We disprove a conjecture of Estrada and Rodríguez-Velázquez [Phys. Rev. E 71, 056103 (2005)] that if a graph has identical subgraph centrality for all nodes, then the closeness and betweenness centralities are also identical for all nodes.

Temporal decorrelations in compressible isotropic turbulence are studied using the space-time correlation theory and direct numerical simulation. A swept-wave model is developed for dilatational components, while the classic random sweeping model is proposed for solenoidal components. The swept-wave model shows that the temporal decorrelations in dilatational fluctuations are dominated by two physical processes: random sweeping and wave propagation. These models are supported by the direct numerical simulation of compressible isotropic turbulence, in the sense that all curves of normalized time correlations for different wave numbers collapse into a single one using the normalized time separations. The swept-wave model is further extended to account for a constant mean velocity.

A five-species predator-prey model is studied on a square lattice where each species has two prey and two predators on the analogy to the rock-paper-scissors-lizard-Spock game. The evolution of the spatial distribution of species is governed by site exchange and invasion between the neighboring predator-prey pairs, where the cyclic symmetry can be characterized by two different invasion rates. The mean-field analysis has indicated periodic oscillations in the species densities with a frequency becoming zero for a specific ratio of invasion rates. When varying the ratio of invasion rates, the appearance of this zero-eigenvalue mode is accompanied by neutrality between the species associations. Monte Carlo simulations of the spatial system reveal diverging fluctuations at a specific invasion rate, which can be related to the vanishing dominance between all pairs of species associations.

We investigate the performance of a linear electromechanical oscillator as an energy harvester of finite-bandwidth random vibrations. We derive exact analytical expressions for the net electrical power and the efficiency of the conversion of the power supplied by the noise into electrical power for arbitrary colored noise. We apply our results to the important case of exponentially correlated noise and discuss the tuning of parameters to achieve good performance of the device.

The dynamics of individual colloidal particles in random potential energy landscapes was investigated experimentally and by Monte Carlo simulations. The value of the potential at each point in the two-dimensional energy landscape follows a Gaussian distribution. The width of the distribution, and hence the degree of roughness of the energy landscape, was varied and its effect on the particle dynamics studied. This situation represents an example of Brownian dynamics in the presence of disorder. In the experiments, the energy landscapes were generated optically using a holographic setup with a spatial light modulator, and the particle trajectories were followed by video microscopy. The dynamics is characterized using, e.g., the time-dependent diffusion coefficient, the mean squared displacement, the van Hove function, and the non-Gaussian parameter. In both experiments and simulations the dynamics is initially diffusive, showing an extended subdiffusive regime at intermediate times before diffusive motion is recovered at very long times. The dependence of the long-time diffusion coefficient on the width of the Gaussian distribution agrees with theoretical predictions. Compared to the dynamics in a one-dimensional potential energy landscape, the localization at intermediate times is weaker and the diffusive regime at long times reached earlier, which is due to the possibility to avoid local maxima in two-dimensional energy landscapes.

We used a configuration-based kinetic Monte Carlo model to explain important features related to formation of the ($\sqrt{3}$$\times$$\sqrt{3}$)$R30$${}^{\circ }$ mosaic of metal and semiconductor atoms on the Si(111) surface. Using first-order desorption processes, we simulate the surprising zero-order desorption spectra, reported in some cases of metal desorption from the Si(111) surface. We show that the mechanism responsible for the zerolike order of desorption is the enhanced desorption from disordered areas. Formation of the $\sqrt{3}$$\times$$\sqrt{3}$ mosaic with properties of a strongly frustrated antiferromagnetic Ising model is simulated by a configuration-sensitive desorption. For substitution of desorbed metal atoms by Si adatoms, fast diffusion of the adatoms on top of a 1$\times$1 layer is proposed as the most probable. Simulations of desorption-induced structural transitions provide us a link between underlying atomistic processes and the observed evolving morphologies with resultant macroscopic desorption fluxes. An effect of the desorption sensitivity on a configuration of neighboring atoms is emphasized.

I compute exact partition function zeros of $\beta$ hairpins, using both analytic and numerical methods, extending previous work [J. Lee, Phys. Rev. Lett. 110, 248101 (2013)] where only a restricted class of hairpins was considered. The zeros of $\beta$ hairpins with an odd number of peptide bonds are computed and the difference of the distribution of zeros from those for an even number of peptide bonds is explained in terms of additional entropy of liberating the extra bond at the turn region. Upon the introduction of a hydrophobic core in the central region of the hairpin, the zeros are distributed uniformly on two concentric circles corresponding to the hydrophobic collapse and the transition to the fully folded conformation. One of the circles dissolves as the core moves toward the turn or the tip region, which is explained in terms of the similarity of the intermediate state with the folded or unfolded states. The exact partition function zeros for a hairpin with a more complex structure of native contacts, the 16 C-terminal residues of streptococcal protein G B1, are numerically computed and their loci are closely approximated by concentric circles.

KIF1A is a single-headed molecular motor that moves processively and unidirectionally along a microtubule by using the chemical energy released by hydrolyzing adenosine triphosphate (ATP) into adenosine diphosphate (ADP) and inorganic phosphate (${\mathrm{P}}_{\mathrm{i}}$). Although the movement of KIF1A seems to have successfully been explained by a simple Brownian motor model of the flashing ratchet type, this model is not suited to discuss the energetics of KIF1A. We introduce an elaborated model of the ratchet type to investigate how the chemical free energy is converted into mechanical work by taking account of the binding and release of reactant (ATP) and product (ADP and ${\mathrm{P}}_{\mathrm{i}}$) molecules to and from the motor. The efficiency of energy transduction, the power output, and other quantities are calculated from the analytically obtained steady-state solution of the Fokker-Planck equations. It turns out that the concentrations of the reactant and product molecules that optimize both the efficiency and the power are close to those in the cell.

Coarse-grained simulations of protein translocation across narrow pores suggest that the transport is characterized by long stall events. The translocation bottlenecks and the associated free-energy barriers are found to be strictly related to the structural properties of the protein native structure. The ascending ramps of the free-energy profile systematically correspond to regions of the chain denser in long range native contacts formed with the untranslocated portion of the protein. These very regions are responsible for the stalls occurring during the protein transport along the nanopore. The decomposition of the free energy in internal energyand entropic terms shows that the dominant energetic contribution can be estimated on the base of the protein native structure only. Interestingly, the essential features of the dynamics are retained in a reduced phenomenological model of the process describing the evolution of a suitable collective variable in the associated free-energy landscape.

We examine the evolution of a liquid drop on an inclined substrate oscillating vertically. The oscillations are weak and slow, which makes the liquid's inertia and viscosity negligible (so that the drop's shape is determined by a balance of surface tension, gravity, and vibration-induced inertial force). No assumptions are made about the drop's thickness, which extends our previous results on thin drops [Benilov, Phys. Rev. E 84, 066301 (2011)] to more realistic situations. It is shown that, if the amplitude of the substrate's oscillations exceeds a certain threshold value ${\varepsilon }_{*}$, the drop climbs uphill. ${\varepsilon }_{*}$, however, strongly depends on the thickness of the drop, which, in turn, depends on the liquid's equilibrium contact angle $\overline{\beta }$. In particular, there is a dramatic decrease in ${\varepsilon }_{*}$ when $\overline{\beta }$ exceeds a certain threshold, which means that thick drops climb uphill for a much weaker vibration of the substrate. At the same time, the frequency range of the substrate's vibration within which drops climb uphill becomes much narrower.

The nonlinear dynamics of the interface between two deep dielectric fluids in the presence of a vertical electric field is studied. We consider the limit of a strong external electric field where electrostatic forces dominate over gravitational and capillary forces. The nonlinear integrodifferential equations for the interface motion are derived under the assumption of small interfacial slopes. It is shown in the framework of these equations that, in the generic case, the instability development leads to the formation of root singularities at the interface in a finite time. The interfacial curvature becomes infinite at singular points, while the slope angles remain relatively small. The curvature is negative in the vicinity of singularities if the ratio of the permittivities of the fluids exceeds the inverse ratio of their densities, and it is positive in the opposite case (we consider that the lower fluid is heavier than the upper one). In the intermediate case, the interface evolution equations describe the formation and sharpening of dimples at the interface. The results obtained are applicable for the description of the instability of the interface between two magnetic fluids in a vertical magnetic field.

In this work, we study the resonance behavior of mechanically oscillated, sessile water drops. By mechanically oscillating sessile drops vertically and within prescribed ranges of frequencies and amplitudes, a rich collection of resonance modes are observed and their dynamics subsequently investigated. We first present our method of identifying each mode uniquely, through association with spherical harmonics and according to their geometric patterns. Next, we compare our measured resonance frequencies of drops to theoretical predictions using both the classical theory of Lord Rayleigh and Lamb for free, oscillating drops, and a prediction by Bostwick and Steen that explicitly considers the effect of the solid substrate on drop dynamics. Finally, we report observations and analysis of drop mode mixing, or the simultaneous coexistence of multiple mode shapes within the resonating sessile drop driven by one sinusoidal signal of a single frequency. The dynamic response of a deformable liquid drop constrained by the substrate it is in contact with is of interest in a number of applications, such as drop atomization and ink jet printing, switchable electronically controlled capillary adhesion, optical microlens devices, as well as digital microfluidic applications where control of droplet motion is induced by means of a harmonically driven substrate.

The bed slope in the shallow-water equations reflects the bed topography. It is not a flow variable and cannot be determined in the solution to the flow equations. An immovable nonflat bed affects a flow as a force term, but the flow has no effect on it. Only when the bed term is correctly represented in a numerical method can it generate an accurate solution. In the enhanced lattice Boltzmann method for the shallow-water equations (eLABSWE), using an individual Chapman-Enskog analysis, it is found that such a correct representation can be achieved by retaining $C_{\alpha }=2{\lambda }_{\alpha }$, in which $C_{\alpha }$ is the coefficient for bed elevation in the lattice Boltzmann equation and ${\lambda }_{\alpha }$ is that for the water depth in the local equilibrium distribution function. The finding has been validated through simulations of a water at rest in a dish-shaped lake, a wind-induced shallow flow in the same lake, and a steady flow over a two-dimensional bed hump.

In this paper, we formally demonstrate that the nonequilibrium density matrix developed by Hershfield for the steady state has the form of a McLennan-Zubarev nonequilibrium ensemble. The correction term in this pseudoequilibrium Gibbs-like ensemble is directly related to the entropy production in the quantum open system. The fact that both methods state that a nonequilibrium steady state can be mapped onto a pseudoequilibrium, permits us to develop nonequilibrium quantities from formal expressions equivalent to the equilibrium case. We provide an example: the derivation of a nonequilibrium distribution function for the electron population in a scattering region in the context of quantum transport.

We study the effect of thermal fluctuations on the wetting phase transitions of infinite order and of continuously varying order, recently discovered within a mean-field density-functional model for three-phase equilibria in systems with short-range forces and a two-component order parameter. Using linear functional renormalization group calculations within a local interface Hamiltonian approach, we show that the infinite-order transitions are robust. The exponential singularity (implying $2-{\alpha }_s=\infty$) of the surface free energy excess at infinite-order wetting as well as the precise algebraic divergence (with ${\beta }_s=-1$) of the wetting layer thickness are not modified as long as $\omega <2$, with $\omega$ the dimensionless wetting parameter that measures the strength of thermal fluctuations. The interface width diverges algebraically and universally (with ${\nu }_{\perp }=1/2$). In contrast, the nonuniversal critical wetting transitions of finite but continuously varying order are modified when thermal fluctuations are taken into account, in line with predictions from earlier calculations on similar models displaying weak, intermediate, and strong fluctuation regimes.

A continuum model for the dynamics of a single step with the strongly anisotropic line energy is formulated and analyzed. The step grows by attachment of adatoms from the lower terrace, onto which atoms adsorb from a vapor phase or from a molecular beam, and the desorption is nonnegligible (the “one-sided” model). Via a multiscale expansion, we derived a long-wave, strongly nonlinear, and strongly anisotropic evolution PDE for the step profile. Written in terms of the step slope, the PDE can be represented in a form similar to a convective Cahn-Hilliard equation. We performed the linear stability analysis and computed the nonlinear dynamics. Linear stability depends on whether the stiffness is minimum or maximum in the direction of the step growth. It also depends nontrivially on the combination of the anisotropy strength parameter and the atomic flux from the terrace to the step. Computations show formation and coarsening of a hill-and-valley structure superimposed onto a long-wavelength profile, which independently coarsens. Coarsening laws for the hill-and-valley structure are computed for two principal orientations of a maximum step stiffness, the increasing anisotropy strength, and the varying atomic flux.

Cable theory has been developed over the last decade, usually assuming that the extracellular space around membranes is a perfect resistor. However, extracellular media may display more complex electrical properties due to various phenomena, such as polarization, ionic diffusion, or capacitive effects, but their impact on cable properties is not known. In this paper, we generalize cable theory for membranes embedded in arbitrarily complex extracellular media. We outline the generalized cable equations, then consider specific cases. The simplest case is a resistive medium, in which case the equations recover the traditional cable equations. We show that for more complex media, for example, in the presence of ionic diffusion, the impact on cable properties such as voltage attenuation can be significant. We illustrate this numerically, always by comparing the generalized cable to the traditional cable. We conclude that the nature of intracellular and extracellular media may have a strong influence on cable filtering as well as on the passive integrative properties of neurons.

Despite several experiments on chaotic quantum transport in two-dimensional systems such as semiconductor quantum dots, corresponding quantum simulations within a real-space model have been out of reach so far. Here we carry out quantum transport calculations in real space and real time for a two-dimensional stadium cavity that shows chaotic dynamics. By applying a large set of magnetic fields we obtain a complete picture of magnetoconductance that indicates fractal scaling. In the calculations of the fractality we use detrended fluctuation analysis—a widely used method in time-series analysis—and show its usefulness in the interpretation of the conductance curves. Comparison with a standard method to extract the fractal dimension leads to consistent results that in turn qualitatively agree with the previous experimental data.

We investigate the emergent dynamical behavior of hydrodynamically coupled microrotors. The two rotors are confined in a plane and move along circles driven by active forces. The three-dimensional fluid is described by the linearized, time-dependent Navier-Stokes equations instead of the usually adopted Stokes equations. We demonstrate that time-dependent hydrodynamic interactions lead to synchronization of the rotational motion. The time dependence of the phase difference between the rotors is determined and synchronization times are extracted for various external torques and rotor separations by solving the underlaying integrodifferential equations numerically. In addition, an analytical expression is provided for the synchronization time.

The zero-temperature random-field Ising model is solved analytically for magnetization versus external field for a bilayered Bethe lattice. The mechanisms of infinite avalanches which are observed for small values of disorder are established. The effects of variable interlayer interaction strengths on infinite avalanches are investigated. The spin-field correlation length is calculated and its critical behavior is discussed. Direct Monte Carlo simulations of spin-flip dynamics are shown to support the analytical findings. We find, paradoxically, that a reduction of the interlayer bond strength can cause a phase transition from a regime with continuous magnetization reversal to a regime where magnetization exhibits a discontinuity associated with an infinite avalanche. This effect is understood in terms of the proposed mechanisms for the infinite avalanche.