This paper explores the dynamics of a ball bouncing on a ferrite rod in an alternating magnetic field. Using linear magnetostriction theory, we derive the equation for the rod's vibration and analyze the influence of frequency doubling effect on the ball's motion. We analytically determined the probability distribution function (PDF) of the ball's rebound velocity and validated our analysis with numerical simulations and experimental results. In both simulations and experiments, the analytically deduced PDF accurately predicts the rebound velocity distribution with high velocities, but shows minor discrepancies in low velocities due to the nonlinear relationship between the incoming and rebounding relative velocity. Additionally, simulation results also show that the ball will eventually enter a “locking region” and undergoes periodic motion.

In previous studies, the propagation of extreme events across nodes in monolayer networks was studied extensively. In this work, we extend this investigation to explore the propagation of extreme events between two distinct layers in a multiplex network. We consider a two-layer network, where one layer is globally coupled and exhibits extreme events, while the second layer remains uncoupled. The interlayer connections between the layers are either unidirectional or bidirectional. We find that unidirectional coupling between the layers can induce extreme events in the uncoupled layer, whereas bidirectional coupling tends to mitigate extreme events in the globally coupled layer. To characterize extreme and nonextreme states, we use probability plots to identify distinct regions in the parameter space. Additionally, we study the robustness of extreme events emergence by examining various network topologies in the uncoupled layer. The mechanism behind the occurrence of extreme events is explored, with a particular focus on the transition from asynchronous state to a fully synchronized excitable state. For numerical simulations, we use nonidentical FitzHugh-Nagumo neurons at each node, which captures the dynamical behavior of both coupled and uncoupled layers. Our findings suggest that extreme events in the uncoupled layer emerge through the gradual disappearance of disordered state, accompanied by occasional bursts of synchronized activity. Results obtained in this work will serve as a starting point in understanding the dynamics behind the propagation of extreme events in real-world networks.

Synergistic contagions are common in natural and social systems, with network topology playing a crucial role in shaping these dynamics. Despite extensive researches, a comprehensive understanding of how specific structural features influence synergistic contagions, especially their phase transitions, remains lacking. This study demonstrates that the spectral approach can serve as a high-precision analytical tool to describe the impact of network structure, particularly degree heterogeneity and degree correlations, on synergistic contagions. By comparing this approach with numerical simulations and conventional analytical approaches, such as the heterogeneous mean-field (HMF) approach, its high accuracy in predicting the critical synergistic strength is illustrated. Furthermore, the analysis based on the spectral approach reveals that the heterogeneity of the principal eigenvector of the network is the key structural factor determining the phase transition of synergistic contagions. As this heterogeneity increases, which can be promoted by increasing degree heterogeneity or degree correlations, the critical synergistic strength required for an explosive phase transition is enhanced.

This study quantifies the probabilities of evolutionary rescue (ER) in populations facing abrupt environmental changes. We consider a population of asexual haploid individuals that evolves without recombination. The research integrates standing genetic variation and de novo mutations within a framework beyond traditional single-locus models. Utilizing Fisher's geometric model and a combination of analytical derivations and stochastic simulations, the study examines how the likelihood of ER is influenced by factors such as the number of traits, the magnitude of environmental change, and the interplay between preexisting genetic variation and newly arising mutations. The results provide insights into the governing factors of ER, including the roles of mutation effect size and probability.

Inhibitory interneurons, ubiquitous in the central nervous system, form networks connected through both chemical synapses and gap junctions. These networks are essential for regulating the activity of principal neurons, especially by inducing temporally patterned dynamic states. Here, we aim to understand the dynamic mechanisms that allow for synchronisation to arise in networks of electrically and chemically coupled interneurons. To this end, we use the exact mean-field reduction to derive a neural mass model for both homogeneous and clustered networks. We first analyze a single population of neurons to understand how the two couplings interact with one another. We demonstrate that the network transitions from an asynchronous to a synchronous regime either by increasing the strength of the gap junction connectivity or the strength of the background input current. Conversely, the strength of inhibitory synapses affects the population firing rate, suggesting that electrical and chemical coupling strengths act as complementary mechanisms by which networks can tune synchronous oscillatory behavior. Next, inspired by the existence of multiple interconnected interneuron subtypes in the cerebellum, we analyze networks consisting of two clusters of cell types defined by differing chemical versus electrical coupling strengths. We show that breaking the electrical and chemical coupling symmetry between these clusters induces bistability, so that a transient external input can switch the network between synchronous and asynchronous firing. Together, our results show the variety of cell-intrinsic and network properties that contribute to synchronisation of interneuronal networks with multiple types of coupling.

Cargo transport mostly involves multiple molecular motors that move along cytoskeletal filaments. Such motors have the ability to detach and reattach on a filament and possibly switch onto another filament. Cargo transport by multiple motors on a single filament has been widely studied; however, cargo transport involving motors switching between filaments remains poorly understood. Here, we use lattice-based Monte Carlo simulations to investigate the properties of transport on multiple filaments, such as velocity, run length, and mean first passage time, compared with transport on a single filament. We provide an analytical expression for cargo velocity for multiple lanes as an extension of the expression for a single lane with a limited number of binding sites. We find this expression is sufficient to describe the force-velocity curves of clusters of motors on multiple lanes in our simulations. Our results show that cargoes being transported on multiple filaments move faster and further than those transported by a single filament. The time taken to deliver cargo to a given target distance is characterized by the mean first passage time, and our results showed a decrease in the time taken for transport on multiple filaments compared with single filaments. Moreover, we consider the effect of molecular motors' intrinsic properties in binding kinetics on their transport. Highly nonprocessive molecular motors with fast binding on and off rates, which are less persistent on filaments, transport cargo more slowly and for shorter run lengths compared with the same number of more processive motors with slow binding on and off rates. Consequently, nonprocessive motors with fast binding kinetics require more time than motors with slow binding kinetics to reach the same target.

The mechanism of density segregation of fine particles under vertical vibration was investigated. The role of permeation air flow on inverse segregation (low-density particles accumulate at the bottom and high-density particles at the top) and the sandwich segregation (low-high-low density profiles) was examined quantitatively. The air pressure in the vibrated particle bed was measured directly under various vibration conditions. The numerical analysis on the coupling motion of particle bed and permeation flow was also performed. It was found that air pressure inside the particle bed changed periodically, which was due to relative motion of the particle bed to the vessel caused by vertical vibration. This periodic pressure change has a significant effect on the mechanism of density segregation. The pressure fluctuation at the bottom of the bed due to the “piston effect,” and the upward propagation of pressure variance play major roles in segregations. The timescales of these two pressure changes determine the segregation patterns, i.e., inverse or sandwich segregations. When the former timescale is large, the pressure in the bed changes monotonically in the vertical direction and, as a result, inverse segregation develops. When the latter timescale is large, an inflection point appears in vertical pressure profiles, resulting in sandwich segregation where high-density particles accumulate at the center.

Two-temperature induced phase separation (2-TIPS) is a phenomenon observed in mixtures of active and passive particles modeled by scalar activity where the temperature of the particle is proportional to its activity. The binary mixture of “hot” and “cold” particles phase separates when the relative temperature difference between hot and cold particles, defined as activity $\chi$, exceeds a density-dependent critical value. The study of kinetics in 2-TIPS, a nonequilibrium phase separation, is of fundamental importance in statistical physics. In this paper, we investigate 2-TIPS kinetics using molecular dynamics (MD) and coarse-grained (CG) modeling in three and two dimensions. The coarse-grained model couples two passive model B equations for hot and cold particles, with coupling terms emulating the energy transfer between them by raising the temperature of cold particles and lowering that of hot particles, a key observation from the MD simulations. MD simulations reveal that, at high densities, phase separation begins immediately after the quench, forming bicontinuous domains rich in hot or cold particles, similar to spinodal decomposition in passive systems. These interconnected domains are also observed in the coarse-grained model for the mixture's critical composition. Both MD and CG models show dynamic scaling of the correlation function, indicating self-similar domain growth. Regardless of dimensionality, both methods report algebraic growth in domain length with a growth exponent of 1/3, known as the Lifshitz-Slyozov exponent, widely observed in passive systems. Our results demonstrate that the universality of phase-separation kinetics observed in passive systems also extends to the nonequilibrium binary mixture undergoing 2-TIPS.

The effective conductivity ($T^{\text{eff}}$) of two- (2D) and three-dimensional (3D) random resistor networks (RRNs) with random edge conductivity is studied. The combined influence of geometrical disorder, which controls the overall connectivity of the medium, and leads to percolation effects, and conductivity randomness is investigated. A formula incorporating connectivity aspects and second-order averaging methods, widely used in the stochastic hydrology community, is derived and extrapolated to higher orders using a power averaging formula based on a mean-field argument. This approach highlights the role of the so-called resistance distance, introduced by graph theorists. Simulations are performed on various RRN geometries constructed from 2D and 3D bond-percolation lattices. The results confirm the robustness of the power averaging technique and the relevance of the mean-field assumption.

In the field of computational biology, AlphaFold has facilitated remarkable progress in predicting protein structures. However, for some multimeric complexes, the accuracy of its predictions still needs improvement. Enhancing the prediction of binding sites in protein oligomers contributes to the prediction of overall structures, and the details of binding sites are crucial for understanding the functional mechanism, affinity, and specificity of complexes. The approach presented here is independent of black-box modeling, thereby facilitating a clearer elucidation of the underlying biological mechanisms of protein-protein interaction interfaces. The study investigates protein interaction sites, mainly for trimers and tetramers, in the Protein Data Bank (PDB) database, using a modular division method. By ranking modules based on the linear combination of the square of the solvent-accessible surface area and the internal contact area (SSAIA), it was found that interface modules are more likely to appear in surface modules with lower values. Among 44 964 monomers, 92.25% of the monomer interface residues are found in the three modules with the smallest SSAIA values. In 5240 trimers, 98.63% of the complexes had at least one chain correctly predicted, and in 7311 tetramers, 98.92% of the complexes had at least one chain correctly predicted, with an average of approximately 3 out of 4 residues in the top-ranked interface modules being interface residues. The results of comparison with other methods in the Benchmark 3.0 dataset and 12 targets of the CASP15 competition validated the effectiveness of our approach, providing a new perspective for predicting binding sites in multimer interactions.

Particle aggregation plays a crucial role in determining the performance of nanofluids. A particle-scale understanding of nanoparticle dynamics and aggregation behavior is a prerequisite for accurately characterizing their functionality. In this study, the complex factors affecting nanoparticle aggregation are innovatively condensed into two key dimensionless numbers, the Brownian number (Br) and the adhesion number (Ad). The influence mechanisms of Br and Ad on aggregation are investigated through simulations of typical particle dynamics, including collision, adhesion, rebound, and separation, using discrete element method coupled with a lattice Boltzmann model and immersed moving boundary (DEM-LBM-IMB), along with comprehensive force analysis. Simulation results reveal that both Brownian motion and adhesion exert nonmonotonic effects on aggregation. Specifically, Brownian motion promotes aggregation by increasing the frequency of particle collisions. However, excessive Brownian motion beyond the interparticle adhesion threshold reduces the adhesion ratio after collisions and amplifies particle separation, thus inhibiting aggregation. On the other hand, enhanced interparticle adhesion improves particle capture after collisions, but excessive adhesion restricts continuous particle movement and collisions, moderately suppressing aggregation. Based on these findings, an aggregation phase diagram is proposed as a function of Br and Ad and further validated by experiments, providing insights into predicting the aggregation behavior of nanofluids under complex conditions.

The ability to control the morphology of the nanotube deposit formed during the evaporation of a sessile droplet on a substrate is of theoretical and practical interest. Such deposits are required for various applications, including nanotechnology, medicine, biotechnology, and optronics. In the experiment of Zhao et al. [J. Colloid Interface Sci. 440, 68 (2015)], an annular deposit was formed near the contact line. The deposition geometry is caused by the coffee ring effect. This deposit is unusual in its morphology. It changes gradually in space from a disordered structure in the inner part of the ring to an aligned structure of nanotubes close to the periphery. To understand the mechanisms that lead to this, we have developed a mathematical model that takes into account the effects of advection, diffusion, and electrostatic interactions on particle transport. Results of numerical calculations have confirmed that all these factors together have an influence on the formation of such a variable morphology. Qualitative agreement with the experiment is shown for some values of the model parameters.

The general epidemic process is a paradigmatic model in nonequilibrium statistical physics displaying a continuous phase transition between active and absorbing states. The dynamic isotropic percolation universality class captures its universal properties, which we aim to quantitatively study by means of the field-theoretic formulation of the model augmented with a perturbative renormalization-group analysis. The main purpose of this work consists in determining the critical dynamic exponent $z$ to the three-loop approximation. This allows us to finalize the quantitative description of the dynamic isotropic percolation class to this order of perturbation theory. The calculations are performed within the dimensional regularization with the minimal subtraction scheme, and actual perturbative expansions are carried out in a formally small parameter $\varepsilon$, where $\varepsilon =6-d$ is a deviation from the upper critical dimension $d_c=6$.

We study the dynamical aspects of the top rank statistics of particles, performing Brownian motions on a half-line, which are ranked by their distance from the origin. For this purpose, we introduce an observable $\mathrm{\Omega }\left(t\right)$ which we call the overlap ratio. The average overlap ratio is equal to the probability that a particle that is on the top-$n$ list at some time will also be on the top-$n$ list after time $t$. The overlap ratio is a local observable which is concentrated at the top of the ranking and does not require the full ranking of all particles. In practice, the overlap ratio is easy to measure. We derive an analytical formula for the average overlap ratio for a system of $N$ particles in the stationary state that undergo independent Brownian motion on the positive real half-axis with a reflecting wall at the origin and a drift towards the wall. In particular, we show that for $N\to \infty$, the overlap ratio takes a rather simple form $\langle \mathrm{\Omega }\left(t\right)\rangle =\mathrm{erfc}\left(a\sqrt{t}\right)$ for $n\gg 1$ with some scaling parameter $a>0$. This result is a very good approximation even for moderate sizes of the top-$n$ list such as $n=10$. Moreover, we observe in numerical studies that the overlap ratio exhibits universal behavior in many dynamical systems including geometric Brownian motion, Brownian motion with asymptotically linear drift, the Bouchaud-Mézard wealth distribution model, and Kesten processes. We conjecture the universality to hold for a broad class of one-dimensional stochastic processes.

This paper proposes a data-driven method for obtaining the bifurcation points of a system utilizing a method based on Extreme Learning Machine with input parameter channels (ELM-IPC) trained on the time-series datasets from discrete dynamical systems. The input parameter channels permit the proposed method to align the original parameter spaces of the time-series datasets with the derived parameter spaces of the ELM-IPC model; this results in the accurate analysis of the bifurcation points of a system. To demonstrate the effectiveness of this approach, we apply it to two discrete dynamical systems: the two-dimensional Hénon map and the four-dimensional system comprising two conservatively coupled Hénon maps. Our results indicate that it is possible to obtain the bifurcation points of a system even in parameter spaces where multiple solutions coexist or periodic solutions with periods exceeding 100 are present.

Partial amplitude death is a phenomenon related to both the phase and amplitude in coupled oscillators, where some oscillators converge to their equilibrium points and others oscillate with a particular phase difference. Although partial amplitude death in delay-coupled oscillators has been numerically observed, it has seldom been analyzed theoretically. Here, we analytically investigate partial amplitude death in delay-coupled oscillators with complete multipartite graphs. We analytically derive the amplitude and phase relationship of the oscillators during partial amplitude death. It is shown that various phase-locked patterns of the partial amplitude death state exist in a given network topology. Furthermore, we find that the coupling strength controls the number of oscillators quenched and that the connection delay does not affect the existence of partial amplitude death, but affects its stability. It is shown that the local stability of partial amplitude death can be reduced to that of a time-invariant linear system, which is useful for analyzing the stability of partial amplitude death with a specific phase-locked pattern.

Inferring control parameters in nonlinear dynamical systems is an important task in analyzing general dynamical behaviors, particularly in the presence of inherently deterministic chaos. Traditional approaches often rely on system-specific models and involve heavily parametrized formulations, which can limit their general applicability. In this study, we present a methodology that employs recurrence plots as structured representations of nonlinear trajectories, which are then used to train convolutional neural networks to infer the values of the control parameter associated with the analyzed trajectories. We focus on two representative nonlinear systems, namely, the logistic map and the standard map, and show that our approach enables accurate estimation of the parameters governing their dynamics. When compared to regression models trained directly on raw time-series data, the use of recurrence plots yields significantly more robust results. Although the methodology does not aim to predict future states explicitly, we argue that accurate parameter inference, when combined with predetermined initial conditions, enables the reconstruction of a system's evolution due to its deterministic nature. These findings highlight the potential of recurrence-based learning frameworks for the automated identification and characterization of nonlinear dynamical behaviors.

We introduce the one-dimensional Morse-soft-Coulomb (MsC) potential to model the dynamics of an electron in an atomic potential. This potential has a single parameter that controls the softness of the repulsive barrier and the well depth. When this softening-depth parameter tends to zero, the MsC potential approaches the Coulomb potential with an infinite repulsive barrier, a known successful model for the hydrogen atom. We investigate the ionization under strong XUV laser fields by considering the classical chaotic dynamics in the MsC potential subjected to time-dependent external fields and comparing the results with the ones for the Coulomb potential. We show that the MsC potential reproduces the dynamics and the ionization probabilities of the Coulomb potential for sufficiently small values of the softening parameter. We also investigate the role of the softening parameter in the ionization probability and in the phase-space structures, showing that an increase in its value widens the chaotic sea and consequently elevates the ionization probability. Finally, we address the problem of controlling the dynamics of an electron in the MsC potential from the perspective of optimal control theory whose solution cannot be easily obtained in the case of the Coulomb potential due to the singularity at the origin. We analyze a particular analytical solution to the problem of transferring a given amount of energy to the atom at minimum cost, which has been previously termed the intrinsic solution. We find that the energy deposited in the atom essentially grows when the electron collides with the nucleus. At each collision, the optimal field follows the abrupt change of the electron momentum in the form of a single-cycle pulse. Thus, the optimal intrinsic solution is essentially composed of a sequence of single-cycle pulses separated by increasing time intervals as the electron climbs the anharmonic potential well. Our results show that the MsC potential is a useful simple model for investigating and furnishing insights into the physics of atomic excitation by external fields.

Seeking for a high-gain fusion scheme is a hot issue in inertial confinement fusion community, especially after the successful fusion ignition at National Ignition Facility. Fast ignition provides an alternative due to its potential to reduce the energy of driven lasers and achieve higher target gain, whose key step is efficiently generating fast electron beam using picosecond lasers. The properties of the electron beam, such as energy spectra, determine heating efficiency and neutron yield. In this paper, with two-dimensional particle-in-cell simulations, we studied how the dual-color lasers affect the fast electron generation. We find that the energy transfer ratio from laser to fast electrons would significantly increase, and the fast electron energy spectra would be adjusted in the dual-color injecting scheme, where an extra weak low-frequency laser is injected with the main pulse. These phenomena are attributed to the longitudinal electric field modulation in the relatively low-density region and relativistic electromagnetically induced transparency (EIT) process in microchannels formed in the over-dense region. Our results can be applied to fast ignition schemes and applications based on relativistic electron generation with different pulses.