For a microchamber filled with a binary electrolyte and containing a flat unbiased center electrode at one wall, we employ three numerical models to study the strength of the resulting induced-charge electro-osmotic (ICEO) flow rolls: (i) a full nonlinear continuum model resolving the double layer, (ii) a linear slip-velocity model not resolving the double layer and without tangential charge transport inside this layer, and (iii) a nonlinear slip-velocity model extending the linear model by including the tangential charge transport inside the double layer. We show that, compared to the full model, the slip-velocity models significantly overestimate the ICEO flow. This provides a partial explanation of the quantitative discrepancy between observed and calculated ICEO velocities reported in the literature. The discrepancy increases significantly for increasing Debye length relative to the electrode size, i.e., for nanofluidic systems. However, even for electrode dimensions in the micrometer range, the discrepancies in velocity due to the finite Debye length can be more than 10% for an electrode of zero height and more than 100% for electrode heights comparable to the Debye length.

A form of the linear mixing rule involving the equality of excess pressures is tested with various mole fractions and various types of orbital-free molecular dynamics simulations. For all the cases considered, this mixing rule yields, within statistical error, the pressure of a mixture of helium and iron obtained by a direct simulation. In an attempt to interpret the robustness of the mixing rule, we show that it can be derived from thermodynamic stability if the system is regarded as a mixture of independent effective average atoms. The success of the mixing rule applied with equations of state including various degrees of approximation leads us to suggest its use in the thermodynamic domain where quantum molecular dynamics can be implemented.

We use momentum-transfer arguments to predict the friction factor $f$ in two-dimensional turbulent soap film flows with rough boundaries (an analog of three-dimensional pipe flow) as a function of Reynolds number Re and roughness $r$, considering separately the inverse energy cascade and the forward enstrophy cascade. At intermediate Re, we predict a Blasius-like friction factor scaling of $f\propto {\text{Re}}^{-1/2}$ in flows dominated by the enstrophy cascade, distinct from the energy cascade scaling of ${\text{Re}}^{-1/4}$. For large Re, $f\sim r$ in the enstrophy-dominated case. We use conformal map techniques to perform direct numerical simulations that are in satisfactory agreement with theory and exhibit data collapse scaling of roughness-induced criticality, previously shown to arise in the three-dimensional pipe data of Nikuradse.

Intermolecular forces are known to precipitate adhesion events between solid bodies. Inspired by a macroscale experiment showing the hysteretic adhesion of a piece of flexible tape over a plastic substrate, we develop here a model of far-field dry adhesion between two flexible sheets interacting via a power-law potential. We show that phase transitions from unadhered to adhered states occur as dictated by a dimensionless bending parameter representing the ratio of interaction strength to bending stiffness. The order of the adhesion transitions, as well as their hysteretic nature, is shown to depend on the form of the interaction potential between the flexible sheets. When three or more sheets interact, additional geometrical considerations determine the hierarchical or sequential nature of the adhesion transitions.

We consider a Taylor-Dean-type flow of an electrically conducting liquid in an annulus between two infinitely long perfectly conducting cylinders subject to a generally helical magnetic field. The cylinders are electrically connected through a remote, perfectly conducting endcap, which allows a radial electric current to pass through the liquid. The radial current interacting with the axial component of magnetic field gives rise to the azimuthal electromagnetic force, which destabilizes the base flow by making its angular momentum decrease radially outwards. This instability, which we refer to as the pseudo–magnetorotational instability (MRI), looks like an MRI although its mechanism is basically centrifugal. In a helical magnetic field, the radial current interacting with the azimuthal component of the field gives rise to an axial electromagnetic force, which drives a longitudinal circulation. First, this circulation advects the Taylor vortices generated by the centrifugal instability, which results in a traveling wave as in the helical MRI (HMRI). However, the direction of travel of this wave is opposite to that of the true HMRI. Second, at sufficiently strong differential rotation, the longitudinal flow becomes hydrodynamically unstable itself. For electrically connected cylinders in a helical magnetic field, hydrodynamic instability is possible at any sufficiently strong differential rotation. In this case, there is no hydrodynamic stability limit defined in the terms of the critical ratio of rotation rates of inner and outer cylinders that would allow one to distinguish a hydrodynamic instability from the HMRI. These effects can critically interfere with experimental as well as numerical determination of MRI.

In a recent paper [S. B. Lee, Physica A 387, 1567 (2008)] the epidemic spread of the contact process (CP) in deterministic fractals, already studied by I. Jensen [J. Phys. A 24, L1111 (1991)], has been investigated by means of computer simulations. In these previous studies, epidemics are started from randomly selected sites of the fractal, and the obtained results are averaged all together. Motivated by these early works, here we also studied the epidemic behavior of the CP in the same fractals, namely, a Sierpinski carpet and the checkerboard fractals but averaging epidemics started from the same site. These fractal media have spatial discrete scale invariance symmetry, and consequently the dynamic evolution of some physical observables may become coupled to the topology, leading to the logarithmic-oscillatory modulation of the corresponding power laws. In fact, by means of extensive simulations we shown that the topology of the substrata causes the oscillatory behavior of the epidemic observables. However, in order to observe these oscillations, which have not been reported in earlier works, the interference effect arising during the averaging of epidemics started from nonequivalent sites should be eliminated. Finally, by analyzing our data and those available on the literature for the dependence of the exponents $\eta$ and $\delta$ on the dimensionality of substrata, we conjectured that for integer dimensions $\left(2\le d\le d_c=4\right)$ the following exact relationship may hold: $\delta +\eta =\frac{d+2}{6}$.

We find that some equilibrium systems and their nonequilibrium counterparts actually show the same jerky response or avalanche behavior on many scales in response to slowly changing external conditions. In other words, their static and dynamic avalanches behave statistically the same. This suggests that their critical properties are much more generally applicable than previously assumed. In this case, systems far from equilibrium may be used to predict equilibrium critical behavior and vice versa.

In this work, we examine the validity of quantum adiabatic theorem in thermodynamic systems. For a $d$-dimensional quantum many-body system, we show that the duration time ${\tau }_0$ required by its ground-state adiabatic process does not depend on the microscopic details but the scaling dimension of the fidelity susceptibility $d_a$. Our result, therefore, provides a quantitative time scale of the quantum adiabatic theorem in thermodynamic systems. The quantum adiabatic theorem might be violated in case that the scaling dimension of the fidelity susceptibility is larger than the system’s real dimension $\left(d_a>d\right)$.

Spike packet propagation is modeled in mesoscopic-scale networks, composed of locally and recurrently coupled neural pools, and embedded in a two-dimensional lattice. Site dynamics is governed by three key parameters—pool connectedness probability, synaptic strength (following the steady-state distribution of some realizations of spike-timing-dependent plasticity learning rule), and the neuron refractoriness. Formation of spatiotemporal patterns in our model, synfire chains, exhibits critical behavior, with the emerging percolation phase transition controlled by the probability for nonzero synaptic strength value. Applying the finite-size scaling method, we infer the critical probability dependence on synaptic strength and refractoriness and determine the effects of connection topology on the pertaining percolation clusters fractal dimensions. We find that the directed percolation and the pair contact process with diffusion constitute the relevant universality classes of phase transitions observed in a class of mesoscopic-scale network models, which may be related to recently reported data on in vitro cultures.

We numerically investigate the six-species predator-prey game in complex networks as well as in $d$-dimensional regular hypercubic lattices with $d=1,2,\dots ,6$. The food-web topology of the six species contains two directed loops, each of which is composed of cyclically predating three species. As the mutation rate is lowered below the well-defined phase transition point, the $Z_2$ symmetry related with the interchange in the two loops is spontaneously broken, and it has been known that the system develops the defensive alliance in which three cyclically predating species defend each other against the invasion of other species. In the Watts-Strogatz small-world network structure characterized by the rewiring probability $\alpha$, the phase diagram shows the reentrant behavior as $\alpha$ is varied, indicating a twofold role of the shortcuts. In $d$-dimensional regular hypercubic lattices, the system also exhibits the reentrant phase transition as $d$ is increased. We identify universality class of the phase transition and discuss the proper mean-field limit of the system.

We analytically determine when a range of abstract social contagion models permit global spreading from a single seed on degree-correlated undirected random networks. We deduce the expected size of the largest vulnerable component, a network’s tinderboxlike critical mass, as well as the probability that infecting a randomly chosen individual seed will trigger global spreading. In the appropriate limits, our results naturally reduce to standard ones for models of disease spreading and to the condition for the existence of a giant component. Recent advances in the distributed infinite seed case allow us to further determine the final size of global spreading events when they occur. To provide support for our results, we derive exact expressions for key spreading quantities for a simple yet rich family of random networks with bimodal degree distributions.

In this paper, the scalings incorporating the Prandtl number (Pr) dependence have been obtained by a scaling analysis for the unsteady natural convection boundary layer of an initially quiescent isothermal Newtonian fluid of $\text{Pr}>1$ produced by the sudden imposition of a higher temperature on a vertical plate. It is shown that the transient flow behavior of the resulting boundary layer can be described by a three-region structure and at the start-up stage the boundary layer development is one dimensional and independent of height due to the dominance of pure conduction; however, at steady state it becomes two dimensional and height dependent as the flow becomes dominated by convection. Numerical results demonstrate that the scalings representing the thermal boundary layer development accurately represent their Pr dependence over the whole stage of flow development. The scalings representing the viscous boundary layer development are generally in good agreement with the numerical results with the Pr variation over the whole stage of flow development, although there are small deviations from the numerical results with the Pr variation that are within acceptable limits for scaling.

Brown, Preston, and Singleton (BPS) produced an analytic calculation for energy exchange processes for a weakly to moderately coupled plasma: the electron-ion temperature equilibration rate and the charged particle stopping power. These precise calculations are accurate to leading and next-to-leading order in the plasma coupling parameter and to all orders for two-body quantum scattering within the plasma. Classical molecular dynamics can provide another approach that can be rigorously implemented. It is therefore useful to compare the predictions from these two methods, particularly since the former is theoretically based and the latter numerically. An agreement would provide both confidence in our theoretical machinery and in the reliability of the computer simulations. The comparisons can be made cleanly in the purely classical regime, thereby avoiding the arbitrariness associated with constructing effective potentials to mock up quantum effects. We present here the classical limit of the general result for the temperature equilibration rate presented in BPS. In particular, we examine the validity of the $m_{\text{electron}}/m_{\text{ion}}\to 0$ limit used in BPS to obtain a very simple analytic evaluation of the long-distance collective effects in the background plasma.

Random critical branching trees (CBTs) are generated by the multiplicative branching process, where the branching number is determined stochastically, independent of the degree of their ancestor. Here we show analytically that despite this stochastic independence, there exists the degree-degree correlation (DDC) in the CBT and it is disassortative. Moreover, the skeletons of fractal networks, the maximum spanning trees formed by the edge betweenness centrality, behave similarly to the CBT in the DDC. This analytic solution and observation support the argument that the fractal scaling in complex networks originates from the disassortativity in the DDC.

A quantitative approach was constructed for detecting phase locking in a chaotic system with complex attractor structure via stroboscopic method. We study the route to weak phase locking by analyzing the stroboscopic points. The onset of weak phase locking detected by using this statistical approach and the critical coupling strength calculated by Lyapunov exponent are matched well. Detailed structure of phase locking intensity is described by the Arnold tongue diagram.

In a recent publication, Plerou and Stanley [Phys. Rev. E 76, 046109 (2007)] use the Meerschaert-Scheffler estimator to verify the “inverse half-cubic law” of trade size distributions. We show that this procedure systematically underestimates these tail exponents.

Analyzing trade-by-trade data for three distinct markets, we showed that the cumulative distributions of trade size display power-law tails $P\left\{q>x\right\}\sim x^{-{\zeta }_q}$, with exponents ${\zeta }_q$ in the “Lévy stable domain” $\left({\zeta }_q<{\zeta }_q^{\ast }=2\right)$. Moreover we reported that the exponent values are consistent for all stocks irrespective of stock-specific variables such as market capitalization, industry sector, or the specific market where the stock is traded. Our conclusions were based on using two distinct estimation methods. Rácz et al. now propose that one of the estimators we used has slow convergence for a pure power law, particularly as tail exponents approach the boundary ${\zeta }_q^{\ast }=2$. We examine the robustness of our results to specific estimation method by additional analysis using five distinct techniques to estimate ${\zeta }_q$. We find results that are fully consistent with those we had reported, providing compelling evidence that our conclusions hold regardless of estimation procedure.

We study heat conduction in one-dimensional granular gases. In particular, we consider two mechanisms of viscous dissipation during intergrain collisions. In one, the dissipative force is proportional to the grain’s velocity and dissipates not only energy but also momentum. In the other, the dissipative force is proportional to the relative velocity of the grains and therefore conserves momentum even while dissipating energy. This allows us to explore the role of momentum conservation in the heat conduction properties of this one-dimensional nonlinear system. We find normal thermal conduction whether or not momentum is conserved.

At the $A$ to $C$ transition, smectic elastomers have recently been observed to undergo $\sim 35\%$ spontaneous shear strains. We first explicitly describe how strains of up to twice this value could be mechanically or electrically induced in Sm-$C$ elastomers by rotation of the director on a cone around the layer normal with an elastic cost dependent on constraints. Second, for typical sample geometries, we give the various microstructures in Sm-$C$ akin to those seen in nematic elastomers under distortions with constraints. It is possible to give explicit results for the nature of the textures. Chiral Sm-$C$ elastomers are ferroelectric. We calculate how the polarization could be mechanically reversed by large, hard, or soft strains of the rubber depending upon sample geometry.