A vertical soap film is maintained by injection of a soap solution from the top. The film is then locally heated. Thermal plumes may be observed to rise in the film, depending on the magnitude of the heating and injected flows. The nearly two-dimensional nature of the system allows to visualize the motion of the plumes using an infrared camera. A model is proposed to describe the growth, emergence, and stationarity of the plumes in the film by taking into account both magnitudes of the heating $\Delta T$ and injected flow $Q$.

Including the ion-gyroradius effect, a general low-frequency kinetic dispersion equation is presented, which simultaneously takes account of a field-aligned current and temperature anisotropy in plasmas. Based on this dispersion equation, kinetic Alfvén wave (KAW) instability driven by the field-aligned current, which is carried by the field-aligned drift of electrons relative to ions at a drift velocity $V_D$, is investigated in a high-$\beta$ plasma, where $\beta$ is the kinetic-to-magnetic pressure ratio in the plasma. The numerical results show that the KAW instability driven by the field-aligned current has a nonzero growth rate in the parallel wave-number range $0<k_z<k_z^u$, where the growth rate reaches a maximum at $k_z\sim k_z^u/2$. On the other hand, in the perpendicular wave-number range $0<k_{\perp }<k_{\perp }^u$ the growth rate monotonously decreases with the wave number $k_{\perp }$ from a maximum at $k_{\perp }=0$ to zero at $k_{\perp }=k_{\perp }^u$. In particular, the upper boundaries of the growing ranges in the wave-number space, $k_z^u$ and $k_{\perp }^u$, as well as the growth rate increase with $V_D$, imply that there are wider growing ranges and larger growth rate for larger drift velocities. Including the temperature anisotropy of plasma particles, the result shows that the instability conditions for these two driven mechanisms are both modified considerably, in which the growing parametric ranges of KAWs widen. The results have potential importance in understanding the physics of space and astrophysical plasma active phenomena since the field-aligned current, also called the Birkeland current, is one of the most active factors in plasma phenomena.

We demonstrate in this work a unique approach for watching outside while hiding in a carpet cloaking based on transformation optics. Unlike conventional carpet cloaking, which screens all the incident electromagnetic waves, we break the cloak and allow incident light get into the carpet. Hence outside information is detected inside the cloak. To recover the invisible cloaking, complementary techniques are applied in the broken space. Consequently, a hiding-inside and watching-outside (HIWO) carpet cloak is sewed, which works as an invisible cloaking and allows surveillance of the outside at the same time. Our work provides a strategy for an ideal cloak with “hiding” and “watching” functions simultaneously.

Motivated by the Harris criterion, the absorbing phase transitions of the conserved lattice gas (CLG) model were studied on lattices with a quenched disorder, i.e., on infinite percolation networks, in two and three dimensions. The Harris criterion suggests that, in a magnetic system, the pure fixed point will be unstable if the specific-heat exponent is positive. For the CLG model, the specific-heat exponent $\alpha$ calculated by the hyperscaling relation $\alpha =2-d\nu$, where $\nu$ is the spatial correlation length exponent in $d$ dimensions, will be positive in two dimensions if the value of $\nu$ obtained earlier by Lübeck and Heger is employed. On the other hand, it will be close to 0 if the more recent value by Lee and Lee is used and it is positive in three dimensions with the available value of $\nu$. Extensive numerical simulations showed that, when the concentration of disordered sites is less than the critical concentration, the critical exponents were similar to those on a regular lattice both in two and three dimensions. When the concentration of disordered sites becomes critical, the density of active particles showed nonuniversal power-law behavior for all particle densities considered in both dimensions. These results were in contrast to the results for the diluted contact process. The cause of such a nonuniversal behavior was addressed.

The Bak-Sneppen model is a well-known stochastic model of evolution that exhibits self-organized criticality; only a few analytical results have been established for it so far. We report a surprising connection between Bak-Sneppen-type models and more tractable Markov processes that evolve without any reference to an underlying topology. Specifically, we show that in the case of a large number of species, the long time behavior of the fitness profile in the Bak-Sneppen model can be replicated by a model with a purely rank-based update rule whose asymptotics can be studied rigorously.

We present exact expressions for the sum of states of noninteracting classical and quantum particles occupying a finite number of modes with arbitrary spacings. Exploiting a probabilistic analogy, we derive an analytic fourth-order approximation to the density of states, which captures its variance and kurtosis, and is superior to the previous, commonly used methods for all three particle statistics. Our approach employs a simple exact method of calculating the moments of the microcanonical density of states for quantum particles, which requires less computational effort than the commonly used saddle-point approximation. We test our methods numerically and discuss their applicability to various physical systems.

Diffusion on a diluted hypercube has been proposed as a model for glassy relaxation and is an example of the more general class of stochastic processes on graphs. In this article we determine numerically through large-scale simulations the eigenvalue spectra for this stochastic process and calculate explicitly the time evolution for the autocorrelation function and for the return probability, all at criticality, with hypercube dimensions $N$ up to $N=28$. We show that at long times both relaxation functions can be described by stretched exponentials with exponent $1/3$ and a characteristic relaxation time which grows exponentially with dimension $N$. The numerical eigenvalue spectra are consistent with analytic predictions for a generic sparse network model.

We present a performance analysis of a two-state heat engine model working with a single-mode radiation field in a cavity. The heat engine cycle consists of two adiabatic and two isoenergetic processes. Assuming the wall of the potential moves at a very slow speed, we determine the optimization region and the positive work condition of the heat engine model. Furthermore, we generalize the results to the performance optimization for a two-state heat engine with a one-dimensional power-law potential. Based on the generalized model with an arbitrary one-dimensional potential, we obtain the expression of efficiency as $\eta =1-\frac{E_C}{E_H}$, with $E_H$ ($E_C$) denoting the expectation value of the system Hamiltonian along the isoenergetic process at high (low) energy. This expression is an analog of the classical thermodynamical result of Carnot, ${\eta }_c=1-\frac{T_C}{T_H}$, with $T_H$ ($T_C$) being the temperature along the isothermal process at high (low) temperature. We prove that under the same conditions, the efficiency $\eta =1-\frac{E_C}{E_H}$ is bounded from above the Carnot efficiency, ${\eta }_c=1-\frac{T_C}{T_H}$, and even quantum dynamics is reversible.

We report the results of a study of single-particle diffusion in dense colloid fluids confined in a ribbon channel geometry that is intermediate between quasione dimensional (q1D) and quasitwo dimensional (q2D). This paper complements a previous paper about pair diffusion in the same system [Phys. Rev. E 82, 031403 (2010)]. In all of the systems studied, the colloid density distribution transverse to the ribbon channel is stratified with peak amplitudes that depend on the colloid density. Although the virtual walls that confine a stratum are structured with a scale length of the colloid diameter, that structure does not have an apparent influence on the single-particle diffusion, which shows the characteristic features of diffusion in a q1D channel with smooth walls. We find that, for all channel widths and packing fractions studied, the single-particle transverse diffusion coefficient in a stratum is smaller than the single-particle longitudinal diffusion coefficient in the same stratum and that the single-particle longitudinal diffusion coefficient varies very little from stratum to stratum, being only slightly smaller in the dense strata next to the walls than in the central strata. The lack of variation in the longitudinal diffusion coefficient with apparent stratum density is explained by the application of the Fischer-Methfessel approximation to the local density in an inhomogeneous liquid. The ratio of the transverse to longitudinal diffusion coefficients varies very slowly with ribbon width, implying a very slow transition from q1D to q2D behavior.

Infrared reflection-absorption spectroscopy results on stearic acid Langmuir monolayers containing Mn, Co, and Cd ions show that on the water surface, the ions induce unidentate and bidentate (both chelate and bridged) coordination in the carboxylate headgroup with some trace of undissociated acid. Moreover, with Cd and Mn ions in subphase, the preferred coordination is found to be unidentate, whereas for Co, bidentate chelate is most preferred. After transfer onto amorphous substrate, not all coordinations are found to exist in the same ratio for the deposited metal stearate monolayers. More specifically, after transfer, Mn is found to coordinate with the carboxylate group as bidentate chelate, Cd as unidentate and bidentate bridged (with unidentate as the preferred coordination), and Co as preferably bidentate bridged (although all coordinations are present). Results suggest a specific interaction in each case, as the metal-carboxylate pair at the water surface is transferred to the substrate surface during Langmuir-Blodgett deposition.

We show that in experimental atomic force microscopy studies of the lifetime distribution of mechanically stressed folded proteins the effects of externally applied fluctuations cannot be distinguished from those of internally present fluctuations. In certain circumstances this leads to artificially nonexponential lifetime distributions, which can be misinterpreted as a signature of protein complexity. This work highlights the importance of fully characterizing and controlling external sources of fluctuation in mechanical studies of proteins before drawing conclusions on the physics at play on the molecular level.

Quorum sensing refers to the change in the cooperative behavior of a collection of elements in response to the change in their population size or density. This behavior can be observed in chemical and biological systems. These elements or cells are coupled via chemicals in the surrounding environment. Here we focus on the change of dynamical behavior, in particular from quiescent to oscillatory, as the cell population changes. For instance, the silent behavior of the elements can become oscillatory as the system concentration or population increases. In this work, two simple models are constructed that can produce the essential representative properties in quorum sensing. The first is an excitable or oscillatory phase model, which is probably the simplest model one can construct to describe quorum sensing. Using the mean-field approximation, the parameter regime for quorum sensing behavior can be identified, and analytical results for the detailed dynamical properties, including the phase diagrams, are obtained and verified numerically. The second model consists of FitzHugh-Nagumo elements coupled to the signaling chemicals in the environment. Nonlinear dynamical analysis of this mean-field model exhibits rich dynamical behaviors, such as infinite period bifurcation, supercritical Hopf, fold bifurcation, and subcritical Hopf bifurcations as the population parameter changes for different coupling strengths. Analytical result is obtained for the Hopf bifurcation phase boundary. Furthermore, two elements coupled via the environment and their synchronization behavior for these two models are also investigated. For both models, it is found that the onset of oscillations is accompanied by the synchronized dynamics of the two elements. Possible applications and extension of these models are also discussed.

We consider a single Brownian particle confined in a double well potential (DWP) and investigate its response to a linear shear flow by means of the probability density and current determined via numerical solution of the Fokker-Planck equation. Besides a shear-dependent distortion of the probability distribution, we find that the associated current crossing the potential barrier exhibits a convex dependency on the shear rate when the DWP's minima are far apart. With decreasing distance this functional dependency changes from a convex to concave characteristics accompanied with an increase of the probability current crossing the DWP's barrier. Through the difference map of the particle density distribution it is possible to extract the shear-flow-induced contribution to the particle density driving the barrier-crossing current. This may open the possibility to design specific flow profiles to optimize flow-induced activated transport of nanoparticles.

We study spectra of directed networks with inhibitory and excitatory couplings. We investigate in particular eigenvector localization properties of various model networks for different values of correlation among their entries. Spectra of random networks with completely uncorrelated entries show a circular distribution with delocalized eigenvectors, whereas networks with correlated entries have localized eigenvectors. In order to understand the origin of localization we track the spectra as a function of connection probability and directionality. As connections are made directed, eigenstates start occurring in complex-conjugate pairs and the eigenvalue distribution combined with the localization measure shows a rich pattern. Moreover, for a very well distinguished community structure, the whole spectrum is localized except few eigenstates at the boundary of the circular distribution. As the network deviates from the community structure there is a sudden change in the localization property for a very small value of deformation from the perfect community structure. We search for this effect for the whole range of correlation strengths and for different community configurations. Furthermore, we investigate spectral properties of a metabolic network of zebrafish and compare them with those of the model networks.

A simple scheme of forcing turbulence away from decay was introduced by Lundgren some time ago, the “linear forcing,” which amounts to a force term that is linear in the velocity field with a constant coefficient. The evolution of linearly forced turbulence toward a stationary final state, as indicated by direct numerical simulations (DNS), is examined from a theoretical point of view based on symmetry arguments. In order to follow closely the DNS, the flow is assumed to live in a cubic domain with periodic boundary conditions. The simplicity of the linear forcing scheme allows one to rewrite the problem as one of decaying turbulence with a decreasing viscosity. Its late-time behavior can then be studied by scaling symmetry considerations. The evolution of the system in the description of “decaying” turbulence can be understood as the gradual symmetry breaking of a larger approximate symmetry to a smaller symmetry that is exact at late times. The latter symmetry implies a stationary state: In the original description all correlators are constant in time, while, in the “decaying” turbulence description, that state possesses constant Reynolds number and integral length scale. The finiteness of the domain is intimately related to the evolution of the system to a stationary state at late times: In linear forcing there is no other large scale than the domain size, therefore, it is the only scale available to set the magnitude of the necessarily constant integral length scale in the stationary state. A high degree of local isotropy is implied by the late-time exact symmetry, the symmetries of the domain itself, and the solenoidal nature of the velocity field. The fluctuations observed in the DNS for all quantities in the stationary state can be associated with deviations from isotropy that is necessarily broken at the large scale by the finiteness of the domain. Indeed, to strengthen this conclusion somewhat, self-preserving isotropic turbulence models are used to study evolution from a direct dynamical point of view. Simultaneously, the naturalness of the Taylor microscale as a self-similarity scale in this system is emphasized. In this context the stationary state emerges as a stable fixed point. We also note that self-preservation seems to be the reason behind a noted similarity of the third-order structure function between the linearly forced and freely decaying turbulence, where, again, the finiteness of the domain plays a significant role.

Entrainment of a ferrofluid contained in a sphere by a rotating uniform magnetic field is studied on the basis of spin-diffusion theory. The equations for flow velocity and spin velocity, coupled to Maxwell’s equations of magnetostatics, are solved analytically to second order in the applied magnetic field. A similar derivation holds in electrohydrodynamics for a polar liquid contained in a sphere and subject to a rotating electrical field.

We investigate here water flow passing a single-walled carbon nanotube (CNT), through analysis based on combined atomistic and continuum mechanics simulations. The relation between drag coefficient $C_{\mathrm{D}}$ and Reynolds number Re is obtained for a wide range of flow speed $u$ from 5 to 600 m/s. The results suggest that Stokes law for creep flow works well for small Reynolds numbers up to 0.1 ($u$ ≈ 100 m/s), and indicates a linear dependence between drag force and flow velocity. Significant deviation is observed at elevated Re values, which is discussed by considering the interfacial slippage, reduction of viscosity due to friction-induced local heating, and flow-induced structural vibration. We find that interfacial slippage has a limited contribution to the reduction of the resistance, and excitations of low-frequency vibration modes in the carbon nanotube play an important role in energy transfer between water and carbon nanotubes, especially at high flow speeds where drastic enhancement of the carbon nanotube vibration is observed. The results reported here reveal nanoscale fluid-structure interacting mechanisms, and lay the ground for rational design of nanofluidics and nanoelectromechanical devices operating in a fluidic environment.

Assuming perfect collision efficiency, we demonstrate that turbulence can initiate and sustain the rapid growth of very small water droplets in air even when these droplets are too small to cluster, and even without having to take gravity and small-scale intermittency into account. This is because the range of local Stokes numbers of identical droplets in the turbulent flow field is broad enough even when small-scale intermittency is neglected. This demonstration is given for turbulence which is one order of magnitude less intense than is typical in warm clouds but with a volume fraction which, even though small, is nevertheless large enough for an estimated a priori frequency of collisions to be ten times larger than in warm clouds. However, the time of growth in these conditions turns out to be one order of magnitude smaller than in warm clouds.

We present turbulent properties of electrostatic drift waves in a nonuniform collisional plasma composed of magnetized electrons and ions in the presence of immobile dust particles. For this purpose, we derive a pair of nonlinear quasi-two-dimensional equations exhibiting the coupling between the generalized ion vorticity and the density fluctuations associated with collisional drift waves. The effect of a dust density gradient on the initial drift instability and fully developed turbulence is examined numerically.

The nonlinear-oscillating system in action-angle variables is characterized by the dependence of frequency of oscillation $\omega \left(I\right)$ on action $I$. Periodic perturbation is capable of realizing in the system a stable nonlinear resonance at which the action $I$ adapts to the resonance condition $\omega \left(I_0\right)\simeq \omega$, that is, “sticking” in the resonance frequency. For a particular physical problem there may be a case when $I\gg \hslash$ is the classical quantity, whereas its correction $\Delta I\simeq \hslash$ is the quantum quantity. Naturally, dynamics of $\Delta I$ is described by the quantum equation of motion. In particular, in the moderate nonlinearity approximation $\varepsilon \ll (d\omega /dI)(I/\omega )\ll 1/\varepsilon$, where $\varepsilon$ is the small parameter, the description of quantum state is reduced to the solution of the Mathieu-Schrödinger equation. The state formed as a result of sticking in resonance is an eigenstate of the operator $\Delta \widehat{I}$ that does not commute with the Hamiltonian $\widehat{H}$. Expanding the eigenstate wave functions in Hamiltonian eigenfunctions, one can obtain a probability distribution of energy level population. Thus, an inverse level population for times lower than the relaxation time can be obtained.