It is a commonly observed phenomenon that spherical particles with inertia in an incompressible fluid do not behave as ideal tracers. Due to the inertia of the particle, the planar dynamics are described in a four-dimensional phase space and thus can differ considerably from the ideal tracer dynamics. Using finite-time Lyapunov exponents, we compute the sensitivity of the final position of a particle with respect to its initial velocity, relative to the fluid, and thus partition the relative velocity subspace at each point in configuration space. The computations are done at every point in the relative velocity subspace, thus giving a sensitivity field. The Stokes number, being a measure of the independence of the particle from the underlying fluid flow, acts as a parameter in determining the variation in these partitions. We demonstrate how this partition framework can be used to segregate particles by Stokes number in a fluid. The fluid model used for demonstration is a two-dimensional cellular flow.

Droplets coalescing at a planar fluid-fluid interface are studied in detail in the Stokes regime with high speed photography. Attention is paid to the expansion of the interfacial bridge, formed between the droplet and interface, as it expands during the process. We report a hydrodynamic instability at the rim of the interfacial bridge. As the rim becomes unstable, it forms a series of tendrils which themselves become unstable and produce micron sized droplets. We show that rim stability depends on drop and medium viscosities as well as the rim geometry.

Consider a random medium consisting of $N$ points randomly distributed so that there is no correlation among the distances separating them. This is the random link model, which is the high dimensionality limit (mean-field approximation) for the Euclidean random point structure. In the random link model, at discrete time steps, a walker moves to the nearest point, which has not been visited in the last $\mu$ steps (memory), producing a deterministic partially self-avoiding walk (the tourist walk). We have analytically obtained the distribution of the number $n$ of points explored by the walker with memory $\mu =2$, as well as the transient and period joint distribution. This result enables us to explain the abrupt change in the exploratory behavior between the cases $\mu =1$ (memoryless walker, driven by extreme value statistics) and $\mu =2$ (walker with memory, driven by combinatorial statistics). In the $\mu =1$ case, the mean newly visited points in the thermodynamic limit $(N⪢1)$ is just $⟨n⟩=e=2.72\dots$ while in the $\mu =2$ case, the mean number $⟨n⟩$ of visited points grows proportionally to $N^{1∕2}$. Also, this result allows us to establish an equivalence between the random link model with $\mu =2$ and random map (uncorrelated back and forth distances) with $\mu =0$ and the abrupt change between the probabilities for null transient time and subsequent ones.

We have calculated the phase diagrams of one-component fluids made of five types of biaxial particles differing in their cross sections. The orientation of the principal particle axis is fixed in space, while the second axis is allowed to freely rotate. We have constructed a free-energy density functional based on fundamental-measure theory to study the relative stability of nematic and smectic phases with uniaxial, biaxial, and tetratic symmetries. Minimization of the density functional allows us to study the phase behavior of the biaxial particles as a function of the cross-section geometry. For low values of the aspect ratio of the particle cross section, we obtain smectic phases with tetratic symmetry, although metastable with respect to the crystal, as our Monte Carlo simulation study indicates. For large particle aspect ratios and in analogy with previous work [A. G. Vanakaras, M. A. Bates, and D. J. Photinos, Phys. Chem. Chem. Phys. 5, 3700 (2003)], we have found a four-phase point where four spinodals, corresponding to phase transitions between phases with different symmetries, meet together. The location of this point is quite sensitive to particle cross section, which suggests that optimizing the particle geometry could be a useful criterion in the design of colloidal particles that can exhibit an increased stability of the biaxial nematic phase with respect to other competing phases with spatial order.

We study in detail the recent suggestions by Tshiprut et al. [Phys. Rev. Lett. 95, 016101 (2005)] to tune tribological properties at the nanoscale by subjecting a substrate to periodic mechanical oscillations. We show that both in stick-slip and sliding regimes of motion friction can be tuned and reduced by controlling the frequency and amplitude of the imposed substrate lateral excitations. We demonstrate that the mechanisms of oscillation-induced reduction of friction are different for stick-slip and sliding dynamics. In the first regime the effect results from a giant enhancement of surface diffusion, while in the second regime it is due to the interplay between washboard and oscillation frequencies that leads to the occurrence of parametric resonances. Moreover, we show that for a particular set of parameters it is possible to sustain the motion with only the oscillations.

We derive an exact formula to calculate the absorption strength in absorbing chaotic systems such as microwave cavities or acoustic resonators. The formula allows us to estimate the absorption strength as a function of the averaged reflection coefficient and the real coupling parameter. We also define the weak and strong absorption regimes in terms of the coupling parameter and the absorption strength.

Using a recently developed geometrical method, we study the transition from order to chaos in an important class of Hamiltonian systems. We show agreement between this geometrical method and the surface of section technique applied to detect chaotic behavior. We give, as a particular illustration, detailed results for an important class of potentials obtained from the perturbation of an oscillator Hamiltonian by means of higher-order polynomials.

A class of controlled synchronization systems under information constraints imposed by limited information capacity of the coupling channel is analyzed. It is shown that the framework proposed by Fradkov et al., [Phys. Rev. E 73, 066209 (2006)] is suitable not only for observer-based synchronization but also for controlled master-slave synchronization via a communication channel with limited information capacity. A simple first-order coder-decoder scheme is proposed and a theoretical analysis for multidimensional master-slave systems represented in the Lurie form (linear part plus nonlinearity depending only on measurable outputs) is provided. An output feedback control law is proposed based on the passification method. It is shown that for systems with passifiable linear part (satisfying the hyperminimum phase condition) the upper bound of the limiting synchronization error is proportional to the upper bound of the transmission error. As a consequence, both upper and lower bounds of the limiting synchronization error are proportional to the maximum rate of the coupling signal and inversely proportional to the information transmission rate (channel capacity). The results are applied to controlled synchronization of two chaotic Chua systems coupled via a controller and a channel with limited capacity. It is shown by computer simulation that, unlike for the case of observer-based synchronization, the hyperminimum phase property cannot be violated for controlled synchronization.

We address the analysis of the energy flow properties of lattice Hamiltonian systems: precisely, we investigate, by using analytical methods, a schematically anharmonic and inhomogeneous model: namely, the chain of oscillators with self-consistent reservoirs. We obtain a symmetric thermal conductivity even for a system with inhomogeneous interparticle interactions or with graded particle masses. Our results show that inhomogeneity in a system obeying Fourier’s law does not guarantee an asymmetric heat flow, and they pose the question if only anharmonicity and inhomogeneity are sufficient to assure a significative thermal rectification in a system, as suggested in the recent literature for graded structures.

We study the influence of thermal fluctuations in the phase diagram of a recently introduced two-dimensional phase field crystal model with an external pinning potential. The model provides a continuum description of pinned lattice systems allowing for both elastic deformations and topological defects. We introduce a nonconserved version of the model and determine the ground-state phase diagram as a function of lattice mismatch and strength of the pinning potential. Monte Carlo simulations are used to determine the phase diagram as a function of temperature near commensurate phases. The results show a rich phase diagram with commensurate, incommensurate, and liquidlike phases with a topology strongly dependent on the type of ordered structure. A finite-size scaling analysis of the melting transition for the $c(2\times 2)$ commensurate phase shows that the thermal correlation length exponent $\nu$ and specific heat behavior are consistent with the Ising universality class as expected from analytical arguments.

The synchrony and variability of the coupled Langevin model subjected to spatially correlated additive and multiplicative noise are discussed. We have employed numerical simulations and the analytical augmented-moment method, which is the second-order moment method for local and global variables [H. Hasegawa, Phys. Rev. E 67, 041903 (2003)]. It has been shown that the synchrony of an ensemble is increased (decreased) by a positive (negative) spatial correlation in both additive and multiplicative noise. Although the variability for local fluctuations is almost insensitive to spatial correlations, that for global fluctuations is increased (decreased) by positive (negative) correlations. When a pulse input is applied, the synchrony is increased for the correlated multiplicative noise, whereas it may be decreased for correlated additive noise coexisting with uncorrelated multiplicative noise. An application of our study to neuron ensembles has demonstrated the possibility that information is conveyed by the variance and synchrony in input signals, which accounts for some neuronal experiments.

We study the rheology of sheared granular flows close to a jamming transition. We use the approach of partially fluidized theory (PFT) with a full set of equations extending the thin layer approximation derived previously for the description of the granular avalanches phenomenology. This theory provides a picture compatible with a local rheology at large shear rates [G. D. R. Midi, Eur. Phys. J. E 14, 341 (2004)] and it works in the vicinity of the jamming transition, where a description in terms of a simple local rheology comes short. We investigate two situations displaying important deviations from local rheology. The first one is based on a set of numerical simulations of sheared soft two-dimensional circular grains. The next case describes previous experimental results obtained on avalanches of sandy material flowing down an incline. Both cases display, close to jamming, significant deviations from the now standard Pouliquen’s flow rule [O. Pouliquen, Phys. Fluids 11, 542 (1999); 11, 1956 (1999)]. This discrepancy is the hallmark of a strongly nonlocal rheology and in both cases, we relate the empirical results and the outcomes of PFT. The numerical simulations show a characteristic constitutive structure for the fluid part of the stress involving the confining pressure and the material stiffness that appear in the form of an additional dimensionless parameter. This constitutive relation is then used to describe the case of sandy flows. We show a quantitative agreement as far as the effective flow rules are concerned. A fundamental feature is identified in PFT as the existence of a jammed layer developing in the vicinity of the flow arrest that corroborates the experimental findings. Finally, we study the case of solitary erosive granular avalanches and relate the outcome with the PFT analysis.

Colloidal particles that are confined to an interface such as the air-water interface are an example of a two-dimensional fluid. Such dispersions have been observed to spontaneously form cluster and stripe morphologies in certain systems with isotropic pair potentials between the particles, due to the fact that the pair interaction between the colloids has competing attraction and repulsion over different length scales. Here we present a simple density functional theory for a model of such a two-dimensional fluid. The theory predicts a bulk phase diagram exhibiting cluster, stripe, and bubble modulated phases, in addition to homogeneous fluid phases. Comparing with simulation results for this model from the literature, we find that the theory is qualitatively reliable. The model allows for a detailed investigation of the structure of the fluid and we are able to obtain simple approximate expressions for the static structure factor and for the length scale characterizing the modulations in the microphase separated phases. We also investigate the behavior of the system under confinement between two parallel hard walls. We find that the confined fluid phase behavior can be rather complex.

Extensive two-dimensional Langevin dynamics simulations are used to determine the effect of steady shear flows on the crystal nucleation kinetics of charge stabilized colloids and colloids whose pair potential possess an attractive shallow well of a few $k_{B}T$’s (attractive colloids). Results show that in both types of systems small amounts of shear speeds up the crystallization process and enhances the quality of the growing crystal significantly. Moderate shear rates, on the other hand, destroy the ordering in the system. The very high shear rate regime where a reentering transition to the ordered state could exist is not considered in this work. In addition to the crystal nucleation phenomena, the analysis of the transport properties and the characterization of the steady state regime under shear are performed.

Cyclic dominance of three species is a commonly occurring interaction dynamics, often denoted the rock-paper-scissors (RPS) game. Such a type of interactions is known to promote species coexistence. Here, we generalize recent results of Reichenbach et al. [Nature (London) 448, 1046 (2007)] of a four-state variant of the RPS game. We show that spiral formation takes place only without a conservation law for the total density. Nevertheless, in general, fast diffusion can destroy species coexistence. We also generalize the four-state model to slightly varying reaction rates. This is shown both analytically and numerically not to change pattern formation, or the effective wavelength of the spirals, and therefore not to alter the qualitative properties of the crossover to extinction.

The equilibrium free-energy landscape of off-lattice model heteropolymers as a function of an internal coordinate, namely the end-to-end distance, is reconstructed from out-of-equilibrium steered molecular dynamics data. This task is accomplished via two independent methods: By employing an extended version of the Jarzynski equality and the inherent structure formalism. A comparison of the free energies estimated with these two schemes with equilibrium results obtained via the umbrella sampling technique reveals a good quantitative agreement among all the approaches in a range of temperatures around the “folding transition” for the two examined sequences. In particular, for the sequence with good foldability properties, the mechanically induced structural transitions can be related to thermodynamical aspects of folding. Moreover, for the same sequence the knowledge of the landscape profile allows for a good estimation of the lifetimes of the native configuration for temperatures ranging from the folding to the collapse temperature. For the random sequence, mechanical and thermal unfolding appear to follow different paths along the landscape.

Social, technological, and economic time series are divided by events which are usually assumed to be random, albeit with some hierarchical structure. It is well known that the interevent statistics observed in these contexts differs from the Poissonian profile by being long-tailed distributed with resting and active periods interwoven. Understanding mechanisms generating consistent statistics has therefore become a central issue. The approach we present is taken from the continuous-time random-walk formalism and represents an analytical alternative to models of nontrivial priority that have been recently proposed. Our analysis also goes one step further by looking at the multifractal structure of the interevent times of human decisions. We here analyze the intertransaction time intervals of several financial markets. We observe that empirical data describe a subtle multifractal behavior. Our model explains this structure by taking the pausing-time density in the form of a superstatistics where the integral kernel quantifies the heterogeneous nature of the executed tasks. A stretched exponential kernel provides a multifractal profile valid for a certain limited range. A suggested heuristic analytical profile is capable of covering a broader region.

We study chemical patterns arising from instabilities in reaction-diffusion-advection systems under the influence of shear flow. Turing pattern formation without shear flow can occur in an activator-inhibitor system as long as the diffusivity of the inhibitor is larger than the diffusivity of the activator. In the presence of shear flow, a homogeneous steady state can become unstable even if this condition is not satisfied. Chemical patterns arise as a result of this instability. We study this instability in a simple system consisting of two layers moving relative to each other. We carry out a linear stability analysis showing the onset of the instability as a function of the relative speed between the layers. We solve numerically the nonlinear reaction-diffusion-advection equations to obtain these patterns. We find stationary, oscillatory, and drifting patterns extending along each layer. We also find regions of bistability that allow the formation of localized structures. The instability is analyzed in terms of Taylor dispersion.

Tossing the dice is commonly considered a paradigm for chance. But where in the process of throwing a cube does the randomness reside? After all, for all practical purposes the motion is described by the laws of deterministic classical mechanics. Therefore the undisputed status of dice as random number generators calls for a careful analysis. This paper is an attempt in that direction. As a simplified model of a dice a barbell with two marked masses at its tips and only two final positions is considered. It is shown how, depending on initial conditions and the degree of dissipation during bounces, the outcome is only more or less unpredictable: the system is not truly random but pseudorandom—even under conditions where it appears to be random.

The dynamics of capillary filling in the presence of chemically coated heterogeneous boundaries is investigated both theoretically and numerically. In particular, by mapping the equations of front motion onto the dynamics of a dissipative driven oscillator, an analytical criterion for front pinning is derived under the condition of diluteness of the coating spots. The criterion is tested against two-dimensional lattice Boltzmann simulations and found to provide satisfactory agreement as long as the width of the front interface remains much thinner than the typical heterogeneity scale of the chemical coating.