Reservoir computing is a useful framework for predicting critical transitions of a dynamical system if the bifurcation parameter is also provided as an input. This work shows how the dynamical system theory provides the underlying mechanism behind the prediction. Using numerical methods, by considering dynamical systems which show Hopf bifurcation, we demonstrate that the map produced by the reservoir after a successful training undergoes a Neimark-Sacker bifurcation such that the critical point of the map is in immediate proximity to that of the original dynamical system. Also, we compare and analyze how the framework learns to distinguish between different structures in the phase space. Our findings provide insight into the functioning of machine learning algorithms for predicting critical transitions.

In many realistic systems, such as neural networks in the brain, the coupling strength between neurons is not fixed, but adaptively adjusts according to their activities. The suprachiasmatic nucleus (SCN), as the main clock in the mammalian brain, has been found to be a plastic neural network, and the coupling strength between neurons is highly dynamical. An important function of the SCN is entrainment, reflecting the ability of the SCN to synchronize with the external light-dark cycle. The entrainment ability is reflected by the entrainment range, which is a period range for the external light-dark cycle to which the SCN can entrain. In this article, we investigated whether the entrainment range of the SCN is affected by the adaptive coupling. We use a modified Kuramoto model with external light-dark cycle. We found that when the light sensitivity is larger than the fixed coupling strength (the coupling strength without adaptive rules), adaptive coupling can widen the entrainment range. Our findings help to understand the impact of the adaptive coupling between oscillatorty neurons on the collective behavior of the SCN, and provides a possible explanation for the plasticity of coupling in the master clock network.

The stochastic block model is widely used to generate graphs with a community structure, but no simple alternative currently exists for hypergraphs, in which more than two nodes can be connected together through a hyperedge. We discuss here such a hypergraph generalization, based on the clustering connection probability $P_{ij}$ between nodes of communities $i$ and $j$, and that uses an explicit and modulable hyperedge formation process. We focus on the standard case where $P_{ij}=p{\delta }_{ij}+q(1-{\delta }_{ij})$ when $0\le q\le p$ (${\delta }_{ij}$ is the Kronecker symbol). We propose a simple model that satisfies three criteria: it should be as simple as possible, when $p=q$ the model should be equivalent to the standard hypergraph random model, and it should use an explicit and modulable hyperedge formation process so that the model is intuitive and can easily express different real-world formation processes. We first show that for such a model the degree distribution and hyperedge size distribution can be approximated by binomial distributions with effective parameters that depend on the number of communities and $q/p$. Also, the composition of hyperedges goes for $q=0$ from ‘pure’ hyperedges (comprising nodes belonging to the same community) to ‘mixed’ hyperedges that comprise nodes from different communities for $q=p$. We test various formation processes and our results suggest that when they depend on the composition of the hyperedge, they tend to favor the dominant community and lead to hyperedges with a smaller diversity. In contrast, for formation processes that are independent from the hyperedge structure, we obtain hyperedges comprising a larger diversity of communities. The advantages of the model proposed here are its simplicity and flexibility that make it a good candidate for testing community-related problems, such as their detection, impact on various dynamics, and visualization.

DNA replication in yeast and in many other organisms starts from well-defined locations on the DNA known as replication origins. The spatial distribution of these origins in the genome is particularly important in ensuring that replication is completed quickly. Cells are more vulnerable to DNA damage and other forms of stress while they are replicating their genome. This raises the possibility that the spatial distribution of origins is under selection pressure. In this paper we investigate the hypothesis that natural selection favors origin distributions leading to shorter replication times. Using a simple mathematical model, we show that this hypothesis leads to two main predictions about the origin distributions: that neighboring origins that are inefficient (less likely to fire) are more likely to be close to each other than efficient origins; and that neighboring origins with larger differences in firing times are more likely to be close to each other than origins with similar firing times. We test these predictions using next-generation sequencing data, and show that they are both supported by the data.

The endothelial glycocalyx layer (EGL) plays a crucial role in regulating blood flow in microvessels. Experimental evidence suggests that there is greater blood flow resistance in vivo compared to in vitro, partially due to the presence of the EGL. However, the complex relationship between EGL deformation and blood cell behavior in shear flow and its quantification remains incompletely understood. To address this gap, we employ a particle-based numerical simulation technique to examine the interaction of the EGL with flowing red blood cells (RBCs) in microtubes. We examine changes in EGL deformation in response to variations in shear rate, EGL graft density, and contour height. Our results indicate that the alterations in EGL height are influenced by the mechanical properties of the EGL, flow conditions, and the RBC-EGL interaction. The flowing RBC compresses the EGL, causing a notable reduction in EGL height near the RBC flow. Additionally, we find that the presence of the EGL in the microtube results in increased RBC deformation and a wider gap between the RBC and tube wall due to spatial occupancy. The significant impact of the EGL on RBC flow is particularly evident in microtubes with diameters ranging from 7 to $10\mu \mathrm{m}$, a range consistent with notable differences in vascular flow resistance observed between in vivo and in vitro experiments. The simulation results shed insight on the dynamic interplay between RBC and the EGL in microvascular blood flow.

Nanoparticles (NPs) that are forcefully driven through a brush-decorated nanochannel form a nonequilibrium system with a rich physical behavior, including a dynamical phase transition between two modes of propagation that correspond to either separate clusters of NPs or a continuous flow channel. The peculiar properties of this system make it an ideal benchmark candidate for a comparison of three thermostat settings, the dissipative particle dynamics (DPD), the Langevin (LGV) dynamics, and a modified LGV setup, denoted as ${\mathrm{LGV}}^{-}$, in which the thermostatting is disabled in the direction of the driving force. We demonstrate that the choice of the thermostat has little influence on the conformations of NPs, and that, due to differences in the dissipation modes, notable differences arise in their dynamical properties, such as effective friction constants and average velocities. This also includes differences in the coupling between NP clusters and the surrounding brush and affects the corresponding phase diagrams of the two propagation modes. We conclude that the conventional DPD and LGV thermostats yield results that display a reasonable degree of coincidence, but we cannot recommend the use of the ${\mathrm{LGV}}^{-}$ algorithm for the present system.

Escape of active agents from metastable states is of great interest in statistical and biological physics. In this paper, we investigate the escape of a flexible active ring, composed of active Brownian particles, from a flat attractive surface using Brownian dynamics simulations. To systematically explore the effects of activity, persistence time, and the shape of attractive potentials, we calculate escape time ${\tau }_e$ and effective temperature $T_{\mathrm{eff}}.$ We observe two distinct escape mechanisms: Kramers-like thermal activation at small persistence times, where $ln\left({\tau }_e\right)\sim 1/\left(k_B{T}_{\mathrm{eff}}\right)$, and the maximal force problem at large persistence time, where ${\tau }_e$ is determined by persistence time. The escape time explicitly depends on the shape of the potential barrier at high activity and large persistence time. Moreover, when the propulsion force is biased along the ring's contour, escape becomes more difficult and is primarily driven by thermal noise. Our findings highlight that, despite its intricate configuration, the active ring can be effectively modeled as a self-propelled Brownian particle when studying its escape from a smooth surface.

The self-assembly of liquid crystal droplets and shells represents a captivating frontier in soft matter physics, promising precision engineering of functional materials. In this study, we delve into the phase behavior and investigate defect formation patterns in spherical shell-confined discotic liquid crystals (DLCs) through $NpT$ Monte Carlo simulations. These shells are created by confining DLCs between two spherical surfaces, promoting the same anchoring. In this study, we focus on the case when both surfaces promote edge-on (planar) anchoring. Our study confirms a general result which states that, when a liquid crystal is under strong confinement, the nature of the isotropic-nematic transition changes from first order into continuous. Furthermore, as expected, topological defects at the spherical surface arise due to the topological constraints on the director field. Notably, our investigation reveals a unique topological defect configuration, characterized by the formation of four disclination lines that bridge the inner and external surfaces. Additionally, we observe a mixed $\pm 1/2$ wedge-twist disclination line that forms an arch that terminates at the outer surface. This arch decreases its length with decreasing temperature to eventually disappear.

A new phase-field approach is designed to model surface diffusion of crystals with strongly anisotropic surface energy. The model can be shown to asymptotically converge toward the sharp-interface equation for surface diffusion in the limit of vanishing interface width. It is employed to investigate the dynamical evolution of a thermodynamically metastable crystal surface. We find that nucleation and growth by surface diffusion of the newly formed surface induce the formation of additional stable surfaces at its wake. This induced nucleation mechanism is found to produce domains composed of several stable surfaces of prescribed width. The domains propagate on the crystal surface and then coalesce to form a hill-and-valley structure. The resulting morphology is more regular than the typical hill-and-valley surface produced by random thermal nucleation, i.e., when motion-by-curvature controls the phase separation dynamics. Moreover, the induced nucleation mechanism is found to be peculiar to surface diffusion and to dominate the phase separation at high degree of metastability. Once the hill-and-valley structure is formed, coarsening operates by motion and elimination of facet junctions, points where two facets merge to form one and we find the following scaling law $L\sim t^{1/6}$, for the growth in time $t$ of the characteristic length scale $L$ during this coarsening stage. The density of junctions is found to exhibit a $t^{-2/3}$ regime. Our results elucidate the role of the induced nucleation mechanism on the dynamics of interfacial phase separation and corroborate surface faceting experiments on ceramics.

Recent experiments have established negative energetic elasticity, the negative contribution of energy to the elastic modulus, as a universal property of polymer gels. To reveal the microscopic origin of this phenomenon, Shirai and Sakumichi investigated a polymer model on a cubic lattice with the energy effect from the solvent in finite-size calculations [Phys. Rev. Lett. 130, 148101 (2023)]. Motivated by this work, we provide a simple platform to study negative energetic elasticity by considering a one-dimensional random walk with the energy effect. This model can be mapped onto the classical Ising chain, leading to an exact form of the free energy in the thermodynamic or continuous limit. Our analytical results are qualitatively consistent with Shirai and Sakumichi's results. Our model serves as a fundamental benchmark for studying the elasticity of polymer chains.

Deterministic and stochastic coupled oscillators with inertia are studied on the rectangular lattice under the shear-velocity boundary condition. Our coupled oscillator model exhibits various nontrivial phenomena and there are various relationships with wide research areas such as the coupled limit-cycle oscillators, the dislocation theory, a block-spring model of earthquakes, and the nonequilibrium molecular dynamics. We show numerically several unique nonequilibrium properties of the coupled oscillators. We find that the spatial profiles of the average value and variance of the velocity become nonuniform when the dissipation rate is large. The probability distribution of the velocity sometimes deviates from the Gaussian distribution. The time evolution of kinetic energy becomes intermittent when the shear rate is small and the temperature is small but not zero. The intermittent jumps of the kinetic energy cause a long tail in the velocity distribution.

Animal behavior occurs on timescales much longer than the response times of individual neurons. In many cases, it is plausible that these long timescales emerge from the recurrent dynamics of electrical activity in networks of neurons. In linear models, timescales are set by the eigenvalues of a dynamical matrix whose elements measure the strengths of synaptic connections between neurons. It is not clear to what extent these matrix elements need to be tuned to generate long timescales; in some cases, one needs not just a single long timescale but a whole range. Starting from the simplest case of random symmetric connections, we combine maximum entropy and random matrix theory methods to construct ensembles of networks, exploring the constraints required for long timescales to become generic. We argue that a single long timescale can emerge generically from realistic constraints, but a full spectrum of slow modes requires more tuning. Langevin dynamics that generates patterns of synaptic connections drawn from these ensembles involves a combination of Hebbian learning and activity-dependent synaptic scaling.

We report on the synthesis and characterization of a colloidal graphitic carbon nitride (g-${\mathrm{C}}_3{\mathrm{N}}_4$) system exhibiting complex memfractance behavior. The g-${\mathrm{C}}_3{\mathrm{N}}_4$ colloid was prepared through thermal polymerization of urea, followed by dispersion in deionized water. X-ray diffraction and scanning electron microscopy confirmed the successful synthesis of g-${\mathrm{C}}_3{\mathrm{N}}_4$. Electrical characterization revealed nonpinched hysteresis loops in current-voltage curves, indicative of memristive behavior with additional capacitive components. The device demonstrated stable resistive switching between high ($\sim 50\mathrm{k}\mathrm{\Omega }$) and low ($\sim 22\mathrm{k}\mathrm{\Omega }$) impedance states over 500 cycles, as well as synaptic plasticity-like conductance modulation. To capture these complex dynamics, we employed a generalized memfractance model that interpolates between memristive, memcapacitive, and second-order memristive elements. This model, employing fractional-order derivatives, accurately fitted the experimental data, revealing the device's memory effects. The emergence of memfractance in this colloidal system opens new avenues for neuromorphic computing and unconventional information processing architectures, leveraging the unique properties of liquid-state memory devices.

A mathematical model is developed to jointly analyze elastic and inelastic scattering data of fluctuating membranes within a single theoretical framework. The model builds on a nonhomogeneously clipped time-dependent Gaussian random field. This specific approach provides one with general analytical expressions for the intermediate scattering function for any number of sublayers in the membrane and arbitrary contrasts. The model is illustrated with the analysis of small-angle x-ray and neutron scattering as well as with neutron spin-echo data measured on unilamellar vesicles prepared from phospholipids extracted from porcine brain tissues. The parameters fitted on the entire data set are the lengths of the chain and the head of the molecules that make up the membrane, the amplitude and lateral sizes of the bending deformations, the thickness fluctuation, and a single parameter characterizing the dynamics.

We study the rheology of bidisperse non-Brownian suspensions using particle-based simulation, mapping the viscosity as a function of the size ratio of the species, their relative abundance, and the overall solid content. The variation of the viscosity with applied stress exhibits shear-thickening phenomenology irrespective of composition, though the stress-dependent limiting solids fraction governing the viscosity and its divergence point are nonmonotonic in the mixing ratio. Contact force data demonstrate an asymmetric exchange in the dominant stress contribution from large-large to small-small particle contacts as the mixing ratio of the species evolves. Combining a prior model for shear thickening with one for composition-dependent jamming, we obtain a full description of the rheology of bidisperse non-Brownian suspensions capable of predicting effects such as the viscosity reduction observed upon adding small particles to a suspension of large particles.

For bichromatically excited diatomic molecules modeled in a shifted Tietz-Wei molecular potential, we demonstrate the occurrence of vibrational resonance (VR) when a saddle-node (SN) bifurcation takes place and its nonoccurrence in the absence of an SN bifurcation. We have examined the VR phenomenon and its connection with SN bifurcation for eight diatomic molecules, namely, ${\mathrm{H}}_2, {\mathrm{N}}_2, {\mathrm{Cl}}_2, {\mathrm{I}}_2, {\mathrm{O}}_2$, HF, CO, and NO, consisting of homogeneous, heterogenous, and halogen molecules. We demonstrate that each of them vibrates at a distinct resonant frequency but with a spread in frequency. The high-frequency amplitude at which VR occurs corresponds to the SN-bifurcation point. We validate our analytic results by numerical simulations and show that the homonuclear halogens respond only weakly to bichromatic fields, which may perhaps be linked to their absence of SN bifurcation.

We study the emergent dynamics of quantum self-sustained oscillators induced by the simultaneous presence of attraction and repulsion in the coupling path. We consider quantum Stuart-Landau oscillators under attractive-repulsive coupling and construct the corresponding quantum master equation in the Lindblad form. We discover an interesting symmetry-breaking transition from quantum limit cycle oscillation to a quantum inhomogeneous steady state. This transition is contrary to the previously known symmetry-breaking transition from a quantum homogeneous state to an inhomogeneous steady state. The result is supported by the analysis on the noisy classical model of the quantum system in the weak quantum regime. Remarkably, we find the generation of entanglement associated with the symmetry-breaking transition that has no analog in the classical domain. This study enriches our understanding of the collective behaviors shown by coupled oscillators in the quantum domain.

Information about the nonlinear magnetic response of dispersions of magnetic particles is the basis for biomedical applications. In this paper, using analytical and numerical methods, the third harmonic of the dynamic susceptibility of an ensemble of moving magnetic particles in an ac magnetic field with an arbitrary amplitude is studied, taking into account interparticle interactions. A simple approximation formula is proposed to predict the third harmonic as a function of two parameters: the Langevin susceptibility ${\chi }_L$, which is used to estimate the particle dipole-dipole interactions, and the Langevin parameter $\xi$, which represents the ratio of the energy of the magnetic moment interacting with the magnetic field to the thermal energy. The derived approximation formula corresponds with the known single-particle theories in the limit case of a small particle's concentration and is valid for concentrated dispersions of magnetic particles (with the Langevin susceptibility up to ${\chi }_L\le 3$) in high-amplitude ac fields (with the Langevin parameter up to $\xi \le 10$).

The structure, thermodynamics, and slow activated dynamics of the equilibrated metastable regime of glass-forming fluids remain a poorly understood problem of high theoretical and experimental interest. We apply a highly accurate microscopic equilibrium liquid state integral equation theory, in conjunction with naïve mode coupling theory of particle localization, to study in a unified manner the structural correlations, thermodynamic properties, and dynamic elastic shear modulus in deeply metastable hard sphere fluids. Distinctive behaviors are predicted including divergent inverse critical power laws for the contact value of the pair correlation function, pressure, and inverse dimensionless compressibility, and a splitting of the second peak and large suppression of interstitial configurations of the pair correlation function. The dynamic elastic modulus is predicted to exhibit two distinct exponential growth regimes with packing fraction that have strongly different slopes. These thermodynamic, structural, and elastic modulus results are consistent with simulations and experiments. Perhaps most unexpectedly, connections between the amplitude of long wavelength density fluctuations, dimensionless compressibility, local structure, and the dynamic elastic shear modulus have been theoretically elucidated. These connections are more broadly relevant to understanding the slow activated relaxation and mechanical response of colloidal suspensions in the ultradense metastable region and deeply supercooled thermal liquids in equilibrium.

Charged and quasineutral beams propagating through an unmagnetized plasma are subject to numerous collisionless instabilities on the small scale of the plasma skin depth. The electrostatic two-stream instability, driven by longitudinal and transverse wakefields, dominates for dilute beams. This leads to modulation of the beam along the propagation direction and, for wide beams, transverse filamentation. A three-dimensional spatiotemporal two-stream theory for warm beams with a finite extent is developed. Unlike the cold beam limit, diffusion due to a finite emittance gives rise to a dominant wave number and a cutoff wave number above which filamentation is suppressed. Particle-in-cell simulations with quasineutral electron-positron beams in the relativistic regime give excellent agreement with the theoretical model. This paper provides deeper insights into the effect of diffusion on filamentation of finite beams, crucial for comprehending plasma-based accelerators in laboratory and cosmic settings.