Nanocolloids trapped at the depleted side (anodic) of a fluidic nanoslot entrance are shown to sensitively regulate dc ion transport through the nanoslot, such that a second limiting-overlimiting transition occurs in its nonlinear current-voltage characteristics. The nanocolloids, brought to the entrance by electro-osmosis, are not stationary but are confined to closed circular and toroidal streamlines, driven by a back-pressure corner vortex and an orthogonal electroconvection vortex instability. The transition from the corner vortex to a complex torus with both vortical motions coincides with the first overlimiting transition, while electrostatic interaction of nanocolloids in these vortices with the nanoslot entrance drives the second limiting transition.

A simplified thermodynamic approach of the incompressible axisymmetric Euler equations is considered based on the conservation of helicity, angular momentum, and microscopic energy. Statistical equilibrium states are obtained by maximizing the Boltzmann entropy under these sole constraints. We assume that these constraints are selected by the properties of forcing and dissipation. The fluctuations are found to be Gaussian, while the mean flow is in a Beltrami state. Furthermore, we show that the maximization of entropy at fixed helicity, angular momentum, and microscopic energy is equivalent to the minimization of macroscopic energy at fixed helicity and angular momentum. This provides a justification of this selective decay principle from statistical mechanics. These theoretical predictions are in good agreement with experiments of a von Kármán turbulent flow and provide a way to measure the temperature of turbulence and check fluctuation-dissipation relations. Relaxation equations are derived that could provide an effective description of the dynamics toward the Beltrami state and the progressive emergence of a Gaussian distribution. They can also provide a numerical algorithm to determine maximum entropy states or minimum energy states.

In order to perform numerical simulations of the Kardar-Parisi-Zhang (KPZ) equation, in any dimensionality, a spatial discretization scheme must be prescribed. The known fact that the KPZ equation can be obtained as a result of a Hopf-Cole transformation applied to a diffusion equation (with multiplicative noise) is shown here to strongly restrict the arbitrariness in the choice of spatial discretization schemes. On one hand, the discretization prescriptions for the Laplacian and the nonlinear (KPZ) term cannot be independently chosen. On the other hand, since the discretization is an operation performed on space and the Hopf-Cole transformation is local both in space and time, the former should be the same regardless of the field to which it is applied. It is shown that whereas some discretization schemes pass both consistency tests, known examples in the literature do not. The requirement of consistency for the discretization of Lyapunov functionals is argued to be a natural and safe starting point in choosing spatial discretization schemes. We also analyze the relation between real-space and pseudospectral discrete representations. In addition we discuss the relevance of the Galilean-invariance violation in these consistent discretization schemes and the alleged conflict of standard discretization with the fluctuation-dissipation theorem, peculiar of one dimension.

Cyclic (rock-paper-scissors-type) population models serve to mimic complex species interactions. Focusing on a paradigmatic three-species model with mutations in one dimension, we observe an interplay between equilibrium and nonequilibrium processes in the stationary state. We exploit these insights to obtain asymptotically exact descriptions of the emerging reactive steady state in the regimes of high and low mutation rates. The results are compared to stochastic lattice simulations. Our methods and findings are potentially relevant for the spatiotemporal evolution of other nonequilibrium stochastic processes.

The paper investigates stochastic processes forced by independent and identically distributed jumps occurring according to a Poisson process. The impact of different distributions of the jump amplitudes are analyzed for processes with linear drift. Exact expressions of the probability density functions are derived when jump amplitudes are distributed as exponential, gamma, and mixture of exponential distributions for both natural and reflecting boundary conditions. The mean level-crossing properties are studied in relation to the different jump amplitudes. As an example of application of the previous theoretical derivations, the role of different rainfall-depth distributions on an existing stochastic soil water balance model is analyzed. It is shown how the shape of distribution of daily rainfall depths plays a more relevant role on the soil moisture probability distribution as the rainfall frequency decreases, as predicted by future climatic scenarios.

In this work, we test the ability of the Ornstein-Zernike equation in the Percus-Yevick approximation (OZPY) to generate interaction potentials from pair correlation functions (PCFs) of monatomic and diatomic Lennard-Jones fluids. The PCFs are generated by solving OZPY equation (monatomic fluid) and molecular-dynamics (MD) simulations (diatomic fluid). Since the interaction potentials are inputs in the OZPY method and the MD simulation, the extraction of the potential from the PCFs using OZPY is a test of self-consistency. This test is necessary if the procedure is to be used to generate coarse-grained (CG) potentials from PCFs. We find that the procedure is completely self-consistent for the monatomic fluid in the whole range of densities studied (reduced density up to 0.55, under reduced temperature of 2.0). In the diatomic case, we find that the procedure is generally self-consistent under both low and high densities, although there is a systematic deviation at high densities. The method is able to reproduce the two parameters ($\epsilon$ and $\sigma$) of the input Lennard-Jones potential model to within about 1%. This CG potential generating procedure can be straightforwardly extended to more complicated molecules.

Thermal energy provides random motion to particles that leads to the well-known entropic force, which favors the clumping of linear and circular molecules. We evaluate the entropic force which resists the radial dilation and subsequent twisting out of plane of circular polymers by developing mechanical models and performing molecular dynamics simulations. We find that dilating a circular chain is analogous to stretching its linear counterpart. We also find that the torque applied to an already dilated ring and the resulting twist out of plane are related by a linear relationship for a wide range of deformed configurations and, using this result, we are able to predict the angular fluctuations of such a macromolecule.

When neurons in layer 1 fire irregularly under stochastic noise, it is found synchronous firings can develop gradually in latter layers within a feed-forward multilayer neural network, which is consistent with experimental findings. The underlying mechanism of propagation of firing rate is explored, then rate encoding realized by synchronization is clarified. Furthermore, the effects of connection probability between nearest layers, stochastic noise, and ratio of inhibitory connections to total connection on (i) propagation of firing rate by synchronization and (ii) coherence of firing pattern are investigated, respectively. It is observed that (i) there is a threshold for connection probability, beyond which firing rate of each layer can propagate successfully through the whole network by synchronization. The dependence of firing rate on layer index is very different for different connection probability. In addition, larger the connection probability is, more rapidly the synchrony is built up. (ii) Increasing intensity of stochastic noise enhances firing rate in output layer. Stochastic noise plays a constructive role in improving synchrony by causing the synchronization more quickly. (iii) The inhibitory connection offsets excitatory input therefore reduces firing rate and synchrony. As layer index increases, coherence measure goes through a peak, i.e., the coherence of firing pattern is the worst at certain a layer. With increasing the ratio of inhibitory connections, the variability of firing train is enhanced, exhibiting destructive role of inhibitory connections on coherence of firing pattern.

The space-time cross-correlation function $C_T\left(r,\tau \right)$ of local temperature fluctuations in turbulent Rayleigh-Bénard convection is obtained from simultaneous two-point time series measurements. The obtained $C_T\left(r,\tau \right)$ is found to have the scaling form $C_T\left(r_E,0\right)$ with $r_E={\left[{\left(r-U\tau \right)}^2+V^2{\tau }^2\right]}^{1/2}$, where $U$ and $V$ are two characteristic velocities associated with the mean and rms velocities of the flow. The experiment verifies the theory and demonstrates its applications to a class of turbulent flows in which the requirement of Taylor’s frozen flow hypothesis is not met.

We study the behavior of U.S. markets both before and after U.S. Federal Open Market Commission meetings and show that the announcement of a U.S. Federal Reserve rate change causes a financial shock, where the dynamics after the announcement is described by an analog of the Omori earthquake law. We quantify the rate $n\left(t\right)$ of aftershocks following an interest-rate change at time $T$ and find power-law decay which scales as $n\left(t-T\right)\sim {\left(t-T\right)}^{-\Omega }$, with $\Omega$ positive. Surprisingly, we find that the same law describes the rate $n^{\prime }\left(\left|t-T\right|\right)$ of “preshocks” before the interest-rate change at time $T$. This study quantitatively relates the size of the market response to the news which caused the shock and uncovers the presence of quantifiable preshocks. We demonstrate that the news associated with interest-rate change is responsible for causing both the anticipation before the announcement and the surprise after the announcement. We estimate the magnitude of financial news using the relative difference between the U.S. Treasury Bill and the Federal Funds effective rate. Our results are consistent with the “sign effect,” in which “bad news” has a larger impact than “good news.” Furthermore, we observe significant volatility aftershocks, confirming a “market under-reaction” that lasts at least one trading day.

We use analytical techniques based on an expansion in the inverse system size to study the stochastic evolutionary dynamics of finite populations of players interacting in a repeated prisoner’s dilemma game. We show that a mechanism of amplification of demographic noise can give rise to coherent oscillations in parameter regimes where deterministic descriptions converge to fixed points with complex eigenvalues. These quasicycles between cooperation and defection have previously been observed in computer simulations; here we provide a systematic and comprehensive analytical characterization of their properties. We are able to predict their power spectra as a function of the mutation rate and other model parameters and to compare the relative magnitude of the cycles induced by different types of underlying microscopic dynamics. We also extend our analysis to the iterated prisoner’s dilemma game with a win-stay lose-shift strategy, appropriate in situations where players are subject to errors of the trembling-hand type.

Sea-ice floe-size distribution (FSD) in ice-pack covered seas influences many aspects of ocean-atmosphere interactions. However, data concerning FSD in the polar oceans are still sparse and processes shaping the observed FSD properties are poorly understood. Typically, power-law FSDs are assumed although no feasible explanation has been provided neither for this one nor for other properties of the observed distributions. Consequently, no model exists capable of predicting FSD parameters in any particular situation. Here I show that the observed FSDs can be well represented by a truncated Pareto distribution $P\left(x\right)=x^{-1-\alpha }\text{exp}\left[\left(1-\alpha \right)/x\right]$, which is an emergent property of a certain group of multiplicative stochastic systems, described by the generalized Lotka-Volterra (GLV) equation. Building upon this recognition, a possibility of developing a simple agent-based GLV-type sea-ice model is considered. Contrary to simple power-law FSDs, GLV gives consistent estimates of the total floe perimeter, as well as floe-area distribution in agreement with observations.

We report on an experimental study of the behavior of a number of commercially available quartz tuning forks oscillating in a classical cryogenic fluid, in the form of either liquid helium I or gaseous helium, extending our previous studies [M. Blazkova et al. Phys. Rev. E 75, 025302 (2007)]. Measurements of the damping of the oscillations allowed us to deduce the drag on the prong of a fork, as a function of the velocity with which the prong moves, for various sizes of fork and various oscillation frequencies. Transitions to turbulent flow have been identified, and the dependence of the critical velocity, expressed as a dimensionless critical Keulegan-Carpenter number, on the dimensionless Stokes number has been established. These measurements have not allowed us to visualize the flow, so we have carried out visualization experiments with oscillating rods in water, the rod dimensions, and the frequencies of oscillation, being chosen so that the relevant dimensionless parameters are similar to those for the prongs of the forks. Some information about the nature of the instability that leads to turbulence has been obtained in this way, and the results for the critical Keulegan-Carpenter number for the rods in water have been compared with values for the tuning forks in a cryogenic fluid.

We derive the Euler-Lagrange equations for a large class of variational problems on curves. Our result generalizes a recent result obtained in the literature. Moreover, it is simple and self-contained. It directly yields Euler-Lagrange equations in the form of equilibrium equations for the internal force and moment.

A lattice Boltzmann model with complex distribution function for the complex Ginzburg-Landau equation (CGLE) is proposed. By using multiscale technique and the Chapman-Enskog expansion on complex variables, we obtain a series of complex partial differential equations. Then, complex equilibrium distribution function and its complex moments are obtained. Based on this model, the rotation and oscillation properties of stable spiral waves and the breaking-up behavior of unstable spiral waves in CGLE are investigated in detail.

Molecular dynamics computer simulations are used to study the aging dynamics of ${\text{SiO}}_2$ (modeled by the BKS model). Starting from fully equilibrated configurations at high temperatures $T_{\text{i}}∊\left\{5000\text{K},3760\text{K}\right\}$, the system is quenched to lower temperatures $T_{\text{f}}∊\left\{2500\text{K},2750\text{K},3000\text{K},3250\text{K}\right\}$ and observed after a waiting time $t_{\text{w}}$. Since the simulation runs are long enough to reach equilibrium at $T_{\text{f}}$, we are able to study the transition from out-of-equilibrium to equilibrium dynamics. We present results for the partial structure factors, for the generalized incoherent intermediate scattering function $C_q\left(t_{\text{w}},t_{\text{w}}+t\right)$, and for the mean-square displacement $\Delta r^2\left(t_{\text{w}},t_{\text{w}}+t\right)$. We conclude that there are three different $t_{\text{w}}$ regions: (I) At very short waiting times, $C_q\left(t_{\text{w}},t_{\text{w}}+t\right)$ decays very fast without forming a plateau. Similarly $\Delta r^2\left(t_{\text{w}},t_{\text{w}}+t\right)$ increases without forming a plateau. (II) With increasing $t_{\text{w}}$ a plateau develops in $C_q\left(t_{\text{w}},t_{\text{w}}+t\right)$ and $\Delta r^2\left(t_{\text{w}},t_{\text{w}}+t\right)$. For intermediate waiting times the plateau height is independent of $t_{\text{w}}$ and $T_{\text{i}}$. Time superposition applies, i.e., $C_q=C_q\left(t/t_{\text{r}}^{\text{Cq}}\right)$ where $t_{\text{r}}^{\text{Cq}}=t_{\text{r}}^{\text{Cq}}\left(t_{\text{w}}\right)$ is a waiting time-dependent decay time. Furthermore $C_q=C\left(q,t_{\text{w}},t_{\text{w}}+t\right)$ scales as $C_q=C(q,z\left(t_{\text{w}},t\right)\phantom{)}$ where $z$ is a function of $t_{\text{w}}$ and $t$ only, i.e., independent of $q$. (III) At large $t_{\text{w}}$ the system reaches equilibrium, i.e., $C_q\left(t_{\text{w}},t_{\text{w}}+t\right)$ and $\Delta r^2\left(t_{\text{w}},t_{\text{w}}+t\right)$ are independent of $t_{\text{w}}$ and $T_{\text{i}}$. For $C_q\left(t_{\text{w}},t_{\text{w}}+t\right)$ we find that the time superposition of intermediate waiting times (II) includes the equilibrium curve (III).

We present a method of measuring the frequency-dependent specific heat at the glass transition applied to 5-polyphenyl-4-ether. The method employs thermal waves effusing radially out from the surface of a spherical thermistor that acts as both a heat generator and a thermometer. It is a merit of the method compared to planar effusion methods that the influence of the mechanical boundary conditions is analytically known. This implies that it is the longitudinal rather than the isobaric specific heat that is measured. As another merit the thermal conductivity and specific heat can be found independently. The method has highest sensitivity at a frequency where the thermal diffusion length is comparable to the radius of the heat generator. This limits in practice the frequency range to 2–3 decades. An account of the $3\omega$ technique used including higher-order terms in the temperature dependence of the thermistor and in the power generated is furthermore given.

The infinitesimal phase response curve (PRC) of a neural oscillator to a weak input is a powerful predictor of network dynamics; however, many networks have strong coupling and require direct measurement of the PRC for strong inputs under the assumption of pulsatile coupling. We incorporate measured noise levels in firing time maps constructed from PRCs to predict phase-locked modes of activity, phase difference, and locking strength in 78 heterogeneous hybrid networks of 2 neurons constructed using the dynamic clamp. We show that noise may either destroy or stabilize a phase-locked mode of activity.

Chimera states are a recently new discovered dynamical phenomenon that appears in arrays of nonlocally coupled oscillators and displays a spatial pattern of coherent and incoherent regions. We report here an additional feature of this dynamical regime: an irregular motion of the position of the coherent and incoherent regions, i.e., we reveal the nature of the chimera as a spatiotemporal pattern with a regular macroscopic pattern in space, and an irregular motion in time. This motion is a finite-size effect that is not observed in the thermodynamic limit. We show that on a large time scale, it can be described as a Brownian motion. We provide a detailed study of its dependence on the number of oscillators $N$ and the parameters of the system.

We consider words as a network of interacting letters, and approximate the probability distribution of states taken on by this network. Despite the intuition that the rules of English spelling are highly combinatorial and arbitrary, we find that maximum entropy models consistent with pairwise correlations among letters provide a surprisingly good approximation to the full statistics of words, capturing $\sim 92\mathrm{\%}$ of the multi-information in four-letter words and even “discovering” words that were not represented in the data. These maximum entropy models incorporate letter interactions through a set of pairwise potentials and thus define an energy landscape on the space of possible words. Guided by the large letter redundancy we seek a lower-dimensional encoding of the letter distribution and show that distinctions between local minima in the landscape account for $\sim 68\mathrm{\%}$ of the four-letter entropy. We suggest that these states provide an effective vocabulary which is matched to the frequency of word use and much smaller than the full lexicon.