We consider synchronization of chaotic systems coupled indirectly through common environment where the environment has an intrinsic dynamics of its own modulated via feedback from the systems. We find that a rich variety of synchronization behavior, such as in-phase, antiphase, complete, and antisynchronization, is possible. We present an approximate stability analysis for the different synchronization behaviors. The transitions to different states of synchronous behavior are analyzed in the parameter plane of coupling strengths by numerical studies for specific cases such as Rössler and Lorenz systems and are characterized using various indices such as correlation, average phase difference, and Lyapunov exponents. The threshold condition obtained from numerical analysis is found to agree with that from the stability analysis.

An effective characterization of chaotic conservative Hamiltonian systems in terms of the curvature associated with a Riemannian metric tensor derived from the structure of the Hamiltonian has been extended to a wide class of potential models of standard form through definition of a conformal metric. The geodesic equations reproduce the Hamilton equations of the original potential model through an inverse map in the tangent space. The second covariant derivative of the geodesic deviation in this space generates a dynamical curvature, resulting in (energy-dependent) criteria for unstable behavior different from the usual Lyapunov criteria. We show here that this criterion can be constructively used to modify locally the potential of a chaotic Hamiltonian model in such a way that stable motion is achieved. Since our criterion for instability is local in coordinate space, these results provide a minimal method for achieving control of a chaotic system.

Although potential flows are irrotational, Lagrangian chaos can occur when these are unsteady, with rapid global mixing observed upon flow parameter optimization. What is unknown is whether Lagrangian chaos in potential flows results in accelerated scalar dispersion, to what magnitude, how robustly, and via what mechanisms. We consider scalar dispersion in a model unsteady potential flow, the Lagrangian topology of which is well understood. The asymptotic scalar dispersion rate $q$ and corresponding scalar distribution (strange eigenmode) are calculated over the flow parameter space $\mathcal{Q}$ for Peclét numbers $\text{Pe}={10}^1–{10}^4$. The richness of solutions over $\mathcal{Q}$ increases with Pe, with pattern mode locking, symmetry breaking transitions to chaos and fractally distributed maxima observed. Such behavior suggests detailed global resolution of $\mathcal{Q}$ is necessary for robust optimization, however localization of local optima to bifurcations between periodic and subharmonic eigenmodes suggests novel efficient means of optimization. Acceleration rates of 150 fold at $\text{Pe}={10}^4$ are observed; significantly greater than corresponding values for chaotic Stokes flows, suggesting significant scope for dispersion acceleration in potential flows in general.

The paper extends one-body effective-medium theory to incorporate the correct second-order interactions in a two-dimensional Maxwell-Garnett theory. The two-body inclusion problem is solved using the averaged dipole moments that are induced by the scattering electromagnetic field on the medium/inclusion system. By incorporating the appropriate polarizability factor in the solutions, conventional right-handed media with binary embeddings are analyzed while a different form for the polarizability term allows the study of the effective properties of a metasurface. In both cases, it is shown that the two-body coefficient to second order in the low area fraction of inclusions is exact, while the corresponding results of the Maxwell-Garnett and Bruggeman theories are incorrect. This is especially true in the superconducting and holes limits, respectively. In the study of metasurfaces, the requirement for electromagnetic screening of the inclusions as well as the requirement needed to achieve the Fröhlich condition are stated. Negative permittivity and permeability are presented for strong-scattering showing negative resonances for a given frequency spectrum. It is shown that these resonances disappear when we derive the weak-scattering limit. The possibility of obtaining doubly negative effective permittivity and permeability is discussed by using an appropriate polarization for the applied electromagnetic field propagating in the metasurface. Finally, the potential difference and hence voltage and capacitance between binary inclusions is determined for surfaces/metasurfaces which allows, in the case of metasurfaces, the behavior of split-ring-type resonators to be investigated.

We extend here the finite-difference-time-domain (FDTD) algorithm working in oblique incidence to dispersive media. The split-field method (SFM) is used and adapted for taking into account the metal dispersion. The additional equations to the FDTD algorithm are given. Instead of the 24 field components usually used in the SFM, 38 and 112 field components are needed to implement the cases of Drude and Drude-Lorentz dispersion models, respectively. Some tests are presented to validate our code as long as the angle of incidence is lower than $76°$ in addition to an application dealing with enhanced transmission and showing original results.

We discuss the propagation of electromagnetic waves in layered structures made up of alternate layers of air and metamaterials. The role played by absorption on the existence of electric and magnetic plasmon polaritons is investigated. Results show that plasmon-polariton modes are robust even in the presence of rather large absorption.

We present a renormalization-group (RG) approach to explain universal features of extreme statistics applied here to independent identically distributed variables. The outlines of the theory have been described in a previous paper, the main result being that finite-size shape corrections to the limit distribution can be obtained from a linearization of the RG transformation near a fixed point, leading to the computation of stable perturbations as eigenfunctions. Here we show details of the RG theory which exhibit remarkable similarities to the RG known in statistical physics. Besides the fixed points explaining universality, and the least stable eigendirections accounting for convergence rates and shape corrections, the similarities include marginally stable perturbations which turn out to be generic for the Fisher-Tippett-Gumbel class. Distribution functions containing unstable perturbations are also considered. We find that, after a transitory divergence, they return to the universal fixed line at the same or at a different point depending on the type of perturbation.

We explicitly calculate the distance dependent correlation functions in a maximal entropy ensemble of random trees. We show that correlations remain disassortative at all distances and vanish only as a second inverse power of the distance. We discuss in detail the example of scale-free trees where the diverging second moment of the degree distribution leads to some interesting phenomena.

When an object is dropped into a bed of fine, loosely packed sand, a surprisingly energetic jet shoots out of the bed. In this work we study the effect that boundaries have on the granular jet formation. We did this by (i) decreasing the depth of the sand bed and (ii) reducing the container diameter to only a few ball diameters. These confinements change the behavior of the ball inside the bed, the void collapse, and the resulting jet height and shape. We map the parameter space of impact with Froude number, ambient pressure, and container dimensions as parameters. From these results we propose an explanation for the thick-thin structure of the jet reported by several groups ([J. R. Royer et al., Nat. Phys. 1, 164 (2005)], [G. Caballero et al., Phys. Rev. Lett. 99, 018001 (2007)], and [J. O. Marston et al., Phys. Fluids 20, 023301 (2008)]).

We study smooth, slightly inelastic particles flowing under gravity on a bumpy inclined plane using event-driven and discrete-element simulations. Shallow layers (ten particle diameters) are used to enable simulation using the event-driven method within reasonable computational times. Steady flows are obtained in a narrow range of angles $\left(13°–14.5°\right)$; lower angles result in stopping of the flow and higher angles in continuous acceleration. The flow is relatively dense with the solid volume fraction, $\nu \approx 0.5$, and significant layering of particles is observed. We derive expressions for the stress, heat flux, and dissipation for the hard and soft particle models from first principles. The computed mean velocity, temperature, stress, dissipation, and heat flux profiles of hard particles are compared to soft particle results for different values of stiffness constant $\left(k\right)$. The value of stiffness constant for which results for hard and soft particles are identical is found to be $k\ge 2\times {10}^{6}mg/d$, where $m$ is the mass of a particle, $g$ is the acceleration due to gravity, and $d$ is the particle diameter. We compare the simulation results to constitutive relations obtained from the kinetic theory of Jenkins and Richman [J. T. Jenkins and M. W. Richman, Arch. Ration. Mech. Anal. 87, 355 (1985)] for pressure, dissipation, viscosity, and thermal conductivity. We find that all the quantities are very well predicted by kinetic theory for volume fractions $\nu <0.5$. At higher densities, obtained for thicker layers ($H=15d$ and $H=20d$), the kinetic theory does not give accurate prediction. Deviations of the kinetic theory predictions from simulation results are relatively small for dissipation and heat flux and most significant deviations are observed for shear viscosity and pressure. The results indicate the range of applicability of soft particle simulations and kinetic theory for dense flows.

We discuss wetting layers in phase-separated colloid-polymer mixtures adsorbed at a vertical wall, observed in recent laser scanning confocal microscopy experiments. Matching of colloid and solvent dielectric properties renders van der Waals forces negligible and provides a system governed by short-range forces and thermal fluctuations on which the subtle predictions of renormalization group (RG) theory for wetting can be tested. The width $w$ of the fluid-fluid (“liquid-gas”) interface bounding the wetting layer scales with the square root of the wetting layer thickness $\ell$, in qualitative agreement with RG theory for short-range complete wetting in three dimensions. The measured wetting layer thickness $\ell$ as a function of the height $h$ above the horizontal plane of bulk phase separation is compared with two distinct theoretical predictions. A simple heuristic interface potential $V\left(\ell \right)$, first proposed in a previous report, is now fully derived, and confronted here with the interface potential based on the linear RG theory. The heuristic approach does not capture fully the RG treatment. While fundamental differences exist between the two approaches, the resulting predictions for $\ell \left(h\right)$ are almost identical. However, the theory does not follow the precise shape of the experimental curve of $\ell \left(h\right)$.

We study dynamic scaling in a model with collective diffusion (CD) of isolated atoms in terraces and irreversible aggregation at step edges. Simulations are performed in two-dimensional substrates with several diffusion to deposition ratios $R\equiv D/F$. Data collapse of scaled roughness distributions confirms that this model is in the class of the fourth-order nonlinear growth equation by Villain, Lai, and Das Sarma (VLDS) with negligible finite-size effects, while estimates of scaling exponents show some discrepancies. This result is consistent with the prediction of a recent renormalization group approach and improves previous numerical works on related models. The roughness follows dynamic scaling as $W=L^{\alpha }/R^{1/2}f\left(\xi /L\right)$, with correlation length $\xi ={\left(Rt\right)}^{1/z}$, where $z$ is the dynamic exponent. We also propose a limited mobility (LM) model where the incident atom executes up to $G$ steps before a new atom is adsorbed, and irreversibly aggregates at step edges. This model is also shown to belong to the VLDS class. The size of the plateaus in the film surface increases as $G^{1/2}$ and the lateral correlation scales as $G^{1/2}{t}^{1/z}$. The time evolution of the roughness reproduces that of the CD model if an equivalent parameter $G\sim R^{2/z}$ is chosen. This suggests the possibility of using LM models with tunable diffusion length to simulate processes with simultaneous diffusion of many atoms. A scaling approach is used to justify exponent values and dynamic relations for both models, including the significant decrease of surface roughness as $R$ or $G$ increases.

In this work, we study the adhesion of multicomponent vesicle membrane to both flat and curved substrates, based on the conventional Helfrich bending energy for multicomponent vesicles and adhesion potentials of different forms. A phase field formulation is used to describe the different components of the vesicle. For the axisymmetric case, a number of representative equilibrium vesicle shapes are computed and a few energy diagrams are presented which reveal the dependence of the calculated shapes and solution branches on various parameters including both bending moduli and spontaneous curvatures as well as the adhesion potential constants. Our computation also confirms a recent experimental observation that the adhesion may promote phase separation in two-component vesicle membranes.

Mechanotactic cell motility has recently been shown to be a key player in the initial aggregation of crawling cells such as leukocytes and amoebae. The effects of mechanotactic signaling in the early aggregation of amoeboid cells are here investigated using a general mathematical model based on known biological evidence. We elucidate the hydrodynamic fundamentals of the direct guiding of a cell through mechanotaxis in the case where one cell transmits a mechanotactic signal through the fluid flow by changing its shape. It is found that any mechanosensing cells placed in the stimulus field of mechanical stress are able to determine the signal transmission direction with a certain angular dispersion which does not preclude the aggregation from happening. The ubiquitous presence of noise is accounted for by the model. Finally, the mesoscopic pattern of aggregation is obtained which constitutes the bridge between, on one hand, the microscopic world where the changes in the cell shape occur and, on the other hand, the cooperative behavior of the cells at the mesoscopic scale.

The Olami-Feder-Christensen model describes a limiting case of an elastic surface that slides on top of a substrate and is one of the simplest models that display some features observed in actual seismicity patterns. However, temporal and spatial correlations of real earthquakes are not correctly described by this model in its original form. I propose and study a modified version of the model, which includes a mechanism of structural relaxation. With this modification, realistic features of seismicity emerge, which are not obtained with the original version, mainly: aftershocks that cluster spatially around the slip surface of the main shock and follow the Omori law, and averaged frictional properties similar to those observed in rock friction, in particular the velocity-weakening effect. In addition, a Gutenberg-Richter law for the decaying of number of earthquakes with magnitude is obtained, with a decaying exponent within the range of experimentally observed values. Contrary to the original version of the model, a realistic value of the exponent appears without the necessity to fine tune any parameter.

We analyze gene coexpression network under the random matrix theory framework. The nearest-neighbor spacing distribution of the adjacency matrix of this network follows Gaussian orthogonal statistics of random matrix theory (RMT). Spectral rigidity test follows random matrix prediction for a certain range and deviates afterwards. Eigenvector analysis of the network using inverse participation ratio suggests that the statistics of bulk of the eigenvalues of network is consistent with those of the real symmetric random matrix, whereas few eigenvalues are localized. Based on these IPR calculations, we can divide eigenvalues in three sets: (a) The nondegenerate part that follows RMT. (b) The nondegenerate part, at both ends and at intermediate eigenvalues, which deviates from RMT and expected to contain information about important nodes in the network. (c) The degenerate part with zero eigenvalue, which fluctuates around RMT-predicted value. We identify nodes corresponding to the dominant modes of the corresponding eigenvectors and analyze their structural properties.

We investigate the onset of collective oscillations in a excitatory pulse-coupled network of leaky integrate-and-fire neurons in the presence of quenched and annealed disorder. We find that the disorder induces a weak form of chaos that is analogous to that arising in the Kuramoto model for a finite number $N$ of oscillators [O. V. Popovych et al., Phys. Rev. E 71 065201(R) (2005)]. In fact, the maximum Lyapunov exponent turns out to scale to zero for $N\to \infty$, with an exponent that is different for the two types of disorder. In the thermodynamic limit, the random-network dynamics reduces to that of a fully homogeneous system with a suitably scaled coupling strength. Moreover, we show that the Lyapunov spectrum of the periodically collective state scales to zero as $1/N^2$, analogously to the scaling found for the “splay state.”

We determined the critical Rayleigh numbers ${\text{Ra}}_c$ for the onset of convection in cylindrical containers with aspect ratios $1\lesssim \Gamma \equiv D/L\lesssim 9$ ($D$ is the diameter and $L$ the height) and the patterns that form just above ${\text{Ra}}_c$, both from experiment and by direct numerical simulation (DNS). Results for ${\text{Ra}}_c$ agree well with the linear stability analysis by Buell and Catton for containers with finite sidewall conductivity. For $\Gamma \le 1.58\pm 0.10$, we found that the patterns correspond to an azimuthal Fourier mode with mode number $m=1$, corresponding to a single convection roll. For $1.58\lesssim \Gamma \lesssim 3.26\pm 0.02$, the pattern was a concentric roll, corresponding to $m=0$. For $3.26\le \Gamma \lesssim 4$, an $m=1$ mode was found again, but near $\Gamma =4$ either $m=1$ or $m=2$ was observed in different runs. These results are consistent with the marginal stability curves calculated by Buell and Catton in the sense that the mode that is the first as a function of Ra to acquire a positive growth rate is the one that is observed. For $\Gamma \gtrsim 4$, the theoretical marginal curves for the four lowest modes lie very close together. There we found patterns near onset that corresponded to various modes, including $m=2$ and 4. At relatively large $\Gamma \gtrsim 6$, we observed parallel straight rolls quite close to onset. Our patterns agree with several DNS investigations by others, but at some $\Gamma$ values differ from those observed experimentally by Stork and Müller. Some results for the pattern evolution with increasing Ra are reported as well.

A quantum kinetic approach for the energy relaxation in strongly coupled plasmas with different electron and ion temperatures is presented. Based on the density operator formalism, we derive a balance equation for the energies of electrons and ions connecting kinetic, correlation, and exchange energies with a quite general expression for the electron-ion energy-transfer rate. The latter is given in terms of the correlation function of density fluctuations which allows for a derivation of increasingly realistic approximation schemes including a coupled-mode expression. The equilibration of the contributions of the total energy including the species temperatures in dense hydrogen and beryllium relevant for inertial confinement fusion is investigated as an example.