We demonstrate theoretically and experimentally that the unstable delayed feedback controller is an efficient tool for stabilizing torsion-free unstable periodic orbits in nonautonomous chaotic systems. To improve the global control performance we introduce a two-step control algorithm. The problem of a linear stability of the system under delayed feedback control is treated analytically. Theoretical results are confirmed by electronic circuit experiments for a forced double-well oscillator.

We report on the experimental observations of chaos synchronizations among orthogonally polarized emissions in a dual-polarization laser. With a three-mode scheme with a single mode in one polarization and two modes in orthogonal polarizations, synchronization was achieved by the cross-saturation dynamics of population inversions when one of the dual-polarized emissions was subjected to external perturbations, i.e., self-mixing modulation or optical fiber feedback. In-phase synchronization or lag synchronization among orthogonally polarized emissions was achieved depending on the degree of cross saturation in the self-mixing modulation. Synchronization of random bursting was observed in the fiber feedback, in which two chaotic-spiking modes in one polarization with anticorrelated intensity variations synchronize the remaining mode in the orthogonal polarization cooperatively with their total intensity variation. Information sender-mediator-receiver relationships among modes, which represent the dynamical roles of individual modes for establishing the observed three types of collective synchronizations, were identified in terms of an information circulation analysis.

In this paper, we study the thermal conductivity of an anharmonically coupled chain of atoms. Numerical studies using classical dynamics have shown that the conductivity of a chain with nearest neighbor couplings diverges with chain length $L$ as $L^{\alpha }$; earlier studies found $\alpha \approx 0.4$ under a range of conditions, but a recent study on longer chains claims $\alpha =1∕3$. Analytically, this problem has been studied by calculating the relaxation rate ${\Gamma }_q$ of the normal modes of vibration as a function of its wave vector $q$. Two theoretical studies of classical chains, one using the mode-coupling formulation and the other the Boltzmann equation method, led to ${\Gamma }_q\propto q^{5∕3}$, which is consistent with $\alpha =0.4$. Here we study the problem for a quantum anharmonic chain with quartic anisotropy. We develop a low-temperature expansion for ${\Gamma }_q$ and find that, in the regime $\hslash {\omega }_q⪡k_{B}T$, ${\Gamma }_q\propto q^{5∕3}{T}^2$, where ${\omega }_q$ is the frequency of the mode. In our analysis, the relaxation arises due to umklapp scattering processes. We further evaluate the thermal conductivity of the chain using the Kubo formula, which enables us to take into account the transport relaxation time through vertex corrections for the current-current correlator. This calculation also yields $\alpha =0.4$.

In this work, we use the same strategy studied in our previous work [J. I. Jiménez-Aquino and M. Romero-Bastida, Phys. Rev. E 74, 041117 (2006)] to solve exactly the Fokker-Planck (FP) and Fokker-Planck-Kramers (FPK) equations of a charged Brownian particle in a fluid (a heavy ion in a light gas) under the influence of external fields: a constant magnetic field and, in general, time-varying mechanical and electric fields. In our proposal, a time-dependent rotation matrix is introduced to transform the Langevin equation in the phase-space $\left(\mathbf{r},\mathbf{u}\right)$ to a new space $\left({\mathbf{r}}^{\prime },{\mathbf{u}}^{\prime }\right)$. As a result, the transformed Langevin equations are very similar to those of ordinary Brownian motion in the presence of those time-varying external forces only, without the magnetic field; therefore, the associated FP and FPK equations can easily be solved in those transformed spaces. To solve these equations, we use the methods of solution developed by Chandrasekhar in the field-free case of ordinary Brownian motion. We also calculate a more general transition probability density in the velocity space by assuming an initial heavy-ion Maxwellian distribution at a temperature generally different from that corresponding to equilibrium, the same as that used by Ferrari [Physica A 163, 596 (1990)].

We investigate the emergence of correlations in granular shear flow. By increasing the density of a simulated granular flow, we observe a transition from a dilute regime, where interactions are dominated by binary collisions, to a dense regime characterized by large force networks and collective motions. With increasing density, interacting grains tend to form networks of simultaneous contacts due to the dissipative nature of collisions. We quantify the size of these networks by measuring two-point force correlations and find dramatic changes in the statistics of contact forces as the size of the networks increases.

Numerical simulations are used to test the kinetic theory constitutive relations of inertial granular shear flow. These predictions are shown to be accurate in the dilute regime, where only binary collisions are relevant, but underestimate the measured value in the dense regime, where force networks of size $\xi$ are present. The discrepancy in the dense regime is due to non-collisional forces that we measure directly in our simulations and arise from elastic deformations of the force networks. We model the non-collisional stress by summing over all paths that elastic waves travel through force networks. This results in an analytical theory that successfully predicts the stress tensor over the entire inertial regime without any adjustable parameters.

An experimental strategy has been developed specifically for the study of composition-dependent phase behavior in multicomponent artificial membranes. The strategy is based on steady-state measurements of fluorescence resonance energy transfer between freely diffusing membrane probe populations, and it is well suited for the rapid generation of large data sets. Presented in this paper are the basic principles that guide the experiment’s design, the derivation of an underlying mathematical model that serves to interpret the data, and experimental results that confirm the model’s predictive power.

We show that two coupled map lattices that are mutually coupled to one another with a delay can display zero delay synchronization if they are driven by a third coupled map lattice. We analytically estimate the parametric regimes that lead to synchronization and show that the presence of mutual delays enhances synchronization to some extent. The zero delay or isochronal synchronization is reasonably robust against mismatches in the internal parameters of the coupled map lattices, and we analytically estimate the synchronization error bounds.

The emission of electromagnetic radiation by localized complex electric charge and current distributions is studied. A statistical formalism in terms of general dynamical multipole fields is developed. The appearing coefficients are treated as stochastic variables. Hereby as much as possible a priori physical knowledge is exploited. First results of simulated statistical electromagnetic fields as a function of position are presented. Sampling this field at one point approximates its resulting probability density.

We investigate the performance of Brownian motors in environments governed by the “porous medium” equation ${\partial }_t\rho =D{\partial }_x\left({\rho }^{\nu -1}{\partial }_x\rho \right)$, where $\rho$ is the density and $D$ and $\nu$ positive constants. This nonlinear equation yields anomalous diffusion when $\nu \ne 1$: subdiffusion for $\nu >1$ and superdiffusion for $\nu <1$. The thermal ratchet is modeled by an overdamped Brownian particle subject to a one-dimensional, spatially periodic, asymmetric potential, modulated by time-periodic fluctuations. We scrutinize the transport properties in the adiabatic limit. The superdiffusive regime, in comparison with the normal one, exhibits transport enhancement for small amplitudes of the temporal fluctuations. Meanwhile, the subdiffusive regime displays more strident features: The flux may become forbidden in one or in both directions. As a consequence, when the blockade is unidirectional, purely directed transport occurs.

Large-scale Monte Carlo simulations are used to explore the effect of quenched disorder on one-dimensional, nonequilibrium kinetic Ising models with locally broken spin symmetry, at zero temperature (the symmetry is broken through spin-flip rates that differ for “+” and “−”spins). The model is found to exhibit a continuous phase transition to an absorbing state. The associated critical behavior is studied at zero branching rate of kinks, through analysis spreading of + and − spins, and of the kink density. Impurities exert a strong effect on the critical behavior only for a particular choice of parameters, corresponding to the strongly spin-anisotropic kinetic Ising model introduced by Majumdar et al. [Phys Rev. Lett 86, 2301 (2001)]. Typically, disorder effects become evident for impurity strengths such that diffusion is nearly blocked. In this regime, the critical behavior is similar to that arising, for example, in the one-dimensional diluted contact process, with Griffiths-like behavior for the kink density. We find variable cluster exponents, which obey a hyperscaling relation, and are similar to those reported by Cafiero et al. [Phys Rev. E 57, 5060 (1998)]. We also show that the isotropic two-component $AB\to \stackrel{̸}{0}$ model is insensitive to reaction disorder, and that only logarithmic corrections arise, induced by strong disorder in the diffusion rate.

Zeros of the partition function of the one-dimensional ferromagnetic and antiferromagnetic Blume-Capel models have been studied by using the transfer matrix method in the thermodynamic limit and for finite size chains. The equation for the distribution of zeros of the partition function in the thermodynamic limit is derived. The distribution of the Yang-Lee and Fisher zeros are studied for a variety of values of the parameters of the model. Densities of the Yang-Lee and Fisher zeros are investigated and a singular behavior of the corresponding densities of zeros at the edge points is shown. The edge singularity exponents are calculated analytically for the densities of the Yang-Lee and Fisher zeros. It is found that for both cases edge singularity exponents are universal and equal to $\sigma =-\frac{1}{2}$.

We present a systematic investigation of the morphology and space-filling properties of polydisperse densely packed granular media in two dimensions. A numerical procedure is introduced to generate collections of circular particles with size distributions of variable shape and span constrained by explicit criteria of statistical representativity. We characterize the domain of statistically accessible distribution parameters for a bounded number of particles. This particle generation procedure is used with two different deposition protocols in order to build large close-packed samples of prescribed polydispersity. We find that the solid fraction is a strongly nonlinear function of the size span, and the highest levels of solid fraction occur for the uniform distribution by volume fractions. As the span is increased, a transition occurs from a regime of topological disorder where the packing properties are governed by particle connectivity to a regime of metric disorder where pore-filling small particles prevail. The polydispersity manifests itself in the first regime through the variability of local coordination numbers. We observe a continuous decrease of the number of particles with four contacts and the growth of two populations of particles with three and five contacts. In the second regime, radial distribution functions show that the material is homogeneous beyond only a few average particle diameters. We also show that the packing orientational order is linked with fabric anisotropy and it declines with size span.

We study the length distribution of a particular class of DNA sequences known as the $5^{\prime }$ untranslated regions exons. These exons belong to the messenger RNA of protein coding genes, but they are not coding (they are located upstream of the coding portion of the mRNA) and are thus less constrained from an evolutionary point of view. We show that in both mice and humans these exons show a very clean power law decay in their length distribution and suggest a simple evolutionary model, which may explain this finding. We conjecture that this power law behavior could indeed be a general feature of higher eukaryotes.

We study the flow of a viscoelastic fluid flowing in an occluded tube due to either central or peripheral obstructions. We show that, by driving the fluid with a dynamic pressure gradient at the frequency that maximizes the dynamic permeability of the obstructed system, the magnitude of the flow can partially be recovered without the removal of the obstruction. We compare the results obtained for the two types of occlusions studied and find that flow recovering is larger in the case of central occlusions.

The critical behavior of the Ising model on a one-dimensional network, which has long-range connections at distances $l>1$ with the probability $\Theta \left(l\right)\sim l^{-m}$, is studied by using Monte Carlo simulations. Through analyzing the Ising model on networks with different $m$ values, this paper discusses the impact of the global correlation, which decays with the increase of $m$, on the phase transition of the Ising model. Adding the analysis of the finite-size scaling of the order parameter $\left[⟨M⟩\right]$, it is observed that in the whole range of $0<m<2$, a finite-temperature transition exists, and the critical exponents show consistence with mean-field values, which indicates a mean-field nature of the phase transition.

A covariant Fokker-Planck-type equation for a simple gas and an equation for the Brownian motion are derived from a relativistic kinetic theory based on the Boltzmann equation. For the simple gas the dynamic friction four-vector and the diffusion tensor are identified and written in terms of integrals which take into account the collision processes. In the case of Brownian motion, the Brownian particles are considered as nonrelativistic, whereas the background gas behaves as a relativistic gas. A general expression for the semirelativistic viscous friction coefficient is obtained and the particular case of constant differential cross section is analyzed for which the nonrelativistic and ultrarelativistic limiting cases are calculated.

Effects of sequence disorder on looping and cyclization of the double-stranded DNA are studied theoretically. Both random intrinsic curvature and inhomogeneous bending rigidity are found to result in a remarkably wide distribution of cyclization probabilities. For short DNA segments, the range of the distribution reaches several orders of magnitude for even completely random sequences. The ensemble averaged values of the cyclization probability are also calculated, and the connection to the recent experiments is discussed.

The entanglement density of amorphous glassy polymers is well known to control their fracture mechanisms under tensile loading. There have been some reports indicating substantial deformation of a glassy polymer’s surface region when exposed to interfacial friction. It is shown conclusively here that there is a direct correlation between the entanglement density of a glassy polymer and the deformation mechanisms that facilitate sliding friction. This correlation was shown experimentally by studying the topography of polymer surfaces following a single sliding pass by an inorganic glass sphere. Four different polymers were studied, including polystyrene cross linked to different degrees. It is also shown that permanent plastic deformation accompanies interfacial friction, and, furthermore, that the type of deformation is a direct function of the respective polymer’s entanglement density. In contrast, no difference in the observed friction force could be attributed to the entanglement density of the respective polymers. The findings can be explained by the state- and rate-dependent friction model.