We evaluate the efficiency at maximum power of a quantum-dot Carnot heat engine. The universal values of the coefficients at the linear and quadratic order in the temperature gradient are reproduced. Curzon-Ahlborn efficiency is recovered in the limit of weak dissipation.

The mean time to reach a threshold (MTT) is the mean first passage time for the number of bound molecules to reach a given value. In the theory of chemical reactions involving a small number of ligands and molecules, the MTT represents the first time a given number of binding sites is formed. In that context, the MTT can be used to characterize the stability of chemical processes, especially when they underlie a biological function. Using a Markov-chain description, we compute here the MTT, in terms of fundamental parameters, such as the number of molecules, the ligands and the forward and backward binding rates. We find that the MTT depends non-linearly on the threshold $T$, and this result may have several applications, ranging from cellular biology to synaptic plasticity. We confirm our analytical computations with Brownian simulations.

Dense ensembles of monodisperse hard spheres spontaneously assemble into regions of local crystalline order (grains) that are separated by relatively disordered grain-boundary (GB) regions. It is well known that grains and grain boundaries (GB) profoundly affect the material properties of polycrystalline materials and plastic deformation and transport in this ubiquitous class of materials can be particularly influenced by GB structure and dynamics. We experimentally investigate the nature of particle motion in the GB regions of a quasi-two-dimensional driven system of hard spheres and find, in accord with recent molecular-dynamics simulations of metallic polycrystalline materials, that particle motion in the GB regions involves a highly cooperative stringlike motion as in glass-forming liquids. Moreover, we show that the addition of small particles to a granular fluid allows the scale of this collective motion to be modulated, a phenomenon that is also observed in simulations and measurements on glass-forming fluids.

Granger causality analysis is a popular method for inference on directed interactions in complex systems of many variables. A shortcoming of the standard framework for Granger causality is that it only allows for examination of interactions between single (univariate) variables within a system, perhaps conditioned on other variables. However, interactions do not necessarily take place between single variables but may occur among groups or “ensembles” of variables. In this study we establish a principled framework for Granger causality in the context of causal interactions among two or more multivariate sets of variables. Building on Geweke’s seminal 1982 work, we offer additional justifications for one particular form of multivariate Granger causality based on the generalized variances of residual errors. Taken together, our results support a comprehensive and theoretically consistent extension of Granger causality to the multivariate case. Treated individually, they highlight several specific advantages of the generalized variance measure, which we illustrate using applications in neuroscience as an example. We further show how the measure can be used to define “partial” Granger causality in the multivariate context and we also motivate reformulations of “causal density” and “Granger autonomy.” Our results are directly applicable to experimental data and promise to reveal new types of functional relations in complex systems, neural and otherwise.

Through one-dimensional and two-dimensional (2D) particle-in-cell simulations of stimulated Raman scattering (SRS), we show that nonlinear plasma wave packets that are created during SRS and convect through the system after saturation can have a dramatic effect on the recurrence of the instability. The recurrence rate is shown to depend on the propagation speed and frequency content of these packets. Furthermore, SRS can be driven to higher amplitudes via backscattered light traveling between packets. In 2D, the influence of the plasma wave packets is also seen, but the average reflectivity is substantially less due to geometric effects and transverse localization of the packets.

We explore the effect of correlations between the in and out degrees of random directed networks on the synchronization of identical pulse-coupled oscillators. Numerical experiments demonstrate that the proportion of initial conditions resulting in a globally synchronous state (prior to a large but finite time) is an increasing function of node-degree correlation. For those networks observed to globally synchronize, both the mean and standard deviation of time to synchronization are decreasing functions of node-degree correlation. Pulse-coupled oscillator networks with negatively correlated node degree often exhibit multiple coherent attracting states, with trajectories performing fast transitions between them. These effects of node-degree correlation on dynamics of pulse-coupled oscillators are consistent with aspects of network topology (e.g., the effect of node-degree correlation on the eigenvalues of the Laplacian matrix) that have been shown to affect synchronization in other contexts.

An infinite square well with a discontinuous step is one of the simplest systems to exhibit non-Newtonian ray-splitting periodic orbits. This system is analyzed using both time-independent perturbation theory (PT) and periodic-orbit theory and the approximate formulas for the energy eigenvalues derived from these two approaches are compared. The periodic orbits of the system can be divided into classes according to how many times they reflect from the potential step. Different classes of orbits contribute to different orders of PT. The dominant term in the second-order PT correction is due to non-Newtonian orbits that reflect from the step exactly once. In the limit in which PT converges, the periodic-orbit theory results agree with those of PT, but outside of this limit the periodic-orbit theory gives much more accurate results for energies above the potential step.

We explore analytically, numerically, and experimentally the spectral properties of the flexural vibrations of micron scale cantilevers in a viscous fluid that are driven externally or by Brownian motion. Although the physical origins of driven and thermal cantilever dynamics are quite different, we show that in each case the dynamics can be calculated deterministically using an impulse or step force, respectively. The stochastic dynamics of the cantilever are related to the removal of a step force by the fluctuation-dissipation theorem to yield the autocorrelation and noise spectral density of equilibrium fluctuations. The dynamics of a cantilever driven externally is related to an impulse in force by transfer function theory. Using this approach, we explore the differences between the driven and thermal spectra of microcantilevers. We find that higher order cantilever modes and the spatial distribution of the applied load for the external drive can be critical to the relationship between the thermal and driven spectra.

We study a singular limit of tumbled granular flows in quasi-two-dimensional rotating drums, demonstrating that the limiting dynamical system, as the shear layer vanishes, belongs to a class of discrete discontinuous mappings called piecewise isometries. In doing so, we identify a mechanism of mixing, in the absence of the usual streamline crossing mediated by the flowing layer. By considering the exceptional case of a 50% full square tumbler, this mechanism (streamline jumping) is related to the horizontal motion of the free surface of the flow in non-half-full tumblers. The limiting dynamics are quite complex, if not (technically) chaotic.

This work presents a simulation technique that can be used to compute the thermal interaction between a gas and a cylindrically shaped wall. The method is computationally simple and is based on the Maxwell-Smoluchowski thermal wall scenario often used for the slit pore geometry. A geometric argument is used to find the corresponding thermalization mechanism for the cylindrical confinement. The algorithm serves as a thermostat, which enables one to perform constant-temperature simulations. By means of simple numerical simulations, Smoluchowski’s expression for self-diffusivity $D_s$ is then recovered in reduced units. The tangential momentum accommodation coefficient is interpreted as a coupling constant for the thermostat similar to the one used for the ordinary Andersen thermostat but applied locally onto the boundary crossing particles.

We show the existence of a competition-induced resonance effect for a generic globally coupled bistable system. In particular, we demonstrate that the response of the macroscopic variable to an external signal is optimal for a particular proportion of repulsive links. Furthermore, we show that a resonance also occurs for other system parameters, like the coupling strength and the number of elements. We relate this resonance to the appearance of a multistable region, and we predict the location of the resonance peaks, by a simple spectral analysis of the Laplacian matrix.

Using the Weiss mean-field approximation theory and the particles’ transport theory for the spatially periodic stochastic systems, we derive an exact analytical expression for the stationary probability current of a coupled lattice system driven by dichotomous noise. It is shown that, for this coupled lattice system, the spatial asymmetry of the system, the asymmetry of the dichotomous noise, and the coupling among nearest neighbors are the ingredients for the stationary probability current. By applying our theory to two special models, we find that (1) the coupling can lead to the directional transport of the particles (even when the potential and the dichotomous noise are symmetric) and (2) the coupling among nearest neighbors can enhance the transport of the particles in some circumstances. Our results are applied to a device of two-dimensional Josephson-junction arrays and a large protein motors cluster.

Stochastic partial differential equations can be used to model second-order thermodynamical phase transitions, as well as a number of critical out-of-equilibrium phenomena. In $\left(2+1\right)$ dimensions, many of these systems are conjectured (and some are indeed proved) to be described by conformal field theories. We advance, in the framework of the Martin-Siggia-Rose field-theoretical formalism of stochastic dynamics, a general solution of the translation Ward identities, which yields a putative conformal energy-momentum tensor. Even though the computation of energy-momentum correlators is obstructed, in principle, by dimensional reduction issues, these are bypassed by the addition of replicated fields to the original $\left(2+1\right)$-dimensional model. The method is illustrated with an application to the Kardar-Parisi-Zhang (KPZ) model of surface growth. The consistency of the approach is checked by means of a straightforward perturbative analysis of the KPZ ultraviolet region, leading, as expected, to its $c=1$ conformal fixed point.

We have investigated analytically and numerically the liquid-glass transition of hard spheres for dimensions $d\to \infty$ in the framework of mode-coupling theory. The numerical results for the critical collective and self-nonergodicity parameters $f_c\left(k;d\right)$ and $f_c^{\left(s\right)}\left(k;d\right)$ exhibit non-Gaussian $k$ dependence even up to $d=800$. $f_c^{\left(s\right)}\left(k;d\right)$ and $f_c\left(k;d\right)$ differ for $k\sim d^{1/2}$, but become identical on a scale $k\sim d$, which is proven analytically. The critical packing fraction ${\phi }_c\left(d\right)\sim d^2{2}^{-d}$ is above the corresponding Kauzmann packing fraction ${\phi }_K\left(d\right)$ derived by a small cage expansion. Its quadratic pre-exponential factor is different from the linear one found earlier. The numerical values for the exponent parameter and therefore the critical exponents $a$ and $b$ depend on $d$, even for the largest values of $d$.

The possible correlation profiles of networks with a given scale-free degree distribution are restricted and bounded by maximally correlated configurations. Dissortative networks consist of nested bilayers, in which low-degree vertices are connected to high-degree vertices. The number of these bilayers attains a constant value for large network size $N$. Assortative networks exhibit monolayers of low-degree vertices, the number of which grows monotonously with $N$. Analytical relations for the Pearson correlation coefficient $r$ of these extremal configurations are derived and shown to provide lower and upper bounds on the possible $r$ values. Both bounds are found to vanish for large networks.

We study the topological properties of the multinetwork of commodity-specific trade relations among world countries over the 1992–2003 period, comparing them with those of the aggregate-trade network, known in the literature as the international-trade network (ITN). We show that link-weight distributions of commodity-specific networks are extremely heterogeneous and (quasi) log normality of aggregate link-weight distribution is generated as a sheer outcome of aggregation. Commodity-specific networks also display average connectivity, clustering, and centrality levels very different from their aggregate counterpart. We also find that ITN complete connectivity is mainly achieved through the presence of many weak links that keep commodity-specific networks together and that the correlation structure existing between topological statistics within each single network is fairly robust and mimics that of the aggregate network. Finally, we employ cross-commodity correlations between link weights to build hierarchies of commodities. Our results suggest that on the top of a relatively time-invariant “intrinsic” taxonomy (based on inherent between-commodity similarities), the roles played by different commodities in the ITN have become more and more dissimilar, possibly as the result of an increased trade specialization. Our approach is general and can be used to characterize any multinetwork emerging as a nontrivial aggregation of several interdependent layers.

Recent atomic force microscope (AFM) experiments have shown that the low-friction sliding of incommensurate graphite flakes on graphite can be destroyed by torque-induced rotations. Here we theoretically investigate the stability of superlubric sliding against rotations of the flake. We find that the occurrence of superlubric motion critically depends on the physical parameters and on the experimental conditions: particular scan lines, thermal fluctuations, and high loading forces can destroy the stability of superlubric orbits. We find that the optimal conditions to achieve superlubric sliding are given by large flakes, low temperature, and low loads, as well as scanning velocities higher than those used in AFM experiments.

The phase relationship between the streamwise and the wall-normal velocity disturbances induced by a traveling-wave-like blowing or suction control [T. Min et al., J. Fluid Mech. 558, 309 (2006)] in a two-dimensional laminar Poiseuille flow is investigated. The investigation is done by solving the linearized Navier-Stokes equation and by using the identity equation between the skin-friction drag and the Reynolds shear stress [K. Fukagata et al., Phys. Fluids 14, L73 (2002)]. It has been known that a traveling wave creates a nonquadrature between the velocity disturbances and generates the positive phase shift of the streamwise velocity disturbance in the case of a skin-friction drag reduction. The present analysis further reveals that this nonquadrature consists of an inviscid base phase relationship and a near-wall phase shift induced by the viscosity. The analogy between the present control and Stokes’ second problem is discussed. The thickness of the near-wall region in which the viscous phase shift takes place is found to be scaled similarly to the Stokes’ second problem.

We report experiments in which the nonaxisymmetric sectorial oscillations of water drops have been excited using acoustic levitation and an active modulation method. The observed stable sectorial oscillations are up to the seventh mode. These oscillations are excited by parametric resonance. The oblate initial shape of the water drops is essential to this kind of excitations. The oscillation frequency increases with mode number but decreases with equatorial radius for each mode number. The data can be well described by a modified Rayleigh equation, without the use of additional parameters.

Most systems, when pushed out of equilibrium, respond by building up currents of locally conserved observables. Understanding how microscopic dynamics determines the averages and fluctuations of these currents is one of the main open problems in nonequilibrium statistical physics. The additivity principle is a theoretical proposal that allows to compute the current distribution in many one-dimensional nonequilibrium systems. Using simulations, we validate this conjecture in a simple and general model of energy transport, both in the presence of a temperature gradient and in canonical equilibrium. In particular, we show that the current distribution displays a Gaussian regime for small current fluctuations, as prescribed by the central limit theorem, and non-Gaussian (exponential) tails for large current deviations, obeying in all cases the Gallavotti-Cohen fluctuation theorem. In order to facilitate a given current fluctuation, the system adopts a well-defined temperature profile different from that of the steady state and in accordance with the additivity hypothesis predictions. System statistics during a large current fluctuation is independent of the sign of the current, which implies that the optimal profile (as well as higher-order profiles and spatial correlations) are invariant upon current inversion. We also demonstrate that finite-time joint fluctuations of the current and the profile are well described by the additivity functional. These results suggest the additivity hypothesis as a general and powerful tool to compute current distributions in many nonequilibrium systems.