The nonlinear stage of modulation instability (MI) starting with either purely periodic or localized periodic modulation is investigated analytically and numerically in the model of long wave-short wave (LS) resonance. Exact multiparametric solutions of Akhmediev breathers (ABs) and super-regular breathers (SRBs) are constructed based on an eigenvalue analysis. Physical spectra of ABs in analytic form are derived. The spectra of the short-wave component show expansion of energy from a single component to the sidebands and recurrence back to the same mode. However, the long-wave component shows complex oscillations in the sidebands, but the central mode remains constant. The evolution of LS-resonance-induced SRB is studied through its exact link with the MI. Our predictions based on exact analytical equations are confirmed by direct numerical simulations. We show that even nonideal single-wave excitations may lead asymptotically to the exact solutions. The connection of our exact solutions with results for the nonintegrable LS resonance model is also considered.

We consider a cigar-shaped Bose-Einstein condensate (BEC) of two-level atoms subjected to laser-induced Rabi coupling. By expanding the geometric vector potential to second order in the density-dependent fields and developing a quasi-one-dimensional (1D) reduction of the full three-dimensional problem via wave-function factorization, we derive an extended chiral Gross-Pitaevskii (GP) equation. We also derive traveling-wave solutions of the extended chiral GP equation using a projection (orthogonality) method, obtaining both bright and dark chiral solitons whose amplitudes and widths depend explicitly on the propagation direction. The chiral character of these solutions is confirmed through analytical analysis and numerical simulations. A BEC confined in a ring-shaped trap is also analyzed, leading to chiral soliton ring geometries. We show that a subtle interplay among density-dependent gauge potentials, confinement-induced interaction corrections, and higher-order current nonlinearities can give rise to alternative topological states, including chiral solitons and chiral ring solitons, in quasi-1D ultracold Bose gases. These results illustrate how higher-order corrections enrich BEC dynamics and provide means to control spatiotemporal structures in density-dependent condensates.

Explanations of societal polarization often rely on one of three mechanisms: homophily, bounded confidence, and community-based interactions. Opinion dynamics models based on these mechanisms consider the lack of interactions as the main cause of polarization. Given the increasing connectivity in modern society, this explanation of polarization may be insufficient. To understand how society becomes more polarized as its connectedness increases, we propose a voter-type model (called I-voter) that incorporates involvement as a key mechanism in opinion formation and study its dependence on the network connectivity. We describe the steady-state behavior of the model analytically, at the mean-field and the moment-hierarchy levels, and stress the generality of our findings by considering various extensions and different network topologies.

When following a sequence—such as reading a text or tracking a user's activity—one can measure how the “dictionary” of distinct elements (types) grows with the number of observations (tokens). When this growth follows a power law, it is referred to as Heaps' law, a regularity often associated with Zipf's law and frequently used to characterize human discovery processes. While random sampling from a Zipf-like distribution can reproduce Heaps' law, this connection relies on the assumption of temporal independence—an assumption often violated in real-world systems although frequently found in the literature. Here, we investigate how temporal correlations in token sequences affect the type-token curve. In human behaviors such as music listening and web browsing, domain-specific correlations in token ordering lead to systematic deviations from the Heaps-Zipf framework, effectively decoupling the type-token plot from the rank-frequency distribution. Using a minimal one-parameter model, we reproduce a wide variety of type-token trajectories, including the extremal cases that bound all possible behaviors compatible with a given frequency distribution. Our results demonstrate that type-token growth reflects not only the empirical distribution of type frequencies, but also the domain-specific, temporal structure of the sequence—a factor often overlooked in empirical applications of scaling laws to characterize human behavior.

The Peyrard-Bishop-Dauxois (PBD) model of DNA denaturation, although successful in the description of melting profiles, fails to predict melting entropies, unzipping forces, and dynamical properties, e.g., hairpin dynamics. The paper presents an atomistic “toy model” of the intra-base-pair motion which suggests that the thermodynamics may be better described by a planar vector—rather than a scalar—order parameter. This leads to correct estimates of melting entropy, unzipping force, hairpin opening rates, and the equilibrium constant of open/closed base pair states during imino proton exchange.

Inhibitory interneurons in the cortex are classified into cell types differing in their morphology, electrophysiology, and connectivity. Although it is known that parvalbumin (PV), somatostatin (SST), and vasoactive intestinal polypeptide-expressing neurons (VIP), the major inhibitory neuron subtypes in the cortex, have distinct modulatory effects on excitatory neurons, how heterogeneous spatial connectivity properties relate to network computations is not well understood. Here, we study the implications of heterogeneous inhibitory neurons on the dynamics and computations of spatially structured neural networks. We develop a mean-field model of the system in order to systematically examine excitation-inhibition balance, dynamical stability, and cell-type specific gain modulations. The model incorporates three inhibitory cell types and excitatory neurons with distinct connectivity probabilities and recent evidence of long-range spatial projections of SST neurons. Position-dependent firing-rate predictions are validated against simulations, and balanced solutions under Gaussian assumptions are derived from scaling arguments. Stability analysis shows that while long-range inhibitory projections in E-I circuits with a homogeneous inhibitory population result in instability, the heterogeneous network maintains stability with long-range SST projections. This suggests that a mixture of short- and long-range inhibitions may be key to providing diverse computations while maintaining stability. We further find that conductance-based synaptic transmissions are necessary to reproduce experimentally observed cell-type-specific gain modulations of inhibition by PV and SST neurons. These gain modulations are distance dependent, and a linear response analysis suggested that shifts in the excitation-inhibition balance of the network underlie these effects. Our theoretical approach offers insight into the computational function of cell-type-specific and distance-dependent network structure.

We present a theoretical framework for unidirectional electromagnetohydrodynamic flow of dilute electrolytes under perpendicular magnetic fields. Starting from the Navier-Stokes equation coupled with the Poisson-Nernst-Planck formulation, we show that the problem admits a sequential decoupling: the Stokes equation is solved first to obtain the velocity profile, which defines a hydrodynamic potential entering the Nernst-Planck description of ions. This Lorentz-force-induced potential competes with electrostatic attraction and significantly alters ionic distributions. We analyze this mechanism in two canonical geometries. In planar Couette shear, it produces a Manning-Oosawa-like condensation transition in one dimension, a phenomenon absent in classical electrostatics. We derive an eigenvalue equation predicting a sharp threshold between counterion enrichment and depletion at the charged wall. In cylindrical Taylor-Couette flow, the same effect shifts the classical Manning criterion by a magnetic parameter, enabling tunable control of condensation. These findings extend Manning-Oosawa phenomenology to driven, nonequilibrium systems and provide a basis for magnetic manipulation of screening in electrolytes, with implications for microfluidics, electrochemical systems, and nonlinear boundary-value theory.

We develop a quantitative framework to determine the minimal periodic supercell required for representative simulations of capillarity-screened Darcy flow in stationary random, polydisperse granular media. The microstructure is characterized by two-point statistics (covariance and spectral density) that govern finite-size fluctuations. Capillarity is modeled as a screened, modified-Helmholtz problem with phase-dependent transport under periodic boundary conditions; periodic homogenization yields an apparent conductivity, an apparent screening parameter, and a macroscopic capillary decay length. Because screening imparts a spatial low-pass response, we introduce a distribution-aware treatment of polydispersity consisting of a capillarity-weighted volume fraction and a screened analog of the integral range that preserves variance units and recovers classical descriptors in the appropriate limits. These descriptors lead to two sizing rules: (i) a length criterion on the shortest cell edge controlled by a microstructural correlation length, the macroscopic decay length, and a high quantile of grain size; and (ii) a volume criterion that links the target coefficient of variation to the screened integral range and the phase contrast. The framework couples statistical microstructure information to capillary response and yields reproducible, distribution-aware supercell selection for image-based finite-element or fast-Fourier-transform solvers. The resulting criteria are therefore intended for representativity of the coarse-grained screened response, rather than for isolated nonlinear pore-scale events.

In indirect-drive inertial confinement fusion (ICF), a hohlraum serves the purpose of converting laser energy into thermal x-ray energy. This process involves the interaction of low-density ablated plasmas, which can give rise to weakly collisional shocks characterized by the Knudsen number $\text{Kn}$ on the order of 1. The Knudsen number highlights the importance of kinetic effects. Preliminary investigations have demonstrated that the kinetic effects associated with weakly collisional shocks significantly impact the efficiency of the ICF process. The study explores the development and structural properties of weakly collisional shocks in hohlraums, focusing on ion mixing and separation in multicomponent plasmas, based on large-scale kinetic simulations. Key findings include the behavior of ions and electrons, which is different from strongly collisional shocks in hydrodynamic theory. The influence of charge-to-mass ratios on ion species separation results in two subshocks and deviations in hydrogen ion concentration from hydrodynamic predictions. The effects of weakly collisional shocks on electron and ion distributions are crucial for understanding laser energy coupling and improving diagnostics. Increased collision frequency could transition shock wave physical behavior from kinetically dominated to fluid-dominated. It further clarifies the impact of these shocks on electron and ion kinetics, providing valuable insights for future research in ICF and astrophysics.

Three-dimensional x-ray microtomography, coupled to rheometric measurements, enables a morphology-resolved reconstruction of capillary stresses at the grain scale in unsaturated wet granular materials. Liquid domains are automatically classified into capillary bridges, dimers, trimers, and larger clusters, and their spatial organization is tracked as a function of shear deformation and liquid content. We show that shear localization governs the redistribution of the liquid phase: capillary bridges remain uniformly distributed throughout the sample, while higher-order morphologies accumulate preferentially near the lower boundary of the shear zone through a shear-driven coalescence mechanism. Despite this spatial localization, simple two-grain bridges generate the dominant contribution to the isotropic capillary pressure, accounting for nearly 85% of the total at liquid-to-solid volume ratio $\epsilon =0.05$, whereas more complex liquid clusters contribute only weakly to the overall cohesion. Incorporating the morphology-resolved capillary pressure into an effective-stress framework qualitatively reproduces the macroscopic friction coefficient across the full range of investigated liquid contents, without adjustable parameters. These results establish a predictive micro-macro link between liquid morphology and the rheology of wet granular materials.

A slightly tilted permanent magnet rotating at high speed can induce a magnetic field capable of trapping another permanent magnet in a gravity independent levitated bound state, bypassing Earnshaw's theorem. During levitation, the floater magnet is locked in a conical orbit at the same frequency as the rotor. This rotation allows the sides of the same polarity of each magnet to face each other, which is responsible for the dynamic equilibrium of the floater magnet. Here, we theoretically explain the motion of the floater in-axis and off-axis and highlight levitation stability conditions and their dependence on the size of the floater and the speed of the rotor. We also experimentally studied the levitation conditions with respect to the rotational speed of the rotor for various floater's sizes and shapes. We observed and analyzed the lower and upper limits of levitation. Finally, we explained the off-axis motion of the center of mass of the floater from its equilibrium position by an extension of the dipole moment model.

Physical models aimed to reproduce basic features of the solar sunspot cycle are typically based on the solar dynamo mechanism. Usually qualitative arguments are used to define parameters of the model, among which a challenging component is the nonlinear form of quenching of the $\alpha$ effect governing regeneration of the magnetic field. We propose an approach, in which the functional form of the $\alpha$ quenching is represented by a neural network model embedded into neural differential dynamo equations trained on observational data. For demonstration, we consider a low-mode dynamo model and find a wide set of $\alpha$-quenching functions and corresponding dynamo numbers that provide an accurate fit to the average profile of the solar cycle data given by sunspot numbers. Within this set, we observe a strong relationship between the dynamo number and the shape of the $\alpha$-quenching function indicating that additional magnetic field data or constraints are essential to unambiguously infer parameters of the dynamo model. In our opinion, the neural differential approach opens a prospect for data-driven investigation of the closure problem in dynamo theory.

We propose a tensor-network-based algorithm to study the classical Ising model on an infinitely large hyperbolic lattice with a regular 3D tesselation of identical dodecahedra. We reformulate the corner transfer matrix renormalization group (CTMRG) algorithm from 2D to 3D to reproduce the known results on the cubic lattice. We subsequently generalize the CTMRG to a hyperbolic lattice with dodecahedral cells, which is an infinite-dimensional lattice. We analyze the spontaneous magnetization, von Neumann entropy, and correlation length to find a continuous noncritical phase transition on the dodecahedral lattice. We estimate the phase-transition temperature and find the magnetic critical exponents $\beta =0.4999$ and $\delta =3.007$, which confirm the mean-field universality class, in accord with predictions from Monte Carlo and high-temperature series expansions. The algorithm can be applied to arbitrary multistate spin models.

In the present work, we review two well-established quasicontinuum models of a Fermi-Pasta-Ulam lattice with Hertzian potentials, and we utilize these two models to approximate the discrete dispersive shock waves which are numerically observed in the simulation of the lattice. To perform analysis on various characteristics of the discrete dispersive shock wave, we analytically derive the Whitham modulation equations of the two quasicontinuum models, which govern the slowly varying spatial and temporal dynamics of distinct parameters of the periodic solutions. We then perform a very useful reduction of the Whitham modulation system to gain a system of initial-value problems whose solutions can provide important insights on edge features of the dispersive shock waves such as their edge speeds. In addition, we also study the numerical rarefaction waves of the lattice based on the two quasicontinuum models. In particular, we analytically compute and compare their self-similar solutions with the numerical discrete rarefaction wave of the lattice. These comparisons made for both dispersive shock waves and rarefaction waves reveal to be reasonably good, which suggest the impressive performance of both quasicontinuum models in approximating the nonlinear dispersive wave patterns of the granular crystal lattice.

In the context of the Kundu-Eckhaus equation, we study the nonlinear stage of modulational instability (MI) driven by a purely continuous spectrum and then analyze the nonlinear interactions in the presence of an additional soliton generated by the discrete spectrum. Specifically, investigating the characteristics of spontaneous oscillations generated by nonlinear MI, we show that the oscillation structure asymptotically evolves into a soliton ensemble as time goes to infinity. Meanwhile, the quintic and derivative nonlinearities can modulate the boundary expansion velocities and peak velocities of the oscillation structure, leading to the loss of spatial symmetry. When the presence of a discrete spectrum gives rise to an extra soliton independent of the initial perturbation, we identify four types of interactions between the soliton and the oscillation structure and accordingly present the partition of the discrete spectrum on the spectral plane, which varies with the strength of the higher-order nonlinearities.

Scroll waves are the three-dimensional counterparts of spiral waves in excitable media, and their filaments can form closed loops known as vortex rings. In systems with negative filament tension, such vortex rings tend to expand and may develop into Winfree turbulence, which is regarded as one of the key mechanisms underlying fibrillationlike activity in cardiac tissue. Therefore, controlling the formation and evolution of scroll-wave vortex rings is crucial for treatment of fibrillation. Motivated by recent advances in pulsed electric field (PEF) ablation for fibrillation therapy, we numerically investigate how PEF modulates the dynamics of free scroll-wave vortex rings in the three-dimensional Barkley model. By systematically varying pulse amplitude, pulse duration, pulse number, and field orientation, we show that when the PEF is applied opposite to the natural drift direction of the vortex ring, sufficiently strong and long pulses can reverse ring expansion and induce collapse, thereby suppressing the onset of turbulence. We further propose a kinematic model that combines intrinsic filament dynamics with the electric-field-induced drift of two-dimensional spiral waves to explain the observed transition from expansion to contraction. These results clarify how pulsed electric forcing can control scroll-wave filaments in media with negative filament tension and may provide mechanistic insight for electrical control of cardiac reentry.

Chimera states, characterized by the coexistence of coherent and incoherent domains, represent a paradigm of self-organization in complex systems. In this study, we introduce a topological analysis method based on winding numbers to characterize the dynamics of spiral wave chimeras in a two-dimensional phase oscillator network. Our investigation reveals distinct scaling laws governing the system's evolution across the phase lag $\alpha$. Perturbation analysis in the limit $\alpha \to 0$ demonstrates that the incoherent core radius scales linearly with $\alpha$. In contrast, within the stable chimera regime, the average total positive winding number $\mu$ follows a clear exponential growth law $\mu =a{e}^{b\alpha }$. This scaling disparity signals a physical crossover from a regime dominated by geometric core expansion to one driven by active topological excitation. Furthermore, we identify a statistical transition in the defect distribution from binomial-like to Poisson-like behavior at a critical threshold ${\alpha }^{*}$. These results demonstrate that topological defects possess intrinsic statistical order, establishing $\mu$ as a robust macrovariable for analyzing the structural complexity of chimera states.

The transient evolution and established states of color domains in fiber lasers with a doublet radiation spectrum are investigated by constructing a Lyapunov functional. In the transient process, the constructed functional decreases monotonically and reaches its minimum, regardless of the initial conditions. This evolution of the constructed functional allows one to determine the direction of the transient process for the generated radiation and its steady-state structure that minimizes this functional. The analysis using variational principles is based on an approximation neglecting the chromatic dispersion and refractive-index nonlinearity of the intracavity medium. The obtained results are useful for understanding the features of the transient evolution of the laser generation and for the development of methods for controlling the generation regimes of fiber lasers.

Microbial adaptation to extreme stress, such as starvation, antimicrobial exposure, or freezing, often reveals fundamental trade-offs between survival and proliferation. Understanding how populations navigate these trade-offs in fluctuating environments remains a central challenge. We develop a quantitative model to investigate the adaptation of populations of yeast (Saccharomyces cerevisiae) subjected to cycles of growth and extreme freeze-thaw stress, focusing on the role of quiescence as a mediator of survival. Our model links key life-history traits—growth rate, lag time, quiescence probability, and stress survival—to a single underlying phenotype, motivated by the role of intracellular trehalose in the adaptation of yeast to freeze-thaw stress. Through stochastic population simulations and analytical calculation of the long-term growth rate, we identify the evolutionary attractors of the system. We find that the strength of the growth-survival trade-off depends critically on environmental parameters, such as the duration of the growth phase. Crucially, our analysis reveals that populations optimized for growth-stress cycles can maintain viability alongside growth-optimized populations even in the absence of stress. This demonstrates that underlying physiological trade-offs do not necessarily translate into fitness trade-offs at the population level, providing general insights into the complex interplay between environmental fluctuations, physiological constraints, and evolutionary dynamics.

Antimicrobial resistance (AMR) threatens global health. A promising and underexplored strategy to tackle this problem is sequential therapies exploiting collateral sensitivity (CS), whereby resistance to one drug increases sensitivity to another. Here, we develop a four-genotype stochastic birth-death model with two bacteriostatic antibiotics to identify switching periods that maximize bacterial extinction under subinhibitory concentrations. We show that extinction probability depends nonlinearly on switching period, with stepwise increases aligned to discrete switch events: fast sequential therapies are suboptimal as they do not allow for the evolution of resistance, a key ingredient in these therapies. A geometric distribution framework accurately predicts cumulative extinction probabilities, where the per-switch extinction probability rises with switching period. We further derive a heuristic approximation for the extinction probability based on times to fixation of single-resistant mutants. Sensitivity analyses reveal that strong reciprocal CS is required for this strategy to work, and we explore how increasing antibiotic doses and higher mutation rates modulate extinction in a nonmonotonic manner. Finally, we discuss how longer therapies maximize extinction but also cause higher resistance, leading to a Pareto front of optimal switching periods. Our results provide quantitative design principles for in vitro and clinical sequential antibiotic therapies, underscoring the potential of CS‐guided regimens to suppress resistance evolution and eradicate infections.