Many real-world complex networks contain a significant amount of structural redundancy, in which multiple vertices play identical topological roles. Such redundancy arises naturally from the simple growth processes which form and shape many real-world systems. Since structurally redundant elements may be permuted without altering network structure, redundancy may be formally investigated by examining network automorphism (symmetry) groups. Here, we use a group-theoretic approach to give a complete description of spectral signatures of redundancy in undirected networks. In particular, we describe how a network’s automorphism group may be used to directly associate specific eigenvalues and eigenvectors with specific network motifs.

The recent information technology revolution has enabled the analysis and processing of large-scale data sets describing human activities. The main source of data is represented by the web, where humans generally use to spend a relevant part of their day. Here, we study three large data sets containing the information about web activities of humans in different contexts. We study in details interevent and waiting-time statistics. In both cases, the number of subsequent operations which differs by $\tau$ units of time decays powerlike as $\tau$ increases. We use nonparametric statistical tests in order to estimate the significance level of reliability of global distributions to describe activity patterns of single users. Global interevent time probability distributions are not representative for the behavior of single users: the shape of single users’ interevent distributions is strongly influenced by the total number of operations performed by the users and distributions of the total number of operations performed by users are heterogeneous. A universal behavior can be anyway found by suppressing the intrinsic dependence of the global probability distribution on the activity of the users. This suppression can be performed by simply dividing the interevent times with their average values. Differently, waiting-time probability distributions seem to be independent of the activity of users and global probability distributions are able to significantly represent the replying activity patterns of single users.

We investigate front propagation and synchronization transitions in dependence on the information transmission delay and coupling strength over scale-free neuronal networks with different average degrees and scaling exponents. As the underlying model of neuronal dynamics, we use the efficient Rulkov map with additive noise. We show that increasing the coupling strength enhances synchronization monotonously, whereas delay plays a more subtle role. In particular, we found that depending on the inherent oscillation frequency of individual neurons, regions of irregular and regular propagating excitatory fronts appear intermittently as the delay increases. These delay-induced synchronization transitions manifest as well-expressed minima in the measure for spatial synchrony, appearing at every multiple of the oscillation frequency. Larger coupling strengths or average degrees can broaden the region of regular propagating fronts by a given information transmission delay and further improve synchronization. These results are robust against variations in system size, intensity of additive noise, and the scaling exponent of the underlying scale-free topology. We argue that fine-tuned information transmission delays are vital for assuring optimally synchronized excitatory fronts on complex neuronal networks and, indeed, they should be seen as important as the coupling strength or the overall density of interneuronal connections. We finally discuss some biological implications of the presented results.

We demonstrate experimentally how nonlinear optical phase dynamics can be generated with an electro-optic delay oscillator. The presented architecture consists of a linear phase modulator, followed by a delay line, and a differential phase-shift keying demodulator (DPSK-d). The latter represents the nonlinear element of the oscillator effecting a nonlinear transformation. This nonlinearity is considered as nonlocal in time since it is ruled by an intrinsic differential delay, which is significantly greater than the typical phase variations. To study the effect of this specific nonlinearity, we characterize the dynamics in terms of the dependence of the relevant feedback gain parameter. Our results reveal the occurrence of regular GHz oscillations (approximately half of the DPSK-d free spectral range), as well as a pronounced broadband phase-chaotic dynamics. Beyond this, the observed dynamical phenomena offer potential for applications in the field of microwave photonics and, in particular, for the realization of novel chaos communication systems. High quality and broadband phase-chaos synchronization is also reported with an emitter-receiver pair of the setup.

The dynamic response of highly viscous droplets to a sharp increase in the surrounding liquid velocity is experimentally investigated in a square microchannel junction. The local injection of the continuous phase from symmetric side channels onto a train of droplets produces a large velocity contrast between the front and the rear of droplets, yielding a broad range of time-dependent deformation and breakup. In particular, due to microscale confinement, the system displays a nonlinear behavior with the initial droplet size. Deformations, relaxation times, and fragmentation processes are examined as a function of flow parameters and fluids properties with emphasis on the formation of slender viscous structures such as spoon-shaped droplets, i.e., asymmetrical droplets.

We study the influence of a wall on the dynamics of a low-Reynolds-number three-sphere swimmer. A far swimmer whose arm makes an angle $\theta$ with the horizon experiences the wall presence as an angle-dependent quadrupole force proportional to ${\left(a/L\right)}^2{\left(L/z\right)}^2\text{cos}\theta$, where $a$, $L$, and $z$ are the radius of spheres, the arm length, and the swimmer distance to the wall, respectively. The wall-induced translational velocity of swimmer is perpendicular to the arms. A far swimmer prefers to orient its arms parallel to the plate. This state is stable. Remarkably, the parallel state is unstable when the swimmer is close to the wall. In this regime, the velocity of swimmer decreases as ${\left(z/L\right)}^2$. Numerical solution of the equations of motion for arbitrary initial $z/L$ and $\theta$ reveals four different phases of locomotion.

We follow the diffusive motion of colloidal particles in soap films with varying $h/d$, where $h$ is the thickness of the film and $d$ is the diameter of the particles. The hydrodynamics of these films are determined by looking at the correlated motion of pairs of particles as a function of separation $R$. The Trapeznikov approximation [A. A. Trapeznikov, Proceedings of the 2nd International Congress on Surface Activity (Butterworths, London, 1957), p. 242] is used to model soap films as an effective two-dimensional (2D) fluid in contact with bulk air phases. The flow fields determined from correlated particle motions show excellent agreement with what is expected for the theory of 2D fluids for all our films where $0.6\le h/d\le 14.3$, with the 2D shear viscosity matching that predicted by Trapeznikov. However, the parameters of these flow fields change markedly for thick films $\left(h/d>7\pm 3\right)$. Our results indicate that three-dimensional effects become important for these thicker films, despite the flow fields still having a 2D character.

We study the impact of inlet channel geometry on microfluidic drop formation. We show that drop makers with $T$-junction style inlets form monodisperse emulsions at low and moderate capillary numbers and those with Flow-Focus style inlets do so at moderate and high capillary numbers. At low and moderate capillary number, drop formation is dominated by interfacial forces and mediated by the confinement of the microchannels; drop size as a function of flow-rate ratio follows a simple functional form based on a blocking-squeezing mechanism. We summarize the stability of the drop makers with different inlet channel geometry in the form of a phase diagram as a function of capillary number and flow-rate ratio.

Inertial particles suspended in many natural and industrial flows undergo coagulation upon collisions and fragmentation if their size becomes too large or if they experience large shear. Here we study this coagulation-fragmentation process in time-periodic incompressible flows. We find that this process approaches an asymptotic dynamical steady state where the average number of particles of each size is roughly constant. We compare the steady-state size distributions corresponding to two fragmentation mechanisms and for different flows and find that the steady state is mostly independent of the coagulation process. While collision rates determine the transient behavior, fragmentation determines the steady state. For example, for fragmentation due to shear, flows that have very different local particle concentrations can result in similar particle size distributions if the temporal or spatial variation in shear forces is similar.

The formation and dynamics of spatially extended compositional domains in multicomponent lipid membranes both in vivo and in vitro lie at the heart of many important biological and biophysical phenomena. While the thermodynamic basis for domain formation has been explored extensively in the past, the roles of membrane and exterior fluid hydrodynamics on domain formation kinetics have received less attention. A case in point is the impact of hydrodynamics on the dynamics of compositional heterogeneities in lipid membranes in the vicinity of a critical point. In this Rapid Communication it is argued that the asymptotic dynamic behavior of a lipid membrane system in the vicinity of a critical point is strongly influenced by hydrodynamic interactions. More specifically, a mode-coupling argument is developed which predicts a scaling behavior of lipid transport coefficients near the critical point for both symmetric and asymmetric bilayers immersed in a bulk fluid.

We present a lattice spin model that mimics a system of interacting particles through a short-range repulsive potential and a long-range attractive power-law decaying potential. We perform a detailed analysis of the general equilibrium phase diagram of the model at finite temperature, showing that the only possible equilibrium phases are the ferromagnetic and the antiferromagnetic ones. We then study the nonequilibrium behavior of the model after a quench to subcritical temperatures, in the antiferromagnetic region of the phase diagram region, where the pair interaction potential behaves in the same qualitative way as in a Lennard-Jones gas. We find that even in the absence of quenched disorder or geometric frustration, the competition between interactions gives rise to nonequilibrium disordered structures at low enough temperatures that strongly slow down the relaxation of the system. This nonequilibrium state presents several features characteristic of glassy systems such as subaging, nontrivial fuctuation dissipation relations, and possible logarithmic growth of free-energy barriers to coarsening.

We study the nondiffusive Brownian motion of both rigid and deformable mesoscopic particles by cross-correlated dynamic light scattering with microsecond temporal resolution. Whereas rigid particles show the classical long-time tail prediction, the transition to diffusive motion of deformable particles presents a striking behavior not explained by the existing hydrodynamic treatments. This observation can be interpreted in terms of a damped oscillatory deformational motion on time scales of the order of the Brownian time. Finally, we show that the nondiffusive Brownian motion depends on the specific flexibility of the particles.

Ionic current through a 3 nm in diameter nanopore has been investigated using molecular dynamics. Results indicate that the ionic current increases linearly as the electrolyte concentration increases from 0.4 to 0.9 M, beyond which the ionic current increases at a slower rate. In contradiction to the expectation that higher surface charge density will lead to more ions in the nanopore, and therefore, higher ionic current, the ionic current shows an increase-decrease profile as the surface charge density increases. These unusual observations are attributed to the fact that ions close to the wall experience large viscous force, leading to low mobility.

We study the effect of noisy oscillatory input on the signal discrimination by spontaneously firing neurons. Using analytically tractable model, we contrast signal detection in two situations: (i) when the neuron is driven by coherent oscillations and (ii) when the coherence of oscillations is destroyed. Analytical calculations revealed a region in the parameter space of the model where oscillations act to reduce the variability of neuronal firing and to enhance the discriminability of weak signals. These analytical results are employed to unveil a possible role of coherent oscillations in peripheral electrosensory system of paddlefish in improvement of detection of weak stimuli. The proposed mechanism may be relevant to a wide range of phenomena involving coherently driven oscillators.

The topological structure of basin boundaries plays a fundamental role in the sensitivity to the final state in chaotic dynamical systems. Herewith we present a study on the dynamics of dissipative systems close to the Hamiltonian limit, emphasizing the increasing number of periodic attractors, and on the structural changes in their basin boundaries as the dissipation approaches zero. We show numerically that a power law with nontrivial exponent describes the growth of the total number of periodic attractors as the damping is decreased. We also establish that for small scales the dynamics is governed by effective dynamical invariants, whose measure depends not only on the region of the phase space but also on the scale under consideration. Therefore, our results show that the concept of effective invariants is also relevant for dissipative systems.

We study the fast irreversible bimolecular reaction in a two-dimensional chaotic flow. The reactants are initially segregated and together fill the whole domain. Simulations show that the reactant concentration decays exponentially with rate $\lambda$ and then crosses over to the algebraic law of chemical kinetics in the final stage of the reaction. We estimate the crossover time from the reaction rate constant and the flow parameters. The exponential decay phase of the reaction can be described in terms of an equivalent passive scalar problem, allowing us to predict $\lambda$ using the theory of passive scalar advection. Depending on the relative length scale between the velocity and the concentration fields, $\lambda$ is either related to the distribution of the finite-time Lyapunov exponent of the flow or given in terms of an effective diffusivity which is independent of the small-scale stretching properties of the flow. For the former case, we suggest an optimal choice of flow parameters at which $\lambda$ is maximum.

With a device that uses microscopic imaging as the signal detection method for online laser light scattering of solutions driven to flow in a capillary tube, we have found that mixing of a solution with water and vice versa induce large numbers of aggregates in the free flow stream. The degrees of aggregation as measured from the total number of aggregates and the corresponding light-scattering intensities are dependent on the species of the solution. This species dependence of the mixing aggregation in the capillary flow has the potential for the development of new protocols or even spectroscopic methods for the detection of solute molecules and the assessment of solution qualities. Furthermore, even with pure-distilled and de-ionized water in the steady-state capillary flow, there are still countable numbers of aggregates detectable in the free flow stream, although of extremely low concentration of an estimated value of no more than ${10}^{-15}\text{M}$.

Faussurier et al. [Phys. Rev. E 65, 016403 (2001)] proposed to use a variational principle relying on Jensen-Feynman (or Gibbs-Bogoliubov) inequality in order to optimize the accounting for two-particle interactions in the calculation of canonical partition functions. It consists of a decomposition into a reference electron system and a first-order correction. The procedure appears to be very efficient in order to evaluate the free energy and the orbital populations. In this work, we present numerical applications of the method and propose to extend it using a reference energy which includes the interaction between two electrons inside a given orbital. This is possible, thanks to our efficient recursion relation for the calculation of partition functions. We also show that a linear reference energy, however, is usually sufficient to achieve a good precision and that the most promising way to improve the approach of Faussurier et al. is to apply Jensen’s inequality to a more convenient convex function.

Master equations can be conveniently used to investigate many particle systems driven out of equilibrium by time-dependent external fields. This topic is of vital interest in connection with fluctuation theorems and the associated microscopic work and heat distributions. We present an exact Monte Carlo simulation algorithm, which allows us to study interaction effects on these distributions. The method is applied to an Ising chain with Glauber dynamics. We find that the distributions are characterized by $\delta$ and step functions with a smooth part in between. With decreasing sweeping rate of the external field or decreasing interaction strength, the singular part becomes less dominant and the Gaussian fluctuation regime is approached.

A theory to predict the steady-state position of a dissipative flow-controlled system, as defined by a control volume, is developed based on the maximum entropy principle of Jaynes, involving minimization of a generalized free-energy-like potential. The analysis provides a theoretical justification of a local, conditional form of the maximum entropy production principle, which successfully predicts the observable properties of many such systems. The analysis reveals a very different manifestation of the second law of thermodynamics in steady-state flow systems, which provides a driving force for the formation of complex systems, including life.