Lévy-type walks with correlated jumps, induced by the topology of the medium, are studied on a class of one-dimensional deterministic graphs built from generalized Cantor and Smith-Volterra-Cantor sets. The particle performs a standard random walk on the sets but is also allowed to move ballistically throughout the empty regions. Using scaling relations and the mapping onto the electric network problem, we obtain the exact values of the scaling exponents for the asymptotic return probability, the resistivity, and the mean-square displacement as a function of the topological parameters of the sets. Interestingly, the system undergoes a transition from superdiffusive to diffusive behavior as a function of the filling of the fractal. The deterministic topology also allows us to discuss the importance of the choice of the initial condition. In particular, we demonstrate that local and average measurements can display different asymptotic behavior. The analytic results are compared to the numerical solution of the master equation of the process.

We examine different types of heterogeneous hydraulic conductivity fields to ascertain the basic structural features that dominate the transport behavior. We contrast two approaches to the analysis, within the framework of the continuous time random walk (CTRW), considering recent simulations of particle transport in two correlated flow fields to discern these key features. These flow fields are the steady-state solutions of Darcy flow in systems with correlated distributions, $\mathcal{P}\mathbf{\left(}K\left(\mathbf{x}\right)\mathbf{\right)}$, of hydraulic conductivity values $K\left(\mathbf{x}\right)$. One approach uses the organizational structure of the Lagrangian velocities determined from simulations to derive correlated space-time distributions for particle tracking, which are used to fit simulated breakthrough curve (BTC) data. These fits emphasize the ability to account for both early arrival times and late-time long tailing. The other approach, in this paper, treats the simulated BTCs as “measurements” and uses a truncated power-law form of $\psi \left(t\right)$, the probability density function (pdf) of local transit times, in a partial differential equation form of CTRW. Excellent fits to both data sets are obtained with a single value of $\beta$, the key parameter that characterizes the nature of the dispersive transport. The value of $\beta$ is derivable from the high $\xi$ behavior of the pdf histogram $\Phi \left(\xi \right)$ (where $\xi$ is the inverse velocity) of the Darcy field, which determines the late-time tail within $\psi \left(t\right)$. The quality of the two fits obtained herein with a physically derived parameter set is a probe of how heterogeneous hydraulic conductivity fields with different types of correlation can affect the larger-scale transport behavior. The features that give rise to a power-law tail of local transition times and a limit of the time range for non-Fickian behavior dominate the transport. The correlation structures of the different $\mathcal{P}\mathbf{\left(}K\left(\mathbf{x}\right)\mathbf{\right)}$ play a secondary role compared to the spectrum of less frequent events (e.g., low velocity regions) that have a large effect on the aggregate of median time transitions.

We study experimentally the motion of an intruder dragged into an amorphous monolayer of horizontally vibrated grains at high packing fractions. This motion exhibits two transitions. The first transition separates a continuous motion regime at comparatively low packing fractions and large dragging force from an intermittent motion one at high packing fraction and low dragging force. Associated to these different motions, we observe a transition from a linear rheology to a stiffer response. We thereby call “fluidization” this first transition. A second transition is observed within the intermittent regime when the intruder’s motion is made of intermittent bursts separated by long waiting times. We observe a peak in the relative fluctuations of the intruder’s displacements and a critical scaling of the burst amplitudes’ distributions. This transition occurs at the jamming point ${\varphi }_J$ defined as the point where the static pressure (i.e., the pressure measured in the absence of vibration) vanishes. Investigating the motion of the surrounding grains, we show that below the fluidization transition, there is a permanent wake of free volume behind the intruder. This transition is marked by the evolution of the reorganization patterns around the intruder, which evolve from compact aggregates in the flowing regime to long-range branched shapes in the intermittent regime, suggesting an increasing role of the stress fluctuations. Remarkably, the distributions of the kinetic energy of these reorganization patterns also exhibit a critical scaling at the jamming transition.

In common with many other structured fluids, block copolymers can be effectively oriented by shear. This susceptibility to shear alignment has previously been shown to hold even in thin films, containing as few as two layers of spherical microdomains, or even a single layer of cylindrical microdomains. A phenomenological model has been proposed [M. W. Wu, R. A. Register, and P. M. Chaikin, Phys. Rev. E 74, 040801(R) (2006)] to describe the alignment of such block-copolymer films, yielding the microdomain lattice order parameter as a function of shearing temperature, stress, and time. Here we directly test the central idea of that model, that the grains which are most misaligned with the shear direction are selectively destroyed, to reform in a direction more closely aligned with the shear. Films are first shear aligned from a polygrain state into a monodomain orientation and are then subjected to a second shear, at a variable stress $\left(\sigma \right)$ and misorientation angle $\left(\delta \theta \right)$ relative to the monodomain director, allowing the effects of $\sigma$ and $\delta \theta$ to be independently and systematically probed. For both cylinder-forming and sphere-forming block copolymers, these experiments confirm the basic premise of the model, as the stress required for realignment increases monotonically as $\delta \theta$ becomes smaller. For a cylinder-forming block copolymer, we find that the characteristic stress ${\sigma }_c$ required to realign cylinders from one monodomain orientation to another is indistinguishable from that required to generate a monodomain orientation from the polygrain state. By contrast, the hexagonal lattice of spheres requires a value of ${\sigma }_c$ more than 3 times as high for reorientation than for generation of the initial monodomain orientation.

The regularity of a noisy system can modulate in various ways. It is well known that coupling in a population can lower the variability of the entire network; the collective activity is more regular. Here, we show that diffusive (reciprocal) coupling of two simple Ornstein-Uhlenbeck (O-U) processes can regularize the individual, even when it is coupled to a noisier process. In cellular networks, the regularity of individual cells is important when a select few play a significant role. The regularizing effect of coupling surprisingly applies also to general nonlinear noisy oscillators. However, unlike with the O-U process, coupling-induced regularity is robust to different kinds of coupling. With two coupled noisy oscillators, we derive an asymptotic formula assuming weak noise and coupling for the variance of the period (i.e., spike times) that accurately captures this effect. Moreover, we find that reciprocal coupling can regularize the individual period of higher dimensional oscillators such as the Morris-Lecar and Brusselator models, even when coupled to noisier oscillators. Coupling can have a counterintuitive and beneficial effect on noisy systems. These results have implications for the role of connectivity with noisy oscillators and the modulation of variability of individual oscillators.

The analysis of many natural time series and especially those related to ice core records often suffers from uneven sampling intervals. For fractional Brownian motion, we show that standard estimates of the volatility can be strongly biased due to uneven sampling. Taking these limitations into account, we study high-resolution records of temperature proxies obtained from Antarctic ice cores. We find that the volatility properties reveal a strong nonlinear component in the temperature time series for time scales of 5–200 kyr extending earlier results. These findings suggest in particular that temperature increments over these time scales appear in clusters of big and small increments—a big (positive or negative) change is most likely followed by a big (positive or negative) change and a small change is most likely followed by a small change.

We present results demonstrating the occurrence of changes in the collective dynamics of a Hamiltonian system which describes a confined microplasma characterized by long-range Coulomb interactions. In its lower energy regime, we first detect macroscopically the transition from a “crystallinelike” to a “liquidlike” behavior, which we call the “melting transition.” We then proceed to study this transition using a microscopic chaos indicator called the smaller alignment index (SALI), which utilizes two deviation vectors in the tangent dynamics of the flow and is nearly constant for ordered (quasiperiodic) orbits, while it decays exponentially to zero for chaotic orbits as $\text{exp}\left[-\left({\lambda }_1-{\lambda }_2\right)t\right]$, where ${\lambda }_1>{\lambda }_2>0$ are the two largest Lyapunov exponents. During the melting phase, SALI exhibits a peculiar stairlike decay to zero, reminiscent of “sticky” orbits of Hamiltonian systems near the boundaries of resonance islands. This alerts us to the importance of the $\Delta \lambda ={\lambda }_1-{\lambda }_2$ variations in that regime and helps us identify the energy range over which “melting” occurs as a multistage diffusion process through weakly chaotic layers in the phase space of the microplasma. Additional evidence supporting further the above findings is given by examining the ${\text{GALI}}_k$ indices, which generalize SALI $\left(={\text{GALI}}_2\right)$ to the case of $k>2$ deviation vectors and depend on the complete spectrum of Lyapunov exponents of the tangent flow about the reference orbit.

We numerically investigated the quantum-classical transition in rf-superconducting quantum interference device (SQUID) systems coupled to a dissipative environment. It is found that chaos emerges and the degree of chaos, the maximal Lyapunov exponent ${\lambda }_m$, exhibits nonmonotonic behavior as a function of the coupling strength $D$. By measuring the proximity of quantum and classical evolution with the uncertainty of dynamics, we show that the uncertainty is a monotonic function of ${\lambda }_m/D$. In addition, the scaling holds in SQUID systems to a relatively smaller ${\hslash }_{eff}$, suggesting the universality for this scaling.

The interplay between physical gelation and equilibrium phase transitions in asymmetric binary mixtures is analyzed from the effective fluid approach, in which the big particles interact via a short-range effective attraction beyond the core due to the depletion mechanism. The question of the universality of the scenario for dynamical arrest is then addressed. The comparison of the phase diagrams of the hard-sphere mixture and the Asakura-Oosawa models at various size ratios shows that strong specificity is observed for nonideal depletants. In particular, equilibrium gelation, without the competition with fluid-fluid transition is possible in mixtures of hard-sphere colloids. This is interpreted from the specificities of the effective potential, such as its oscillatory behavior and its complex variation with the physical parameters. The consequences on the dynamical arrest and the fluid-fluid transition are then investigated by considering in particular the role of the well at contact and the first repulsive barrier. This is done for the actual effective potential in the hard-sphere mixture and for a square well and shoulder model, which allows a separate discussion of the role of the different parameters, in particular on the localization length and the escape time. This study is next extended to mixtures of “hard-sphere-like” colloids with residual interactions. It confirms the trends relative to equilibrium gelation and illustrates a diversity of the phase behavior well beyond the scenarios expected from simple models.

Dense suspensions under sufficiently high shear stress can exhibit a dramatic transition to a solidlike state. This is known as extreme shear thickening and is sometimes accompanied by dilatancy. This behavior is contradictory; the material is solidlike but only when flowing. To probe the elasticity of the dilatant state, we measure the transient inertio-elastic oscillations that occur in response to step changes in applied stress. As the volume fraction of solids increases the apparent flow elasticity also increases, and the suspension flows more slowly, approaching an elastic solid, which will support stress statically.

We have studied mesogenic properties in the smectic-$A_d{P}_A$ phase of an asymmetric bent-core liquid crystal by means of polarizing optical microscopy, second-harmonic generation (SHG), electro-optical (EO), and dielectric measurements. In homeotropically aligned cells, EO switching is clearly observed from a schlieren texture with both four- and two-brush defects to a uniform bright domain under the application of very low in-plane electric field below $1\text{V}/\mu \text{m}$. The phase is SHG active under an electric field, i.e., SHG gradually increases without a threshold and saturates with the increasing field. In homogeneous cells, by applying triangular wave field at saturated voltage, the splitting of the polarization switching current peak is observed, indicating that the mesophase is antiferroelectric. The dielectric studies indicate a Debye-type relaxation of the transverse dipoles associated with the rotation of the molecules about their long axis. The dc bias-dependent dielectric relaxation time and the dielectric strength suggest that a field-induced antiferroelectric-ferroelectric phase transition occurs continuously beyond $1.2\text{V}/\mu \text{m}$ and is reversible. The field-dependent texture observation is consistent with the dielectric measurements. Two possible models are proposed to interpret the continuous phase transition.

A two-dimensional computer simulation model was proposed for tank-treading and tumbling motions of an elastic biconcave red blood cell (RBC) under steady shear flow. The RBC model consisted of an outer cellular membrane and an inner fluid; the membrane’s elastic properties were modeled by springs for stretch/compression and bending to consider the membrane’s natural state in a practical manner. Membrane deformation was coupled with incompressible viscous flow of the inner and outer fluids of the RBC using a particle method. The proposed simulation model was capable of reproducing tank-treading and tumbling motions of an RBC along with rotational oscillation, which is the transition between the two motions. In simulations using the same initial RBC shape with different natural states of the RBC membrane, only tank-treading motion was exhibited in the case of a uniform natural state of the membrane, and a nonuniform natural state was necessary to generate the rotational oscillation and tumbling motion. Simulation results corresponded to published data from experimental and computational studies. In the range of simulation parameters considered, the relative membrane elastic force versus fluid viscous force was $\sim 1$ at the transition when the natural state nonuniformity was taken into account in estimating the membrane elastic force. A combination of natural state nonuniformity and elastic spring constant determined that change in the RBC deformation at the transition is that from a large compressive deformation to no deformation, such as rigid body.

In this Brief Report we extend the classical analysis performed on the schematic model proposed in [T. Moreira, G. Q. Pellegrino, J. G. Peixoto de Faria, M. C. Nemes, F. Camargo, and A. F. R. Toledo Piza, Phys. Rev. E 77, 051102 (2008)] concerning quantum phase transitions in a bilayer system. We show that appropriate integrations along the classical periodic orbits reproduce with excellent agreement both the quantum spectrum and the expected mean value for the number of excitons in the system, quantities which are directly related to the observed boson-fermion quantum phase transition.

The nonequilibrium effective potential is calculated for the Frank model of spontaneous mirror-symmetry breaking in chemistry in which external noise is introduced to account for random environmental effects. The well-mixed limit, corresponding to negligible diffusion, and the case of diffusion in two space dimensions are studied in detail. White noise has a disordering effect in the former case, whereas in the latter case a phase transition occurs for external noise exceeding a critical intensity which racemizes the system.

The dynamics of two-dimensional thin premixed flames is addressed in the framework of mathematical models where the flow field on either side of the front is piecewise incompressible and vorticity free. Flames confined in channels with asymptotically straight impenetrable walls are considered. Besides a few free propagations along straight channels, attention is focused on flames propagating against high-speed flows and positioned near a round central obstacle or near two symmetric bumps protruding inward. Combining conformal maps and Green’s functions, a regularized generalization of Frankel’s integro-differential equation for the instantaneous front shape in each configuration is derived and solved numerically. This produces a variety of real looking phenomena: steady fronts (symmetric or not), noise-induced subwrinkles, flashback events, and breathing fronts in pulsating flows. Perspectives and open mathematical and physical problems are finally evoked.

We have made an investigation to study the plasma screening effect of dense quantum plasmas on the photodetachment cross section of hydrogen negative ion within the framework of dipole approximation. Plasma screening effect has been taken care of by the exponential cosine-screened Coulomb potential (ECSCP). The asymptotic forms of highly correlated wave functions for the initial bound states of ${\text{H}}^{-}$ and the plane wave form for the final $e^{-}-\text{H}$ states are used to evaluate the transition matrix elements. Results for photodetachment cross section in dense quantum plasmas are reported for the plasma screening parameter in the range [0.0,0.6] (in $a_0^{-1}$). In respect of the photodetachment process of ${\text{H}}^{-}$, we have also compared the plasma screening effect of a dense quantum plasma with that of a weakly coupled plasma for which plasma screening effect has been represented by the Debye model. Our results for the unscreened case agree nicely with some of the most accurate results available in the literature.

We investigate the dynamics of solitons of the cubic nonlinear Schrödinger equation (NLSE) with the following perturbations: nonparametric spatiotemporal driving of the form $f\left(x,t\right)=a\text{exp}\left[iK\left(t\right)x\right]$, damping, and a linear term which serves to stabilize the driven soliton. Using the time evolution of norm, momentum and energy, or, alternatively, a Lagrangian approach, we develop a collective-coordinate-theory which yields a set of ordinary differential equations (ODEs) for our four collective coordinates. These ODEs are solved analytically and numerically for the case of a constant, spatially periodic force $f\left(x\right)$. The soliton position exhibits oscillations around a mean trajectory with constant velocity. This means that the soliton performs, on the average, a unidirectional motion although the spatial average of the force vanishes. The amplitude of the oscillations is much smaller than the period of $f\left(x\right)$. In order to find out for which regions the above solutions are stable, we calculate the time evolution of the soliton momentum $P\left(t\right)$ and the soliton velocity $V\left(t\right)$: This is a parameter representation of a curve $P\left(V\right)$ which is visited by the soliton while time evolves. Our conjecture is that the soliton becomes unstable, if this curve has a branch with negative slope. This conjecture is fully confirmed by our simulations for the perturbed NLSE. Moreover, this curve also yields a good estimate for the soliton lifetime: the soliton lives longer, the shorter the branch with negative slope is.

Optical properties of inhomogeneous materials are, in general, scale dependent. We show that, when observed at mesoscopic scales, the local anisotropic polarizabilities depend on the volume of interaction, which may be limited by either the excitation field or material dimensions. We demonstrate the existence of a specific interaction length scale corresponding to the maximum degree of local anisotropy and discuss its relation to the detailed morphology of a disordered medium. Probing these mesoscopic scales provides information about the local structure and allows characterizing material systems that otherwise may appear similar.

Exact extended traveling wave and spatiotemporal soliton solutions to the generalized $\left(3+1\right)$-dimensional Gross-Pitaevskii equation with time-dependent coefficients are obtained. The case with constant diffraction and parabolic potential strength, but with variable gain, is discussed in some detail. It is found that gain in the system is necessary for the appearance of stable solitons.

In this paper, we propose a finite-difference-based lattice Boltzmann equation (LBE) model with multiple-relaxation times (MRT), in which the distribution functions of individual species evolve on a same regular lattice without any interpolations. Furthermore, the use of the MRT enables the model more flexible so that it can be applied to mixtures of species with different viscosities and adjustable Schmidt number. Some numerical tests are conducted to validate the model, the numerical results are found to agree well with analytical solutions/or other numerical results, and good numerical stability of the proposed LBE model is also observed.