The type-I intermittency route to (or out of) chaos is investigated within the horizontal visibility (HV) graph theory. For that purpose, we address the trajectories generated by unimodal maps close to an inverse tangent bifurcation and construct their associated HV graphs. We show how the alternation of laminar episodes and chaotic bursts imprints a fingerprint in the resulting graph structure. Accordingly, we derive a phenomenological theory that predicts quantitative values for several network parameters. In particular, we predict that the characteristic power-law scaling of the mean length of laminar trend sizes is fully inherited by the variance of the graph degree distribution, in good agreement with the numerics. We also report numerical evidence on how the characteristic power-law scaling of the Lyapunov exponent as a function of the distance to the tangent bifurcation is inherited in the graph by an analogous scaling of block entropy functionals defined on the graph. Furthermore, we are able to recast the full set of HV graphs generated by intermittent dynamics into a renormalization-group framework, where the fixed points of its graph-theoretical renormalization-group flow account for the different types of dynamics. We also establish that the nontrivial fixed point of this flow coincides with the tangency condition and that the corresponding invariant graph exhibits extremal entropic properties.

We investigate the dependence of the average bursting frequency on time delay for neuron networks with randomly distributed time-delayed chemical synapses. The result is compared with the corresponding curve for the phase synchronization and it turns out that, in some intervals, these have a very similar shape and appear as almost mirror images of each other. We have analyzed both the map-based chaotic Rulkov model and the continuous Hindmarsh-Rose model, yielding the same conclusions. In order to gain further insight, we also analyzed time-delayed Kuramoto models displaying an overall behavior similar to that observed on the neuron network models. For the Kuramoto models, we were able to derive analytical formulas providing an implicit functional relationship between the mean frequency and the phase synchronization. These formulas suggest a strong dependence between those two measures, which could explain the similarities in shape between the curves.

We discuss the effect of triplet synchrony in oscillatory networks. In this state the phases and the frequencies of three coupled oscillators fulfill the conditions of a triplet locking, whereas every pair of systems remains asynchronous. We suggest an easy to compute measure, a triplet synchronization index, which can be used to detect such states from experimental data.

The exponentially decaying acoustic pressure of scattered surface acoustic waves (SAWs) at the contact line of a liquid film pinned to filter paper is shown to sustain a high curvature conic tip with micron-sized modulations whose dimension grows exponentially from the tip. The large negative capillary pressure in the film, necessary for offsetting the large positive acoustic pressure at the contact line, also creates significant negative hydrodynamic pressure and robust wicking action through the paper. An asymptotic analysis of this intricate pressure matching between the quasistatic conic film and bulk drop shows that the necessary SAW power to pump liquid from the filter paper and aerosolize, expressed in terms of the acoustic pressure scaled by the drop capillary pressure, grows exponentially with respect to twice the acoustic decay constant multiplied by the drop length, with a universal preexponential coefficient. Global rapid aerosolization occurs at a SAW power twice as high, beyond which the wicking rate saturates.

We investigate the effects of boundary conditions on the surface of self-propelled spherical swimmers moving in a viscous fluid with a low Reynolds number. We first show that collisions between the swimmers are impossible under the commonly used no-slip conditions. Next we demonstrate that collisions do occur if the more general Navier boundary conditions, allowing for a finite slip on the surface that produces drag, are imposed on the boundary of swimmers. The presence of a small inertia for each swimmer does not influence whether collisions occur between swimmers.

Plasma defocusing and higher-order Kerr effects on multiple filamentation and pattern formation of ultrashort laser pulse propagation in air are investigated. Linear analyses and numerical results show that these two saturable nonlinear effects can destroy the coherent evolution of the laser field, and small-scale spatial turbulent structures rapidly appear. For the two-dimensional case, numerical simulations show that blow-up-like solutions, spatial chaos, and pseudorecurrence can appear at higher laser intensities if only plasma defocusing is included. These complex patterns result from the stochastic evolution of the higher- or shorter-wavelength modes of the laser light spectrum. From the viewpoint of nonlinear dynamics, filamentation can be attributed to the modulational instability of these spatial incoherent localized structures. Furthermore, filament patterns associated with multiphoton ionization of the air molecules with and without higher-order Kerr effects are compared.

We consider electric conductance through a narrow nanochannel in the thick-double-layer limit, where the space-charge Debye layers adjacent to the channel walls overlap. At moderate surface-charge densities the electrolyte solution filling the channel comprises mainly of counterions. This allows to derive an analytic closed-form approximation for the channel conductance, independent of the salt concentration in the channel reservoirs. The derived expression consists of two terms. The first, representing electromigratory transport, is independent of the channel depth. The second, representing convective transport, depends upon it weakly.

We study the evolution of cooperation in the spatial public goods game, focusing on the effects that are brought about by the delayed distribution of goods that accumulate in groups due to the continuous investments of cooperators. We find that intermediate delays enhance network reciprocity because of a decelerated invasion of defectors, who are unable to reap the same high short-term benefits as they do in the absence of delayed distribution. Long delays, however, introduce a risk because the large accumulated wealth might fall into the wrong hands. Indeed, as soon as the curvature of a cooperative cluster turns negative, the engulfed defectors can collect the heritage of many generations of cooperators and by doing so start a waning-moon pattern that nullifies the benefits of decelerated invasion. Accidental meeting points of growing cooperative clusters may also act as triggers for the waning-moon effect, thus linking the success of cooperators with their propensity to fail in a rather bizarre way. Our results highlight that “investing in the future” is a good idea only if that future is sufficiently near and not likely to be burdened by inflation.

Neither a purely deterministic rotary nanomotor nor a purely orientational diffuser exhibits long-term translational motion, but coupling rotation to orientational diffusion yields translational diffusion. We demonstrate that this effective translational diffusion can easily dominate the ordinary thermal translational diffusion for experimentally relevant nanomotors, and that this effective diffusion is chiral. Unpowered chiral particles do not exhibit chiral diffusion, but a nanorotor has both handedness and an instantaneous direction of powered motion, thus—unlike an unpowered particle—its diffusional motion can distinguish left from right.

The heat flow and thermal profile in a one-dimensional (1D) harmonic lattice with coordinate-dependent masses have been calculated in the thermodynamic limit. It is shown in the particular example of a 1D harmonic lattice with linearly increasing masses that in standard Langevin conditions of contact, a temperature gradient can form, and Fourier's law can be obeyed.

We establish a set of nonequilibrium quantum phase transitions in the Lipkin-Meshkov-Glick model under monochromatic modulation of the interparticle interaction. We show that the external driving induces a rich phase diagram that characterizes the multistability in the system. Interestingly, the number of stable configurations can be tuned by increasing the amplitude of the driving field. Furthermore, by studying the quantum evolution, we demonstrate that the system exhibits a set of quantum phases that correspond to dynamically stabilized states.

We study phonon modes in two-dimensional colloidal crystals composed of soft microgel particles with hard polystyrene particle dopants distributed randomly on the triangular lattice. This experimental approach produces close-packed lattices of spheres with random bond strength disorder, i.e., the effective springs coupling nearest neighbors are very stiff, very soft, or of intermediate stiffness. Particle tracking video microscopy and covariance matrix techniques are then employed to derive the phonon modes of the corresponding “shadow” crystals with bond strength disorder as a function of increasing dopant concentration. At low frequencies, hard and soft particles participate equally in the phonon modes, and the samples exhibit Debye-like density of states behavior characteristic of crystals. For mid- and high-frequency phonons, the relative participation of hard versus soft particles in each mode is found to vary systematically with dopant concentration. Additionally, a few localized modes, primarily associated with hard particle motions, are found at the highest frequencies.

Random sequential adsorption (RSA) of polymer, modeled as a chain of identical spheres, is systematically studied. In order to control precisely anisotropy and number of degrees of freedom, two different kinds of polymers are used. In the first one, monomers are placed along a straight line, whereas in the second, relative orientations of particles are random. Such polymers fill a flat homogeneous surface randomly. The paper focuses on maximal random coverage ratio and adsorption kinetics dependence on polymer size, shape anisotropy, and numbers of degrees of freedom. Obtained results were discussed and compared with other numerical experiments and theoretical predictions.

Two-dimensional lattices of $N$ synchronized oscillators with reactive coupling are considered as high-precision frequency sources in the case where a spiral pattern is formed. The improvement of the frequency precision is shown to be independent of $N$ for large $N$, unlike the case of purely dissipative coupling where the improvement is proportional to $N$, but instead depends on just those oscillators in the core of the spiral that acts as the source region of the waves. Our conclusions are based on numerical simulations of up to $N=29929$ oscillators and analytic results for a continuum approximation to the lattice in an infinite system. We derive an expression for the dependence of the frequency precision on the reactive component of the coupling constant, depending on a single parameter given by fitting the frequency of the spiral waves to the numerical simulations.

We simulate the bond and site percolation models on a simple-cubic lattice with linear sizes up to $L=512$, and estimate the percolation thresholds to be $p_c\left(\mathrm{bond}\right)=0.24881182\left(10\right)$ and $p_c\left(\mathrm{site}\right)=0.3116077\left(2\right)$. By performing extensive simulations at these estimated critical points, we then estimate the critical exponents $1/\nu =1.1410\left(15\right)$, $\beta /\nu =0.47705\left(15\right)$, the leading correction exponent $y_i=-1.2\left(2\right)$, and the shortest-path exponent $d_{\min }=1.3756\left(3\right)$. Various universal amplitudes are also obtained, including wrapping probabilities, ratios associated with the cluster-size distribution, and the excess cluster number. We observe that the leading finite-size corrections in certain wrapping probabilities are governed by an exponent $\approx$$-2$, rather than $y_i\approx -1.2$.

One interesting yet difficult computational issue has recently been posed in biophysics in regard to the implementation of thermodynamic constraints to complex networks. Biochemical networks of enzymes inside cells are among the most efficient, robust, differentiated, and flexible free-energy transducers in nature. How is the second law of thermodynamics encoded for these complex networks? In this article it is demonstrated that for chemical reaction networks in the steady state the exclusion (presence) of closed reaction cycles makes possible (impossible) the definition of a chemical potential vector. Interestingly, this statement is encoded in one of the key results in combinatorial optimization, i.e., the Gordan theorem of the alternatives. From a computational viewpoint, the theorem reveals that calculating a reaction's free energy and identifying infeasible loops in flux states are dual problems whose solutions are mutually exclusive, and this opens the way for efficient and scalable methods to perform the energy balance analysis of large-scale biochemical networks.

Shocks and blasts can be readily obtained in granular flows be they dense or dilute. Here, by examining the propagation of a blast shock in a dilute granular flow, we show that such a front is unstable with respect to transverse variations of the density of grains. This instability has a well-defined wavelength which depends on the density of the medium and has an amplitude which grows as an exponential of the distance traveled. These features can be understood using a simple model for the shock front, including dissipation which is inherent to granular flows. While this instability bears much resemblance to that anticipated in gases, it is distinct and has special features we discuss here.

Symmetric $\mathsf{T}$ junctions have been used widely in microfluidics to generate equal-sized microdroplets, which are applicable in drug delivery systems. A newly proposed method for generating unequal-sized microdroplets at a $\mathsf{T}$ junction is investigated theoretically and experimentally. Asymmetric $\mathsf{T}$ junctions with branches of identical lengths and different cross sections are utilized for this aim. An equation for the critical breakup of droplets at asymmetric $\mathsf{T}$ junctions and one for determining the breakup point of droplets are developed. A good agreement was observed between the theories (present and previous) and the experiments.