Temporal correlations of time series or event sequences in natural and social phenomena have been characterized by power-law decaying autocorrelation functions with decaying exponent $\gamma$. Such temporal correlations can be understood in terms of power-law distributed interevent times with exponent $\alpha$ and/or correlations between interevent times. The latter, often called correlated bursts, has recently been studied by measuring power-law distributed bursty trains with exponent $\beta$. A scaling relation between $\alpha$ and $\gamma$ has been established for the uncorrelated interevent times, while little is known about the effects of correlated interevent times on temporal correlations. In order to study these effects, we devise the bursty-get-burstier model for correlated bursts, by which one can tune the degree of correlations between interevent times, while keeping the same interevent time distribution. We numerically find that sufficiently strong correlations between interevent times could violate the scaling relation between $\alpha$ and $\gamma$ for the uncorrelated case. A nontrivial dependence of $\gamma$ on $\beta$ is also found for some range of $\alpha$. The implication of our results is discussed in terms of the hierarchical organization of bursty trains at various time scales.

We show that two intriguing features of mesoscopic transport, namely, the modulation of Coulomb blockade peak heights and the transmission phase lapses occurring between subsequent peaks, are closely related. Our analytic arguments are corroborated by numerical simulations for chaotic ballistic quantum dots. The correlations between the two properties are experimentally testable. The statistical distribution of the partial-width amplitude, at the heart of the previous relationship, is determined, and its characteristic parameters are estimated from simple models.

We revisit the numerical calculation of generalized Lyapunov exponents, $L\left(q\right)$, in deterministic dynamical systems. The standard method consists of adding noise to the dynamics in order to use importance sampling algorithms. Then $L\left(q\right)$ is obtained by taking the limit noise-amplitude $\to$ 0 after the calculation. We focus on a particular method that involves periodic cloning and pruning of a set of trajectories. However, instead of considering a noisy dynamics, we implement an imperfect (noisy) cloning. This alternative method is compared with the standard one and, when possible, with analytical results. As a workbench we use the asymmetric tent map, the standard map, and a system of coupled symplectic maps. The general conclusion of this study is that the imperfect-cloning method performs as well as the standard one, with the advantage of preserving the deterministic dynamics.

We study the dynamics of mobile, locally coupled identical oscillators in the presence of coupling delays. We find different kinds of chimera states in which coherent in-phase and antiphase domains coexist with incoherent domains. These chimera states are dynamic and can persist for long times for intermediate mobility values. We discuss the mechanisms leading to the formation of these chimera states in different mobility regimes. This finding could be relevant for natural and technological systems composed of mobile communicating agents.

We report that explosive synchronization of networked oscillators (a process through which the transition to coherence occurs without intermediate stages but is rather characterized by a sudden and abrupt jump from the network's asynchronous to synchronous motion) is related to self-similarity of synchronous clusters of different size. Self-similarity is revealed by destructing the network synchronous state during the backward transition and observed with the decrease of the coupling strength between the nodes of the network. As illustrative examples, networks of Kuramoto oscillators with different topologies of links have been considered. For each one of such topologies, the destruction of the synchronous state goes step by step with self-similar configurations of interacting oscillators. At the critical point, the invariance of the phase distribution in the synchronized cluster with respect to the cluster size is reported.

Cortical spreading depression (CSD) along with migraine waves and spreading depolarization events with stroke or injures are the front-line examples of extreme physiological behaviors of the brain cortex which manifest themselves via the onset and spreading of localized areas of neuronal hyperactivity followed by their depression. While much is known about the physiological pathways involved, the dynamical mechanisms of the formation and evolution of complex spatiotemporal patterns during CSD are still poorly understood, in spite of the number of modeling studies that have been already performed. Recently we have proposed a relatively simple mathematical model of cortical spreading depression which counts the effects of neurovascular coupling and cerebral blood flow redistribution during CSD. In the present study, we address the main dynamical consequences of newly included pathways, namely, the changes in the formation and propagation speed of the CSD front and the pattern formation features in two dimensions. Our most notable finding is that the combination of vascular-mediated spatial coupling with local regulatory mechanisms results in the formation of stationary Turing-like patterns during a CSD event.

We seek general principles of the structure of the cellular collective activity associated with conscious awareness. Can we obtain evidence for features of the optimal brain organization that allows for adequate processing of stimuli and that may guide the emergence of cognition and consciousness? Analyzing brain recordings in conscious and unconscious states, we followed initially the classic approach in physics when it comes to understanding collective behaviours of systems composed of a myriad of units: the assessment of the number of possible configurations (microstates) that the system can adopt, for which we use a global entropic measure associated with the number of connected brain regions. Having found maximal entropy in conscious states, we then inspected the microscopic nature of the configurations of connections using an adequate complexity measure and found higher complexity in states characterized not only by conscious awareness but also by subconscious cognitive processing, such as sleep stages. Our observations indicate that conscious awareness is associated with maximal global (macroscopic) entropy and with the short time scale (microscopic) complexity of the configurations of connected brain networks in pathological unconscious states (seizures and coma), but the microscopic view captures the high complexity in physiological unconscious states (sleep) where there is information processing. As such, our results support the global nature of conscious awareness, as advocated by several theories of cognition. We thus hope that our studies represent preliminary steps to reveal aspects of the structure of cognition that leads to conscious awareness.

Many organisms can remember locations they have previously visited during a search. Visual search experiments have shown exploration is guided away from these locations, reducing redundancies in the search path before finding a hidden target. We develop and analyze a two-layer neural field model that encodes positional information during a search task. A position-encoding layer sustains a bump attractor corresponding to the searching agent's current location, and search is modeled by velocity input that propagates the bump. A memory layer sustains persistent activity bounded by a wave front, whose edges expand in response to excitatory input from the position layer. Search can then be biased in response to remembered locations, influencing velocity inputs to the position layer. Asymptotic techniques are used to reduce the dynamics of our model to a low-dimensional system of equations that track the bump position and front boundary. Performance is compared for different target-finding tasks.

We develop an extended classical density-functional theory to describe clustering of imidazolium-based cations into linear chains, driven by $\pi \text{−}\pi$ stacking. We find that the associating system displays a similar short-ranged structure to the completely dissociated fluid. We also construct a restricted primitive model for associating ionic species in an RTIL+solvent mixture. The double-layer formed in these systems exhibits strong overscreening by the cation chains, as expected. Significantly enhanced capacitance is also observed for the case where counterions are the associating species. The established density-functional method can be also used to describe polydisperse polyelectrolyte models.

Interparticle interactions and bulk properties of colloidal suspensions can be substantially modified by the addition of nanoparticles. Extreme asymmetries in size and charge between colloidal particles and nanoparticles present severe computational challenges to molecular-scale modeling of such complex systems. We present a statistical mechanical theory of effective electrostatic interactions that can greatly ease large-scale modeling of charged colloid-nanoparticle mixtures. By applying a sequential coarse-graining procedure, we show that a multicomponent mixture of charged colloids, nanoparticles, counterions, and coions can be mapped first onto a binary mixture of colloids and nanoparticles and then onto a one-component model of colloids alone. In a linear-response approximation, the one-component model is governed by a single effective pair potential and a one-body volume energy, whose parameters depend nontrivially on nanoparticle size, charge, and concentration. To test the theory, we perform molecular dynamics simulations of the two-component and one-component models and compute structural properties. For moderate electrostatic couplings, colloid-colloid radial distribution functions and static structure factors agree closely between the two models, validating the sequential coarse-graining approach. Nanoparticles of sufficient charge and concentration enhance screening of electrostatic interactions, weakening correlations between charged colloids and destabilizing suspensions, consistent with experiments.

Diffusing-wave spectroscopy (DWS) extends dynamic light scattering measurements to samples with strong multiple scattering. DWS treats the transport of photons through turbid samples as a diffusion process, thereby making it possible to extract the dynamics of scatterers from measured correlation functions. The analysis of DWS data requires knowledge of the path length distribution of photons traveling through the sample. While for flat sample cells this path length distribution can be readily calculated and expressed in analytical form; no such expression is available for cylindrical sample cells. DWS measurements have therefore typically relied on dedicated setups that use flat sample cells. Here we show how DWS measurements, in particular DWS-based microrheology measurements, can be performed in standard dynamic light scattering setups that use cylindrical sample cells. To do so we perform simple random-walk simulations that yield numerical predictions of the path length distribution as a function of both the transport mean free path and the detection angle. This information is used in experiments to extract the mean-square displacement of tracer particles in the material, as well as the corresponding frequency-dependent viscoelastic response. An important advantage of our approach is that by performing measurements at different detection angles, the average path length through the sample can be varied. For measurements performed on a single sample cell, this gives access to a wider range of length and time scales than obtained in a conventional DWS setup. Such angle-dependent measurements also offer an important consistency check, as for all detection angles the DWS analysis should yield the same tracer dynamics, even though the respective path length distributions are very different. We validate our approach by performing measurements both on aqueous suspensions of tracer particles and on solidlike gelatin samples, for which we find our DWS-based microrheology data to be in good agreement with rheological measurements performed on the same samples.

The present study is devoted to the investigation of the nonlinear optical properties of a smectic liquid crystal doped with gold nanorods. Using the $Z$-scan technique, we investigate the changes in the optical birefringence of a homeotropic sample upon laser exposure, considering the configurations of normal and oblique incidence. Our results reveal that the birefringence variations may be governed by distinct physical mechanisms, depending on the relative angle between the far-field director and the wave vector of the excitation laser beam. In particular, we observe that the position dependence of the far-field transmittance exhibits different behaviors as the incidence angle is changed, indicating that distortions in the beam wavefront may be associated with the thermal lens phenomenon or an optically induced reorientation of the nematic director. The temperature dependence of the nonlinear refractive and absorptive coefficients is investigated close to the smectic-$A$–nematic phase transition. A detailed analysis of the interplay between smectic order and plasmon resonance is performed, thus unveiling the capability of plasmonic liquid crystal to be used in optical devices.

Barchan dunes are crescentic shape dunes with horns pointing downstream. The present paper reports the formation of subaqueous barchan dunes from initially conical heaps in a rectangular channel. Because the most unique feature of a barchan dune is its horns, we associate the time scale for the appearance of horns to the formation of a barchan dune. A granular heap initially conical was placed on the bottom wall of a closed conduit and it was entrained by a water flow in turbulent regime. After a certain time, horns appear and grow, until an equilibrium length is reached. Our results show the existence of the time scales $0.5t_c$ and $2.5t_c$ for the appearance and equilibrium of horns, respectively, where $t_c$ is a characteristic time that scales with the grains diameter, gravity acceleration, densities of the fluid and grains, and shear and threshold velocities.

We have found that in two-dimensional Kolmogorov flow a spatially localized turbulent state (SLT) exists stably and travels with a constant speed on average switching the moving direction randomly and intermittently for moderate values of the control parameters: Reynolds number and the flow rate. We define the coarse-grained position and velocity of an SLT and separate the motion of the SLT from its internal turbulent dynamics by introducing a co-moving frame. The switching process of an SLT represented by the coarse-grained velocity seems to be a random telegraph signal. Focusing on the asymmetry of the internal turbulence we introduce two coarse-grained variables characterizing the internal dynamics. These quantities follow the switching process reasonably. This suggests that the twin attracting invariant sets each of which corresponds to a one-way traveling SLT are embedded in the attractor of the moving SLT and the connection of the two sets is too complicated to be represented by a few degrees of freedom but the motion of an SLT is correlated with the internal turbulent dynamics.

We present a concise yet effective central-moments-based lattice Boltzmann method with an accelerated convergence to the steady state through preconditioning. It is demonstrated that the proposed scheme reduces to a slight modification of the unaccelerated one, as the preconditioning affects only the equilibrium state. Different from previous efforts carried out within the lattice Boltzmann community, the present scheme is built on an original model. In fact, the corresponding collision operator loses the pyramidal orchestrated nature that is typical of the cascaded scheme, hence we coin the name “noncascaded.” Our model is very general, characterized by highly intelligible formulations, simple to implement, and it can be derived for any lattice velocity space.

Through the integration of the power spectral density, we obtain temperature profiles of both multisegment harmonic and anharmonic systems, showing the presence of an anomalous negative temperature gradient inside the interfacial segment. Via investigating patterns of the power spectral density, we found that the counterintuitive phenomenon comes from the presence of interfacial localized phonon modes. Two out-band localized modes of the harmonic model, which make no contributions to local temperature due to the absence of phonon interactions, result in the concave temperature profile and overcooling effect. For the anharmonic model, thanks to the phonon-phonon interactions, the localized modes are excited and make considerable contributions to interfacial temperature, which is clearly shown by examining the temperature accumulation function. When anharmonicity is considerably large, the negative temperature gradient is absent since the localized phonon modes are fully mixed. The presence of localized modes are evidently demonstrated by the inverse participation ratio and normal mode analysis for the isolated harmonic model. The localized modes make contribution to interfacial temperature profiles of the harmonic system when they are excited in initial conditions of simulations.

Based upon our compact group approach and the Hashin-Shtrikman variational theorem, we propose a solution, which effectively incorporates many-particle effects in concentrated systems, to the problem of the effective quasistatic permittivity of dispersions of graded dielectric particles. After the theory is shown to recover existing analytical results and simulation data for dispersions of hard dielectric spheres with power-law permittivity profiles, we use it to describe the effective dielectric response of nonconducting polymer-ceramic composites modeled as dispersions of dielectric core-shell particles. Possible generalizations of the results are specified.

In recent years it was shown both theoretically and experimentally that in certain systems exhibiting anomalous diffusion the time- and ensemble-averaged mean-squared displacement are remarkably different. The ensemble-averaged diffusivity is obtained from a scaling Green-Kubo relation, which connects the scale-invariant nonstationary velocity correlation function with the transport coefficient. Here we obtain the relation between time-averaged diffusivity, usually recorded in single-particle tracking experiments, and the underlying scale-invariant velocity correlation function. The time-averaged mean-squared displacement is given by $\langle \overline{{\delta }^2}\rangle \sim 2D_{\nu }{t}^{\beta }{\mathrm{\Delta }}^{\nu -\beta }$, where $t$ is the total measurement time and $\mathrm{\Delta }$ is the lag time. Here $\nu$ is the anomalous diffusion exponent obtained from ensemble-averaged measurements $\langle x^2\rangle \sim t^{\nu }$, while $\beta \ge -1$ marks the growth or decline of the kinetic energy $\langle v^2\rangle \sim t^{\beta }$. Thus, we establish a connection between exponents that can be read off the asymptotic properties of the velocity correlation function and similarly for the transport constant $D_{\nu }$. We demonstrate our results with nonstationary scale-invariant stochastic and deterministic models, thereby highlighting that systems with equivalent behavior in the ensemble average can differ strongly in their time average. If the averaged kinetic energy is finite, $\beta =0$, the time scaling of $\langle \overline{{\delta }^2}\rangle$ and $\langle x^2\rangle$ are identical; however, the time-averaged transport coefficient $D_{\nu }$ is not identical to the corresponding ensemble-averaged diffusion constant.

We report exact results on one of the best studied models in statistical physics: the classical antiferromagnetic Ising chain in a magnetic field. We show that the model possesses an infinite cascade of thermal phase transitions (also known as disorder lines or geometric phase transitions). The phase transition is signaled by a change of asymptotic behavior of the nonlocal string-string correlation functions when their monotonic decay becomes modulated by incommensurate oscillations. The transitions occur for rarefied ($m$-periodic) strings with arbitrary odd $m$. We propose a duality transformation which maps the Ising chain onto the $m$-leg Ising tube with nearest-neighbor couplings along the legs and the plaquette four-spin interactions of adjacent legs. Then the $m$-string correlation functions of the Ising chain are mapped onto the two-point spin-spin correlation functions along the legs of the $m$-leg tube. We trace the origin of these cascades of phase transitions to the lines of the Lee-Yang zeros of the Ising chain in $m$-periodic complex magnetic field, allowing us to relate these zeros to the observable (and potentially measurable) quantities.

Critical point of liquid-gas (LG) transition does not conform with the paradigm of spontaneous symmetry breaking because there is no broken symmetry in both phases. We revisit the conjecture that this critical point belongs to the Ising class by performing large scale Monte Carlo simulations in two-dimensional free space in combination with the numerical flowgram method. Our main result is that the critical indices do agree with the Onsager values within the error of 1%–2%. This significantly improves the accuracy reported in the literature. The related problem about the role of higher order odd terms in the (real) ${\phi }^4$ field model as a mapping of the LG transition is addressed too. The scaling dimension of the ${\phi }^5$ term at criticality is shown to be the same as that of the linear one $\phi$. We suggest that the role of all higher order odd terms at criticality is simply in generating the linear field operator with the critical dimension consistent with the Ising universality class.