We report studies on the rheological properties of a liquid crystalline analog of Abrikosov phase in type-II superconductors known as twist-grain-boundary-$A$ (${\mathrm{TGB}}_A$) phase. The ${\mathrm{TGB}}_A$ phase shows a large apparent yield stress compared to the cholesteric (${\mathrm{N}}^{*}$) phase. The storage modulus ($G^{{}^{\prime }}$) of the ${\mathrm{TGB}}_A$ phase is significantly larger than the loss modulus ($G^{{}^{\prime \prime }}$). The dynamic relaxation measurements indicate a solid-like behavior of ${\mathrm{N}}^{*}$, ${\mathrm{TGB}}_A$, and smectic-$C$${}^{*}$ phases. The complex shear modulus of the ${\mathrm{TGB}}_A$ phase exhibits a power-law behavior $G^{*}$($\omega$) $\sim$ ${\omega }^{\alpha }$ with $\alpha \simeq 0.5$. The relative amplitude of $G^{{}^{\prime }}$ and $G^{{}^{\prime \prime }}$ at various temperatures indicate that the enhanced elasticity of ${\mathrm{TGB}}_A$ phase is due to the structural defects.

Repeating patterns of spike sequences from a neuronal network have been proposed to be useful in the reconstruction of the network topology. Reverberations in a physiologically realistic model with various physical connection topologies (from random to scale free) have been simulated to study the effectiveness of the pattern-matching method in the reconstruction of network topology from network dynamics. Simulation results show that functional networks reconstructed from repeating spike patterns can be quite different from the original physical networks; even global properties, such as the degree distribution, cannot always be recovered. However, the pattern-matching method can be effective in identifying hubs in the network. Since the form of reverberations is quite different for networks with and without hubs, the form of reverberations together with the reconstruction by repeating spike patterns might provide a reliable method to detect hubs in neuronal cultures.

To control infection spreading on networks, we investigate the effect of observer nodes that recognize infection in a neighboring node and make the rest of the neighbor nodes immune. We numerically show that random placement of observer nodes works better on networks with clustering than on locally treelike networks, implying that our model is promising for realistic social networks. The efficiency of several heuristic schemes for observer placement is also examined for synthetic and empirical networks. In parallel with numerical simulations of epidemic dynamics, we also show that the effect of observer placement can be assessed by the size of the largest connected component of networks remaining after removing observer nodes and links between their neighboring nodes.

Velocity correlations are measured in a dusty plasma with only two microparticles. These correlations allow a characterization of the oscillatory modes and an identification of the effects of ion wakes. Ion wake effects are isolated by comparing two experiments with the microparticles aligned parallel vs perpendicular to the ion flow. From records of microparticle velocities, the one- and two-particle distribution functions $f_1$ and $f_2$ are obtained, and the two-particle correlation function $g_2\equiv f_2-f_1{f}_1$ is calculated. Comparing the two experiments, we find that motion is much more correlated when the microparticles are aligned with the ion flow and the character of the oscillatory modes depends on the ion flow direction due to the ion wake.

We explore spatially localized solitonic configurations of a director field, generated using optical realignment and laser-induced heating, in frustrated chiral nematic liquid crystals confined between substrates with perpendicular surface anchoring. We demonstrate that, in addition to recently studied torons and Hopf-fibration solitonic structures (hopfions), one can generate a host of other axially symmetric stable and metastable director field configurations where local twist is matched to the surface boundary conditions through introduction of point defects and loops of singular and nonsingular disclinations. The experimentally demonstrated structures include the so-called “baby-skyrmions” in the form of double twist cylinders oriented perpendicular to the confining substrates where their double twist field configuration is matched to the perpendicular boundary conditions by loops of twist disclinations. We also generate complex textures with arbitrarily large skyrmion numbers. A simple back-of-the-envelope theoretical analysis based on free energy considerations and the nonpolar nature of chiral nematics provides insights into the long-term stability and diversity of these inter-related solitonic field configurations, including different types of torons, cholestric-finger loops, two-dimensional skyrmions, and more complex structures comprised of torons, hopfions, and various disclination loops that are experimentally observed in a confinement-frustrated chiral nematic system.

Bipartite networks are a common type of network data in which there are two types of vertices, and only vertices of different types can be connected. While bipartite networks exhibit community structure like their unipartite counterparts, existing approaches to bipartite community detection have drawbacks, including implicit parameter choices, loss of information through one-mode projections, and lack of interpretability. Here we solve the community detection problem for bipartite networks by formulating a bipartite stochastic block model, which explicitly includes vertex type information and may be trivially extended to $k$-partite networks. This bipartite stochastic block model yields a projection-free and statistically principled method for community detection that makes clear assumptions and parameter choices and yields interpretable results. We demonstrate this model's ability to efficiently and accurately find community structure in synthetic bipartite networks with known structure and in real-world bipartite networks with unknown structure, and we characterize its performance in practical contexts.

In network science, assortativity refers to the tendency of links to exist between nodes with similar attributes. In social networks, for example, links tend to exist between individuals of similar age, nationality, location, race, income, educational level, religious belief, and language. Thus, various attributes jointly affect the network topology. An interesting problem is to detect community structure beyond some specific assortativity-related attributes $\rho$, i.e., to take out the effect of $\rho$ on network topology and reveal the hidden community structures which are due to other attributes. An approach to this problem is to redefine the null model of the modularity measure, so as to simulate the effect of $\rho$ on network topology. However, a challenge is that we do not know to what extent the network topology is affected by $\rho$ and by other attributes. In this paper, we propose a distance modularity, which allows us to freely choose any suitable function to simulate the effect of $\rho$. Such freedom can help us probe the effect of $\rho$ and detect the hidden communities which are due to other attributes. We test the effectiveness of distance modularity on synthetic benchmarks and two real-world networks.

Many physical, chemical, and biological systems can be modeled by means of random-frequency harmonic oscillator systems. Even though the noise-free evolution of harmonic oscillator systems can be easily implemented, the way to experimentally introduce, and control, noise effects due to a surrounding environment remains a subject of lively interest. Here, we experimentally demonstrate a setup that provides a unique tool to generate a fully tunable environment for classical electrical oscillator systems. We illustrate the operation of the setup by implementing the case of a damped random-frequency harmonic oscillator. The high degree of tunability and control of our scheme is demonstrated by gradually modifying the statistics of the oscillator's frequency fluctuations. This tunable system can readily be used to experimentally study interesting noise effects, such as noise-induced transitions in systems driven by multiplicative noise, and noise-induced transport, a phenomenon that takes place in quantum and classical coupled oscillator networks.

We show that the presence of a driven bond in an otherwise diffusive lattice gas with simple exclusion interaction results in long-range density-density correlation in its stationary state. In dimensions $d>1$ we show that in the thermodynamic limit this correlation decays as $C(\mathbf{r},\mathbf{s})\sim {(r^2+s^2)}^{-d}$ at large distances $r$ and $s$ away from the drive with $|\mathbf{r}-\mathbf{s}|\gg 1$. This is derived using an electrostatic analogy whereby $C(\mathbf{r},\mathbf{s})$ is expressed as the potential due to a configuration of electrostatic charges distributed in $2d$ dimension. At bulk density $\rho =1/2$ we show that the potential is that of a localized quadrupolar charge. At other densities the same is correct in leading order in the strength of the drive and it is argued numerically to be valid at higher orders.

We investigate pressure-driven motion of liquid-liquid menisci in circular tubes, for systems in pseudopartial wetting conditions. The originality of this type of wetting lies in the coexistence of a macroscopic contact angle with a wetting liquid film covering the solid surface. Focusing on small capillary numbers, we report observations of an apparent contact angle hysteresis at first sight similar to the standard partial wetting case. However, this apparent hysteresis exhibits original features. We observe very long transient regimes before steady state, up to several hundreds of seconds. Furthermore, in steady state, the velocities are nonzero, meaning that the contact line is not strongly pinned to the surface defects, but are very small. The velocity of the contact line tends to vanish near the equilibrium contact angle. These observations are consistent with the thermally activated depinning theory that has been proposed to describe partial wetting systems on disordered substrates and suggest that a single physical mechanism controls both the hysteresis (or the pinning) and the motion of the contact line. The proposed analysis leads to the conclusion that the depinning activated energy is lower with pseudopartial wetting systems than with partial wetting ones, allowing the direct observation of the thermally activated motion of the contact line.

We present a dynamically equivalent transformation between time series and complex networks based on coarse geometry theory. In terms of quasi-isometric maps, we characterize how the underlying geometrical characters of complex systems are preserved during transformations. Fractal dimensions are shown to be the same for time series (or complex network) and its transformed counterpart. Results from the Rössler system, fractional Brownian motion, synthetic networks, and real networks support our findings. This work gives theoretical evidences for an equivalent transformation between time series and networks.

The evolution of surface water waves in finite depth under wind forcing is reduced to an antidissipative Korteweg–de Vries–Burgers equation. We exhibit its solitary wave solution. Antidissipation accelerates and increases the amplitude of the solitary wave and leads to blow-up and breaking. Blow-up occurs in finite time for infinitely large asymptotic space so it is a nonlinear, dispersive, and antidissipative equivalent of the linear instability which occurs for infinite time. Due to antidissipation two given arbitrary and adjacent planes of constant phases of the solitary wave acquire different velocities and accelerations inducing breaking. Soliton breaking occurs in finite space in a time prior to the blow-up. We show that the theoretical growth in amplitude and the time of breaking are both testable in an existing experimental facility.

In this work, we investigate the balance between the nonlinear and linear interaction energy of an interparticle anharmonic system in the vicinity of the ground state condensate. As a result, we find that the nonlinear interaction energy is very significant in the vicinity of each degree of freedom. We address some potential applications of the findings to miscellaneous areas of interests such as soliton theory, hydrodynamics, solid state physics, ferromagnetic and ferroelectric domain walls, condensed matter physics, and particle physics, among others.

We demonstrate diffusing-wave spectroscopy (DWS) in a localized region of a viscoelastically inhomogeneous object by measurement of the intensity autocorrelation $[g_2\left(\tau \right)]$ that captures only the decay introduced by the temperature-induced Brownian motion in the region. The region is roughly specified by the focal volume of an ultrasound transducer which introduces region specific mechanical vibration owing to insonification. Essential characteristics of the localized non-Markovian dynamics are contained in the decay of the modulation depth $\left[M\right(\tau )]$, introduced by the ultrasound forcing in the focal volume selected, on $g_2\left(\tau \right)$. The modulation depth $M\left({\tau }_i\right)$ at any delay time ${\tau }_i$ can be measured by short-time Fourier transform of $g_2\left(\tau \right)$ and measurement of the magnitude of the spectrum at the ultrasound drive frequency. By following the established theoretical framework of DWS, we are able to connect the decay in $M\left(\tau \right)$ to the mean-squared displacement (MSD) of scattering centers and the MSD to $G^{*}\left(\omega \right)$, the complex viscoelastic spectrum. A two-region composite polyvinyl alcohol phantom with different viscoelastic properties is selected for demonstrating local DWS-based recovery of $G^{*}\left(\omega \right)$ corresponding to these regions from the measured region specific $M\left({\tau }_i\right)$vs${\tau }_i$. The ultrasound-assisted measurement of MSD is verified by simulating, using a generalized Langevin equation (GLE), the dynamics of the particles in the region selected as well as by the usual DWS experiment without the ultrasound. It is shown that whereas the MSD obtained by solving the GLE without the ultrasound forcing agreed with its experimental counterpart covering small and large values of $\tau$, the match was good only in the initial transients in regard to experimental measurements with ultrasound.

We investigate the nonlinearity of a liquid crystal cell doped with gold nanoparticles by considering their selective absorption. Such nonlinearities are promising for optical processing applications and optical limiters. Systems displaying thermal nonlinearities are particularly attractive as the maximum nonlinearity may occur in the absence of an applied field and additionally this nonlinearity can be controlled by the reorientation of the liquid crystal. We show that there exists a theoretical optimum concentration of absorbers, which maximizes the nonlinearity. Further we show that the nonlinearity of the system can be tuned by the reorientation of the liquid crystal host, with the nonlinearity decreasing from $9\times 10{}^{-5}$ ${\mathrm{cm}}^2{\mathrm{W}}^{-1}$ to zero by the application of a magnetic field of the order of 0.01 Tesla. This allows a fine control of the diffraction efficiency and, in principle, many other nonlinear effects.

In a system of interdependent networks, an initial failure of nodes invokes a cascade of iterative failures that may lead to a total collapse of the whole system in the form of an abrupt first-order transition. When the fraction of initial failed nodes $1-p$ reaches criticality $p=p_c$, the abrupt collapse occurs by spontaneous cascading failures. At this stage, the giant component decreases slowly in a plateau form and the number of iterations in the cascade $\tau$ diverges. The origin of this plateau and its increasing with the size of the system have been unclear. Here we find that, simultaneously with the abrupt first-order transition, a spontaneous second-order percolation occurs during the cascade of iterative failures. This sheds light on the origin of the plateau and how its length scales with the size of the system. Understanding the critical nature of the dynamical process of cascading failures may be useful for designing strategies for preventing and mitigating catastrophic collapses.

The dynamics in a variant of globally coupled Sakaguchi-Kuramoto phase oscillators is studied. The model consists of two subpopulations, each with a different phase lag and interaction strength. Using Ott-Antonson ansatz, we analyze the dynamics in the model and present the numerical results. There exist stationary synchronous states which are generalized $\pi$ states and two types of traveling wave states. We find that the traveling wave states are the dominant dynamics in comparison with the stationary states. Particularly, we find that the stationary and traveling wave states can be smoothly connected through the properly chosen parameter paths.

We study the chaotic motion of a small rigid sphere, lighter than the fluid in a three-dimensional vortex of finite height. Based on the results of Eulerian and Lagrangian measurements, a sequence of models is set up. The time-independent model is a generalization of the Burgers vortex. In this case, there are two types of attractors for the particle: a fixed point on the vortex axis and a limit cycle around the vortex axis. Time dependence might combine these regular attractors into a single chaotic attractor, however its robustness is much weaker than what the experiments suggest. To construct an aperiodically time-dependent advection dynamics in a simple way, Gaussian noise is added to the particle velocity in the numerical simulation. With an appropriate choice of the noise properties, mimicking the effect of local turbulence, a reasonable agreement with the experimentally observed particle statistics is found.

We delineate the contact line dynamics of two immiscible fluids in a medium having spatially periodic porous structures. The flow is driven by an external applied pressure gradient. We bring out the combined consequences of the solid fraction distribution and the substrate wettability on the resulting dynamics of the contact line, by employing phase-field formalism. We capture the sequence of spatiotemporal events leading to formation of liquid bridges by trapping a small amount of displaced phase fluid between two consecutive porous blocks, as dictated by the combinations of substrate wettability and solid fraction. We also demonstrate the existence of a regime of complete interfacial recovery, depending on the parametric space of the governing parameters under concern. Our results essentially demonstrate the intricate mechanisms by virtue of which the wettabilities of the substrates alter the dynamical evolutions of interfaces and the subsequent shapes and sizes of the adsorbed dispersed phases, bearing far-ranging consequences in several practical applications ranging from oil recovery to groundwater flow.

A numerical study of dynamos in rotating convecting plane layers is presented which focuses on magnetic energies and dissipation rates and the generation of mean fields (where the mean is taken over horizontal planes). The scaling of the magnetic energy with the flux Rayleigh number is different from the scaling proposed in spherical shells, whereas the same dependence of the magnetic dissipation length on the magnetic Reynolds number is found for the two geometries. Dynamos both with and without mean field exist in rapidly rotating convecting plane layers.