The effect of geometry in the statistics of nonlinear universality classes for interface growth has been widely investigated in recent years, and it is well known to yield a split of them into subclasses. In this work, we investigate this for the linear classes of Edwards-Wilkinson and of Mullins-Herring in one and two dimensions. From comparison of analytical results with extensive numerical simulations of several discrete models belonging to these classes, as well as numerical integrations of the growth equations on substrates of fixed size (flat geometry) or expanding linearly in time (radial geometry), we verify that the height distributions (HDs) and the spatial and the temporal covariances are universal but geometry-dependent. In fact, the HDs are always Gaussian, and, when defined in terms of the so-called “KPZ ansatz” $[h\simeq v_{\infty }t+{\left(\mathrm{\Gamma }t\right)}^{\beta }\chi ]$, their probability density functions $P\left(\chi \right)$ have mean null, so that all their cumulants are null, except by their variances, which assume different values in the flat and radial cases. The shape of the (rescaled) covariance curves is analyzed in detail and compared with some existing analytical results for them. Overall, these results demonstrate that the splitting of such university classes is quite general, being not restricted to the nonlinear ones.

We consider discrete-time Markov bridges, chains whose initial and final states coincide. We derive exact finite-time formulae for the joint probability distributions of additive functionals of trajectories. We apply our theory to time-integrated currents and frenesy of enzymatic reactions, which may include absolutely irreversible transitions. We discuss the information that frenesy carries about the currents and show that bridges may violate known uncertainty relations in certain cases. Numerical simulations are in perfect agreement with our theory.

A couple of bistable oxidation reactions on Rh(110), the ${\mathrm{CH}}_3\mathrm{OH}+{\mathrm{O}}_2$ and the ${\mathrm{NH}}_3+{\mathrm{O}}_2$ reactions, exhibit localized excitations at the interface between oxygen-poor and oxygen-rich phase that propagate in a pulselike manner along the interface. A three-variable reaction-diffusion model is set up based on a mechanism that explains the localized excitations as being caused by temporary structural defects generated in the vicinity of the interface. The structural defects are a consequence of different densities of surface atoms in the oxygen-induced reconstruction phases and in the nonreconstructed $(1\times 1)$ phase. One- and two-dimensional simulations show that traveling interface pulses (TIPs) exist in a region of so-called double metastability adjacent to the equistability point of the bistable system. As in the experiment, we observe triangular-shaped TIPs that move fast along the interface. Diffusional anisotropy is not required for the occurrence of TIPs. All essential features of the experiment are reproduced by the simulations.

In this work we investigate how the behavior of the Shannon entropy can be used to measure the diffusion exponent of a set of initial conditions in two systems: (i) standard map and (ii) the oval billiard. We are interested in the diffusion near the main island in the phase space, where stickiness is observed. We calculate the diffusion exponent for many values of the nonlinear parameter of the standard map where the size and shape of the main island change as the parameter varies. We show that the changes of behavior in the diffusion exponent are related with the changes in the area of the main island and show that when the area of the main island is abruptly reduced, due to the destruction of invariant tori and, consequently, creation of hyperbolic and elliptic fixed points, the diffusion exponent grows.

With two minimal models, I study how electrode curvature affects the response of electrolytes to applied electrostatic potentials. For flat electrodes, Bazant et al. [Phys. Rev. E 70, 021506 (2004)] popularized the $RC$ timescale ${\lambda }_{\mathrm{D}}L/D$, with ${\lambda }_{\mathrm{D}}$ being the Debye length, $2L$ the electrode separation, and $D$ the ionic diffusivity. For thin electric double layers near concentric spherical and coaxial cylindrical electrodes, I show here that equivalent circuit models again predict the correct ionic relaxation timescales. Importantly, these timescales explicitly depend on both electrode radii, not simply on their difference.

The reverse perturbation method [Phys. Rev. E 59, 4894 (1999)] for shearing simple liquids and measuring their viscosity is extended to the Vicsek model (VM) of active particles [Phys. Rev. Lett. 75, 1226 (1995)] and its metric-free version. The sheared systems exhibit a phenomenon that is similar to the skin effect of an alternating electric current: Momentum that is fed into the boundaries of a layer decays mostly exponentially toward the center of the layer. It is shown how two transport coefficients, i.e., the shear viscosity $\nu$ and the momentum amplification coefficient $\lambda$, can be obtained by fitting this decay with an analytical solution of the hydrodynamic equations for the VM. The viscosity of the VM consists of two parts, a kinetic and a collisional contribution. While analytical predictions already exist for the former, a novel expression for the collisional part is derived by an Enskog-like kinetic theory. To verify the predictions for the transport coefficients, Green-Kubo relations were evaluated and transverse current correlations were measured in independent simulations. Not too far to the transition to collective motion, we find excellent agreement between the different measurements of the transport coefficients. However, the measured values of $\nu$ and $1-\lambda$ are always slightly higher than the mean-field predictions, even at large mean free paths and at state points quite far from the threshold to collective motion, that is, far in the disordered phase. These findings seem to indicate that the mean-field assumption of molecular chaos is much less reliable in systems with velocity-alignment rules such as the VM, compared to models obeying detailed balance such as multiparticle collision dynamics.

The partition of nanoswimmers between a narrow channel and a reservoir is explored by dissipative particle dynamics. In contrast to passive colloids, nanoswimmers prefer to stay in the slit rather than in the reservoir for sufficiently large active force ($F_a$) or run time (τ). The partition ratio ($\phi$) increases with $F_a$ and τ. Interestingly, as the slit height decreases, $\phi$ grows accordingly until the confinement effect dominates. Three types of the concentration profile in the slit are identified as a consequence of the competition between surface accumulation and entropic barrier.

Weakly attractive interactions between the tips of rodlike colloidal particles affect their liquid-crystal phase behavior due to a subtle interplay between enthalpy and entropy. Here we employ molecular dynamics simulations on semiflexible, repulsive bead-spring chains where one of the two end beads attract each other. We calculate the phase diagram as a function of both the volume fraction of the chains and the strength of the attractive potential. We identify a large number of phases that include isotropic, nematic, smectic-$A$, smectic-$B$, and crystalline states. For tip attraction energies lower than the thermal energy, our results are qualitatively consistent with experimental findings: We find that an increase of the attraction strength shifts the nematic to smectic-$A$ phase transition to lower volume fractions, with only minor effect on the stability of the other phases. For sufficiently strong tip attraction, the nematic phase disappears completely, in addition leading to the destabilization of the isotropic phase. In order to better understand the underlying physics of these phenomena, we also investigate the clustering of the particles at their attractive tips and the effective molecular field experienced by the particles in the smectic-$A$ phase. Based on these results, we argue that the clustering of the tips only affects the phase stability if lamellar structures (“micelles”) are formed. We find that an increase of the attraction strength increases the degree of order in the layered phases. Interestingly, we also find evidence for the existence of an antiferroelectric smectic-$A$ phase transition induced by the interaction between the tips. A simple Maier-Saupe-McMillan model confirms our findings.

In a recent numerical and analytical study, Park et al. [Phys. Rev. E 84, 056604 (2011)] presented the statement that a linearly damped harmonic oscillator subject to a linear frequency chirp ${\omega }_f\left(t\right)={\omega }_0+\epsilon t$ experiences “an early onset of resonance, setting in when the ramped forcing frequency is midway between its initial value ${\omega }_0$ and the natural frequency ${\omega }_n$ for resonance in the unforced problem,” i.e., the resonance occurs when the instantaneous frequency ${\omega }_{\text{inst}}$ approaches $({\omega }_0+{\omega }_n)/2$. This statement is not valid because the instantaneous frequency of the forcing function actually grows twice as fast as stated in the paper, and the resonance actually occurs for instantaneous forcing frequency ${\omega }_{\text{inst}}$ approximately equal to the natural frequency ${\omega }_n$. We also highlight the difference between the critical frequency ramp rate for resonance amplitude measurement and the critical frequency ramp rate for resonance frequency and damping measurements.

The nonlinear regime of laser-plasma interactions including both two-plasmon decay (TPD) and stimulated Raman scattering (SRS) instabilities has been studied in three-dimensional (3D) particle-in-cell simulations with parameters relevant to the inertial confinement fusion (ICF) experiments. SRS and TPD develop in the same region in plasmas, and the generation of fast electrons can be described accurately with only the full model including both SRS and TPD. The growth of instabilities in the linear stage is found to be in good agreement with analytical theories. In the saturation stage the low-frequency density perturbations driven by the daughter waves of the SRS side scattering can saturate the TPD and consequently inhibit the fast-electron generation. The fast-electron flux in 3D modeling is up to an order of magnitude smaller than previously reported in 2D TPD simulations, bringing it close to the results of ICF experiments.

Random walks with stochastic resetting provides a treatable framework to study interesting features about central-place motion. In this work, we introduce noninstantaneous resetting as a two-state model being a combination of an exploring state where the walker moves randomly according to a propagator and a returning state where the walker performs a ballistic motion with constant velocity towards the origin. We study the emerging transport properties for two types of reset time probability density functions (PDFs): exponential and Pareto. In the first case, we find the stationary distribution and a general expression for the stationary mean-square displacement (MSD) in terms of the propagator. We find that the stationary MSD may increase, decrease or remain constant with the returning velocity. This depends on the moments of the propagator. Regarding the Pareto resetting PDF we also study the stationary distribution and the asymptotic scaling of the MSD for diffusive motion. In this case, we see that the resetting modifies the transport regime, making the overall transport subdiffusive and even reaching a stationary MSD, i.e., a stochastic localization. This phenomena is also observed in diffusion under instantaneous Pareto resetting. We check the main results with stochastic simulations of the process.

An immobile charged species provides a charged medium for transport of charge carriers that is exploited in many applications, such as permselective membranes, doped semiconductors, biological ion channels, as well as porous media and microchannels with surface charges. In this paper, we theoretically study the electrochemical impedance of electrodiffusion in a charged medium by employing the Nernst-Planck equation and the electroneutrality condition with a background charge density. The impedance response is obtained under different dc bias conditions extending above the diffusion-limiting bias. We find a transition in the impedance behavior around the diffusion-limiting bias and present an analytical approximation for a weakly charged medium under an overlimiting bias.

Optimization of mutual synchronization between a pair of limit-cycle oscillators with weak symmetric coupling is considered in the framework of the phase-reduction theory. By generalizing our previous study [S. Shirasaka, N. Watanabe, Y. Kawamura, and H. Nakao, Optimizing stability of mutual synchronization between a pair of limit-cycle oscillators with weak cross coupling, Phys. Rev. E 96, 012223 (2017)] on the optimization of cross-diffusion coupling matrices between the oscillators, we consider optimization of mutual coupling signals to maximize the linear stability of the synchronized state, which are functionals of the past time sequences of the oscillator states. For the case of linear coupling, optimization of the delay time and linear filtering of coupling signals are considered. For the case of nonlinear coupling, general drive-response coupling is considered and the optimal response and driving functions are derived. The theoretical results are illustrated by numerical simulations.

Networks in the brain consist of different types of neurons. Here we investigate the influence of neuron diversity on the dynamics, phase space structure, and computational capabilities of spiking neural networks. We find that already a single neuron of a different type can qualitatively change the network dynamics and that mixed networks may combine the computational capabilities of ones with a single-neuron type. We study inhibitory networks of concave leaky (LIF) and convex “antileaky” (XIF) integrate-and-fire neurons that generalize irregularly spiking nonchaotic LIF neuron networks. Endowed with simple conductance-based synapses for XIF neurons, our networks can generate a balanced state of irregular asynchronous spiking as well. We determine the voltage probability distributions and self-consistent firing rates assuming Poisson input with finite-size spike impacts. Further, we compute the full spectrum of Lyapunov exponents (LEs) and the covariant Lyapunov vectors (CLVs) specifying the corresponding perturbation directions. We find that there is approximately one positive LE for each XIF neuron. This indicates in particular that a single XIF neuron renders the network dynamics chaotic. A simple mean-field approach, which can be justified by properties of the CLVs, explains the finding. As an application, we propose a spike-based computing scheme where our networks serve as computational reservoirs and their different stability properties yield different computational capabilities.

The coordinated beating of epithelial cilia in human lungs is a fascinating problem from the hydrodynamics perspective. The phase lag between neighboring cilia is able to generate collective cilia motions, known as metachronal waves. Different kinds of waves can occur, antiplectic or symplectic, depending on the direction of the wave with respect to the flow direction. It is shown here, using a coupled lattice Boltzmann-immersed boundary solver, that the key mechanism responsible for their transport efficiency is a blowing-suction effect that displaces the interface between the periciliary liquid and the mucus phase. The contribution of this mechanism on the average flow generated by the cilia is compared to the contribution of the lubrication effect. The results reveal that the interface displacement is the main mechanism responsible for the better efficiency of antiplectic metachronal waves over symplectic ones to transport bronchial mucus. The conclusions drawn here can be extended to any two-layer fluid configuration having different viscosities, and put into motion by cilia-shaped or comb-plate structures, having a back-and-forth motion with phase lags.

We study agitated frictional disks in two dimensions with the aim of developing a scaling theory for their diffusion over time. As a function of the area fraction $\varphi$ and mean-square velocity fluctuations $\langle v^2\rangle$ the mean-square displacement of the disks $\langle d^2\rangle$ spans four to five orders of magnitude. The motion evolves from a subdiffusive form to a complex diffusive behavior at long times. The statistics of $\langle d^n\rangle$ at all times are multiscaling, since the probability distribution function (PDF) of displacements has very broad wings. Even where a diffusion constant can be identified it is a complex function of $\varphi$ and $\langle v^2\rangle$. By identifying the relevant length and time scales and their interdependence one can rescale the data for the mean-square displacement and the PDF of displacements into collapsed scaling functions for all $\varphi$ and $\langle v^2\rangle$. These scaling functions provide a predictive tool, allowing one to infer from one set of measurements (at a given $\varphi$ and $\langle v^2\rangle$) what are the expected results at any value of $\varphi$ and $\langle v^2\rangle$ within the scaling range.

It is crucial to properly describe the associating fluids in terms of phase equilibrium behaviors, which are needed for design, operation, and optimization of various chemical and energy processes. Pseudopotential lattice Boltzmann method (LBM) appears to be a reliable and efficient approach to study thermodynamic behaviors and phase transition of complex fluid systems. However, when cubic equations of state (EOSs) are incorporated into single-component multiphase LBM, simulation results are not well matched with experimental data. This study presents the utilization of cubic-plus-association (CPA) EOS in the LBM structure to obtain more accurate modeling results for associating fluids. An approach based on the global search optimization algorithm is introduced to find the optimal association parameters of CPA EOS for water and primary alcohols in the lattice units. The thermodynamic consistency is verified by the Maxwell construction and is also improved by the forcing scheme of [Q. Li, K. H. Luo, and X. J. Li, Phys. Rev. E 86, 016709 (2012)]. The spurious velocity is reduced with increasing isotropy in the gradient operator. Furthermore, an extended version of CPA EOS is introduced, which increases the system stability at low reduced temperatures. There is a very good match between the LBM results and experimental data, confirming the reliability of the model developed in the present study. The introduced approach has potential to be employed for simulating transport phenomena and interfacial characteristics of associating fluids in porous systems.

The voter model with multiple states has found applications in areas as diverse as population genetics, opinion formation, species competition, and language dynamics, among others. In a single step of the dynamics, an individual chosen at random copies the state of a random neighbor in the population. In this basic formulation, it is assumed that the copying is perfect, and thus an exact copy of an individual is generated at each time step. Here, we introduce and study a variant of the multistate voter model in mean field that incorporates a degree of imperfection or error in the copying process, which leaves the states of the two interacting individuals similar but not exactly equal. This dynamics can also be interpreted as a perfect copying with the addition of noise: a minimalistic model for flocking. We found that the ordering properties of this multistate noisy voter model, measured by a parameter $\psi$ in [0,1], depend on the amplitude $\eta$ of the copying error or noise and the population size $N$. In the case of perfect copying $\eta =0$, the system reaches an absorbing configuration with complete order ($\psi =1$) for all values of $N$. However, for any degree of imperfection $\eta >0$, we show that the average value of $\psi$ at the stationary state decreases with $N$ as $\langle \psi \rangle \simeq 6/\left({\pi }^2{\eta }^{2}N\right)$ for $\eta \ll 1$ and ${\eta }^{2}N\gtrsim 1$, and thus the system becomes totally disordered in the thermodynamic limit $N\to \infty$. We also show that $\langle \psi \rangle \simeq 1-\frac{{\pi }^2}{6}{\eta }^{2}N$ in the vanishing small error limit $\eta \to 0$, which implies that complete order is never achieved for $\eta >0$. These results are supported by Monte Carlo simulations of the model, which allow to study other scenarios as well.

We contrast the generic features of structural relaxation close to the idealized glass transition that are predicted by the self-consistent generalized Langevin equation theory (SCGLE) against those that are predicted by the mode-coupling theory of the glass transition (MCT). We present an asymptotic solution close to conditions of kinetic arrest that is valid for both theories, despite the different starting points that are adopted in deriving them. This in particular provides the same level of understanding of the asymptotic dynamics in the SCGLE as was previously done only for MCT. We discuss similarities and different predictions of the two theories for kinetic arrest in standard glass-forming models, as exemplified through the hard-sphere system. Qualitative differences are found for models where a decoupling of relaxation modes is predicted, such as the generalized Gaussian core model, or binary hard-sphere mixtures of particles with very disparate sizes. These differences, which arise in the distinct treatment of the memory kernels associated to self- and collective motion of particles, lead to distinct scenarios that are predicted by each theory for partially arrested states and in the vicinity of higher-order glass-transition singularities.

It was discovered recently that frictional granular materials can exhibit an important mechanism for instabilities, i.e., the appearance of pairs of complex eigenvalues in their stability matrix. The consequence is an oscillatory exponential growth of small perturbations which are tamed by dynamical nonlinearities. The amplification can be giant, many orders of magnitude, and it ends with a catastrophic system-spanning plastic event. Here we follow up on this discovery, explore the scaling laws characterizing the onset of the instability, the scenarios of the development of the instability with and without damping, and the nature of the eventual system-spanning events. The possible relevance to earthquake physics and to the transition from static to dynamic friction is discussed.