The Preisach model has been useful as a null model for understanding memory formation in periodically driven disordered systems. In amorphous solids, for example, the athermal response to shear is due to localized plastic events (soft spots). As shown recently by Mungan et al. [Phys. Rev. Lett. 123, 178002 (2019)], the plastic response to applied shear can be rigorously described in terms of a directed network whose transitions correspond to one or more soft spots changing states. The topology of this graph depends on the interactions between soft spots and when such interactions are negligible, the resulting description becomes that of the Preisach model. A first step in linking transition graph topology with the underlying soft-spot interactions is therefore to determine the structure of such graphs in the absence of interactions. Here we perform a detailed analysis of the transition graph of the Preisach model. We highlight the important role played by return-point memory in organizing the graph into a hierarchy of loops and subloops. Our analysis reveals that the topology of a large portion of this graph is actually not governed by the values of the switching fields that describe the hysteretic behavior of the individual elements but by a coarser parameter, a permutation $\mathit{\rho }$ which prescribes the sequence in which the individual hysteretic elements change their states as the main hysteresis loop is traversed. This in turn allows us to derive combinatorial properties, such as the number of major loops in the transition graph as well as the number of states $\left|\mathcal{R}\right|$ constituting the main hysteresis loop and its nested subloops. We find that $\left|\mathcal{R}\right|$ is equal to the number of increasing subsequences contained in the permutation $\mathit{\rho }$.

The problem of survival of a Brownian particle diffusing on a disk with a reflective boundary that has two absorbing arcs is treated analytically. The framework of boundary homogenization is applied to calculate the effective trapping rate of the disk boundary, and this enables estimation of the mean first passage time. The method of conformal mapping is applied to transform the original system to a simpler geometrical configuration (a flat reflective boundary with a periodic configuration of identical absorbing strips) for which the analytical solution is known. The expression for the mean first passage time is simplified for some limiting cases (small arc or small gap). The derived analytical expressions compare favorably with the results of Brownian particle simulations and other analytical results from the literature.

The stationary radial distribution, $P\left(\rho \right)$, of a random walk with the diffusion coefficient $D$, which winds at the tangential velocity $V$ around an impenetrable disk of radius $R$ for $R\gg D/V$ converges to the distribution involving the Airy function. Typical trajectories are localized in the circular strip $[R,R+\delta R^{1/3}]$, where $\delta$ is a constant which depends on the parameters $D$ and $V$ and is independent of $R$.

We report on three launches of ballooning Erigone spiders observed in a $0.9{\mathrm{m}}^3$ laboratory chamber, controlled under conditions where no significant air motion was possible. These launches were elicited by vertical, downward-oriented electric fields within the chamber, and the motions indicate clearly that negative electric charge on the ballooning silk, subject to the Coulomb force, produced the lift observed in each launch. We estimate the total charge required under plausible assumptions, and find that at least 1.15 nC is necessary in each case. The charge is likely to be nonuniformly distributed, favoring initial longitudinal mobility of electrons along the fresh silk during extrusion. These results demonstrate that spiders are able to utilize charge on their silk to attain electrostatic flight even in the absence of any aerodynamic lift.

An information-theoretic scheme is proposed to estimate the underlying domain of interactions and the timescale of the interactions for many-particle systems. The crux is the application of transfer entropy which measures the amount of information transferred from one variable to another, and the introduction of a “cutoff distance variable” which specifies the distance within which pairs of particles are taken into account in the estimation of transfer entropy. The Vicsek model often studied as a metaphor of collectively moving animals is employed with introducing asymmetric interactions and an interaction timescale. Based on ensemble data of trajectories of the model system, it is shown that using the interaction domain significantly improves the performance of classification of leaders and followers compared to the approach without utilizing knowledge of the domain. Given an interaction timescale estimated from an ensemble of trajectories, the first derivative of transfer entropy averaged over the ensemble with respect to the cutoff distance is presented to serve as an indicator to infer the interaction domain. It is shown that transfer entropy is superior for inferring the interaction radius compared to cross correlation, hence resulting in a higher performance for inferring the leader-follower relationship. The effects of noise size exerted from environment and the ratio of the numbers of leader and follower on the classification performance are also discussed.

A polydispersed mixture of granular materials composed of different-sized particles segregates whenever it undergoes external actions such as shear. Predicting and controlling segregation pose a challenging problem of industrial interest. One of the most frequent and important causes of segregation is interparticle percolation that occurs when small particles fall down through the voids between large particles as a result of local shear in the presence of a gravitational field. In this paper, we present a theoretical model to predict the percolation velocity in sheared systems, and we validate it experimentally. The experiments were carried out in simple shear conditions. This type of flow was achieved in a shear box which allowed the quantitative study of particle percolation under constant shear conditions. The granular material inside the box was a binary mixture of cohesionless spheres differing only in size. The experiments allowed us to quantify the percolation speed for different size ratios and different shear rates. The collected data confirmed the validity of the proposed theoretical model; the latter can be implemented in a continuum framework to simulate more complex phenomena and geometries.

A walker is a macroscopic coupling of a droplet and a capillary wave field that exhibits several quantumlike properties. In 2009, Eddi et al. [Phys. Rev. Lett. 102, 240401 (2009)] showed that walkers may cross a submerged barrier in an unpredictable manner and named this behavior “unpredictable walker tunneling.” In quantum mechanics, tunneling is one of the simplest arrangements where similar unpredictability occurs. In this paper, we investigate how unpredictability can be unveiled for walkers through an experimental study of walker tunneling with precision. We refine both time and position measurements to take into account the fast bouncing dynamics of the system. Tunneling is shown to be unpredictable until a distance of 2.6 mm from the barrier center, where we observe the separation of reflected and transmitted trajectories in the position-velocity phase-space. The unpredictability is unlikely to be attributable to either uncertainty in the initial conditions or to the noise in the experiment. It is more likely due to changes in the drop's vertical dynamics arising when it interacts with the barrier. We compare this macroscopic system to a tunneling quantum particle that is subjected to repeated measurements of its position and momentum. We show that, despite the different theoretical treatments of these two disparate systems, similar patterns emerge in the position-velocity phase space.

The afterglow emission from Nd:YAG-laser-produced microdroplet-tin plasma is investigated, with a focus on analyzing Stark effect phenomena and the dynamical evolution of the plasma. Time- and space-resolved optical imaging spectroscopy is performed on 11 lines from Sn i–iv ions, in the 315–425-nm wavelength range. Stark shift-to-width ratios serve as the basis for unambiguous experimental tests of atomic physics theory predictions. Experiment and theory, where available, are found to be in poor agreement, and are in disagreement regarding the sign of the ratio in several cases. Spectroscopic measurements of the Stark widths in tandem with Saha-Boltzmann fits to Sn i and Sn ii lines, establish the evolution of the local temperature and density of the plasma afterglow, 20–40 ns after the end of the 15-ns-long temporally box-shaped laser pulse. A clear cool-down from $\sim 2$ to 1 eV is observed of the plasma in this time window, having started at $\sim 30$ eV when emitting extreme-ultraviolet (EUV) light. An exponential reduction of the density of the plasma from $\sim {10}^{18}$–${10}^{17}{e}^{-}$ ${\mathrm{cm}}^{-3}$ is observed in this same time window. Our work is relevant for understanding the dynamics of the decaying, expanding plasma in state-of-the-art EUV nanolithography machines.

Molecular dynamics (MD) simulations is currently the most popular and credible tool to model water flow in nanoscale where the conventional continuum equations break down due to the dominance of fluid-surface interactions. However, current MD simulations are computationally challenging for the water flow in complex tube geometries or a network of nanopores, e.g., membrane, shale matrix, and aquaporins. We present a novel mesoscopic lattice Boltzmann method (LBM) for capturing fluctuated density distribution and a nonparabolic velocity profile of water flow through nanochannels. We incorporated molecular interactions between water and the solid inner wall into LBM formulations. Details of the molecular interactions were translated into true and apparent slippage, which were both correlated to the surface wettability, e.g., contact angle. Our proposed LBM was tested against 47 published cases of water flow through infinite-length nanochannels made of different materials and dimensions―flow rates as high as seven orders of magnitude when compared with predictions of the classical no-slip Hagen-Poiseuille (HP) flow. Using the developed LBM model, we also studied water flow through finite-length nanochannels with tube entrance and exit effects. Results were found to be in good agreement with 44 published finite-length cases in the literature. The proposed LBM model is nearly as accurate as MD simulations for a nanochannel, while being computationally efficient enough to allow implications for much larger and more complex geometrical nanostructures.

We derive generalized Fokker-Planck equations (FPEs) based on two nonextensive entropy measures $S_{\pm }$ that depend exclusively on the probability. These entropies have been originally obtained from the superstatistics framework, therefore they regard nonequilibrium systems outlined by a long-term stationary state in view of a spatiotemporally fluctuating intensive quantity. Moreover, entropies $S_{\pm }$ as well as Boltzmann-Gibbs (BG) entropy $S_B$ both pertain to the same asymptotical equivalence class, thus suggesting that $S_{\pm }$ could depict a consistent thermodynamic generalization of BG. For these reasons, we assert that transport phenomena to be accounted for by our models shall coincide with the portrait given by the conventional FPEs for systems comprehending short-range interactions or a high number of accessible microstates, whereas, for systems composed of a small number of microstates, or those with long-range interactions, the governing equations of motion are to be the FPEs here derived, as long as the system fulfills the attributes mentioned above. We discuss the anomalous diffusion exhibited by the two generalized FPEs and also present some numerical applications. In particular, we find that there are models regarding biological sciences, for the study of congregation and aggregation behavior, the structure of which coincides with the one of our models.

Recently, a number of sufficiency conditions have been shown for the occurrence of a ${\mathbb{Z}}_2$-symmetry breaking phase transition (${\mathbb{Z}}_2$-SBPT) starting from geometric-topological concepts of potential energy landscapes. In particular, a ${\mathbb{Z}}_2$-SBPT can be triggered by double-well potentials, or equivalently by dumbbell-shaped equipotential surfaces. In this paper, we introduce two models with a ${\mathbb{Z}}_2$-SBPT that, due to their essential feature, show in the clearest way the generating mechanism of a ${\mathbb{Z}}_2$-SBPT. Although they cannot be considered physical models, they all have the features of such models with the same kind of SBPT. At the end of the paper, the ${\varphi }^4$ model is revisited in light of this approach. In particular, the landscape of one of the models introduced here turned out to be equivalent to that of the mean-field ${\varphi }^4$ model in a simplified version.

The putative generalization of the thermodynamic uncertainty relation (TUR) to underdamped dynamics is still an open problem. So far, bounds that have been derived for such a dynamics are not particularly transparent and they do not converge to the known TUR in the overdamped limit. Furthermore, it was found that there are restrictions for a TUR to hold such as the absence of a magnetic field. In this article we first analyze the properties of driven free diffusion in the underdamped regime and show that it inherently violates the overdamped TUR for finite times. Based on numerical evidence, we then conjecture a bound for one-dimensional driven diffusion in a potential which is based on the result for free diffusion. This bound converges to the known overdamped TUR in the corresponding limit. Moreover, the conjectured bound holds for observables that involve higher powers of the velocity as long as the observable is odd under time reversal. Finally, we address the applicability of this bound to underdamped dynamics in higher dimensions.

In this study, we investigate thermal transport in $d$-dimensional quantum harmonic lattices coupled to self-consistent reservoirs. The $d$-dimensional system is treated as a set of Klein-Gordon chains by exploiting an orthogonal transformation. For generality, the self-energy that describes the reservoir-system coupling is assumed to be a power function of energy $\mathrm{\Sigma }\propto -i{\varepsilon }^n$, where $n$ is limited to odd integers because of the reality condition. Total momentum conservation is violated for $n=1$ but otherwise preserved. In this approach, we show that for $n=1$, thermal conductivity remains finite in the thermodynamic limit and normal transport takes place for an arbitrary value of $d$. For $n=3,5,7,\cdots$, however, thermal conductivity diverges and thermal transport becomes anomalous as long as $d<n$, whereas normal transport is recovered when $d\ge n$. These criteria derived for quantum-mechanical lattices imply that normal transport emerges in high enough dimensions despite total momentum conservation and reinforce the prevailing conjecture deduced in the classical limit.

The transition from asynchronous dynamics to generalized chaotic synchronization and then to completely synchronous dynamics is known to be accompanied by on-off intermittency. We show that there is another (second) type of the transition called jump intermittency which occurs near the boundary of generalized synchronization in chaotic systems with complex two-sheeted attractors. Although this transient behavior also exhibits intermittent dynamics, it differs sufficiently from on-off intermittency supposed hitherto to be the only type of motion corresponding to the transition to generalized synchronization. This type of transition has been revealed and the underling mechanism has been explained in both unidirectionally and mutually coupled chaotic Lorenz and Chen oscillators. To detect the epochs of synchronous and asynchronous motion in mutually coupled oscillators with complex topology of an attractor a technique based on finding time intervals when the phase trajectories are located on equal or different sheets of chaotic attractors of coupled oscillators has been developed. We have also shown that in the unidirectionally coupled systems the proposed technique gives the same results that may obtained with the help of the traditional method using the auxiliary system approach.

We demonstrate that functionalizing nanoslits with pH-responsive polyelectrolyte brushes can lead to extremely fast electro-osmotic (EOS) water transport, where the maximum centreline velocity and the volume flow rate can be an order of magnitude larger than these quantities in identically charged brush-free nanochannels for a wide range of system parameters. Such an enhancement is most remarkable given that the brushes have been known to retard the transport by imparting additional drag on the fluid flow. We argue that this enhancement stems from the localization of the charge density of the brush-induced electric double layer (and, hence, the EOS body force) away from the nanochannel wall (or the location of the wall-induced drag force). This ensures a much larger impact of the EOS body force triggering such fast water transport. Finally, the calculated flux values for the present brush-grafted nanochannels are found to be significantly larger than those for a wide range of nanofluidic membranes and channels, suggesting that the brush functionalization can be considered as a mechanism for enabling such superfast nanofluidic transport.

We have investigated the effects of a smooth transition layer at the contact discontinuity on the growth of the Richtmyer-Meshkov instability (RMI) by hydrodynamic numerical simulations, and we derived an empirical condition for the suppression of the instability. The transition layer has little influence on the RMI when the thickness $L$ is narrower than the wavelength of an interface modulation $\lambda$. However, if the transition layer becomes broader than $\lambda$, the perturbed velocity associated with the RMI is reduced considerably. The suppression condition is interpreted as the cases in which the shock transit time through the transition layer is longer than the sound crossing time of the modulation wavelength. The fluctuation kinetic energy decreases as $L^{-p}$ with $p=2.5$, which indicates that the growth velocity of the RMI decreases in proportion to $L^{-p/2}$ by the presence of the transition layer. This feature is found to be quite universal and appeared in a wide range of shock-interface interactions.

Lipid vesicles are known to undergo complex conformational transitions, but it remains challenging to systematically characterize nonequilibrium membrane dynamics in flow. Here, we report the direct observation of anisotropic vesicle relaxation from highly deformed shapes using a Stokes trap. Vesicle shape relaxation is described by two distinct characteristic timescales governed by the bending modulus and membrane tension. Interestingly, the fast double-mode timescale is found to depend on vesicle deflation or reduced volume. Experimental results are well described by a viscoelastic model of a deformed membrane. Overall, these results show that vesicle relaxation is governed by an interplay between membrane elastic moduli, surface tension, and vesicle deflation.

This study reveals that injecting a light fluid of density ${\rho }_b$ in the recirculating bubble of a bluff body at $\text{Re}\approx 6.4\times {10}^4$ has a greater drag reduction potential than blowing fluid of a density greater than or equal to that of the free stream $\rho$. It is found that the maximum drag reduction scales as ${({\rho }_b/\rho )}^{-\frac{1}{6}}$. This power law combines the ability of the recirculating bubble to diffuse the injected momentum and the effectiveness of the injection to increase the recirculating bubble length.

This paper presents a unified method for formulating a field-theoretic perturbation theory that encompasses the conventional liquid state theory. First, the free-energy functional of an instantaneous correlation field is obtained from the functional-integral representation of the grand potential. Next, we demonstrate that the instantaneous free-energy functional yields a closure relation between the correlation functions in the mean-field approximation. Notably, the obtained closure relation covers a variety of approximate closures introduced in the liquid state theory.

A one-dimensional modified Nogochi nonlinear electric transmission network with dispersive elements that consist of a large number of identical sections is theoretically studied in the present paper. The first-order nonautonomous rogue waves with quintic nonlinearity and nonlinear dispersion effects in this network are predicted and analyzed using the cubic-quintic nonlinear Schrödinger (CQ-NLS) equation with a cubic nonlinear derivative term. The results show that, in the semidiscrete limit, the voltage for the transmission network is described in some cases by the CQ-NLS equation with a derivative term that is derived employing the reductive perturbation technique. A one-parameter first-order rational solution of the derived CQ-NLS equation is presented and used to investigate analytically the dependency of the characteristics of the first-order rouge wave parameters on the electric transmission network under consideration. Our results show that when we change the quintic nonlinear and nonlinear dispersion parameter, the first-order nonautonomous rogue wave transforms into the bright-like soliton. Our results also reveal that the shape of the first-order nonautonomous rogue waves does not change when we tune the quintic nonlinear and nonlinear dispersion parameter, while the quintic nonlinear term and nonlinear dispersion effect affect the velocity of first-rogue waves and the evolution of their phase. We also show that the network parameters as well as the frequency of the carrier voltage signal can be used to manage the motion of the first-order nonautonomous rogue waves in the electrical network under consideration. Our results may help to control and manage rogue waves experimentally in electric networks.