We study theoretically the linear Saffman-Taylor instability for non-Newtonian fluids in a Hele-Shaw cell. After introducing the notion of generalized Newtonian fluid we calculate the associated Darcy’s law. We derive the relation governing the growth rate of normal modes for a large class of non-Newtonian flows. For shear-thinning fluids at high shear rate our theory provides Darcy’s laws free of the nonphysical divergences appearing in the classical approaches. We characterize fluids which develop instabilities faster than Newtonian fluids under the same hydrodynamical conditions. Another primary result that this paper provides is that for some shear-thickening fluids, all normal modes are stable.

For controllable generation of an isolated attosecond relativistic electron bunch [relativistic electron mirror (REM)] with nearly solid-state density, we proposed [V. V. Kulagin et al., Phys. Rev. Lett. 99, 124801 (2007)] to use a solid nanofilm illuminated normally by an ultraintense femtosecond laser pulse having a sharp rising edge (nonadiabatic laser pulse). In this paper, the REM characteristics are investigated in a regular way for a wide range of parameters. With the help of two-dimensional (2D) particle-in-cell (PIC) simulations, it is shown that, in spite of Coulomb forces, all of the electrons in the laser spot can be synchronously accelerated to ultrarelativistic velocities by the first half-cycle of the field, which has large enough amplitude. For the process of the REM generation, we also verify a self-consistent one-dimensional theory, which we developed earlier (cited above) and which takes into account Coulomb forces, radiation of the electrons, and laser amplitude depletion. This theory shows a good agreement with the results of the 2D PIC simulations. Finally, the scaling of the REM dynamical parameters with the field amplitude and the nanofilm thickness is analyzed.

Optical emission spectroscopy (OES) was used to study the evolution behavior of the neutral Si atoms in the plasma produced by nanosecond pulsed-laser beam irradiating on SiC crystal targets. The OES measurements indicated that the electron temperature and density in the plasma had maximum values around a region about 2mm from the target surface. Based on the temporal and spatial evolution of the spectral line at 633.19 nm originating from excited Si atoms, it was found that these Si atoms have short decay times and long range spatial distribution in vacuum. At the initial growth stage of SiC thin films using pulsed-laser deposition (PLD) technique, these Si atoms were found possibly to arrive at the Si substrate to form defects near the SiC/Si interface. By comparing the OES result measured in vacuum and that measured in ambient air, it was deduced that by properly adjusting the background gas species and pressure, the quality of the films prepared by PLD technique may be improved.

We generalize the Poland-Scheraga model to the case of a circular DNA, taking into account the twisting of the two strains around each other. Guided by recent single-molecule experiments on DNA strands, we assume that the torsional stress induced by denaturation enforces the formation of supercoils whose writhe absorbs the linking number expelled by the loops. Our model predicts that when the entropy parameter of a loop satisfies $c\le 2$, denaturation transition does not take place. On the other hand, for $c>2$, a first-order denaturation transition is consistent with our model and may take place in the actual system, as in the case with no supercoils. These results are in contrast with other treatments of circular DNA melting where denaturation is assumed to be accompanied by an increase in twist rather than writhe on the bound segments.

Negative capacitance (NC), predicted by various electrical double layer (EDL) theories, is critically reviewed. Physically possible for individual components of the EDL, the compact or diffuse layer, it is strictly prohibited for the whole EDL or for an electrochemical cell with two electrodes. However, NC is allowed for the artificial conditions of $\sigma$ control, where an EDL is described by the equilibrium electric response of electrolyte to a field of fixed, and typically uniform, surface charge-density distributions, $\sigma$. The contradiction is only apparent; in fact local $\sigma$ cannot be set independently, but is established by the equilibrium response to physically controllable variables, i.e., applied voltage $\varphi$ ($\varphi$ control) or total surface charge $q$ ($q$ control). NC predictions in studies based on $\sigma$ control signify potential instabilities and phase transitions for physically realizable conditions. Building on our previous study of $\varphi$ control [M. B. Partenskii and P. C. Jordan, Phys. Rev. E 77, 061117 (2008)], here we analyze critical behavior under $q$ control, clarifying the basic picture using an exactly solvable “squishy capacitor” toy model. We find that $\varphi$ can change discontinuously in the presence of a lateral transition, specify stability conditions for an electrochemical cell, analyze the origin of the EDL’s critical point in terms of compact and diffuse serial contributions, and discuss perspectives and challenges for theoretical studies not limited by $\sigma$ control.

Transport of overdamped Brownian particles in a two-dimensional asymmetric tube is investigated in the presence of nonadiabatic periodic driving forces. By using Brownian dynamics simulations we can find that the phenomena in nonadiabatic regime differ from that in adiabatic case. The direction of the current can be reversed by tuning the driving frequency. Remarkably, the current as a function of the driving amplitude exhibits several local maxima at finite driving frequency.

We complement and extend our work on fluctuations arising in nonequilibrium systems in steady states driven by Lévy noise [H. Touchette and E. G. D. Cohen, Phys. Rev. E 76, 020101(R) (2007)]. As a concrete example, we consider a particle subjected to a drag force and a Lévy white noise with tail index $\mu ∊\left(0,2\right]$, and calculate the probability distribution of the work done on the particle by the drag force, as well as the probability distribution of the work dissipated by the dragged particle in a nonequilibrium steady state. For $0<\mu <2$, both distributions satisfy what we call an anomalous fluctuation property characterized by positive and negative fluctuations that asymptotically have the same probability. For $\mu =2$, by contrast, the work and dissipated work distributions satisfy the known conventional and extended fluctuation relations, respectively, which are both characterized by positive fluctuations that are exponentially more probable than negative fluctuations. The difference between these different fluctuation behaviors is discussed in the context of large deviation theory. Experiments that could probe or reveal an anomalous fluctuation property are also discussed.

Evolutionary game dynamics describes the spreading of successful strategies in a population of reproducing individuals. Typically, the microscopic definition of strategy spreading is stochastic such that the dynamics becomes deterministic only in infinitely large populations. Here, we present a microscopic birth-death process that has a fully deterministic strong selection limit in well-mixed populations of any size. Additionally, under weak selection, from this process the frequency-dependent Moran process is recovered. This makes it a natural extension of the usual evolutionary dynamics under weak selection. We find simple expressions for the fixation probabilities and average fixation times of the process in evolutionary games with two players and two strategies. For cyclic games with two players and three strategies, we show that the resulting deterministic dynamics crucially depends on the initial condition in a nontrivial way.

Here, we uncover the load and fault-tolerant backbones of the trans-European gas pipeline network. Combining topological data with information on intercountry flows, we estimate the global load of the network and its tolerance to failures. To do this, we apply two complementary methods generalized from the betweenness centrality and the maximum flow. We find that the gas pipeline network has grown to satisfy a dual purpose. On one hand, the major pipelines are crossed by a large number of shortest paths thereby increasing the efficiency of the network; on the other hand, a nonoperational pipeline causes only a minimal impact on network capacity, implying that the network is error tolerant. These findings suggest that the trans-European gas pipeline network is robust, i.e., error tolerant to failures of high load links.

The Einstein formula for the effective shear viscosity of low Reynolds number suspension flows is generalized to the case of flat, low-concentration, particle-laden interfaces separating two immiscible fluids. The effective surface shear and dilational viscosities of this system is found to be ${\eta }_s=\frac{5}{3}\left({\eta }_1+{\eta }_2\right)R\varphi$ and ${\zeta }_s=5\left({\eta }_1+{\eta }_2\right)R\varphi$, correspondingly, where ${\eta }_1$ and ${\eta }_2$ are the shear viscosities of two bulk fluids and $\varphi$ is the surface concentration of spherical particles of radius $R$. The formula is found to be in excellent agreement with data obtained using multicomponent lattice Boltzmann equation simulation.

Three-dimensional numerical simulations using a front-tracking method are presented on the dynamics of oblate shape capsules in linear shear flow by considering a broad range of viscosity contrast (ratio of internal-to-external fluid viscosity), shear rate (or capillary number), and aspect ratio. We focus specifically on the coupling between the shape deformation and orientation dynamics of capsules, and show how this coupling influences the transition from the tank-treading to tumbling motion. At low capillary numbers, three distinct modes of motion are identified: a swinging or oscillatory (OS) mode at a low viscosity contrast in which the inclination angle $\theta \left(t\right)$ oscillates but always remains positive; a vacillating-breathing (VB) mode at a moderate viscosity contrast in which $\theta \left(t\right)$ periodically becomes positive and negative, but a full tumbling does not occur; and a pure tumbling mode (TU) at a higher viscosity contrast. At higher capillary numbers, three types of transient motions occur, in addition to the OS and TU modes, during which the capsule switches from one mode to the other as (i) VB to OS, (ii) TU to VB to OS, and (iii) TU to VB. Phase diagrams showing various regimes of capsule dynamics are presented. For all modes of motion (OS, VB, and TU), a large-amplitude oscillation in capsule shape and a strong coupling between the shape deformation and orientation dynamics are observed. It is shown that the coupling between the shape deformation and orientation is the strongest in the VB mode, and hence at a moderate viscosity contrast, for which the amplitude of shape deformation reaches its maximum. The numerical results are compared with the theories of Keller and Skalak, and Skotheim and Secomb. Significant departures from the two theories are discussed and related to the strong coupling between the shape deformation, inclination, and transition dynamics.

The results of a theoretical investigation on the stopping power of ions moving in a two-dimensional degenerate electron gas are presented. The stopping power for an ion is calculated employing linear-response theory using the dielectric function approach. The collisions, which lead to a damping of plasmons and quasiparticles in the electron gas, is taken into account through a relaxation-time approximation in the linear-response function. The stopping power for an ion is calculated in both the low- and high-velocity limits. In order to highlight the effects of damping, we present a comparison of our analytical and numerical results, in the case of pointlike ions, obtained for a nonzero damping with those for a vanishing damping. It is shown that the equipartition sum rule first formulated by Lindhard and Winther for three-dimensional degenerate electron gas does not necessarily hold in two dimensions. We have generalized this rule introducing an effective dielectric function. In addition, some results for two-dimensional interacting electron gas have been obtained. In this case, the exchange-correlation interactions of electrons are considered via local-field corrected dielectric function.

The stability of ion plasma perturbations is investigated in a homogeneous isotropic complex plasma, where a balance between plasma creation due to ionization and plasma loss due to the absorption on dust particles has been reached. The analysis is performed on the basis of a self-consistent fluid description including dust charge variations and ion-neutral friction. It is shown that the stability depends primarily on the nature of the ionization source. For an ionization source proportional to the electron density, an instability takes place at wave numbers below a certain threshold, and the instability mechanism is explained in detail. No instability is found for a constant ionization source.

In this paper, we present a nonparametric method to estimate the heterogeneity of a random medium from the angular distribution of intensity of waves transmitted through a slab of random material. Our approach is based on the modeling of forward multiple scattering using compound Poisson processes on compact Lie groups. The estimation technique is validated through numerical simulations based on radiative transfer theory.

Non-Euclidean plates are thin elastic bodies having no stress-free configuration, hence exhibiting residual stresses in the absence of external constraints. These bodies are endowed with a three-dimensional reference metric, which may not necessarily be immersible in physical space. Here, based on a recently developed theory for such bodies, we characterize the transition from flat to buckled equilibrium configurations at a critical value of the plate thickness. Depending on the reference metric, the buckling transition may be either continuous or discontinuous. In the infinitely thin plate limit, under the assumption that a limiting configuration exists, we show that the limit is a configuration that minimizes the bending content, among all configurations with zero stretching content (isometric immersions of the midsurface). For small but finite plate thickness, we show the formation of a boundary layer, whose size scales with the square root of the plate thickness and whose shape is determined by a balance between stretching and bending energies.

We consider a particle, confined to a moving harmonic potential, under the influence of friction and external asymmetric Poissonian shot noise (PSN). We study the fluctuations of the work done to maintain this system in a nonequilibrium steady state. PSN generalizes the usual Gaussian noise and can be considered to be a paradigm of external noise, where fluctuation and dissipation originate from physically independent mechanisms. We consider two scenarios: (i) the noise is given purely by PSN and (ii) in addition to PSN the particle is subject to white Gaussian noise. In both cases we derive exact expressions for the large deviation form of the work distribution, which are characterized by the time scales of the system. We show that the usual steady-state fluctuation theorem does not apply in our model and that in a certain parameter regime large negative work fluctuations are more likely to occur than the corresponding positive ones, though the average work is always positive.

Following the introduction of the Brownian motion model for sediment transport by Einstein, several stochastic models have been explored in the literature motivated by the need to reproduce the observed non-Gaussian probability density functions (PDFs) of the sediment transport rates observed in laboratory experiments. Recent studies have presented evidence that PDFs of bed elevation and sediment transport rates depend on time scale (sampling time), but this dependence is not accounted for in any previous stochastic models. Here we propose an extension of Brownian motion, called fractional Laplace motion, as a model for sediment transport which acknowledges the fact that the time over which the gravel particles are in motion is in itself a random variable. We show that this model reproduces the multiscale statistics of sediment transport rates as quantified via a large-scale laboratory experiment.

When a drop of liquid containing particles is allowed to evaporate from a substrate, the flow induced by the liquid evaporating from the drop edge carries the particles to the edge. If these particles prevent the drop edge from receding as the evaporation proceeds, then more particles will be accumulated near the drop edge resulting in the formation of a deposit that resembles coffee rings. We determine the capillary force on the particles near a drop edge and the effect of the particles on the gas-liquid-substrate contact angle to derive a condition that must be satisfied for particles to form the ringlike pattern.

Feedback circuits are important building blocks of gene regulatory network. Recent studies with simplified models found the advantage of coupled fast and slow feedback loops in creating bistable switch, and interlinked dual-time feedback loops can enhance robustness to stochasticity and persistence of memory. Based on the same feedback structure and mathematical model, the effect of noise on persistence of memory is investigated. It is found that (1) an intermediate amount of single-parameter noise plays a constructive role in persisting memory through noise-induced changing from monostable to bistable region, while larger single-parameter noise destroys the memory ability of the system through noise-induced transition between two stable states. (2) Different from the single-parameter noise, arbitrary amount of the internal noise destroys the memory ability of the system. (3) For the same feedback structure with less nonlinear feedback which is not enough to render the system bistability, the single-parameter noise can play similar constructive role through rendering the system bistability.

Syntheses of protein molecules in a cell are carried out by ribosomes. A ribosome can be regarded as a molecular motor which utilizes the input chemical energy to move on a messenger RNA (mRNA) track that also serves as a template for the polymerization of the corresponding protein. The forward movement, however, is characterized by an alternating sequence of translocation and pause. Using a quantitative model, which captures the mechanochemical cycle of an individual ribosome, we derive an exact analytical expression for the distribution of its dwell times at the successive positions on the mRNA track. Inverse of the average dwell time satisfies a “Michaelis-Menten-type” equation and is consistent with the general formula for the average velocity of a molecular motor with an unbranched mechanochemical cycle. Extending this formula appropriately, we also derive the exact force-velocity relation for a ribosome. Often many ribosomes simultaneously move on the same mRNA track, while each synthesizes a copy of the same protein. We extend the model of a single ribosome by incorporating steric exclusion of different individuals on the same track. We draw the phase diagram of this model of ribosome traffic in three-dimensional spaces spanned by experimentally controllable parameters. We suggest new experimental tests of our theoretical predictions.