We consider a model of a random media with fixed and finite memory time with abrupt losses of memory (renovation model). Within the memory intervals we can observe either amplification or oscillation of the vector field in a given particle. The cumulative effect of amplifications in many subsequent intervals leads to amplification of the mean field and mean energy. Similarly, the cumulative effect of intermittent amplifications or oscillations also leads to amplification of the mean field and mean energy, however, at a lower rate. Finally, the random oscillations alone can resonate and yield the growth of the mean field and energy. These are the three mechanisms that we investigate and compute analytically and numerically the growth rates based on the Jacobi equation with a random curvature parameter.

Geometric Brownian motion is an exemplary stochastic processes obeying multiplicative noise, with widespread applications in several fields, e.g., in finance, in physics, and biology. The definition of the process depends crucially on the interpretation of the stochastic integrals which involves the discretization parameter $\alpha$ with $0\le \alpha \le 1$, giving rise to the well-known special cases $\alpha =0$ (Itô), $\alpha =1/2$ (Fisk-Stratonovich), and $\alpha =1$ (Hänggi-Klimontovich or anti-Itô). In this paper we study the asymptotic limits of the probability distribution functions of geometric Brownian motion and some related generalizations. We establish the conditions for the existence of normalizable asymptotic distributions depending on the discretization parameter $\alpha$. Using the infinite ergodicity approach, recently applied to stochastic processes with multiplicative noise by E. Barkai and collaborators, we show how meaningful asymptotic results can be formulated in a transparent way.

The Kuramoto model describes how coupled oscillators synchronize their phases as the intensity of the coupling increases past a threshold. The model was recently extended by reinterpreting the oscillators as particles moving on the surface of unit spheres in a $D$-dimensional space. Each particle is then represented by a $D$-dimensional unit vector; for $D=2$ the particles move on the unit circle and the vectors can be described by a single phase, recovering the original Kuramoto model. This multidimensional description can be further extended by promoting the coupling constant between the particles to a matrix $\mathbf{K}$ that acts on the unit vectors. As the coupling matrix changes the direction of the vectors, it can be interpreted as a generalized frustration that tends to hinder synchronization. In a recent paper we studied in detail the role of the coupling matrix for $D=2$. Here we extend this analysis to arbitrary dimensions. We show that, for identical particles, when the natural frequencies are set to zero, the system converges either to a stationary synchronized state, given by one of the real eigenvectors of $\mathbf{K}$, or to an effective two-dimensional rotation, defined by one of the complex eigenvectors of $\mathbf{K}$. The stability of these states depends on the set eigenvalues and eigenvectors of the coupling matrix, which controls the asymptotic behavior of the system, and therefore, can be used to manipulate these states. When the natural frequencies are not zero, synchronization depends on whether $D$ is even or odd. In even dimensions the transition to synchronization is continuous and rotating states are replaced by active states, where the module of the order parameter oscillates while it rotates. If $D$ is odd the phase transition is discontinuous and active states can be suppressed for some distributions of natural frequencies.

The nonlinear dynamics induced by the modulation instability (MI) of a binary mixture in an atomic Bose-Einstein condensate (BEC) is investigated theoretically under the joint effects of higher-order residual nonlinearities and helicoidal spin-orbit (SO) coupling in a regime of unbalanced chemical potential. The analysis relies on a system of modified coupled Gross-Pitaevskii equations on which the linear stability analysis of plane-wave solutions is performed, from which an expression of the MI gain is obtained. A parametric analysis of regions of instability is carried out, where effects originating from the higher-order interactions and the helicoidal spin-orbit coupling are confronted under different combinations of the signs of the intra- and intercomponent interaction strengths. Direct numerical calculations on the generic model support our analytical predictions and show that the higher-order interspecies interaction and the SO coupling can balance each other suitably for stability to take place. Mainly, it is found that the residual nonlinearity preserves and reinforces the stability of miscible pairs of condensates with SO coupling. Additionally, when a miscible binary mixture of condensates with SO coupling is modulationally unstable, the presence of residual nonlinearity may help soften such instability. Our results finally suggest that MI-induced formation of stable solitons in mixtures of BECs with two-body attraction may be preserved by the residual nonlinearity even though the latter enhances the instability.

The centrality measures, like betweenness $b$ and degree $k$ in complex networks remain fundamental quantities helping to classify them. It is realized from Barthelemy's paper [Eur. Phys. J. B 38, 163 (2004)] that the maximal $b-k$ exponent for the scale-free (SF) networks is ${\eta }_{\text{max}}=2$, belonging to SF trees, based on which one concludes $\delta \ge \frac{\gamma +1}{2}$, where $\gamma$ and $\delta$ are the scaling exponents for the distribution functions of the degree and the betweenness centralities, respectively. This conjecture was violated for some special models and systems. Here we present a systematic study on this problem for visibility graphs of correlated time series, and show evidence that this conjecture fails in some correlation strengths. We consider the visibility graph of three models: two-dimensional Bak-Tang-Weisenfeld (BTW) sandpile model, one-dimensional (1D) fractional Brownian motion (FBM), and 1D Levy walks, the two latter cases are controlled by the Hurst exponent $H$ and the step index $\alpha$, respectively. In particular, for the BTW model and FBM with $H\lesssim 0.5$, $\eta$ is greater than 2, and also $\delta <\frac{\gamma +1}{2}$ for the BTW model, while the Barthelemy's conjecture remains valid for the Levy process. We assert that the failure of the Barthelemy's conjecture is due to large fluctuations in the scaling $b-k$ relation resulting in the violation of hyperscaling relation $\eta =\frac{\gamma -1}{\delta -1}$ and emergent anomalous behavior for the BTW model and FBM. Universal distribution function of generalized degree is found for these models which have the same scaling behavior as the Barabasi-Albert network.

I show that nonequilibrium two-dimensional interfaces between three-dimensional phase separated fluids exhibit a peculiar “sublogarithmic” roughness. Specifically, an interface of lateral extent $L$ will fluctuate vertically (i.e., normal to the mean surface orientation) a typical rms distance $w\equiv \sqrt{\langle |h(\mathbf{r},t){|}^2\rangle }\propto {[ln(L/a)]}^{1/3}$ [where $a$ is a microscopic length, and $h(\mathbf{r},t)$ is the height of the interface at two-dimensional position $\mathbf{r}$ at time $t]$. In contrast, the roughness of equilibrium two-dimensional interfaces between three-dimensional fluids, obeys $w\propto {[ln(L/a)]}^{1/2}$. The exponent $1/3$ for the active case is exact. In addition, the characteristic timescales $\tau \left(L\right)$ in the active case scale according to $\tau \left(L\right)\propto L^3{[ln(L/a)]}^{1/3}$, in contrast to the simple $\tau \left(L\right)\propto L^3$ scaling found in equilibrium systems with conserved densities and no fluid flow.

We consider a Brownian oscillator whose coupling to the environment may lead to the formation of a localized normal mode. For lower values of the oscillator's natural frequency $\omega \le {\omega }_c$, the localized mode is absent and the unperturbed oscillator reaches thermal equilibrium. For higher values of $\omega >{\omega }_c$ when the localized mode is formed, the unperturbed oscillator does not thermalize but rather evolves into a nonequilibrium cyclostationary state. We consider the response of such an oscillator to an external periodic force. Despite the coupling to the environment, the oscillator shows the unbounded resonance (with the response linearly increasing with time) when the frequency of the external force coincides with the frequency of the localized mode. An unusual resonance (“quasiresonance”) occurs for the oscillator with the critical value of the natural frequency $\omega ={\omega }_c$, which separates thermalizing (ergodic) and nonthermalizing (nonergodic) configurations. In that case, the resonance response increases with time sublinearly, which can be interpreted as a resonance between the external force and the incipient localized mode.

Topological data analysis is a powerful framework for extracting useful topological information from complex data sets. Recent work has shown its application for the dynamical analysis of classical dissipative systems through a topology-preserving embedding method that allows reconstructing dynamical attractors, the topologies of which can be used to identify chaotic behavior. Open quantum systems can similarly exhibit nontrivial dynamics, but the existing toolkit for classification and quantification are still limited, particularly for experimental applications. In this paper, we present a topological pipeline for characterizing quantum dynamics, which draws inspiration from the classical approach by using single quantum trajectory unravelings of the master equation to construct analog quantum attractors and extract their topology using persistent homology. We apply the method to a periodically modulated Kerr-nonlinear cavity to discriminate parameter regimes of regular and chaotic phases using limited measurements of the system.

We revise the encounter-based approach to imperfect diffusion-controlled reactions, which employs the statistics of encounters between a diffusing particle and the reactive region to implement surface reactions. We extend this approach to deal with a more general setting, in which the reactive region is surrounded by a reflecting boundary with an escape region. We derive a spectral expansion for the full propagator and investigate the behavior and probabilistic interpretations of the associated probability flux density. In particular, we obtain the joint probability density of the escape time and the number of encounters with the reactive region before escape, and the probability density of the first-crossing time of a prescribed number of encounters. We briefly discuss generalizations of the conventional Poissonian-type surface reaction mechanism described by Robin boundary condition and potential applications of this formalism in chemistry and biophysics.

Graham has shown [Z. Phys. B 26, 397 (1977)] that a fluctuation-dissipation relation can be imposed on a class of nonequilibrium Markovian Langevin equations that admit a stationary solution of the corresponding Fokker-Planck equation. The resulting equilibrium form of the Langevin equation is associated with a nonequilibrium Hamiltonian. Here we provide some explicit insight into how this Hamiltonian may lose its time-reversal invariance and how the “reactive” and “dissipative” fluxes loose their distinct time-reversal symmetries. The antisymmetric coupling matrix between forces and fluxes no longer originates from Poisson brackets and the “reactive” fluxes contribute to the (“housekeeping”) entropy production, in the steady state. The time-reversal even and odd parts of the nonequilibrium Hamiltonian contribute in qualitatively different but physically instructive ways to the entropy. We find instances where fluctuations due to noise are solely responsible for the dissipation. Finally, this structure gives rise to a new, physically pertinent instance of frenesy.

Efficient processing and transfer of information in neurons have been linked to noise-induced resonance phenomena such as coherence resonance (CR), and adaptive rules in neural networks have been mostly linked to two prevalent mechanisms: spike-timing-dependent plasticity (STDP) and homeostatic structural plasticity (HSP). Thus this paper investigates CR in small-world and random adaptive networks of Hodgkin-Huxley neurons driven by STDP and HSP. Our numerical study indicates that the degree of CR strongly depends, and in different ways, on the adjusting rate parameter $P$, which controls STDP, on the characteristic rewiring frequency parameter $F$, which controls HSP, and on the parameters of the network topology. In particular, we found two robust behaviors. (i) Decreasing $P$ (which enhances the weakening effect of STDP on synaptic weights) and decreasing $F$ (which slows down the swapping rate of synapses between neurons) always leads to higher degrees of CR in small-world and random networks, provided that the synaptic time delay parameter ${\tau }_c$ has some appropriate values. (ii) Increasing the synaptic time delay ${\tau }_c$ induces multiple CR (MCR)—the occurrence of multiple peaks in the degree of coherence as ${\tau }_c$ changes—in small-world and random networks, with MCR becoming more pronounced at smaller values of $P$ and $F$. Our results imply that STDP and HSP can jointly play an essential role in enhancing the time precision of firing necessary for optimal information processing and transfer in neural systems and could thus have applications in designing networks of noisy artificial neural circuits engineered to use CR to optimize information processing and transfer.

Electrohydrodynamic (EHD) jet printing involves the deposition of a liquid jet issuing from a needle stretched under the effect of a strong electric field between the needle and a collector plate. Unlike the geometrically independent classical cone-jet observed at low flow rates and high applied electric fields, at a relatively high flow rate and moderate electric field, EHD jets are moderately stretched. Jetting characteristics of such moderately stretched EHD jets differ from the typical cone-jet due to the nonlocalized cone-to-jet transition. Hence, we describe the physics of the moderately stretched EHD jet applicable to the EHD jet printing process through numerical solutions of a quasi-one-dimensional model of the EHD jet and experiments. Through comparison with experimental measurements, we show that our simulations correctly predict the jet shape for varying flow rates and applied potential difference. We present the physical mechanism of inertia-dominated slender EHD jets based on the dominant driving and resisting forces and relevant dimensionless numbers. We show that the slender EHD jet stretches and accelerates primarily due to the balance of driving tangential electric shear and resisting inertia forces in the developed jet region, whereas in the vicinity of the needle, driving charge repulsion and resisting surface tension forces govern the cone shape. The findings of this study can help in operational understanding and better control of the EHD jet printing process.

In competitive settings that entail several populations, individuals often engage in intra- and interpopulation interactions that determine their fitness and evolutionary success. With this simple motivation, we here study a multipopulation model where individuals engage in group interactions within their own population and in pairwise interactions with individuals from different populations. We use the evolutionary public goods game and the prisoner's dilemma game to describe these group and pairwise interactions, respectively. We also take into account asymmetry in the extent to which group and pairwise interactions determine the fitness of individuals. We find that interactions across multiple populations reveal new mechanisms through which the evolution of cooperation can be promoted, but this depends on the level of interaction asymmetry. If inter- and intrapopulation interactions are symmetric, the sole presence of multiple populations promotes the evolution of cooperation. Asymmetry in the interactions can further promote cooperation at the expense of the coexistence of the competing strategies. An in-depth analysis of the spatiotemporal dynamics reveals loop-dominated structures and pattern formation that can explain the various evolutionary outcomes. Thus, complex evolutionary interactions in multiple populations reveal an intricate interplay between cooperation and coexistence, and they also open up the path toward further explorations of multipopulation games and biodiversity.

Universal properties of turbulence have been associated traditionally with very high Reynolds numbers, but recent work has shown that the onset of the power laws in derivative statistics occurs at modest microscale Reynolds numbers of the order of 10, with the corresponding exponents being consistent with those for the inertial range structure functions at very high Reynolds numbers. In this paper we use well-resolved direct numerical simulations of homogeneous and isotropic turbulence to establish this result for a range of initial conditions with different forcing mechanisms. We also show that the moments of transverse velocity gradients possess larger scaling exponents than those of the longitudinal moments, confirming past results that the former are more intermittent than the latter.

Inspired by vehicular traffic phenomena, we study a three-lane open totally asymmetric simple exclusion process with both-sided lane switching in the companionship of Langmuir kinetics. We calculate the phase diagrams, density profiles, and phase transitions through mean-field theory and successfully validate these findings with Monte Carlo simulation results. It has been found that both the qualitative and quantitative topology of phase diagrams crucially rely on the ratio of lane-switching rates called coupling strength. The proposed model has various unique mixed phases, including a double shock resulting in bulk-induced phase transitions. The interplay between both-sided coupling, third lane, and Langmuir kinetics produces unusual features, including a back-and-forth phase transition, also called a reentrance transition, in two directions for relatively nominal values of coupling strength. The presence of reentrance transition and peculiar phase boundaries leads to a rare type of phase division in which one phase lies entirely within another region. Moreover, we scrutinize the shock dynamics by analyzing four different types of shock and finite-size effects.

We report the observation of nonlinear three-wave resonant interactions between two different branches of the dispersion relation of hydrodynamic waves, namely the gravity-capillary and sloshing modes. These atypical interactions are investigated within a torus of fluid for which the sloshing mode can be easily excited. A triadic resonance instability is then observed due to this three-wave two-branch interaction mechanism. An exponential growth of the instability and phase locking are evidenced. The efficiency of this interaction is found to be maximal when the gravity-capillary phase velocity matches the group velocity of the sloshing mode. For a stronger forcing, additional waves are generated by a cascade of three-wave interactions populating the wave spectrum. Such a three-wave two-branch interaction mechanism is probably not restricted to hydrodynamics and could be of interest in other systems involving several propagation modes.

The control of biopolymer length is mediated by proteins that localize to polymer ends and regulate polymerization dynamics. Several mechanisms have been proposed to achieve end localization. Here, we propose a novel mechanism by which a protein that binds to a shrinking polymer and slows its shrinkage will be spontaneously enriched at the shrinking end through a “herding” effect. We formalize this process using both lattice-gas and continuum descriptions, and we present experimental evidence that the microtubule regulator spastin employs this mechanism. Our findings extend to more general problems involving diffusion within shrinking domains.

The playground swing is a dynamic, coupled oscillator system consisting of the swing as an object and a human as the swinger. Here, we propose a model for capturing the effect of the initial phase of natural upper body motion on the continuous pumping of a swing and validate this model from the motion data of ten participants pumping swings of three different swing chain lengths. Our model predicts that the swing pumps the most if the phase of maximum lean back, which we call the initial phase, occurs when the swing is at a vertical (midpoint) position and moving forward when the amplitude is small. As the amplitude grows, the optimal initial phase gradually shifts towards an earlier phase of the cycle, the back extreme of the swing's trajectory. As predicted by our model, all participants shifted the initial phase of their upper body movements earlier as swing amplitude increased. This indicated that swingers adjust both the frequency and initial phase of their upper body movements to successfully pump a playground swing.

Recently, we argued [Chin. Phys. Lett. 39, 080502 (2022)] that the Ising model simultaneously exhibits two upper critical dimensions $(d_c=4,d_p=6)$ in the Fortuin-Kasteleyn (FK) random-cluster representation. In this paper, we perform a systematic study of the FK Ising model on hypercubic lattices with spatial dimensions $d$ from 5 to 7, and on the complete graph. We provide a detailed data analysis of the critical behaviors of a variety of quantities at and near the critical points. Our results clearly show that many quantities exhibit distinct critical phenomena for $4<d<6$ and $d\ge 6$, and thus strongly support the argument that 6 is also an upper critical dimension. Moreover, for each studied dimension, we observe the existence of two configuration sectors, two lengthscales, as well as two scaling windows, and thus two sets of critical exponents are needed to describe these behaviors. Our finding enriches the understanding of the critical phenomena in the Ising model.

We generalize the previous study on the application of variational autoencoders to the two-dimensional Ising model to a system with anisotropy. Due to the self-duality property of the system, the critical points can be located exactly for the entire range of anisotropic coupling. This presents an excellent test bed for the validity of using a variational autoencoder to characterize an anisotropic classical model. We reproduce the phase diagram for a wide range of anisotropic couplings and temperatures via a variational autoencoder without the explicit construction of an order parameter. Considering that the partition function of $(d+1)$-dimensional anisotropic models can be mapped to that of the $d$-dimensional quantum spin models, the present study provides numerical evidence that a variational autoencoder can be applied to analyze quantum systems via the quantum Monte Carlo method.