The interaction of nanoparticles with surfactants is extensively used in a wide range of applications from enhancing colloidal stability to phase separation processes as well as in the synthesis of noble functional materials. The interaction is highly specific depending on the charged nature of the surfactant. In the case of nonionic surfactants, the micelles adsorb on the surface of nanoparticles. The adsorption of nonionic surfactant C12E10 as a function of surfactant concentration for two different sizes of anionic silica nanoparticles (16 and 27 nm) has been examined using dynamic light scattering (DLS) and small-angle neutron scattering (SANS). SANS measurements have been carried out under different contrast-matched conditions, where nanoparticles, as well as surfactant micelles, have been contrast-matched to the solvent. The adsorption of micelles is determined from the contrast-matched condition of silica nanoparticles with the solvent. SANS data under surfactant contrast-matched condition suggest that there is no modification in the structure and/or interaction of the silica nanoparticles in presence of nonionic micelles. The adsorption of micelles on nanoparticles is found to follow an exponential behavior with respect to the surfactant concentration. These results are consistent with the variation of hydrodynamic size of nanoparticle-surfactant system in DLS. The study on different-sized nanoparticles shows that the lower curvature enhances the packing fraction whereas the loss of surface-to-volume ratio suppresses the fraction of adsorbed micelles with the increase in the nanoparticle size. The adsorption coefficient has higher value for the larger size of the nanoparticles. In the mixed system of two sizes of nanoparticles, no preferential selectivity of micelle adsorption is observed.

We introduce a one-dimensional lattice model to study active particles in narrow channel connecting finite reservoirs. The model describes interacting run-and-tumble swimmers exerting pushing forces on neighboring particles, allowing the formation of long active clusters inside the channel. Our model is able to reproduce the emerging oscillatory dynamics observed in full molecular dynamics simulations of self-propelled bacteria [Paoluzzi et al., Phys. Rev. Lett. 115, 188303 (2015)] and allows us to extend in a simple way the analysis to a wide range of system parameters (box length, number of swimmers), taking into account different physical conditions (presence or absence of tumbling, different forms of the entrance probability into the channel). We find that the oscillatory behavior is suppressed for short channels length $L<L^{*}$ and for high tumbling rates $\lambda >{\lambda }^{*}$, with threshold values $L^{*}$ and ${\lambda }^{*}$ which in general depend on physical parameters. Moreover, we find that oscillations persist by using different entrance probabilities, which, however, affect the oscillation properties and the filling dynamics of reservoirs.

We systematically investigate finite-size effects in the dynamic structure factor $S(q,\omega )$ of the uniform electron gas obtained via the analytic continuation of ab initio path integral Monte Carlo data for the imaginary-time density–density correlation function $F(q,\tau )$. Using the recent scheme by Dornheim et al. [Phys. Rev. Lett. 121, 255001 (2018)], we find that the reconstructed spectra are not afflicted with any finite-size effects for as few as $N=14$ electrons both at warm dense matter (WDM) conditions and at the margins of the strongly correlated electron liquid regime. Our results further corroborate the high quality of our current description of the dynamic density response of correlated electrons, which is of high importance for many applications in WDM theory and beyond.

The out-of-time-order correlator (OTOC) has recently become relevant in different areas where it has been linked to scrambling of quantum information and entanglement. It has also been proposed as a good indicator of quantum complexity. In this sense, the OTOC-RE theorem relates the OTOCs summed over a complete basis of operators to the second Renyi entropy. Here we have studied the OTOC-RE correspondence on physically meaningful bases like the ones constructed with the Pauli, reflection, and translation operators. The evolution is given by a paradigmatic bi-partite system consisting of two perturbed and coupled Arnold cat maps with different dynamics. We show that the sum over a small set of relevant operators is enough in order to obtain a very good approximation for the entropy and, hence, to reveal the character of the dynamics. In turn, this provides us with an alternative natural indicator of complexity, i.e., the scaling of the number of relevant operators with time. When represented in phase space, each one of these sets reveals the classical dynamical footprints with different depth according to the chosen basis.

We derive exact analytical expressions for correlation functions of singular values of the product of $M$ Ginibre matrices of size $N$ in the double scaling limit $M,N\to \infty$. The singular value statistics is described by a determinantal point process with a kernel that interpolates between Gaussian unitary ensemble statistic and Dirac-delta (picket-fence) statistic. In the thermodynamic limit $N\to \infty$, the interpolation parameter is given by the limiting quotient $a=N/M$. One of our goals is to find an explicit form of the kernel at the hard edge, in the bulk, and at the soft edge for any $a$. We find that in addition to the standard scaling regimes, there is a transitional regime which interpolates between the hard edge and the bulk. We conjecture that these results are universal, and that they apply to a broad class of products of random matrices from the Gaussian basin of attraction, including correlated matrices. We corroborate this conjecture by numerical simulations. Additionally, we show that the local spectral statistics of the considered random matrix products is identical with the local statistics of Dyson Brownian motion with the initial condition given by equidistant positions, with the crucial difference that this equivalence holds only locally. Finally, we have identified a mesoscopic spectral scale at the soft edge which is crucial for the unfolding of the spectrum.

Researchers have designed many algorithms to measure the distances between graph nodes, such as average hitting times of random walks, cosine distances from DeepWalk, personalized PageRank, etc. Successful though these algorithms are, still they are either underperforming or too time consuming to be applicable to huge graphs that we encounter daily in this big data era. To address these issues, here we propose a faster algorithm based on an improved version of random walks that can beat DeepWalk results with more than 10 times acceleration. The reason for this significant acceleration is that we can derive an analytical formula to calculate the expected hitting times of this random walk quickly. There is only one parameter (the power expansion order) in our algorithm, and the results are robust with respect to its changes. Therefore, we can directly find the optimal solution without fine tuning of model parameters. Our method can be widely used for fraud detection, targeted ads, recommendation systems, topic-sensitive search, etc.

Exact completely closed homogeneous generalized master equations (GMEs) governing the evolution in time of equilibrium two-time correlation functions for dynamic variables of a subsystem of $s$ particles ($s<N$) selected from $N\gg 1$ particles of a classical many-body system are obtained. These time-convolution and time-convolutionless GMEs differ from the known GMEs (e.g., Nakajima-Zwanzig GME) by the absence of inhomogeneous terms containing correlations between all $N$ particles at the initial moment of time and preventing the closed description of $s$-particle subsystem evolution. Closed homogeneous GMEs describing the subdynamics of fluctuations are obtained by applying a special projection operator to the Liouville-type equation governing the dynamics of the correlation function with the related to the Gibbs distribution initial state, which is more natural than the conventional factorized initial state. No common approximation, like the “molecular chaos,” is needed. In the linear approximation in the particles' density, the linear generalized Boltzmann equation accounting for initial correlations and valid at all timescales is obtained. This equation for a weak interparticle interaction converts into the generalized linear Landau equation in which the initial correlations are also accounted for. The connection of these equations to the nonlinear Boltzmann and Landau equations is discussed. The same approach is applicable to studying the kinetics of the conventional reduced $s$-particle distribution functions for a classical $N$-particle system driven from an equilibrium state by an external force.

Extreme or rogue waves are large and unexpected waves appearing with higher probability than predicted by Gaussian statistics. Although their formation is explained by both linear and nonlinear wave propagation, nonlinearity has been considered a necessary ingredient to generate super rogue waves, i.e., an enhanced wave amplification, where the wave amplitudes exceed by far those of ordinary rogue waves. Here we show, experimentally and theoretically, that optical super rogue waves emerge in the simple case of linear light diffraction in one transverse dimension. The underlying physics is a long-range correlation on the random initial phases of the light waves. When subgroups of random phases appear recurrently along the spatial phase distribution, a more ordered phase structure greatly increases the probability of constructive interference to generate super rogue events (non-Gaussian statistics with superlong tails). Our results consist in a significant advance in the understanding of extreme waves formation by linear superposition of random waves, with applications in a large variety of wave systems.

The properties of long, numerically determined periodic orbits of two low-dimensional chaotic systems, the Lorenz equations and the Kuramoto-Sivashinsky system in a minimal-domain configuration, are examined. The primary question is to establish whether the sensitivity of period averaged quantities with respect to parameter perturbations computed over long orbits can be used as a sufficiently good proxy for the response of the chaotic state to finite-amplitude parameter perturbations. To address this question, an inventory of thousands of orbits at least two orders of magnitude longer than the shortest admissible cycles is constructed. The expectation of period averages, Floquet exponents, and sensitivities over such set is then obtained. It is shown that all these quantities converge to a limiting value as the orbit period is increased. However, while period averages and Floquet exponents appear to converge to analogous quantities computed from chaotic trajectories, the limiting value of the sensitivity is not necessarily consistent with the response of the chaotic state, similar to observations made with other shadowing algorithms.

This paper proposes a method of nonparametric filtering for stochastic nonlinear oscillations with particular interest in their derivative estimation. Based on a second-order ordinary differential equation, a stochastic oscillation is modeled by a two-variate stochastic differential equation without specifying the function form of the drift function, where the first variable is assumed to be observable but not the other. Given the discrete time series with observation error, the proposed method enables us to estimate the values of the drift function and its derivatives including those of the unobservable variable. According to the results of numerical experiments to compare estimation accuracy with a parametric method, the proposed method shows better performance in the estimation of nonlinear models.

The rapid diffusion of information and the adoption of social behaviors are of critical importance in situations as diverse as collective actions, pandemic prevention, or advertising and marketing. Although the dynamics of large cascades have been extensively studied in various contexts, few have systematically examined the impact of network topology on the efficiency of information diffusion. Here, by employing the linear threshold model on networks with communities, we demonstrate that a prominent network feature—the modular structure—strongly affects the speed of information diffusion in complex contagion. Our simulations show that there always exists an optimal network modularity for the most efficient spreading process. Beyond this critical value, either a stronger or a weaker modular structure actually hinders the diffusion speed. These results are confirmed by an analytical approximation. We further demonstrate that the optimal modularity varies with both the seed size and the target cascade size and is ultimately dependent on the network under investigation. We underscore the importance of our findings in applications from marketing to epidemiology, from neuroscience to engineering, where the understanding of the structural design of complex systems focuses on the efficiency of information propagation.

Protein thresholds have been shown to act as an ancient timekeeping device, such as in the time to lysis of Escherichia coli infected with bacteriophage $\lambda$ . The time taken for protein levels to reach a particular threshold for the first time is defined as the first passage time (FPT) of the protein synthesis system, which is a stochastic quantity. The first few moments of the distribution of first passage times were known earlier, but an analytical expression for the full distribution was not available. In this work, we derive an analytical expression for the first passage times for a long-lived protein. This expression allows us to calculate the full distribution not only for cases of no self-regulation, but also for both positive and negative self-regulation of the threshold protein. We show that the shape of the distribution matches previous experimental data on $\lambda$-phage lysis time distributions. We also provide analytical expressions for the FPT distribution with non-zero degradation in Laplace space. Furthermore, we study the noise in the precision of the first passage times described by coefficient of variation (CV) of the distribution as a function of the protein threshold value. We show that under conditions of positive self-regulation, the CV declines monotonically with increasing protein threshold, while under conditions of linear negative self-regulation, there is an optimal protein threshold that minimizes the noise in the first passage times.

Behavior decision making, where individuals can efficiently express their preferences for all options, has a great impact on cooperation. Hereby, we institute a minimal model in well-mixed populations where whether and how to sanction defectors are decided by cooperators via different decision-making mechanisms. The results illustrate that whether cooperation can outbreak depends on the cooperators' preferences for sanction and complying with the electoral outcome. We highlight the role of individuals' preferences in the emergence of cooperation and show that there exists an intermediate degree of the cooperators' preference for sanction at which the cooperators' preference for complying with the electoral outcome has a negligible impact on cooperation. We point out whether conformity facilitates the emergence of cooperation depends on the cooperators' preference for sanction. We find, compared with individual decision making, whether collective decision making is more conducive to promoting cooperation crucially depends on cooperators' preferences as well as the consensus required for employing sanction.

Liquid crystal nanocomposites have been a hot topic of research due to optimization of physical properties with such blending. There are several reports on enhancement of physical properties of nematic liquid crystals due to the blending of the nanomaterials. L. M. Lopatina and J. V. Selinger [Phys. Rev. Lett. 102, 197802 (2009)] have even proposed a theory based on experimental results for the enhancement of the properties of the nematic mesophase in the presence of ferroelectric nanoparticles. However, discotic liquid crystal nanocomposites are less studied. In the present experimental work, we have studied the effect of ferroelectric ($\mathrm{BaTi}{\mathrm{O}}_3$) nanoparticles on a room temperature discotic liquid crystalline material, namely 1,5-dihydroxy-2,3,6,7-tetrakis(3,7-dimethyloctyloxy)-9,10-anthraquinone. We investigated the physical properties of low concentration ferroelectric nanoparticle dispersed discotic columnar structure, using calorimetric, optical, x-ray diffraction, and dielectric spectroscopy tools. Results show that inclusion of ferroelectric nanoparticles in the discotic matrix consolidates the stability of the columnar matrix of the $\mathrm{Co}{\mathrm{l}}_h$ phase by virtue of their ferroic nature. An enhancement in charge carrier conductivity by several orders of magnitude at ambient conditions has been observed which makes such systems highly appropriate for one-dimensional conductors. Low concentration of $\mathrm{BaTi}{\mathrm{O}}_3$ nanoparticles substantially enhanced permittivity of the system also. A molecular relaxation mode has been observed in the middle frequency range of the dielectric spectra. Enhancement of these important parameters could be possible due to the ferroelectric nature of the dispersed nanoparticles.

In this article we show how spherical nanoparticles (NPs) imposing planar anchoring can strongly impact the viscoelastic, dielectric, and electro-optical properties of a nematic liquid crystal when they are not aggregated. We also demonstrate that when the NPs are magnetic, most nematic properties are more impacted than when they are nonmagnetic. With magnetic NPs a molecular disorder is induced that decreases the nematic order parameter, this decrease impacting the values of elastic constants, viscosity, and response time. The impact on 5CB liquid crystal (LC) has been investigated with spherical nanoparticles (NPs) of identical size around 6 nm, magnetic ($\gamma {\mathrm{Fe}}_2{\mathrm{O}}_3$), and nonmagnetic (${\mathrm{CeO}}_2$) ones that are both surface functionalized by poly(aminopropylmethylsiloxane-b-dimethylsiloxane) (PAPMS-b-PDMS) block copolymer ligands to promote planar anchoring. In the presence of nonmagnetic NPs, despite an almost constant nematic order parameter, a significant decrease of elastic constants (25.4%), viscosity (22%), and response time (23%) is measured. It suggests a dilution effect for the intermolecular interactions in the presence of NPs. This hypothesis is supported by the observation of an enhanced decrease of the same nematic parameters in the presence of magnetic NPs that can be fully explained by the corresponding order parameter decrease. This finally leads to a remarkable decrease of the splay elastic constant by 51% in the presence of magnetic NPs. The decrease of the nematic order parameter by 18% in the presence of magnetic NPs demonstrates that the NP magnetic moments are only weakly coupled to the nematic director and consequently only induce a disorder in the composite system. A significant influence of the expected large LC structural modifications in the presence of magnetic NPs is, however, shown by a particularly large increase of the diffusion coefficient 43% and large decrease of the dielectric anisotropy (43%). We believe that the observed impact of NPs with planar anchoring on nematic properties could be extended to most spherical NPs if their aggregation can be avoided. In particular, the difference between magnetic and nonmagnetic NPs could be extended to ferroelectric and nonferroelectric NPs.

Adsorption of liquid on a planar wall decorated by a hydrophilic stripe of width $L$ is considered. Under the condition that the wall is only partially wet (or dry) while the stripe tends to be wet completely, a liquid drop is formed above the stripe. The maximum height ${\ell }_m\left(\delta \mu \right)$ of the drop depends on the stripe width $L$ and the chemical potential departure from saturation $\delta \mu$ where it adopts the value ${\ell }_0={\ell }_m\left(0\right)$. Assuming a long-range potential of van der Waals type exerted by the stripe, the interfacial Hamiltonian model is used to show that ${\ell }_0$ is approached linearly with $\delta \mu$ with a slope which scales as $L^2$ over the region satisfying $L\lesssim {\xi }_{\parallel }$, where ${\xi }_{\parallel }$ is the parallel correlation function pertinent to the stripe. This suggests that near the saturation there exists a universal curve ${\ell }_m\left(\delta \mu \right)$ to which the adsorption isotherms corresponding to different values of $L$ all collapse when appropriately rescaled. Although the series expansion based on the interfacial Hamiltonian model can be formed by considering higher order terms, a more appropriate approximation in the form of a rational function based on scaling arguments is proposed. The approximation is based on exact asymptotic results, namely, that ${\ell }_m\sim \delta {\mu }^{-1/3}$ for $L\to \infty$ and that ${\ell }_m$ obeys the correct $\delta \mu \to 0$ behavior in line with the results of the interfacial Hamiltonian model. All the predictions are verified by the comparison with a microscopic density functional theory (DFT) and, in particular, the rational function approximation—even in its simplest form—is shown to be in a very reasonable agreement with DFT for a broad range of both $\delta \mu$ and $L$.

We study shear-driven jamming of ellipsoidal particles at zero temperature with a focus on the microscopic dynamics. We find that a change from spherical particles to ellipsoids with aspect ratio $\alpha =1.02$ gives dramatic changes of the microscopic dynamics with much lower translational velocities and a new role for the rotations. Whereas the velocity difference at contacts—and thereby the dissipation—in collections of spheres is dominated by the translational velocities and reduced by the rotations, the same quantity is in collections of ellipsoids instead totally dominated by the rotational velocities. By also examining the effect of different aspect ratios we find that the examined quantities show either a peak or a change in slope at $\alpha \approx 1.2$, which thus gives evidence for a crossover between different regions of low and high aspect ratio.

The accumulation of shear transformations (STs) in space and time is responsible for plastic deformation in amorphous solids. Here we study the effect of finite strain rates on STs during simulations of athermal shear deformation in an atomistic model of amorphous silicon. We present a time-resolved analysis of STs by mapping the plastic events identified in the atomistic simulations on a collection of Eshelby inclusions, which are characterized in terms of number, effective volume, lifetime, and orientation. Our analysis led us to distinguish between small and large events. We find that the main effect of a lower strain rate is to allow for a larger number of small events, roughly identified by an effective volume ${\gamma }_0{V}_0<20$ Å${}^3$, while the number and characteristics of larger events are surprisingly independent of the strain rate. We show that at low strains, the decrease of the stress observed at lower strain rates is mainly due to the excess of small events, while at larger strains, when the glass approaches the yield point where a shear band forms, larger events start to play a role and organize due to their elastic interactions. This phenomenology is compared with the predictions of mesoscale elastoplastic models. The technique developed here can be used as a systematic tool to analyze plasticity during molecular dynamics simulations. It can also give valuable information to develop physically grounded mesoscale models of plasticity, providing quantitative predictions of the mechanical properties of amorphous materials.

Intermittent locomotion is a widely used behavioral strategy for fish and birds to reduce the cost of movement. The intermittent locomotion performance of a self-propelled flapping plate is investigated numerically. Two intermittent swimming modes, namely, the multiple-tail-beat mode (MT mode) and the half-tail-beat mode (HT mode), as well as the continuous swimming mode (CT mode), are considered. Performance is evaluated from propulsive speed, efficiency, and cost of transport. The hydrodynamic performances of the intermittent modes are found to be better than the hydrodynamic performance of the CT mode when the bending stiffness $K$ is moderate [i.e., $K\approx O\left(1\right)]$ and the duty cycle is not too small. For the two intermittent modes, the performance of the HT mode is better than that of the MT mode when $K$ is small or moderate, while the situation is opposite when $K$ is large. It is found that compared to the asymmetric wake of the MT mode, the symmetric wake of the HT mode is favorable to generate more thrust force and therefore achieve better performance. Besides, at moderate $K$, the largest bending deformation of the plate in the HT mode, as well as the large normal force, produces the largest thrust during the flapping. The present results can help us to better understand the intermittent locomotion of animals and may be helpful for bionic design.

Investigating the power density spectrum of fluctuations in Rayleigh-Taylor (RT) interfacial mixing is a means of studying characteristic length, timescales, anisotropies, and anomalous processes. Guided by group theory, analyzing the invariance-based properties of the fluctuations, our paper examines raw time series from hot-wire anemometry measurements in the experiment by Akula et al. [J. Fluid Mech. 816, 619 (2017)]. The results suggest that the power density spectrum can be modeled as a compound function presented as the product of a power law and an exponential. The data analysis is based on Whittle's approximation of the power density spectrum for independent zero-mean near-Gaussian signals to construct a maximum likelihood estimator of the parameters. Those that maximize the log-likelihood are computed numerically through Newton-Raphson iteration. The Hessian of the log-likelihood is used to evaluate the Fisher information matrix and provide an estimate of the statistical error on the obtained parameters. The Kolmogorov-Smirnov test is applied to analyze the goodness of fit, by verifying the hypothesis that the ratio between the observed periodogram and the estimated power density spectrum follows a ${\chi }^2$ probability distribution. The dependence of the parameters of the compound function is investigated on the range of mode numbers over which the fit is performed. In the domain where the relative errors of the power-law exponent and the exponential decay rate are small and the goodness of fit is excellent, the parameters of the compound function are clearly defined, in agreement with the theory developed in the paper. The study of the power-law spectra in RT mixing data suggests that rigorous physics-based statistical methods can help researchers to see beyond visual inspection.