We address hysteresis of three-dimensional polydisperse granular packs, comparing macro- and microscopic viewpoints, to reveal their elastic/inelastic mechanics and force network anisotropy. During the uniaxial loading-unloading cycle of an appropriately prepared pack, one can decompose the force network into weak and strong subnetworks. The first stages of loading exhibit arching, where all the fabric displays negative anisotropy. For later stages, the strong (weak) network shows positive (negative) anisotropy. On unloading, the force network progresses to a fabric wide hydrostatic point, where the anisotropies of the weak and strong subnetworks switch signs. During the loading stage, a Mohr circle analysis permits the identification of a well-defined macroscopic internal friction angle, whose value is larger than that of grain-grain interactions. To analyze unloading, a generalized local Coulomb-friction argument predicts a continuously changing friction angle, that vanishes at the hydrostatic point. A suggestive interplay between microscopic friction and fabric structure, at different loding stages, is proposed as the mechanism for the emergence of a macro internal friction angle.

Particle-tracking methods are used to study gelation in a colloidal suspension of Laponite clay particles. We track the motion of small fluorescent polystyrene spheres added to the suspension, and obtain the micron-scale viscous and elastic moduli of the material from their mean-squared displacement. The fluorescent spheres move subdiffusively due to the microstructure of the suspension, with the diffusive exponent decreasing from close to one at early times to near zero as the material gels. The particle-tracking data show that the system becomes more heterogeneous on the microscopic scale as gelation proceeds. We also determine the bulk-scale moduli using small-amplitude oscillatory shear rheometry. Both the macroscopic and microscopic moduli increase with time, and on both scales we observe a transition from a primarily viscous fluid to an elastic gel. We find that the gel point, determined as the time at which the viscous and elastic moduli are equal, is length-scale dependent—gelation occurs earlier on the bulk scale than on the microscopic scale.

Within the general quadrupolar model for biaxial nematic liquid crystals, whose potential of mean torque extends that in the Maier-Saupe theory with two extra interaction terms, we propose a quantitative criterion to identify the dominant biaxial interaction. We show that the ratio of the biaxial-to-uniaxial and uniaxial-to-isotropic transition temperatures is almost independent of one interaction parameter, thus indicating the other as dominant. We also show that there is a significant mismatch between the principal orientational order parameters predicted by the theory and those measured for the biaxial phase of a tetrapode.

We consider how oscillatory activity in networks of excitable systems depends on spatial correlations of random inputs and the spatial range of feedback coupling. Analysis of a neural field model with topographic delayed recurrent feedback reveals how oscillations in certain frequency bands, including the gamma band, are enhanced by increases in the input correlation length. Further, the enhancement is maximal when this length exceeds the feedback coupling range. Suppression of oscillatory power occurs concomitantly in other bands. These effects depend solely on the ratio of input and feedback length scales. The precise positions of these bands are determined by the synaptic constants and the delays. The results agree with numerical simulations of the model and of a network of stochastic spiking neurons, and are expected for any noise-driven excitable element networks.

Extensive all-atom molecular dynamics simulations were performed to characterize the microscopic origin of the force experienced by DNA in a bulk electrolyte and a solid-state nanopore when subject to an external electrostatic field $E$. The effective screening of the DNA charge was found to originate from the hydrodynamic drag of the electro-osmotic flow that is driven by the motion of counterions along the surface of DNA. We show that the effective driving force $F$ in a nanopore obeys the same law as in a bulk electrolyte: $F=\xi \mu E$, where $\xi$ and $\mu$ are the friction coefficient and electrophoretic mobility of DNA, respectively. Using this relationship, we suggest a method for determining the effective driving force on DNA in a nanopore that does not require a direct force measurement.

In chaotically driven nonlinear dynamical systems, weak generalized synchrony can arise through distinct scenarios or routes in a manner similar to the onset of low-dimensional chaos or the creation of strange nonchaotic attractors in quasiperiodically driven systems. The limit sets of the dynamics for weak generalized synchronization are nonchaotic—the Lyapunov exponent is nonpositive—and are geometrically strange. Quantitative measures related to the parameter sensitivity exponent and finite-time Lyapunov exponent distributions can be defined in order to characterize generalized synchronization.

Using soliton amplitude and phase ansatzes, a theory is proposed for searching for stationary soliton solutions to the cubic-quintic complex Ginzburg-Landau (CGL) equation. For arbitrary combinations of system parameters, our approach allows the existence of dissipative solitons together with their specific soliton characteristics to be determined, and we demonstrate this explicitly for the case of a pulsed fiber laser system. The regimes of existence of dissipative solitons and their rules of evolution in a complicated five-dimensional parameter space are also analyzed. This work may open other research opportunities in diverse areas of nonlinear dynamics governed by the CGL equation, and may impact significantly on experimental design.

Large time evolution of concentration profiles is studied analytically for reaction-diffusion systems where the reactants $A$ and $B$ are each initially separately contained in two immiscible solutions and react upon contact and transfer across the interface according to a general $nA+mB\to C$ reaction scheme. This study generalizes to immiscible two-layer systems the large time analytical asymptotic limits of concentrations derived by Koza [J. Stat. Phys. 85, 179 (1996)] for miscible fluids and for reaction rates of the form $A^n{B}^m$ with arbitrary diffusion coefficients and homogeneous initial concentrations. In addition to a dependence on the parameters already characterizing the miscible case, the asymptotic concentration profiles in immiscible systems depend now also on the partition coefficients of the chemical species between the two solution layers and on the ratio of diffusion coefficients of a given species in the two fluids. The miscible time scalings are found to remain valid for the immiscible fluids case. However, for immiscible systems, the reaction front speed is enhanced by increasing the stoichiometry of the invading species over that of the species being invaded. The direction of the front propagation is found to depend on the diffusion coefficient of the invading species in its initial fluid but not on its value in the invading fluid. Hence, a reaction front in immiscible fluids can travel in the opposite direction to the reaction front formed in miscible fluids for a range of parameter values. The value of the invading species partition coefficient affects the magnitude of the front speed but it cannot alter the direction of the front. For sufficiently large times, the total amount of product produced in time is independent of the rate of the reaction. The centre of mass of the product can move in the opposite direction to the center of mass of the reaction rate.

The increasing ubiquity of Internet access and the frequency with which people interact with it raise the possibility of using the Web to better observe, understand, and monitor several aspects of human social behavior. Web sites with large numbers of frequently returning users are ideal for this task. If these sites belong to companies or universities, their usage patterns can furnish information about the working habits of entire populations. In this work, we analyze the properly anonymized logs detailing the access history to Emory University’s Web site. Emory is a medium-sized university located in Atlanta, Georgia. We find interesting structure in the activity patterns of the domain and study in a systematic way the main forces behind the dynamics of the traffic. In particular, we find that linear preferential linking, priority-based queuing, and the decay of interest for the contents of the pages are the essential ingredients to understand the way users navigate the Web.

We numerically investigate quantum dynamics in a one-dimensional double-well system emphasizing influence of a parametrically polychromatic perturbation on the dynamics. It is found that time dependence of transition probability for an initially localized wave packet between the wells shows two types of motion, coherent and incoherent motion, depending on the perturbation parameters. As the strength and/or the number of frequency components of the perturbation increase, coherent motion changes into incoherent one. The former is related to coherent tunneling of the wave packet due to coherence; the latter is related to a delocalized state caused by decoherence. In coherent motion, by virtue of coherence of the dynamics, the expectation value and the standard deviation of a dynamical variable such as the energy of the system show oscillatory time dependence around the initial values. On the contrary in incoherent motion, because of the decoherence, the time dependence fluctuates irregularly around a certain value after a rapid increase due to the resonance. We find that negativity of the Wigner function also show similar time dependence in each type of motion. We compare the classification of the quantum dynamics based on regularity of the time dependence with the one of corresponding classical dynamics based on the Lyapunov exponent. The classifications of the quantum and classical dynamics overlap well in the parameter space. Furthermore, we confirm decoherence of quantum dynamics in a kicked double-well system.

Dynamical properties of neural populations are studied using probabilistic cellular automata. Previous work demonstrated the emergence of critical behavior as the function of system noise and density of long-range axonal connections. Finite-size scaling theory identified critical properties, which were consistent with properties of a weak Ising universality class. The present work extends the studies to neural populations with excitatory and inhibitory interactions. It is shown that the populations can exhibit narrow-band oscillations when confined to a range of inhibition levels, with clear boundaries marking the parameter region of prominent oscillations. Phase diagrams have been constructed to characterize unimodal, bimodal, and quadromodal oscillatory states. The significance of these findings is discussed in the context of large-scale narrow-band oscillations in neural tissues, as observed in electroencephalographic and magnetoencephalographic measurements.

We have shown experimentally that the pattern created by the displacement of a more viscous fluid by a less viscous one in a radial Hele-Shaw cell develops not radially but spirally when a more viscous sodium polyacrylate solution is displaced by a less viscous trivalent iron ion $\left({\mathrm{Fe}}^{3+}\right)$ solution with a sufficiently high concentration of ${\mathrm{Fe}}^{3+}$. Another experiment revealed that an instantaneous chemical reaction takes place between the two fluids, and at high ${\mathrm{Fe}}^{3+}$ concentrations it produces a film of the gel at the contact plane. The gel film is proposed to be responsible for the spiral pattern.

We investigate the representation of Lagrangian velocities in heterogeneous porous media as Markov processes. We use numerical simulations to show that classical descriptions of particle velocities using Markov processes in time fail because low velocities are much more strongly correlated in time than high velocities. We demonstrate that Lagrangian velocities describe a Markov process at fixed distances along the particle trajectories (i.e., a spatial Markov process). This remarkable property has significant implications for modeling effective transport in heterogeneous velocity fields: (i) the spatial Lagrangian velocity transition densities are sufficient to fully characterize these complex velocity field organizations, (ii) classical effective transport descriptions that rely on Markov processes in time for the particle velocities are not suited for describing transport in heterogeneous porous media, and (iii) an alternative effective transport description derives from the Markovian nature of the spatial velocity transitions. It expresses particle movements as a random walk in space time characterized by a correlated random temporal increment and thus generalizes the continuous time random walk model to transport in correlated velocity fields.

Simulations are reported to investigate solid superheating and liquid supercooling of two-dimensional systems with a Yukawa interparticle potential. Motivated by experiments where a dusty plasma is heated and then cooled suddenly, we track particle motion using a simulation with Langevin dynamics. Hysteresis is observed when the temperature is varied rapidly in a heating and cooling cycle. As in the experiment, transient solid superheating, but not liquid supercooling, is observed. Solid superheating, which is characterized by solid structure above the melting point, is found to be promoted by a higher rate of temperature increase.

In this paper, it is shown that a double-negative or a mu-negative shell can be used to achieve a very high gain for an electrically small loop. It is also seen that together with the high gain, the metamaterial shell can be used to achieve a very uniform gain characteristic with respect to the shell dimensions. This is accomplished by a proper choice of the media parameters of the metamaterial shell and the region surrounding the antenna. This significantly eases the fabrication constraints and the close tolerances on the shell which was a major drawback towards the practical realization of the shell. Also, significant power gain can be obtained when the radiated power from the metamaterial shell is compared to the power radiated by a loop of the same radius as the outer radius of the shell. In addition, it is also found that a double-positive shell of the same dimensions as the metamaterial shell can be used to significantly increase the gain of the infinitesimal antenna. The power gain characteristics show distinct resonant peaks in this case. Excellent matching characteristics are observed corresponding to the radiated power gain.

We present an experimental measurement of the slip length of air flow close to solid surfaces using an atomic force microscope (AFM) in dynamic mode. The air was confined between a glass surface and a spherical glass particle glued to an AFM cantilever. The Knudsen number was varied continuously over three decades by varying the distance between the two surfaces. Our results show that the effect of confining the air is purely dissipative. The data are described by an isothermal Maxwell slip-boundary condition, and the measured slip-length value was $118\mathrm{nm}$.

We show that the extension of Casimir-like forces to fluctuating fluids driven out of equilibrium can exhibit two interrelated phenomena forbidden at equilibrium: self-forces can be induced on single asymmetric objects and the action-reaction principle between two objects can be violated. These effects originate in asymmetric restrictions imposed by the objects’ boundaries on the fluid’s fluctuations. They are not ruled out by the second law of thermodynamics since the fluid is in a nonequilibrium state. Considering a simple reaction-diffusion model for the fluid, we explicitly calculate the self-force induced on a deformed circle. We also show that the action-reaction principle does not apply for the internal Casimir forces between a circle and a plate. Their sum, instead of vanishing, provides the self-force on the circle-plate assembly.

We study the diffusion of $N$ particles on an infinite line. The particles obey the standard diffusion equation and interact by a hard-core interaction. The problem has an exact solution, from which we derive the single-particle and two-particle probability distributions for arbitrary initial conditions, as expansions in powers of $t^{-1∕2}$, where $t$ denotes time. Explicit expressions are given for the moments of the displacement for each of the particles and correlations of displacements between any pair of particles. The $m\text{th}$ moment grows as $t^{m∕2}$ in the leading order. Correlations in the system are quite strong. Two of the interesting features are as follows. (1) Correlation between the displacements of the central particle and that of any other particle decays with the label distance exponentially, but with a correlation length of the order of $N$. (2) Correlations of a particle near one edge with those on the other edge are much larger than with those near the center. This implies that the size of the assembly expands quite symmetrically with time as $t^{1∕2}$.

Optical trapping is a powerful tool for the micromanipulation of living cells—especially bacteria—but photodamage induced by the laser beam can adversely affect viability. We have explored optical trapping conditions in the near infrared $(840–930\mathrm{nm})$ that preserve the viability of E. coli, as measured by gene expression of green fluorescent protein. We have found that time-sharing the optical traps, i.e., dwelling only $10\mu \mathrm{s}–1\mathrm{ms}$ on the cell, improves viability relative to continuous wave (CW) exposure for the same exposure time. We have also observed that similar to CW traps the photodamage in a time-shared trap depends weakly on wavelength, but linearly on peak power, implying an effect induced by single photon absorption. Taken altogether, integrating the exposure time and peak power, the data indicate that there is a lethal energy dose of about $5\mathrm{J}$ for E. coli. Thus a single parameter—the energy—can be used to describe the limitation on viability.

Chaotic mixing in a closed vessel is studied experimentally and numerically in different two-dimensional (2D) flow configurations. For a purely hyperbolic phase space, it is well known that concentration fluctuations converge to an eigenmode of the advection-diffusion operator and decay exponentially with time. We illustrate how the unstable manifold of hyperbolic periodic points dominates the resulting persistent pattern. We show for different physical viscous flows that, in the case of a fully chaotic Poincaré section, parabolic periodic points at the walls lead to slower (algebraic) decay. A persistent pattern, the backbone of which is the unstable manifold of parabolic points, can be observed. However, slow stretching at the wall forbids the rapid propagation of stretched filaments throughout the whole domain, and hence delays the formation of an eigenmode until it is no longer experimentally observable. Inspired by the baker’s map, we introduce a 1D model with a parabolic point that gives a good account of the slow decay observed in experiments. We derive a universal decay law for such systems parametrized by the rate at which a particle approaches the no-slip wall.