Papers

We investigate the dynamics of two-component flat-top–bubble vector solitons using a variational approximation and numerical simulations. The system is described by coupled cubic-quintic nonlinear Schrödinger equations with repulsive intercomponent coupling. We introduce a self-induced mechanism in which a localized flat-top soliton (FTS) generates a density bubble in a second component: the localized density acts as a repulsive potential for the background field, creating a composite bound state. A background-subtracted formulation and normalized super-Gaussian profiles yield collective-coordinate equations for the component centers and an effective interaction potential for their relative separation. The potential forms a binding well that is nearly triangular over its global displacement range but smooth and locally parabolic near its minimum. The variational approximation consequently predicts harmonic internal oscillations whose frequency is independent of amplitude in the small-oscillation regime. Real-time simulations verify this weak-kick behavior with good agreement between the variational and numerical frequencies. For strong phase imprints, equating the exact kick energy to the variational binding depth predicts a kick scale \(K_{\mathrm{escape}}\) for the onset of partial FTS escape. Real-time simulations support this prediction: below this scale, the composite remains nearly intact, whereas above it, a substantial fraction of the localized component leaves the bubble.

We consider the open XXZ spin chain with unparallel boundary fields, in the special case in which the Vertex-IRF transform of the K-matrix labelling the boundary field at site 1 is diagonal and invariant under the value of the gauge parameters, the other K-matrix being arbitrary. We discuss here several properties related to this special gauge invariant boundary condition. Such a model can be solved in the Vertex-IRF framework with arbitrary gauge parameters: we can diagonalise the transfer matrix by means of generalised Sklyanin's Separation of Variable (SoV) approach in a family of SoV bases that depend on two arbitrary gauge parameters $\alpha$ and $\beta$, $\beta$ being the so-called dynamical parameter and $\alpha$ an arbitrary shift of the spectral parameter. We show here that such SoV bases depend actually on $\alpha$ and $\beta$ through the difference $\alpha-\beta$ only. Considering the ungauged limit in which $\alpha-\beta$ tends to infinity, we show how to compute all elementary building blocks for the correlation functions of this model. We finally show how to compute overlaps between eigenstates of this model and eigenstates of a spin chain sharing the same boundary condition at site $N$ and in which the gauge invariant boundary condition at site 1 has been changed to a more general one.

We consider a reduced Lorenz-like model that describes two walking droplets interacting through their mutual wave field, and investigate the emergence of strong bipartite correlations in this classical wave-particle system. The coupled nonlinear dynamics admit two invariant synchronization manifolds associated with correlated and anticorrelated states, within which the droplets display synchronized chaotic intermittency. Employing measurement protocols inspired by Bell experiments, we compute position correlations from the long-time dynamics and identify parameter regimes for which the CHSH-Bell parameter $S$ exceeds 2, corresponding to violations of Bell's Inequality. We further introduce a procedure for isolating the two subsystems, thereby ensuring the absence of wave-mediated signaling between them. Changing measurement settings following this isolation allows us to execute dynamic Bell tests in which violations persist. Our results demonstrate that nonlinear deterministic dynamics can produce Bell violations through wave-mediated synchronization mechanisms; moreover, these violations may be rationalized on the grounds that the wave form is influenced by the measurement settings. We thus provide a consistent dynamical framework for the appearance of classical entanglement in pilot-wave systems.

We present a reduced-order semi-analytical model for reorientational nonlinearity in chiral nematic liquid crystals, showing that the chiral pitch acts as the dominant physical length scale governing the onset of nonlinear self-focusing and soliton formation. Starting from the full Frank-Oseen equation, we derive a closed-form expression for the optically induced molecular rotation that captures the essential saturable response of the medium while reducing computational cost by more than two orders of magnitude compared with standard relaxation-method solvers. Despite its simplicity, the model reproduces the essential features of the numerically obtained nonlinear refractive index, the onset of self-localization, and the transition from discrete to continuous solitons in one and two dimensions. It further predicts the formation of fully localized astigmatic nematicons with only minor shifts in the self-localization threshold due to the neglect of nonlocal effects. The proposed model provides direct physical insight into light-matter interactions with soft matter media and offers a computationally efficient tool for the design and optimization of nonlinear photonic devices.

We investigate the propagation of counter-rotating convection rolls in Rayleigh-Bénard convection initiated locally in a quiescent fluid layer under supercritical conditions. The velocity of the front separating quiescent fluid from the forming convection rolls, and the wavenumber of the convection rolls remaining behind the front, are explored. We numerically investigate fronts of forming convection rolls over five orders of magnitude of the reduced Rayleigh number, $\epsilon$, in 2D and 3D domains, for a broad range of boundary conditions, and for different front initiation approaches. In all cases, the front velocity increases as $\epsilon^{1/2}$ with increasing $\epsilon$ for $\epsilon \lesssim 1$ in agreement with predictions using the amplitude equation. The amplitude equation description of the front velocity remains accurate for $\epsilon \lesssim 10$ except when the Prandtl number is large which yields a velocity that is faster than predicted for a fluid layer far from threshold. The wavenumber of the convection rolls increases linearly with $\epsilon$ in agreement with the wavenumber that maximizes the growth rate of perturbations in the linear regime. Farther from onset, the wavenumber growth transitions to a reduced scaling of $\epsilon^{1/4}$ in agreement with predictions using the Swift-Hohenberg equation in the large $\epsilon$ limit. The scalings describing the wavenumber variation with $\epsilon$ are independent of the domain geometry, boundary conditions, and front initiation method. However, the front-selected wavenumber at criticality does not equal the critical wavenumber of the bulk instability, in general, and depends significantly upon these details. We compare our results with experimental measurements where possible.

We investigate the joint effects of stochastic forcing and quenched structural heterogeneity on stochastic resonance (SR) and liquid-state computation in a small-world network of excitable FitzHugh–Nagumo neurons. Heterogeneity is introduced separately through coupling strengths and time delays drawn from Gaussian, bimodal, and shifted-exponential distributions. Weak periodic forcing resolves the stochastic-resonance landscape, whereas weak aperiodic driving probes noise-assisted signal encoding and Liquid State Machine (LSM) forecasting. Heterogeneity is not generically beneficial, but reorganizes the resonance landscape and computational performance in a distribution-dependent manner. Gaussian coupling disorder broadens the strong-response region, whereas bimodal disorder produces a more pronounced enhancement and shifts resonance toward weaker noise. Shifted-exponential coupling disorder behaves differently: increasing its scale broadens and shifts the coupling distribution toward less responsive regions. Time-delay heterogeneity can enhance or suppress SR depending on how the delay distribution samples the structured delay-response landscape. Under aperiodic forcing, stronger input–output coherence accompanies lower LSM prediction error, showing that SR can improve LSM performance and that suitable coupling heterogeneity can further enhance this computational benefit; Gaussian and bimodal coupling disorder shift the optimum toward weaker noise and reduce the noise-optimized root-mean-square prediction error, with the largest reduction obtained for the bimodal case. These results identify stochastic forcing and quenched heterogeneity as coupled control parameters and show that the computational enhancement of LSMs depends on disorder structure rather than magnitude alone.

Conventional electrogastrography (EGG) analyses summarize gastric slow-wave activity using dominant frequency, power, or phase-based metrics, without explicitly modeling amplitude-dependent frequency dynamics. We developed a statistical nonlinear-dynamics framework that represents the gastric-band analytic EGG signal as a stochastic Stuart-Landau oscillator and estimate local effective phase-shear, $\beta_{\mathrm{eff}}$, a normalized measure of amplitude-frequency coupling. In overnight recordings from 60 healthy participants, effective phase-shear was consistently negative, generalized to held-out halves of each recording, and was abolished by amplitude surrogates that disrupted amplitude-phase alignment while preserving amplitude-series structure. We then applied the measure to fasted and fed recordings from 16 healthy participants and 24 participants with gastric dysfunction. Phase-shear magnitude differed between groups and classified dysfunction comparable to the strongest multielectrode phase-based traveling-wave measures. These findings establish amplitude-frequency coupling as a dynamical feature of gastric-band EGG that complements conventional spectral and spatial phase metrics, while motivating future multichannel observation models to determine its relationship to slow-wave propagation and gastric function.

In this paper we investigate the behavior of localized solutions, specifically solitons, in a system of three coupled waveguides. The nonlinearity is modeled by a quasi-periodic modulation influencing the interaction between the waveguides. We analyze the evolution of the soliton profiles and their dynamics under varying modulation parameters, highlighting distinct behaviors such as attraction and repulsion among solitons. Our findings reveal that the system exhibits complex behaviors, depending on the interplay between the quasi-periodic modulation and the waveguide parameters. The study contributes to understanding the impact of quasi-periodic nonlinearity on soliton dynamics in coupled waveguide systems, laying the groundwork for potential applications in nonlinear optics and photonic devices.

We study quantum dynamics through the lens of entanglement generation and characterize the underlying unitary evolution by the distinct signatures it imprints on the time-dependent entangling power. For a unitary operator, we characterize ergodicity by the equality between its long-time-averaged entangling power and the Haar-averaged linear entropy. We define mixing more stringently as the convergence of the time-dependent entangling power itself to the Haar value at long times. Within this framework, we establish the ergodic hierarchy of dynamical behavior, showing in particular that mixing implies ergodicity, whereas ergodicity does not necessarily imply mixing. As an application, we find that two-qubit unitary gates are neither ergodic nor mixing: their long-time-averaged entangling power can take only four discrete values, none of which coincides with the Haar average. We then investigate many-body dynamics using the kicked Ising chain and find that the long-time-averaged entangling power converges to the Haar value in both integrable and nonintegrable cases, indicating ergodicity. Remarkably, however, the nonintegrable chain exhibits mixing, whereas the integrable chain, despite being ergodic, is demonstrably nonmixing. We also introduce a Lyapunov-like exponent to characterize the rate at which the time-dependent entangling power approaches its saturation value. We find that this exponent increases systematically with the degree of integrability breaking in the many-body system. Our results establish entanglement generation as a useful framework for characterizing dynamical systems and reveal qualitatively different signatures of integrability beyond conventional diagnostics.

In this paper we study the dynamics and stability of localized solutions in a saturable nonlinear Schrödinger equation with space- and time-dependent variable coefficients. Using a variational approach and numerical simulations, we analyze the effects of different external potential configurations. Our results reveal that the stability of the solutions is highly sensitive to the modulation parameters, leading to the emergence of alternating stable and unstable regions as a function of the modulation frequency. These findings provide valuable insights into the control of localized structures in nonlinear wave systems, with potential implications for optical waveguides, Bose-Einstein condensates, and other nonlinear media.

Strict thermodynamic scaling relations, such as the Rushbrooke inequality, are fundamentally established for equilibrium critical phenomena in the thermodynamic limit. In finite-size dynamical systems exhibiting synchronization, the direct application of such identities is hindered both by the finiteness of the network and the nonequilibrium nature of the spontaneous synchronization transition. To bypass this difficulty, we rigorously study the dynamical counterparts of the order parameter, susceptibility, and specific heat in finite systems of dynamical oscillators with nonlinear coupling. By measuring these quantities as a function of system size, we extract the associated critical exponents governing the transition. The validity of our thermodynamic mapping is tested by directly confirming the Rushbrooke inequality. Our results establish that standard equilibrium thermodynamic scaling architectures can be systematically applied to the finite-size scaling of nonequilibrium synchronization dynamics.

Nonlinear dynamical systems manifest rich variety of dynamical states and transitions driven by fluctuations. To understand the pattern of fluctuations during dynamical transitions, we investigate the structural features of chaos to order transition in logistic map. We determine fluctuations as amplitude jumps and encode them onto a complex network where nodes represent amplitude levels and links represent transitions between distinct amplitude bins. We discover that global network measures identify points of period doubling, regimes of periodicity and chaos, including interior crises events. Using local network measures, we also unravel novel peculiar parabolic-shaped patterns in the orbit diagram that we show are reminiscent of the distribution of stable and unstable periodic points in the bifurcation diagram.

Periodic surface-wave forcing can reorganise turbulent flows through coherent spectral response, synchronization, intermittency, and changes in short-term predictability, so its dynamical effect need not vary monotonically with forcing frequency. We reanalyse laboratory acoustic Doppler velocimetry records obtained at constant discharge under four conditions (0, 0.5, 0.67, and 1~Hz) using one common KNN–GMAE forecast-error-growth protocol. A distance-weighted $k$-nearest-neighbour predictor generates out-of-sample forecasts over multiple horizons, and the slope of the early quasi-linear region of $\ln(\mathrm{GMAE})$ versus physical forecast time is reported as a finite-horizon forecast-error-growth rate, $\lFEG$. For the full 120-s records, $\lFEG$ is 5.68, 0.85, 3.39, and 4.11~s$^{-1}$ for 0, 0.5, 0.67, and 1~Hz, respectively. The ordering 0~Hz $>$ 1~Hz $>$ 0.67~Hz $>$ 0.5~Hz is preserved in all seven nearby parameter configurations, indicating that the comparative result is not an artefact of a single KNN setting. A 40-s sliding-window analysis with a 10-s step reveals substantial temporal structure. The no-wave condition remains predominantly high and the 0.5-Hz condition predominantly low, whereas the 1-Hz record has weaker local support for a single exponential-growth regime: only 3 of 9 windows satisfy the adopted early-fit criterion $\RFEG\geq0.90$, compared with 8/9, 7/9, and 7/9 for 0, 0.5, and 0.67~Hz.

The Trachenko-Zaccone equation provides a compact nonlinear dynamical framework for describing non-Debye relaxation in disordered condensed matter. Originally developed to rationalize stretched- and compressed-exponential relaxation in liquids and glasses from the dynamics of interacting local relaxation events, the same equation has subsequently appeared in broader contexts, including polymer relaxation and nonlinear models of global population dynamics. This review retraces the conceptual development of the equation, with particular emphasis on its physical origin in Kostya Trachenko's feed-forward interaction mechanism, its mathematical structure, and its possible generalizations. We also include personal recollections of the work with Kostya Trachenko at Queen Mary University of London in August 2019, during which the equation emerged in essentially its present form. After reviewing applications to stress relaxation, glassy materials, polymer relaxation and population dynamics, we discuss future directions including time-dependent feedback parameters, coupled order parameters, heterogeneous and spatially resolved formulations, flux terms, network versions and stochastic extensions. The central theme of the review is that the Trachenko-Zaccone equation should be viewed not only as a model of glassy relaxation, but as a general nonlinear feedback equation with potential applications across complex systems.

We construct representation-independent families of solutions of the non-braided scalene Yang–Baxter equation from quadratic noncommutative algebras. Beginning with two anticommuting generators, we obtain a continuous deformation in terms of quantum-plane algebras and extend the construction to an arbitrary number of generators. In the latter case the scalene Yang–Baxter relation fixes the multiparameter exchange matrix to an exact multiplicative form, thereby selecting a distinguished subclass of multiparameter quantum affine spaces. We construct finite-dimensional realizations using singular matrices and finite Heisenberg–Weyl operators, as well as infinite-dimensional realizations in terms of bilateral weighted shifts and multiplicative-shift operators. The explicit realizations are generically purely scalene: although the ordered triple satisfies the scalene Yang–Baxter equation, its individual constituent operators do not satisfy the ordinary non-braided Yang–Baxter equation. These results provide a representation-independent algebraic framework for constructing Yang–Baxter-irreducible scalene triples and a starting point for investigating their possible applications to quantum integrability.

Extreme events (EEs) in chaotic dynamics are rare broad excursions whose forecastability can be altered by dynamical noise. We investigate how noise changes EE occurrence and prediction skill across forecast horizons in a third-order autonomous chaotic flow. A single clean-data threshold is frozen for all realizations, broad events are defined by one maximum per excursion, and a future window W=15 is predicted from a 15-time-unit history using HistGradientBoosting with chronological data separation. As the forecast gap G between the observed history and the future event window increases, the clean Matthews correlation coefficient (MCC) decreases from 0.641 at G=0 to 0.165 at G=15. Noise dependence is evaluated with ten paired realizations at eight amplitudes. The mean short-horizon score increases from 0.456 in clean data to 0.546 at sigma=0.007; the paired gain is 0.0895 (95% CI 0.0494-0.1295; Holm-adjusted p=0.0234). Noise strongly increases EE occurrence while event amplitude and width remain comparatively stable. Equalizing positive training counts across noise levels substantially attenuates the short-horizon gain, whereas strong noise reduces intermediate-horizon skill. We term this horizon-dependent, nonuniform change in forecast skill noise-induced predictability redistribution (NIPR).

Granovetter's threshold model provides a classical framework for social mobilization, where collective action spreads through cascades as individuals join once movement size reaches their personal threshold. Here, we characterize social tipping points-the minimum seed required for global mobilization-using the initial fraction of instigators, $\rho_0$, as a control parameter. For a finite population of size $N$ with Beta-distributed thresholds $(\alpha, \beta)$, we present an exact analytical study of the cascade dynamics. By evaluating the asymptotic active fraction $\rho_\infty$, we map the thermodynamic phase diagram separating partial cascades ($\rho_0 \le \rho_\infty < 1$) from complete mobilization ($\rho_\infty = 1$), revealing continuous and discontinuous transition lines that meet seamlessly at a critical endpoint. For interior-peaked distributions ($\alpha > 1, \beta > 1$), the regimes are separated by a hybrid phase transition combining a first-order discontinuity with second-order bottleneck singularities. Combining exact finite-$N$ combinatorial formulations with large-deviation theory, we establish how finite-size fluctuations smooth these singularities. For power-law thresholds ($\alpha > 1, \beta = 1$), the critical scaling window shrinks as $N^{-1/3}$, while the expected inactive fraction vanishes as $N^{-1/3}$ at criticality. For interior-peaked distributions ($\beta > 1$), the order parameter is bimodally distributed: realizations either achieve full mobilization or stall near a bottleneck $\rho^*$. Excluding fully mobilized trajectories, $\rho^* - \langle \rho_\infty \rangle$ vanishes as $N^{-1/4}$ and the scaling window compresses to $N^{-1/2}$. Together, these results establish an exact finite-size scaling theory for threshold-driven tipping phenomena.

We propose a minimal adaptive network model with product-form coupling that reduces dimensionality while capturing key features of synaptic plasticity. The system spontaneously self-organizes into adaptive chimera states, where identical oscillators separate into synchronized and desynchronized groups through adaptive weight dynamics. These adaptive chimeras organize into branches with fixed coherent cluster fraction and exhibit transitions between stationary, breathing, and chaotic collective dynamics, revealing a collective bifurcation structure. Crucially, the resulting attractor landscape is highly multistable: repeated cluster reorganizations generate distinct dynamical pathways that coexist within the same parameter regime and depend sensitively on initial conditions.

In the article a new approach to construction of generalized coherent states in quantum billiards is proposed. The coherent states are defined as the projections of a Gaussian wave function on the basis of the eigenstates of the quantum billiard, continued outside. The continuation is built as the solution of the equivalent Balian–Bloch equation, defined on the entire $\mathbb{R}^2$ and the projection operator is built using the resolvent of the Balian–Bloch equation. In the case of the one–dimensional potential well and billiards, belonging to the Coxeter group, the wave functions of the coherent states were expressed analytically via the Jacobi and Riemann theta functions.

It is known that the attractive singular inverse-square potential gives rise to the critical quantum collapse in the framework of the three-dimensional (3D) linear Schroedinger equation. This article summarizes theoretical results which demonstrate suppression of the collapse, caused by this singular potential, and the creation of the otherwise missing ground state (GS) in a 3D gas of bosonic particles, carrying an electric dipole moment, which are pulled to the central electric charge, with repulsive contact interactions between the particles. In the mean-field approximation, the repulsive interactions are represented by the cubic term in the respective Gross-Pitaevskii (GP) equation. In addition to the GS, excited states with angular momentum are briefly considered too. Another topic considered in the article is 1D and 2D bound states in the linear Schroedinger and GP equations with the repulsive potential, which demonstrates a singularity at r –> infinity. A very recent result is that such a potential, growing faster than the negative harmonic-oscillator potential, produces a full spectrum of counter-intuitive normalizable (localized) bound states. The article puts forward perspectives for further studies of linear and nonlinear bound states existing under the action of the potentials with the singularity at r –> 0 or r –> infinity.

The intermediate-energy double pendulum is a prototypical chaotic system. Despite its irregular motion, it exhibits recurrent flips - events in which one of the arms passes over the top. We develop a statistical prediction for the mean flip rate in terms of phase space flux. Applying this flux-based approach to the equal-mass, equal arm ("egalitarian") double pendulum, we find excellent agreement between the statistical prediction and numerical simulations: ensemble-averaged flip rates agree at about the 1% level, while even the statistics of individual chaotic trajectories agree at the few-percent level, quantifying the validity of the ergodic approximation. This agreement holds for flips of either arm and over a broad range of energies. This flux-based approach is closely related to that used for the egalitarian three-body system. A central role is played by the saddle orbits: periodic orbits that tend to the stable saddle eigenmode as the energy approaches the saddle energy from above and approximately follow the ridge of the potential at higher energies. These orbits provide a natural dividing surface for defining flips while avoiding recrossings. Indeed, the resulting distribution of crossing times exhibits a distinct gap. We also present two alternative simplified dividing surfaces, one of which is based on an accurate analytic approximation to the saddle orbits.

We explore quantum Turing pattern zoology, where the same Lindblad equation supports a morphology atlas of stripes, spots, holes, labyrinths, and defects. The stable stripe species provides a quantitatively controlled case in which morphology and Gaussian witness loss separate parametrically. In particular, visible Turing stripes can remain after two Gaussian witness margins associated with the same $k_*$ mode cross zero in a completely positive Lindblad lattice. The witness thresholds on the exact shell fall as $\mathcal{N}^{-1}$. The stripe nematic threshold tends to a nonzero value at fixed lattice size, time window, and morphology criterion. The ratio of the morphology threshold to either witness threshold therefore grows with $\mathcal{N}$. Imaging and momentum-resolved covariance measurements probe these sectors separately.

Weather forecasting and climate projection frequently use multi-model ensembles (MMEs) to improve short-term forecasts by averaging across models. However, this practice is often not well justified or validated. Using reservoir computing (RC) as a computationally efficient alternative to large-scale physical models, we assess the validity of the MME approach for chaotic time series. By training multiple randomly constructed RCs on the same dataset, we create a multi-model ensemble in which each model has its own unique error. These model errors lead to very different forecasting performances, with forecast error distributions that exhibit heavy tails. The arithmetic mean across forecasts from multiple models for the same target is usually closer to the ground truth than most individual forecasts, and further improvement is achieved by weighted arithmetic means where the weights are constructed based on each model's test-set performance. We show that iterated forecasts over many time steps deviate from the ground truth along the unstable manifold of the target point, in both directions, so that, if forecast errors were independent and had zero mean, the arithmetic mean forecast should approach the true target like $1/\sqrt{\nens}$ where $\nens$ is the size of the multi-model ensemble. We observe deviations from this behavior, which we attribute to the tails of the error distribution of random RCs.

Reputation is widely recognized as a key mechanism for sustaining cooperation. However, most existing game-theoretic models treat reputation primarily as an external factor that modulates payoffs, interaction structures, or strategy update rules. In many social contexts, though, reputation operates primarily as information – it shapes how individuals interpret their own experiences and assess the behavior of others. To bridge this gap, we propose a spatial prisoner's dilemma game grounded in the reinforcement learning paradigm, in which agents equipped with Q-learning integrate both individual and social information via a locally defined reputation metric to guide their decisions. Our results reveal that reputation-modulated learning significantly promotes the emergence of cooperative behavior, and we observe a discontinuous phase transition from full cooperation to full defection as the temptation increases. Cooperation spreads through the nucleation of cooperative clusters, whereas the disintegration of these clusters drives the system into an absorbing state of complete defection. Overall, this study demonstrates that reputation facilitates cooperation not only by providing direct incentives but also by reshaping the social information landscape that agents rely on for learning and adaptation.

In this paper, we identify a new mechanism for rogue wave formation in a shallow-water setting. We study a bidirectional shallow-water wave field in the context of the Kaup-Boussinesq equation, and introduce a weak high-wavenumber dissipative perturbation that breaks the underlying integrability of the system. In this setting, dominant solitons grow through successive interactions with weaker, co-propagating solitons, leading to the formation of a "champion soliton" in each direction of propagation. This behaviour is in contrast to the general intuition that dissipation damps coherent structures, and instead shows that weak dissipation can induce their intensification. Moreover, we find that weak dissipation alone is not sufficient for champion soliton formation; the presence of random waves plays a crucial role in the intensification process, catalysing the transfer of energy into dominant coherent structures. While champion solitons have previously been studied in non-integrable systems, these works primarily consider perturbations introduced through modifications of the nonlinear terms (e.g., higher-order Korteweg-de Vries and Schrödinger-type models). In the present work, high-wavenumber dissipation provides a more physically natural perturbation, since such small-scale damping is a common feature in many systems.

Time-varying interaction delays are ubiquitous in active matter, yet their collective effects remain largely unexplored. We show that active particles with internal dynamics and Vicsek-like delayed alignment exhibit intermittent flocking, characterized by long episodes of coherent motion interrupted by brief disordering events. This collective behavior arises from laminar chaos, a form of chaotic dynamics unique to systems with time-varying delays. Changing only the delay parameters qualitatively reshapes collective motion, producing fractal changes in global flocking order. Our results establish the temporal structure of interaction delays as a new control parameter for active matter.

A weakly nonlinear regime of radial tunneling is theoretically considered for a light wave in a spherical dielectric Bragg resonator containing a set of “shell” eigenmodes (both TE and TM) with different azimuthal numbers $l\geqslant 1$, which are concentrated near a defect of the Bragg structure, several layers away from the origin. Also, a single mixed radial mode with $l=1$ is located near the resonator center, either TM or TE. Nonlinearity of Kerr type in the main approximation is actual for the central mode only, while all the shell modes remain in the linear regime. The tunneling occurs between the central mode and the shell $l=1$ mode of the same symmetry. Nontrivial part of the dynamics of optical field is described by a Hamiltonian system of ordinary differential equations for complex vectors ${\bf C}_{1}(t)$ and ${\bf C}_{2}(t)$, which determine the magnitude and spatial orientation of the wave structures at the center and at the shell, respectively. Depending on “asymmetry parameter” of tunnel coupling, the system demonstrates different variants of nonlinear behavior.

Dissipative chaos often exhibits abrupt transitions to periodic windows or vanishing states, but these transitions occur far below macroscopic theoretical boundaries such as the Melnikov threshold. In this study, we re-evaluate the transversal intersections (microscopic) of invariant manifolds from a deterministic and entropic perspective for the “Arnold tongues” shown by synchronization to forced inputs in the parameter space. We applied an algorithm that digitally determines manifold intersections as binary values ($1.0$ or $0.0$) without numerical interpolation. As a result of scanning the $\Omega - F$ parameter plane at a resolution of $5000 \times 5000$ ($25$ million points) with the damping coefficient fixed at $k = 0.2$, it became possible to globally capture the relationship between the macroscopic phase-locked regions shown by the Arnold tongues and the microscopic manifold intersections (chaotic regions). Furthermore, from a one-dimensional cross-section whose computational accuracy was verified, we confirmed a dynamical case where the region with homoclinic intersections (topological entropy $h_T > 0$) is a necessary condition for the region where chaos manifests (Kolmogorov-Sinai entropy $h_{KS} > 0$), and simultaneously confirmed the existence of a region where the intersection of the primary saddle solution does not serve as a necessary condition.

Paleoclimate archives extend climate knowledge beyond the instrumental era, registering different seasons, variables, time averages, and memory lengths. A longstanding problem is to integrate these heterogeneous sources of information within a unified methodology. Here we present a new data-assimilation framework, Last Millennium Reanalysis 4D-Var (LMR4D-Var), which reconstructs climate trajectories from these heterogeneous datasets while balancing errors in the model, observations, and initial conditions. We compare results using LMR4D-Var to assimilate proxies from PAGES2k, Temp12k, and borehole temperature profiles without treating them as instantaneous equivalents. Instrumental verification shows that LMR4D-Var achieves the highest skill compared with previous reconstructions. Borehole assimilation preserves skill against withheld annually resolved records, increases agreement between reconstructed 300–2000-m ocean heat content and independent estimates, and yields a cooler reconstructed Little Ice Age ocean. Results for Temp12k demonstrate assimilation of decadal-to-millennial records and the potential for Holocene and deeper-time applications with suitable emulators.

We define a map from solutions of the Bethe Ansatz equations (BAEs) of four-dimensional $\mathcal{N}=4$ super-Yang–Mills with arbitrary semisimple gauge algebra $\mathfrak{g}$ to extrema and poles of the potential of the untwisted elliptic Calogero–Moser system of type $\mathfrak{g}$. We conjecture the map to be a bijection on the preimage of the Calogero–Moser extrema, and show that it intertwines the symmetries of the two systems, both the gauge ones (torus, Weyl and center invariance) and a $\mathrm{PSL}(2,\mathbb{Z})$ action, so that solutions on both sides organize into orbits, each BAE orbit mapping onto a single orbit of Calogero–Moser extrema or poles. That the system produced is the untwisted one has a consequence: the conjectured correspondence between BAE solutions and vacua of the $\mathcal{N}=1^\ast$ deformation of $\mathcal{N}=4$ on $\mathbb{R}^{3,1}$, which are extrema of the twisted system, cannot extend to non-simply-laced $\mathfrak{g}$. It also fails within the simply-laced cases, though not for $\mathfrak{su}(N)$: we exhibit an $\mathfrak{so}(8)$ solution that flows to a pole of the Calogero–Moser potential rather than to an extremum, and so has no $\mathcal{N}=1^\ast$ counterpart. We illustrate the map in detail for every rank-two $\mathfrak{g}$, classical and exceptional alike, and use these cases as evidence for the conjecture.