Complex networks are made up of communities wherein dynamics occur. Here, a community is defined as an ensemble of identical Wien-bridge oscillators that are nearly synchronized. We explore experimental evidence of community switching, i.e., a subset of oscillators in a community synchronizing their frequencies to those of the other community. We demonstrate this phenomenon by varying the network connectivity and interaction strength. Employing Wien-bridge oscillators, we study experimentally, as well as in LTspice simulations, the phenomenon where an oscillator synchronizes its frequency to that of its neighboring community en route to global synchronization. Our results are in agreement with numerical simulations of the Kuramoto model reported by Kato and Kori in their novel work involving community switching [Phys. Rev. E 107, 014210 (2023)]. Due to the presence of noise, hysteresis is also observed in our experiment but not in LTspice simulations. Lastly, the onset of global synchrony for different topologies is studied.

Following on from previous work [J. F. Scott and C. Cambon, J. Fluid Mech. 979, A17 (2024)], this article concerns weak (small Rossby or Froude number), homogeneous turbulence subject to rotation and stable stratification. The flow is expressed as a combination of particular solutions (modes) of the linearized governing equations without viscosity or diffusion. Modes are of two types: oscillatory ones which represent inertial-gravity waves and time-independent ones that express a nonpropagating (NP) component of the flow. It was shown in the previous work that, at leading order, the NP component evolves independently of the wave component and a specifically adapted direct numerical simulation (DNS) approach was introduced to describe the NP component, the same approach which is employed here. Using wave-turbulence analysis and assuming the NP amplitude is small compared with the wave amplitude, evolution equations for the wave spectra were derived and numerically exploited. Here, those equations are extended to the case when the NP and wave components are of comparable magnitude. The NP spectra then appear in the wave-turbulence equations, which means those equations are no longer closed. As a result, a combination of adapted DNS for the NP component and the wave-turbulence equations is used and numerical solutions of the latter are given. Terms in the wave-turbulence equations arising from the NP component couple pairs of wave modes, adding to the three-wave interactions of the previous work when the latter exist. This is found to considerably increase the wave dissipation. Indeed, it provides the only mechanism for significant dissipation in the cases for which three-wave interactions are absent. The additional dissipation is especially important for wave modes having wave vectors perpendicular to the vertical or rotation axis, but is also effective for other directions.

Radiative hydrodynamics models the interaction between fluid flows and radiation, which is essential for many astrophysical simulations. The M1-multigroup model is widely regarded as the most precise framework for capturing the complex interplay between light and matter, particularly by accounting for the spectral behavior of photons. A critical component of this model is the Eddington factor, which is used in the closure relation linking the radiative pressure to the radiative energy. Although an analytical expression for the Eddington factor does not exist, our research reveals that it depends solely on three parameters: the radiative temperature, the reduced flux, and the group narrowness. To address the challenge of calculating this factor efficiently, we have developed a method that combines neural networks and polynomial approximations. This method achieves computational speeds up to 3000 times faster than traditional line search algorithms while providing precision levels up to 1000 times higher than simplified alternatives based on interpolation or the analytical expression of the M1-gray model. Unlike interpolation-based techniques, it operates without requiring prior knowledge of radiative quantities, offering greater flexibility and applicability in diverse scenarios. Although the test simulations we performed, where radiation pressure is not the dominant factor, demonstrate a limited impact of the precision of the estimation of the Eddington factor on fluid dynamics, our approach lays a solid foundation for future advancements. It is particularly promising for more complex simulations involving out-of-equilibrium, radiative pressure-dominated scenarios. These developments mark a significant step forward in radiative hydrodynamics, offering a robust, accurate, and highly efficient computational tool to advance astrophysical modeling.

We investigate both ensemble and time-averaged mean-squared displacements of particles in a polydisperse granular system in a homogeneous cooling state and derive rigorous analytical expressions valid both at short and long time scales. The discrepancies in ensemble and time-averaged mean-squared displacements indicate ergodicity breaking in granular systems consisting of an arbitrary number of species of different sizes and masses. We compare the results of our study with Monte Carlo simulations in terms of a powerful low-rank algorithm and find a nice agreement.

We have studied the diluted Heisenberg spin glass model in a three-component random field for the commonly used one-dimensional long-range model where the probability that two spins separated by a distance $r$ interact with one another falls as $1/r^{2\sigma }$, for two values of $\sigma$, $0.75$ and $0.85$. No de Almeida–Thouless line is expected at these $\sigma$ values. The spin glass correlation length ${\xi }_{\text{SG}}$ varies with the random field as expected from the Imry-Ma argument and the droplet scaling picture of spin glasses. However, when ${\xi }_{\text{SG}}$ becomes comparable to the system size $L$, there are departures which we attribute to the features deriving from the replica symmetry breaking picture of spin glasses. For the case $\sigma =0.85$ these features go away for system sizes with $L>L^{*}$, where $L^{*}$ is large ($\approx 4000–8000$ lattice spacings). In the case of $\sigma =0.75$ we have been unable to study large enough systems to determine its value of $L^{*}$. We sketch a renormalization group scenario to explain how these features could arise. In this scenario finite size effects on the droplet scaling picture in low-dimensional spin glasses produce some aspects of Parisi's replica symmetry breaking theory of the Sherrington-Kirkpatrick model.

The hydrodynamics of crystals with vacancies is developed on the basis of local-equilibrium thermodynamics, where the chemical potential of vacancies plays a key role together with a constraint relating the concentration of vacancies to the density of mass and the strain tensor. The microscopic foundations are established, leading to Green-Kubo and Einstein-Helfand formulas for the transport coefficients, including the vacancy conductivities and the coefficients of vacancy thermodiffusion. As a consequence of having introduced the chemical potential of vacancies, a relationship is obtained between the conductivities and the Fickian diffusion coefficients for the vacancies. The macroscopic equations are linearized around equilibrium to deduce the dispersion relations of the eight hydrodynamic modes. The theoretical predictions are confirmed by numerical simulations of the hard-sphere crystal with vacancies. The study explicitly shows that the eighth hydrodynamic mode of nonperfect monatomic crystals is indeed a mode of vacancy diffusion.

We explore the dynamics and transport properties of the rational standard nontwist map (RSNM), which works as an extension of the standard nontwist map (SNM). In addition to the usual parameters of the SNM that govern the twist function profile and the intensity of the nonlinear perturbation, we introduce a new perturbation parameter $\mu$ in the RSNM, which makes it possible to break the symmetry of the system. The symmetry breaking leads to directed transport, known as the ratchet effect, where chaotic orbits exhibit a preferential direction of motion. We analyze the impact of $\mu$ on both the phase space and the parameter space structure, focusing on the destruction of transport barriers, which acts as separators between chaotic regions. Through numerical simulations and analysis of the fixed points stability, we demonstrate that an increase in $\mu$ enhances the chaotic volume in the lower half of the phase space, resulting in the destruction of invariant spanning curves, while simultaneously regularizing the upper half. Additionally, we explore the conditions under which partial transport barriers persist and their role in moderating transport across the phase space. We show that even small variations in a control parameter causes crossings of invariant manifolds from different regions of the phase space, enhancing transport with the mechanism of turnstiles and intercrossing. Our analysis of directed transport reveals that the breaking of symmetry by $\mu$ results in either positive or negative net transport in the phase space, depending on the control parameters. We also note that RSNM creates new regions within the parameter space, referred to as holes, due to the emergence of transport within previously null transport regions.

Island formation in strain-free heteroepitaxial deposition of thin films is analyzed using kinetic Monte Carlo simulations of two minimal lattice models and scaling approaches. The transition from layer-by-layer (LBL) to island (ISL) growth is driven by a weaker binding strength of the substrate, which, in the kinetic model, is equivalent to an increased diffusivity of particles on the substrate compared to particles on the film. The LBL-ISL transition region is characterized by particle fluxes between layers 1 and 2 significantly exceeding the net flux between them, which sets a quasiequilibrium condition. Deposition on top of monolayer islands weakly contributes to the second-layer nucleation, in contrast with the homoepitaxial growth case. A thermodynamic approach for compact islands with one or two layers predicts the minimum size in which the second layer is stable. When this is linked to scaling expressions for submonolayer island deposition, the dependence of the ISL-LBL transition point on the kinetic parameters qualitatively matches the simulation results, with quantitative agreement in some parameter ranges. The transition occurs in the equilibrium regime of partial wetting, and the convergence of the transition point upon reducing the deposition rate is very slow and practically unattainable in experiments.

We introduce matrix H theory, a framework for analyzing collective behavior arising from multivariate stochastic processes with hierarchical structure. The theory models the joint distribution of the multiple variables (the measured signal) as a compound of a large-scale multivariate distribution with the distribution of a slowly fluctuating background. The background is characterized by a hierarchical stochastic evolution of internal degrees of freedom, representing the correlations between stocks at different timescales. As in its univariate version, the matrix H-theory formalism also has two universality classes, Wishart and inverse Wishart, enabling a concise description of both the background and the signal probability distributions in terms of Meijer $G$ functions with matrix argument. Empirical analysis of daily returns of stocks within the S&P 500 demonstrates the effectiveness of matrix H theory in describing fluctuations in stock markets. These findings contribute to a deeper understanding of multivariate hierarchical processes and offer potential for developing more informed portfolio strategies in financial markets.

Although neuron models have been well studied for their rich dynamics and biological properties, limited research has been done on the complex geometries that emerge from the basins of attraction and basin boundaries of multistable neuron systems. In this paper, we investigate the geometrical properties of the strange attractors, four-dimensional basins, and fractal basin boundaries of an asymmetrically electrically coupled system of two identical nonchaotic Rulkov neurons. We discover a quasimultistability in the system emerging from the existence of a chaotic spiking-bursting pseudo-attractor, and we classify and quantify the system's basins of attraction, which are found to have complex fractal geometries. Using the method of uncertainty exponents, we also find that the system exhibits extreme final state sensitivity, which results in a dynamical uncertainty that could have important applications in neurobiology.

The phenomenon of high-order ($p/q$) synchronization, induced by two different frequencies in the system, is well known and studied extensively in forced oscillators including neurons and to a lesser extent in coupled oscillators. Their frequencies are locked such that for every $p$ cycles of one oscillator there are $q$ cycles of the other. We demonstrate this phenomenon in a pair of coupled neurons having identical frequencies but asymmetric coupling. Specifically, we focus on an excitatory-inhibitory (E-I) neuron pair where such an asymmetry is naturally present even with equal reciprocal synaptic strengths $\left(g\right)$ and inverse time constant $\left(\alpha \right)$. We thoroughly investigate the asymmetric coupling-induced $p/q$ frequency-locking structure in $(g,\alpha )$ parameter space through simulations and analysis. Simulations display quasiperiodicity, devil staircase, a Farey arrangement of spike sequences, and presence of reducible and irreducible $p/q$ regions. We introduce an analytical method, based on event-driven maps, to determine the existence and stability of any spike sequence of the two neurons in a $p/q$ frequency-locked state. Specifically, this method successfully deals with nonsmooth bifurcations and we could utilize it to obtain solutions for the case of identical E-I neuron pair under arbitrary coupling strength. In contrast to the so-called Arnold tongues, the $p/q$ regions obtained here are not structureless. Instead they have their own internal bifurcation structure with varying levels of complexity. Intrasequence and intersequence multistability, involving spike sequences of same $p/q$ state, are found. Additionally, multistability also arises by overlap of $p/q$ with $p^{\prime }/q^{\prime }$. The boundaries of both reducible and irreducible $p/q$ regions are defined by saddle node and nonsmooth grazing bifurcations of various types.

We consider a versatile matrix model of the form $\mathbf{A}+i\mathbf{B}$, where $\mathbf{A}$ and $\mathbf{B}$ are real random circulant matrices with independent but, in general, nonidentically distributed Gaussian entries. For this model, we derive exact results for the joint probability density function and find that it is a multivariate Gaussian. Arbitrary order marginal density therefore also readily follows. It is demonstrated that by adjusting the averages and variances of the Gaussian elements of $\mathbf{A}$ and $\mathbf{B}$, we can interpolate between a remarkably wide range of eigenvalue distributions in the complex plane. In particular, we can examine the crossover between a random real circulant matrix and a random complex circulant matrix. We also extend our study to include Wigner-like and Wishart-like matrices constructed from our general random circulant matrix. To validate our analytical findings, Monte Carlo simulations are conducted, which confirm the accuracy of our results. Additionally, we compare our analytical results with the spectra of adjacency matrices from various random circulant graphs. Despite the difference in entry distributions—Gaussian in our model and non-Gaussian in the adjacency matrices—the densities show excellent agreement in the large-dimension limit.

The rapid evolution and global impact of coronaviruses, notably SARS-CoV-1 and SARS-CoV-2, underscore the importance of understanding their molecular mechanisms in detail. This study focuses on the receptor-binding motif (RBM) within the spike protein of these viruses, a critical element for viral entry through interaction with the ACE2 receptor. We investigate the sequence variations in the RBM across SARS-CoV-1, SARS-CoV-2, and its early variants of concern (VOCs). Utilizing multicanonical simulations and microcanonical analysis, we examine how these variations influence the folding dynamics, thermostability, and solubility of the RBMs. Our methodology includes calculating the density of states (DoS) to identify structural phase transitions and assess thermodynamic properties. Furthermore, we solve the Poisson-Boltzmann equation to model the solubility of the RBMs in aqueous environments. This methodology is expected to elucidate structural and functional differences in viral evolution and pathogenicity, likely improving targeted treatments and vaccines.

Glassy soft matter is often continuously polydisperse, in which the sizes or various properties of the constituent particles are distributed continuously. However, most of the microscopic theories of the glass transition focus on the monodisperse particles. Here, we developed a replica theory for the dynamic glass transition of continuously polydisperse hard spheres. We focused on the limit of infinite spatial dimension, where replica theory becomes exact. In theory, the cage size $A$, which plays the role of an order parameter, appears to depend on the particle size $\sigma$, and thus, the effective free energy, the so-called Franz-Parisi potential, is a functional of $A\left(\sigma \right)$. We applied this theory to two fundamental systems: a nearly monodisperse system and an exponential distribution system. We found that dynamic decoupling occurs in both cases; the critical particle size ${\sigma }^{*}$ emerges, and larger particles with $\sigma \ge {\sigma }^{*}$ vitrify, while smaller particles $\sigma <{\sigma }^{*}$ remain mobile. Moreover, the cage size $A\left(\sigma \right)$ exhibits a critical behavior at $\sigma \simeq {\sigma }^{*}$, originating from spinodal instability of ${\sigma }^{*}$-sized particles. We discuss the implications of these results for finite dimensional systems.

The thermodynamics and microstructure of confined fluids with small particle number are best described using the canonical ensemble. However, practical calculations can usually only be performed in the grand-canonical ensemble, which can introduce unphysical artifacts. We employ the method of asymptotics to transform grand-canonical observables to the canonical ensemble, where the former can be conveniently obtained using the classical density functional theory of inhomogeneous fluids. By formulating the ensemble transformation as a contour integral in the complex fugacity plane we reveal the influence of the Yang-Lee zeros in determining the form and convergence properties of the asymptotic series. The theory is employed to develop expansions for the canonical partition function and the canonical one-body density. Numerical investigations are then performed using an exactly soluble one-dimensional model system of hard rods.

The behavior of nonlinear systems near critical transitions has significant implications for stability, transients, and resilience in complex systems. Transient times, $\tau$, become extremely long near phase transitions (or bifurcations) in a phenomenon known as critical slowing down, and are observed in electronic circuits, circuit quantum electrodynamics, ecosystems, and gene regulatory networks. Critical slowing down typically follows universal laws of the form $\tau \sim |\mu -{\mu }_c{|}^{\beta }$, with $\mu$ being the control parameter and ${\mu }_c$ its critical value. For instance, $\beta =-1/2$ close to saddle-node bifurcations. Despite intensive research on slowing down phenomena for single bifurcations, both local and global, the behavior of transients when several bifurcations are close to each other remains unknown. Here, we investigate transients near two saddle-node bifurcations merging into a transcritical one. Using a nonlinear gene-regulatory model and a normal form exhibiting a mushroom bifurcation diagram we show, both analytically and numerically, a synergistic, i.e., nonadditive, lengthening of transients due to coupled ghost effects and transcritical slowing down. We also show that intrinsic and extrinsic noise play opposite roles in the slowing down of the transition, allowing us to control the timing of the transition without compromising the precision of timing. This establishes molecular strategies to generate genetic timers with transients much larger than the typical timescales of the reactions involved.

We model charge transfer in B-DNA, the most common form of deoxyribonucleic acid, with the aim of assessing the role of the backbone. We achieve this by employing a four-channel tight binding model, where B-DNA is analyzed at the base and backbone sites level. The significant difference of our model, with other similar models that have appeared in the literature so far, is that we have calculated all tight binding on-site energies and interaction integrals using DFT; these are not roughly estimated or guessed. We study two kinds of sequences: homopolymers and randomly generated sequences. This enables us to effectively compare the relative ease of charge transfer through the backbone channels with that of the $\pi$ pathway formed by the nucleobases' frontier molecular orbitals, since the latter is highly sensitive to sequence periodicity, as it determines the degree of energy uniformity across the base-pair sequence. Results are presented for the electronic structure, the localization of the energy eigenstates, and the ease of carrier transfer. Emphasis is given to results for holes, due to the inherent unreliability of DFT calculations for excited states. We demonstrate that the backbone could be essential for B-DNA charge transfer, provided limited backbone energy disorder.