Multiple transient memories, originally discovered in charge-density-wave conductors, are a remarkable and initially counterintuitive example of how a system can store information about its driving. In this class of memories, a system can learn multiple driving inputs, nearly all of which are eventually forgotten despite their continual input. If sufficient noise is present, the system regains plasticity so that it can continue to learn new memories indefinitely. Recently, Keim and Nagel [Phys. Rev. Lett. 107, 010603 (2011)] showed how multiple transient memories could be generalized to a generic driven disordered system with noise, giving as an example simulations of a simple model of a sheared non-Brownian suspension. Here, we further explore simulation models of suspensions under cyclic shear, focusing on three main themes: robustness, structure, and overdriving. We show that multiple transient memories are a robust feature independent of many details of the model. The steady-state spatial distribution of the particles is sensitive to the driving algorithm; nonetheless, the memory formation is independent of such a change in particle correlations. Finally, we demonstrate that overdriving provides another means for controlling memory formation and retention.

Motivated by empirical data, we develop a statistical description of the queue dynamics for large tick assets based on a two-dimensional Fokker-Planck (diffusion) equation. Our description explicitly includes state dependence, i.e., the fact that the drift and diffusion depend on the volume present on both sides of the spread. “Jump” events, corresponding to sudden changes of the best limit price, must also be included as birth-death terms in the Fokker-Planck equation. All quantities involved in the equation can be calibrated using high-frequency data on the best quotes. One of our central findings is that the dynamical process is approximately scale invariant, i.e., the only relevant variable is the ratio of the current volume in the queue to its average value. While the latter shows intraday seasonalities and strong variability across stocks and time periods, the dynamics of the rescaled volumes is universal. In terms of rescaled volumes, we found that the drift has a complex two-dimensional structure, which is a sum of a gradient contribution and a rotational contribution, both stable across stocks and time. This drift term is entirely responsible for the dynamical correlations between the ask queue and the bid queue.

The ground-state properties of the quasi-one-dimensional spin-$1/2$ antiferromagnetic Heisenberg model is investigated by using a variational method. Spins on chains along the $x$ direction are antiferromagnetically coupled with exchange $J>0$, while spins between chains in the $y$ direction are coupled either ferromagnetically ($J^{\prime }<0$) or antiferromagnetically ($J^{\prime }>0$). The staggered and the colinear antiferromagnetic magnetizations are computed and their dependence on the anisotropy parameter $\lambda =|J^{\prime }|/J$ is analyzed. It is found that an infinitesimal interchain coupling parameter is sufficient to stabilize a long-range order with either a staggered magnetization $m_s$ ($J^{\prime }>0$) or a colinear antiferromagnetic magnetization $m_{caf}$ ($J^{\prime }<0$), both behaving as $\simeq {\lambda }^{1/2}$ for $\lambda \to 0$.

Accurate localization of the epileptic seizure onset zones (SOZs) is crucial for successful surgery, which usually depends on the information obtained from intracranial electroencephalography (IEEG) recordings. The visual criteria and univariate methods of analyzing IEEG recordings have not always produced clarity on the SOZs for resection and ultimate seizure freedom for patients. Here, to contribute to improving the localization of the SOZs and to understanding the mechanism of seizure propagation over the brain, we applied spectral interdependency methods to IEEG time series recorded from patients during seizures. We found that the high-frequency ($>$80 Hz) Granger causality (GC) occurs before the onset of any visible ictal activity and causal relationships involve the recording electrodes where clinically identifiable seizures later develop. These results suggest that high-frequency oscillatory network activities precede and underlie epileptic seizures, and that GC spectral measures derived from IEEG can assist in precise delineation of seizure onset times and SOZs.

The fractal dimension of minimal spanning trees on percolation clusters is estimated for dimensions $d$ up to $d=5$. A robust analysis technique is developed for correlated data, as seen in such trees. This should be a robust method suitable for analyzing a wide array of randomly generated fractal structures. The trees analyzed using these techniques are built using a combination of Prim's and Kruskal's algorithms for finding minimal spanning trees. This combination reduces memory usage and allows for simulation of larger systems than would otherwise be possible. The path length fractal dimension $d_s$ of MSTs on critical percolation clusters is found to be compatible with the predictions of the perturbation expansion developed by T. S. Jackson and N. Read [Phys. Rev. E 81, 021131 (2010)].

The appearance of the spin-$\frac{1}{2}$ and spin-1 representations in the Frieden-Soffer extreme physical information (EPI) statistical approach to the Einstein-Podolsky-Rosen-Bohm (EPR-Bohm) experiment is shown. In order to obtain the EPR-Bohm result, in addition to the observed structural and variational information principles of the EPI method, the condition of the regularity of the probability distribution is used. The observed structural information principle is obtained from the analyticity of the logarithm of the likelihood function. It is suggested that, due to the self-consistent analysis of both information principles, quantum mechanics is covered by the statistical information theory. The estimation of the angle between the analyzers in the EPR-Bohm experiment is discussed.

A study of lateral aggregation, induced by an oscillatory field, in a magnetorheological fluid based on non-Brownian magnetic particles is presented. We investigate the behavior of chains formed by the particles, due to the simultaneous application of a static magnetic field and a sinusoidal magnetic field transverse to each other. We show that the effective oscillating field enhances the aggregation process. We discuss this result in terms of an effective particle concentration induced by the oscillating field when chains oscillate angularly and sweep the area around them. The oscillating field produces a lateral aggregation similar to that observed in systems composed of Brownian particles which is induced by thermal fluctuations. We study the effect of the oscillating field on the angular amplitude described by single chains. It is observed that the angular amplitude decreases as the frequency of the oscillating field increases; we discuss this behavior numerically in terms of a simple model for this system. Lateral aggregation is studied in detail in isolated pairs of chains of equal length at several conditions of separation and displacement. From the results, a phase diagram is obtained showing the conditions under which aggregation is possible.

Network topology and nodal dynamics are two fundamental stones of adaptive networks. Detailed and accurate knowledge of these two ingredients is crucial for understanding the evolution and mechanism of adaptive networks. In this paper, by adopting the framework of the adaptive SIS model proposed by Gross et al. [Phys. Rev. Lett. 96, 208701 (2006)] and carefully utilizing the information of degree correlation of the network, we propose a link-based formalism for describing the system dynamics with high accuracy and subtle details. Several specific degree correlation measures are introduced to reveal the coevolution of network topology and system dynamics.

We analyze the stabilization of unstable steady states by delayed feedback control with a periodic time-varying delay in the regime of a high-frequency modulation of the delay. The average effect of the delayed feedback term in the control force is equivalent to a distributed delay in the interval of the modulation, and the obtained distribution depends on the type of the modulation. In our analysis we use a simple generic normal form of an unstable focus, and investigate the effects of phase-dependent coupling and the influence of the control loop latency on the controllability. In addition, we have explored the influence of the modulation of the delays in multiple delay feedback schemes consisting of two independent delay lines of Pyragas type. A main advantage of the variable delay is the considerably larger domain of stabilization in parameter space.

The turbulent flow originating downstream of the Kelvin-Helmholtz instability in a mixing layer has great relevance in many applications, ranging from atmospheric physics to combustion in technical devices. The mixing of a substance by the turbulent velocity field is usually involved. In this paper, a detailed statistical analysis of fluctuations of a passive scalar in the fully developed region of a turbulent mixing layer from a direct numerical simulation is presented. Passive scalar spectra show inertial ranges characterized by scaling exponents $-4/3$ and $-3/2$ in the streamwise and spanwise directions, in agreement with a recent theoretical analysis of passive scalar scaling in shear flows [Celani et al., J. Fluid Mech. 523, 99 (2005)]. Scaling exponents of high-order structure functions in the streamwise direction show saturation of intermittency with an asymptotic exponent ${\zeta }_{\infty }=0.4$ at large orders. Saturation of intermittency is confirmed by the self-similarity of the tails of the probability density functions of the scalar increments at different scales $r$ with the scaling factor $r^{-{\zeta }_{\infty }}$ and by the analysis of the cumulative probability of large fluctuations. Conversely, intermittency saturation is not observed for the spanwise increments and the relative scaling exponents agree with recent results for homogeneous isotropic turbulence with mean scalar gradient. Probability density functions of the scalar increments in the three directions are compared to assess anisotropy.

The proof of existence of Vlasov-Maxwell equilibria which do not exhibit a functional dependence in terms of the single-particle energy is established. The theory deals with the kinetic treatment of multispecies axisymmetric magnetized plasmas, with particular reference to plasma systems which are slowly time varying. Aside from collisionless laboratory plasmas, the theory concerns important aspects of astrophysical scenarios, such as accretion-disk and coronal plasmas arising in the gravitational field of compact objects. Qualitative properties of the solution are investigated by making use of a perturbative kinetic theory. These concern the realization of the equilibrium kinetic distribution functions in terms of generalized Gaussian distributions and the constraints imposed by the Maxwell equations. These equilibria are shown to be generally non-neutral and characterized by the absence of the Debye screening effect. As a further application, the stability properties of these equilibria with respect to axisymmetric electromagnetic perturbations are addressed. This permits us to establish absolute stability criteria holding in such a case.

We present and numerically solve a modified form of the equation of motion for a charged particle under the influence of an external force, taking into account the radiation reaction. This covariant equation is integro-differential, as Dirac-Röhrlich's, but has several technical improvements. First, the equation has the form of Newton's second law, with acceleration isolated on the left hand side and the force depending only on positions and velocities: Thus, the equation is linear in the highest derivative. Second, the total four-force is by construction perpendicular to the four-velocity. Third, if the external force vanishes for all future times, the total force and the acceleration automatically vanish at the present time. We show the advantages of this equation by solving it numerically for several examples of external force.

We propose a model which explains how power-law crossover behavior can arise in a system which is capable of experiencing cascading failure. In our model the susceptibility of the system to cascades is described by a single number, the propagation power, which measures the ease with which cascades propagate. Physically, such a number could represent the density of unstable material in a system, its internal connectivity, or the mean susceptibility of its component parts to failure. We assume that the propagation power follows an upward drifting Brownian motion between cascades, and drops discontinuously each time a cascade occurs. Cascades are described by a continuous state branching process with distributional properties determined by the value of the propagation power when they occur. In common with many cascading models, pure power-law behavior is exhibited at a critical level of propagation power, and the mean cascade size diverges. This divergence constrains large systems to the subcritical region. We show that as a result, crossover behavior appears in the cascade distribution when an average is performed over the distribution of propagation power. We are able to analytically determine the exponents before and after the crossover.

It is shown that a standard principle of traditional catalysis—that a catalyst does not alter the final thermodynamic equilibrium of a reaction—can fail in low-pressure, heterogeneous gas-surface reactions. Kinetic theory for this epicatalysis is presented, and two well-documented experimental examples are detailed: surface ionized plasmas and hydrogen dissociation on refractory metals. This phenomenon should be observable over a wide range of temperatures and pressures, and for a broad spectrum of heterogeneous reactions. By transcending some constraints of equilibrium thermodynamics, epicatalysis might provide additional control parameters and synthetic routes for reactions, and enable product streams boosted in thermochemical energy or desirable species.

We present a systematic analysis of dynamic scaling in the time evolution of the phase order parameter for coupled oscillators with nonidentical natural frequencies in terms of the Kuramoto model. This provides a comprehensive view of phase synchronization. In particular, we extend finite-size scaling (FSS) in the steady state to dynamics, determine critical exponents, and find the critical coupling strength. The dynamic scaling approach enables us to measure not only the FSS exponent associated with the correlation volume in finite systems but also thermodynamic critical exponents. Based on the extended FSS theory, we also discuss how the sampling of natural frequencies and thermal noise affect dynamic scaling, which is numerically confirmed.

Evolutionary game theory is one of the key paradigms behind many scientific disciplines from science to engineering. In complex networks, because of the difficulty of formulating the replicator dynamics, most of the previous studies are confined to a numerical level. In this paper, we introduce a vectorial formulation to derive three classes of individuals’ payoff analytically. The three classes are pure cooperators, pure defectors, and fence-sitters. Here, fence-sitters are the individuals who change their strategies at least once in the strategy evolutionary process. As a general approach, our vectorial formalization can be applied to all the two-strategy games. To clarify the function of the fence-sitters, we define a parameter, payoff memory, as the number of rounds that the individuals’ payoffs are aggregated. We observe that the payoff memory can control the fence-sitters’ effects and the level of cooperation efficiently. Our results indicate that the fence-sitters’ role is nontrivial in the complex topologies, which protects cooperation in an indirect way. Our results may provide a better understanding of the composition of cooperators in a circumstance where the temptation to defect is larger.

We study the connection between polymers at the $\theta$ temperature on the lattice and Schramm-Loewner chains with constant step length in the continuum. The second of these realize a useful algorithm for the exact sampling of tricritical polymers, where finite-chain effects are excluded. The driving function computed from the lattice model via a radial implementation of the zipper method is shown to converge to Brownian motion of diffusivity $\kappa =6$ for large times. The distribution function of an internal portion of walk is well approximated by that obtained from Schramm-Loewner chains. The exponent of the correlation length $\nu$ and the leading correction-to-scaling exponent ${\Delta }_1$ measured in the continuum are compatible with $\nu =4/7$ (predicted for the $\theta$ point) and ${\Delta }_1=72/91$ (predicted for percolation). Finally, we compute the shape factor and the asphericity of the chains, finding surprising accord with the $\theta$-point end-to-end values.

Spherical Janus particles are one of the most prominent examples for active Brownian objects. Here, we study the diffusiophoretic motion of such microswimmers in experiment and in theory. Three stages are found: simple Brownian motion at short times, superdiffusion at intermediate times, and finally diffusive behavior again at long times. These three regimes observed in the experiments are compared with a theoretical model for the Langevin dynamics of self-propelled particles with coupled translational and rotational motion. Besides the mean square displacement also higher displacement moments are addressed. In particular, theoretical predictions regarding the non-Gaussian behavior of self-propelled particles are verified in the experiments. Furthermore, the full displacement probability distribution is analyzed, where in agreement with Brownian dynamics simulations either an extremely broadened peak or a pronounced double-peak structure is found, depending on the experimental conditions.

Dilute electrolytic cells filled with chlorobenzene containing small amounts of tetrabutylammonium tetraphenylborate show anomalous dielectric dispersions in low-frequency regions. We propose a new model for electrode polarization in order to analyze the dielectric behavior of the dilute electrolytic cells. The model comprises two capacitive components: One is the space-charge polarization accompanied with a specific ionic adsorption on electrodes, and the other is the electrode capacitance which is brought about by an electronic spillover from the electrode surface. This model can primarily explain the anomalous frequency-dependent dielectric behavior of the electrolytic cells not only with low electrolyte concentrations, but also with high concentrations and can correctly describe the characteristics of the electrode polarization reflected in the dielectric spectra.

Spherical CdSe nanoparticles, surface-treated with oleylamine and tri-octylphosphine, dispersed in ferroelectric liquid crystals, can efficiently target disclination lines, substantially altering the macroscopic properties of the host compound. Here we present an ac calorimetry and x-ray diffraction study demonstrating that for a large range of nanoparticle concentrations the smectic-$A$ layer thickness increases monotonically. This provides evidence for enhanced accumulation of nanoparticles at the smectic layers. Our results for the Smectic-$A$ (Sm$A$) to chiral smectic-$C$ (Sm$C^{*}$) phase transition of the liquid crystal S-(+)4-(2${}^{\prime }$-methylbutyl)phenyl-4${}^{\prime }$-n-octylbiphenyl-4-carboxylate (CE8) reveal that the character of the transition is profoundly changed as a function of the nanoparticle concentration. Large transition temperature shifts are recorded. Moreover, the heat-capacity peaks exhibit a crossover trend to a step-like anomaly. This behavior may be linked to the weakening of the Sm$A$ and Sm$C^{*}$ order parameter coupling responsible for the observed near-tricritical, mean-field character of the transition in bulk CE8. At lower temperatures, the presence of nanoparticles disrupts the phase sequence involving the tilted hexatic phases most likely by obstructing the establishment of long-range bond-orientational order.