophases. Here, we report direct evidence for the existence of a mesophase with $C_S$ symmetry. The observations are based on optical studies of director inversion walls in freely suspended films in electric fields under obliquely incident light. This phase is distinguished by the polarization lying in the molecular tilt plane in freely suspended films. Such a low-symmetry polar fluid phase has been long predicted to occur in bent-core liquid crystals. The stability of this phase is attributed to the bent shape of the mesogens and dominating dispersion interactions.

Long-scale dynamic fluctuation phenomena in freely suspended films is analyzed. We consider isotropic films that, say, can be pulled from bulk smectic-$A$ liquid crystals. The key feature of such objects is possibility of bending deformations of the film. The bending (also known as flexular) mode turns out to be anomalously weakly attenuated. In the harmonic approximation there is no viscous-like damping of the bending mode, proportional to $q^2$ $(q$ is the wave vector of the mode), since it is forbidden by the rotational symmetry. Therefore, the bending mode is strongly affected by nonlinear dynamic fluctuation effects. We calculate the dominant fluctuation contributions to the damping of the bending mode due to its coupling to the inplane viscous mode, which restores the viscous-like $q^2$ damping of the bending mode. Our calculations are performed in the framework of the perturbation theory where the coupling of the modes is assumed to be small, then the bending mode damping is relatively weak. We discuss our results in the context of existing experiments and numeric simulations of the freely suspended films and propose possible experimental observations of our predictions.

We report a mechanism of pattern formation in growing bistable systems coupled indirectly. A modified Fujita et al. model is studied as an example of a reaction-diffusion system of nondiffusive activator and inhibitor molecules immersed in the medium of a fast diffusive agent. Here we show that, as the system grows, a new domain nucleates spontaneously in the area where the local level of the agent becomes critical. Newly nucleated domains are stable and the pattern formation is different from Turing's mechanism in monostable systems. Domains are spatially confined by the agent even if the activator and inhibitor molecules diffuse. With the spatial extension of the system, a larger domain may undergo a wave number instability, and the concentrations of active molecules within the neighboring elements of a domain can become sharply different. The mechanism reported in this work could be generic for pattern formation systems involving multistability, growth, and indirect coupling.

Modeling long-range epidemic spreading in a random environment, we consider a quenched, disordered, $d$-dimensional contact process with infection rates decaying with distance as $1/r^{d+\sigma }$. We study the dynamical behavior of the model at and below the epidemic threshold by a variant of the strong-disorder renormalization-group method and by Monte Carlo simulations in one and two spatial dimensions. Starting from a single infected site, the average survival probability is found to decay as $P\left(t\right)\sim t^{-d/z}$ up to multiplicative logarithmic corrections. Below the epidemic threshold, a Griffiths phase emerges, where the dynamical exponent $z$ varies continuously with the control parameter and tends to $z_c=d+\sigma$ as the threshold is approached. At the threshold, the spatial extension of the infected cluster (in surviving trials) is found to grow as $R\left(t\right)\sim t^{1/z_c}$ with a multiplicative logarithmic correction and the average number of infected sites in surviving trials is found to increase as $N_s\left(t\right)\sim {(lnt)}^{\chi }$ with $\chi =2$ in one dimension.

In this paper, a nutrient-phytoplankton system described by a couple of advection-diffusion-reaction equations with delay was studied analytically and numerically. The aim of this research was to provide an understanding of the impact of delay on instability. Significantly, delay cannot only induce instability, but can also promote the formation of spatial pattern via a Turing-like instability. In addition, the theoretical analysis indicates that the flow (advection term) may lead to instability when the delay term exists. By comparison, diffusion cannot result in Turing instability when flow does not exist. Results of numerical simulation were consistent with the analytical results.

Three-dimensional excitable systems can self-organize vortex patterns that rotate around one-dimensional phase singularities called filaments. In experiments with the Belousov-Zhabotinsky reaction and numerical simulations, we pin these scroll waves to translating inert cylinders and demonstrate the controlled repositioning of their rotation centers. If the pinning site extends only along a portion of the filament, the phase singularity is stretched out along the trajectory of the heterogeneity, which effectively writes the singularity into the system. Its trailing end point follows the heterogeneity with a lower velocity. This velocity, its dependence on the placement of the anchor, and the shape of the filament are explained by a curvature flow model.

During thermocapillary transport of a confined long bubble, we unveil the existence of a contrary-to-the-conventional disjoining-pressure-dominant scaling regime characterizing the dynamics of the thin liquid film engulfed between the bubble interface and the channel surface. Such a regime is realized for the limitingly small magnitude of the Marangoni stress (surface tension gradient) when the separating liquid region reaches an ultrathin dimension. Over this regime, we witness a severe breakdown of the seemingly intuitive scaling arguments based on the balance of viscous and capillary forces. Starting from competent balance criteria, we uncover the characteristic length scales involved, leading towards obtaining the new consistent scaling laws of the disjoining-pressure-dominant regime, in a simple closed form analytical fashion. Our scaling estimations are substantiated by full-scale numerical simulations of the pertinent thin-film equations. These new scaling laws appear to be convenient for implementing as a fundamental design basis for multiphase microfluidic systems.

We investigate water infiltration pressure for hydrophobic nanochannels through molecular dynamics simulations. It is found that the entrance energy barrier significantly raises the infiltration pressure, which makes the classic Young-Laplace equation invalid for nanochannels. As the channel surface is tuned from superhydrophobic to hydrophobic, the infiltration pressure is greatly reduced mainly due to the decrease of the capillary pressure (Young-Laplace equation) caused by the contact angle change, while the contribution of the entrance energy barrier to the infiltration pressure, which is termed entrance barrier pressure, increases from 25% to 60%.

We have combined the average-atom model with the hypernetted chain approximation (AAHNC) to describe the electronic and ionic structure in the warm dense matter regime. On the basis of the electronic and ionic structures, the x-ray Thomson scattering (XRTS) spectrum is calculated using the random-phase approximation. While the electronic structure is described within the average-atom model, the effects of other ions on the electronic structure are considered using an integral equation method of the theory of liquids, namely the hypernetted chain approximation. The ion-ion pair potential is calculated using the modified Gordon-Kim model based on the electronic density distribution. Finally, the electronic and ionic structures are determined self-consistently. The XRTS spectrum is calculated according to the Chihara formula, where the scattering contributions are divided into three components: elastic, bound-free, and free-free. Comparison of the present AAHNC results with other theoretical models and experimental data shows very good agreement. Thus the AAHNC model can give a reasonable description of the electronic and ionic structure in warm dense matter.

We study wave propagation in a chain of spherical particles containing a local resonator. The resonant particles are made of an aluminum outer spherical shell and a steel inner mass connected by a polymeric plastic structure acting as a spring. We characterize the dynamic response of individual particles and the transmitted linear spectra of a chain of particles in contact. A wide band gap is observed both in theoretical and experimental results. We show the ability to tune the acoustic transmission by varying the contact interaction between particles. Higher driving amplitude leads to the generation of nonlinearities both in the response of a single particle and that of the whole chain. For a single resonant particle, we observe experimentally a resonant frequency downshift, which follows a complex nonlinear behavior. In the chain of particles, nonlinearity leads to the generation of nonlinear harmonics and the presence of localized modes inside the band gap.

This paper is a continuation of our work on the development of multiscale numerical scheme from low-speed isothermal flow to compressible flows at high Mach numbers. In our earlier work [Z. L. Guo et al., Phys. Rev. E 88, 033305 (2013)], a discrete unified gas kinetic scheme (DUGKS) was developed for low-speed flows in which the Mach number is small so that the flow is nearly incompressible. In the current work, we extend the scheme to compressible flows with the inclusion of thermal effect and shock discontinuity based on the gas kinetic Shakhov model. This method is an explicit finite-volume scheme with the coupling of particle transport and collision in the flux evaluation at a cell interface. As a result, the time step of the method is not limited by the particle collision time. With the variation of the ratio between the time step and particle collision time, the scheme is an asymptotic preserving (AP) method, where both the Chapman-Enskog expansion for the Navier-Stokes solution in the continuum regime and the free transport mechanism in the rarefied limit can be precisely recovered with a second-order accuracy in both space and time. The DUGKS is an idealized multiscale method for all Knudsen number flow simulations. A number of numerical tests, including the shock structure problem, the Sod tube problem in a whole range of degree of rarefaction, and the two-dimensional Riemann problem in both continuum and rarefied regimes, are performed to validate the scheme. Comparisons with the results of direct simulation Monte Carlo (DSMC) and other benchmark data demonstrate that the DUGKS is a reliable and efficient method for multiscale flow problems.

The strong turbulence suppression, mainly for large-scale modes, of two-dimensional self-propelling rods, by increasing the long-range coupling strength $\Gamma$ of low-concentration passive particles, is numerically demonstrated. It is found that large-scale collective rod motion in forms of swirls or jets is mainly contributed from well-aligned dense patches, which can push small poorly aligned rod patches and uncoupled passive particles. The more efficient momentum transfer and dissipation through increasing passive particle coupling leads to the formation of a more ordered and slowed down network of passive particles, which competes with coherent dense active rod clusters. The frustration of active rod alignment ordering and coherent motion by the passive particle network, which interrupt the inverse cascading of forming large-scale swirls, is the key for suppressing collective rod motion with scales beyond the interpassive distance, even in the liquid phase of passive particles. The loosely packed active rods are weakly affected by increasing passive particle coupling due to the weak rod-particle interaction. They mainly contribute to the small-scale modes and high-speed motion.

Based on the availability of an invariant manifold, we develop a model-reduction procedure that preserves thermodynamic structure. More concretely, we construct the Poisson and irreversible brackets of the general equation for the nonequilibrium reversible-irreversible coupling of nonequilibrium thermodynamics by means of the ideas originally introduced for handling constraints. The general ideas are then applied to the Kramers problem, that is, the description of transitions between two potential wells separated by a high barrier. This example reveals how a fortuitous cancellation mechanism that allows a logarithmic entropy to generate a linear diffusion equation is inherited by a master equation resulting from model reduction.

Glass-forming liquids exhibit a dramatic dynamical slowdown as the temperature is lowered. This can be attributed to relaxation proceeding via large structural rearrangements whose characteristic size increases as the system cools. These cooperative rearrangements are well modeled by instantons in a replica effective field theory, with the size of the dominant instanton encoding the liquid's cavity point-to-set correlation length. Varying the parameters of the effective theory corresponds to varying the statistics of the underlying free-energy landscape. We demonstrate that, for a wide range of parameters, replica-symmetry-breaking instantons dominate. The detailed structure of the dominant instanton provides a rich window into point-to-set correlations and glassy dynamics.

We examine the dynamic phase transition properties of ferromagnetic uniaxial nanowires with tunable radius $r$ in the presence of both oscillating and biased magnetic fields. Variation of the transition temperature as a function of amplitude $h_0$ of the oscillating field has been analyzed in the absence of magnetic bias $h_b$ and at constant oscillation period $P$. We find that the transition temperature as a function of $h_0$ exhibits an exponential decay behavior. We also investigate the magnetization dynamics in terms of magnetic hysteresis loops as functions of the parameters $h_b,h_0$, and $P$. Our calculations are qualitatively in agreement with the recent experimental results obtained for uniaxial cobalt films in which it was concluded that the bias field $h_b$ is the conjugate field of the dynamic order parameter.

We investigate the steady-state packing fraction $\varphi$ and force moment tensor $\Sigma$ of quasi-two-dimensional granular columns subjected to tapping. Systems of different height $h$ and width $L$ are considered. We find that $\varphi$ and $\Sigma$, which describe the macroscopic state of the system, are insensitive to $L$ for $L>50d$ (with $d$ the grain diameter). However, results for granular columns of different heights cannot be conciliated. This suggests that comparison between results of different laboratories on this type of experiments can be done only for systems of same height. We show that a parameter $\varepsilon =1+{\left(A\omega \right)}^2/\left(2gh\right)$, with $A$ and $\omega$ the amplitude and frequency of the tap and $g$ the acceleration of gravity, can be defined to characterize the tap intensity. This parameter is based on the effective flight of the granular bed, which takes into account the $h$ dependency. When $\varphi$ is plotted as a function of $\varepsilon$, the data collapses for systems of different $h$. However, this parameter alone is unable to determine the steady state to be reached since different $\Sigma$ can be observed for a given $\varepsilon$ if different column heights are considered.

Adsorption-desorption processes of polydisperse mixtures on a triangular lattice are studied by numerical simulations. Mixtures are composed of the shapes of different numbers of segments and rotational symmetries. Numerical simulations are performed to determine the influence of the number of mixture components and the length of the shapes making the mixture on the kinetics of the deposition process. We find that, above the jamming limit, the time evolution of the total coverage of a mixture can be described by the Mittag-Leffler function $\theta \left(t\right)={\theta }_{\infty }-\Delta \theta E_{\beta }[-{(t/\tau )}^{\beta }]$ for all the mixtures we have examined. Our results show that the equilibrium coverage decreases with the number of components making the mixture and also with the desorption probability, via corresponding stretched exponential laws. For the mixtures of equal-sized objects, we propose a simple formula for predicting the value of the steady-state coverage fraction of a mixture from the values of the steady-state coverage fractions of pure component shapes.

We introduce a formulation for normal mode analyses of globular proteins that significantly improves on an earlier one-parameter formulation [M. M. Tirion, Phys. Rev. Lett. 77, 1905 (1996)] that characterized the slow modes associated with protein data bank structures. Here we develop that empirical potential function that is minimized at the outset to include two features essential to reproduce the eigenspectra and associated density of states in the 0 to $300{\mathrm{cm}}^{-1}$ frequency range, not merely the slow modes. First, introduction of preferred dihedral-angle configurations via use of torsional stiffness constants eliminates anomalous dispersion characteristics due to insufficiently bound surface side chains and helps fix the spectrum thin tail frequencies (100–$300{\mathrm{cm}}^{-1})$. Second, we take into account the atomic identities and the distance of separation of all pairwise interactions, improving the spectrum distribution in the 20 to $300{\mathrm{cm}}^{-1}$ range. With these modifications, not only does the spectrum reproduce that of full atomic potentials, but we obtain stable reliable eigenmodes for the slow modes and over a wide range of frequencies.

Mean-field approximations (MFAs) are frequently used in physics. When a process (such as an epidemic or a synchronization) on a network is approximated by MFA, a major hurdle is the determination of those graphs for which MFA is reasonably accurate. Here, we present an accuracy criterion for Markovian susceptible-infected-susceptible (SIS) epidemics on any network, based on the spectrum of the adjacency and SIS covariance matrix. We evaluate the MFA criterion for the complete and star graphs analytically, and numerically for connected Erdős-Rényi random graphs for small size $N\le 14$. The accuracy of MFA increases with average degree and with $N$. Precise simulations (up to network sizes $N=100$) of the MFA accuracy criterion versus $N$ for the complete graph, star, square lattice, and path graphs lead us to conjecture that the worst MFA accuracy decreases, for large $N$, proportionally to the inverse of the spectral radius of the adjacency matrix of the graph.

We study the synchronization of neuronal networks with dynamical heterogeneity, showing that network structures with the same propensity for synchronization (as quantified by master stability function analysis) may develop dramatically different synchronization properties when heterogeneity is introduced with respect to neuronal excitability type. Specifically, we investigate networks composed of neurons with different types of phase response curves (PRCs), which characterize how oscillating neurons respond to excitatory perturbations. Neurons exhibiting type 1 PRC respond exclusively with phase advances, while neurons exhibiting type 2 PRC respond with either phase delays or phase advances, depending on when the perturbation occurs. We find that Watts-Strogatz small world networks transition to synchronization gradually as the proportion of type 2 neurons increases, whereas scale-free networks may transition gradually or rapidly, depending upon local correlations between node degree and excitability type. Random placement of type 2 neurons results in gradual transition to synchronization, whereas placement of type 2 neurons as hubs leads to a much more rapid transition, showing that type 2 hub cells easily “hijack” neuronal networks to synchronization. These results underscore the fact that the degree of synchronization observed in neuronal networks is determined by a complex interplay between network structure and the dynamical properties of individual neurons, indicating that efforts to recover structural connectivity from dynamical correlations must in general take both factors into account.