Mahadev Sunil Kumar, Adarsh Ganesan
Parametrically driven oscillators provide a natural platform for neuromorphic computation, where nonlinear mode coupling and intrinsic dynamics enable both memory and high-dimensional transformation. Here, we investigate a two-mode system exhibiting 2:1 parametric resonance and demonstrate its operation as a reservoir computer across distinct dynamical regimes, including sub-threshold, parametric resonance, and frequency-comb states. By encoding input signals into the drive amplitude and sampling the resulting temporal and spectral responses, we perform one step-ahead prediction of benchmark chaotic systems, including Mackey-Glass, Rossler, and Lorenz dynamics. We find that optimal computational performance is achieved within the parametric resonance regime, where nonlinear interactions are activated while temporal coherence is preserved. In contrast, although frequency-comb states introduce increased spectral dimensionality, their performance is not consistently good across their existence band and also degrades in the chaotic comb regime due to loss of phase coherence. Mapping prediction error over parameter space reveals a direct correspondence between computational capability and the underlying bifurcation structure, with low-error regions aligned with the parametric resonance boundary. We further show that the input modulation, the detuning from the frequency matching condition, damping ratio, and input data rate systematically control the accessible dynamical regimes and thereby the computational performance. These results establish parametric resonance as a robust operating regime for oscillator-based reservoir computing and provide design principles for tuning physical systems toward optimal neuromorphic functionality.
Alena Kolesnikova, Ivan Pshenichnyuk, Andrey Gelash
Recent advances in manufacturing photonic integrated devices enable efficient coupling between high-Q microresonators in both linear and nonlinear regimes, creating a tunable, complex, hybridized optical system. Considering two coupled microresonators with normal and anomalous dispersion and equal free spectral range (FSR), we theoretically predict a novel nonlinear phenomenon: fully coherent hybridization of dissipative Kerr solitons (DKS) and propose a realistic integrated photonic design for its experimental observation. Using the Lugiato-Lefever equations in the supermode basis, we show that the emergent picture of inter-resonator DKS interactions can be understood as the formation of coherent structures in both supermodes generated by an unusual four-wave mixing process. The found hybridized DKS states can exhibit a broad, flat spectral profile near the pumped mode and remarkable oscillatory features in the spectral wings, promising broad applications in the generation and control of optical Kerr frequency combs.
Filipe Rodrigues da Silva, Azadeh Mohammadi
We present a non-Abelian model for magnetic monopoles in inhomogeneous media, based on a generalization of the standard 't~Hooft-Polyakov model. The medium is described by spatially dependent couplings in the gauge and scalar sectors, constrained by $P(|Φ|,r)M(|Φ|,r)=1$ so that the Bogomol'nyi-Prasad-Sommerfield (BPS) bound is preserved. For static spherically symmetric configurations, we study the first-order monopole equations for the class of generalized permeabilities $M(H,r)=f(r)/H^α$. For the power-law profile $f(r)=r^β$, we determine the domain in the $(α,β)$ plane where regular BPS solutions exist. On the line $α=1$, the system becomes exactly integrable, with closed-form monopole solutions in an inhomogeneous background. Away from this analytical sector, the solutions are constructed numerically. The model supports a rich spectrum of configurations, including effectively point-like monopoles, compact-core monopoles, hollow monopoles, shell-like structures, and multi-shell monopoles characterized by multiple concentric peaks in the energy density.
Ramdhan Wibawa, Birendra Jha
We report the first systematic evidence of hallucination in AI models of fluid dynamics, demonstrated in the canonical problem of hydrodynamically unstable transport known as viscous fingering. AI-based modeling of flow with instabilities remains challenging because rapidly evolving, multiscale fingering patterns are difficult to resolve accurately. We identify solutions that appear visually realistic yet are physically implausible, analogous to hallucinations in large language models. These hallucinations manifest as spurious fluid interfaces and reverse diffusion that violate conservation laws. We show that their origin lies in the spectral bias of AI models, which becomes dominant at high flow rates and viscosity contrasts. Guided by this insight, we introduce DeepFingers, a new framework for AI-driven fluid dynamics that enforces balanced learning across the full spectrum of spatial modes by combining the Fourier Neural Operator with a Deep Operator Network to predict the spatiotemporal evolution of viscous fingers. By conditioning on both time and viscosity contrast, DeepFingers learns mappings between successive concentration fields across regimes. The framework accurately captures tip splitting, finger merging, and channel formation while preserving global metrics of mixing. The results open a new research direction to investigate fundamental limitations in AI models of physical systems.
Fernando Carreño-Navas, Siannah Peñaranda, Renato Alvarez-Nodarse, Niurka R. Quintero
We derive an exact solitary wave solution for the $\PTb$-symmetric nonlinear Dirac equation with a scalar-scalar interaction. We consider a power-law nonlinearity of the form $|\barΨ\,Ψ|^{k}\,Ψ$ for positive values of $k$. The system's energy is conserved despite the presence of a gain-loss term, which is quantified by the parameter $Λ$. We show that the $\PTb$-transition point is defined by the solution's existence condition and is independent of the nonlinearity exponent $k$. Furthermore, momentum is conserved, although neither the canonical momentum nor the charge is a conserved quantity. A notable result is that the stationary solution, obtained from the continuity equations, exhibits nonzero momentum in its rest frame. We also derive a moving soliton solution, where the gain-loss parameter allows the soliton's velocity to be precisely chosen so that the moving soliton possesses zero momentum. Finally, we establish that the presence of a gain-loss mechanism and higher-order nonlinearity restrict the stability domain of the solutions.
Troy I. Johnson, Justin T. Cole
An outstanding challenge in the field of topological insulators is the realization of nonlinear systems that support coherent traveling waves. Highly nonlinear lattices can suffer from significant radiation losses due to Peierls-Nabarro effects. In this work a nonlinear tight-binding model that supports robust traveling edge states is proposed and examined. This system possess a nontrivial local Chern topology and soliton-like states. When a traveling solitary wave collides with a stationary mode, the two are observed to interact inelastically. These results suggest future directions for the modeling, realization, and application of nonlinear Chern insulators.
Rujiang Li, Muhammad Imran, Wencai Wang, Yongtao Jia, Ying Liu
The introduction of nonlinearities into lattices with topological band structures has led to the discovery of various types of solitons. The Su-Schrieffer-Heeger (SSH) lattice, as the most fundamental topological model, has been extended into the nonlinear regime. In particular, nonlinear edge states and bulk solitons exhibiting intensity humps against a zero background have been extensively studied in nonlinear SSH lattices. In this paper, we systematically investigate dark solitons in nonlinear SSH lattices. These dark solitons maintain a nonzero and constant background, featuring intensity dips either in the bulk of the lattice or at its edges, and residing spectrally in the semi-infinite gap or the middle finite gap. Regardless of the specific type of dark soliton, the intensity dip remains wellpreserved and is not affected by the band structure of the original linear lattice. Although the dark solitons we have identified are generally dynamically unstable across a broad range of parameters, several types exhibit linear stability when the intracell coupling is much larger than the intercell coupling. Our findings may provide valuable insights for the exploration of novel types of solitons in nonlinear topological lattices.
Neda Valizadeh, Robabeh Rahimi, Ramin Abolfath
{\bf Purpose}: To develop a geometry-governed diffusion framework that explains differential tissue response under FLASH ultra-high dose rate (UHDR) irradiation by explicitly accounting for structural heterogeneity and anomalous transport in biological tissues. {\bf Methods}: We formulate a generalized diffusion--reaction model on fractal substrates to describe molecular transport in heterogeneous media. Tissue architecture is characterized by a fractal (Hausdorff) dimension \(D\), while scale-dependent transport inefficiency and memory effects are captured by a fractional parameter \(θ\). Analytical solutions for radially symmetric geometries are derived and compared with classical normal (Euclidean) diffusion and a Gaussian reference model under identical physical conditions. Transport behavior is quantified through transient probability distributions and steady-state spatial profiles. {\bf Results}: The model reveals systematic suppression of long-range transport and enhanced localization as tissue structural complexity increases. Increasing \(θ\) leads to subdiffusive dynamics, reduced effective diffusion lengths, and persistent non-Gaussian concentration profiles, even in the steady state. While increasing \(D\) alone enhances spatial accessibility, fractional dynamics dominate transport behavior when \(θ>0\), counteracting geometric connectivity. These effects produce a separation between regimes characterized by efficient inter-track overlap and rapid homogenization, and regimes marked by isolated, long-lived reactive domains.
Gaoqing Meng, Mingshu Zhao
We demonstrate the existence of bright solitons in a repulsively interacting, harmonically trapped quasi-one-dimensional Bose-Einstein condensate described by the Gross-Pitaevskii equation. Using a neural-network quantum state (NNQS) approach, we parametrize the initial wavefunction and optimize it to find solutions that recur after one trap period, effectively balancing repulsion with trap-induced attraction. Aside from the bright solitonic solution, we also report double bright and dark soliton states. Perturbing the initial state with multiplicative phase and amplitude noise confirms that these periodic orbits are orbitally stable. Our results indicate that NNQS provides a powerful framework for uncovering coherent structures in nonlinear wave systems.
Yijun Lin, Adrian van Kan, Edgar Knobloch
We study large-scale dynamics in the Ginzburg-Landau equation (GLE) using a reduced description derived from a WKB expansion. Rigorous mathematical results establishing that this reduced equation accurately approximates the full GLE are currently limited to the real GLE (RGLE) and exclude phase-slip dynamics. For the RGLE, we find that the reduced equation has conserved gradient form and show that, upon inclusion of a higher-order regularization, it admits exact stationary solutions. In the reduced dynamics, all nonuniform steady states are linearly unstable and among them, localized hole solutions identified through the reduced description differ from the classical hole solution of the RGLE due to Langer and Ambegaokar. In the Eckhaus-unstable regime, we derive a self-similar description of the approach to finite-time singularities in the reduced equation, with scaling exponents that agree with direct numerical simulations (DNS), and a similarity profile obtained from a nonlinear 4th-order boundary value problem. Extending the reduction to the complex GLE (CGLE) with nearly real coefficients introduces a Burgers nonlinearity that generates traveling shocks connecting two distinct plane-waves. We obtain exact expressions for the shock profile and perform extensive DNS to demonstrate convergence to the predicted profile in the appropriate large-scale, nearly real-coefficient limit of the CGLE. Away from this limit, the wave number profile loses monotonicity, which we explain in the framework of spatial dynamics. We further show that the exact shock solutions found here are qualitatively distinct from the Nozaki-Bekki solutions. Taken together, our results reveal how a single, scalar reduced equation elucidates unstable stationary states, self-similar collapse toward phase slips, and shock formation, providing an understanding large-scale phase dynamics in pattern-forming systems.
Chang-Quan Zhou, Hua-Shu Dou, Lin Niu, Wen-Qian Xu
Simulations of the transitional flow in Taylor-Couette configuration are carried out to study the effect of the gap width on turbulent transition. The research results show that, under the same radius and the rotating speed of the inner cylinder, as the gap width increases, the flow becomes more stable. It is discovered that the average velocity distribution in the gap approaches the free vortex flow as the width increase and the stability of the flow is enhanced. It is found that, as the gap width increases, the maximum of the energy gradient function (from the energy gradient theory) in the gap decreases, which delays the turbulent transition. As such, the larger the gap width, the later the transition occurs. As the gap width increases, the Reynolds number based on the gap width alone is not able to characterize the flow behavior in Taylor-Couette flows, and the effect of the radius ratio should be taken into account.
Vjekoslav Vulić, Neven Šantić, Hrvoje Buljan, Damir Aumiler
The manipulation of light in periodic structures is fundamental to the development of discrete photonics and provides a versatile platform for controlling light propagation in integrated and quantum photonic systems. This work reports the experimental observation of discrete one-dimensional (1D) solitons in a photonic lattice, optically induced in warm rubidium vapor. The lattice is generated by the interference of two coupling laser fields intersecting at a small angle, which creates a spatially modulated 1D refractive index. When a probe beam is focused into a single lattice site, discrete diffraction is observed. By increasing the probe intensity, discrete solitons emerge as a result of the balance between discrete diffraction and self-focusing within the nonlinear atomic medium. Experimental results are supported by numerical simulations, in which the refractive index is modeled via optical Bloch equations for a multilevel atomic system driven by the coupling and probe fields in a $Λ$ configuration. These results, combined with the inherent controlability of gain and loss in atomic vapors, suggest that this platform provides a versatile foundation for exploring non-Hermitian nonlinear dynamics and parity-time-symmetric photonic lattices.
Francisco-Shu Kitaura
Apr 13, 2026·astro-ph.CO·PDF Complex structures often emerge from initially homogeneous or weakly correlated states. We address the apparent tension between this ordering and entropy growth through a unified framework combining semi-microscopic phase-space dynamics, transport geometry, information theory, and coarse-grained effective modeling. The key point is that entropy depends on the level of description: a coarse-grained spatial field may become more ordered as structure forms, even while the full phase-space description becomes more complex through shell crossing, multistreaming, and the activation of velocity degrees of freedom. Using a Lagrangian--Eulerian transport map, we show how density amplification is governed by the Jacobian of the deformation and how anisotropic collapse arises from the eigenvalues of a hierarchy of deformation tensors. Long-range interaction or information flow is encoded in the displacement field, so that nonlocality enters directly through transport. We connect this geometric description to a maximum-entropy Gaussian baseline and show how nonlinear transport and nonlocal coupling generate scale coupling, higher-order correlations, and non-Gaussianity. We then formulate a Landau--Ginzburg description in which the growth of seed anisotropies is interpreted as the activation of lower effective free-energy branches, providing a coarse-grained realization of self-organization. Applied to generated cosmological fields, this framework indicates that the nonlocal tidal level becomes relevant already at moderate overdensity. Although cosmological structure formation is the main realization considered here, the framework is intended more broadly as a mesoscopic language for systems in which transport, anisotropy, nonlocality, and self-organization are central.
Alok Yadav
The macroscopic dynamics of topological defects in magnetic materials are traditionally modeled using pairwise interactions. However, higher-order quantum exchange mechanisms - such as biquadratic and 4-spin ring exchange-play a critical role in strongly correlated systems. In this work, we introduce the "Simplicial Bridge," an exact analytical framework that maps these high-dimensional, non-linear Landau-Lifshitz partial differential equations onto generalized Kuramoto phase-oscillator networks operating on abstract simplicial complexes. We rigorously demonstrate that spatial overlap in the continuous limit natively generates higher-order topological forces without requiring a supportive discrete atomic lattice. Specifically, the overlap of 1D helimagnetic kinks generates 2-simplices (triadic forces), while the spatial compression of 2D skyrmion tails - governed by modified Bessel function asymptotics - generates true 3-simplices (tetradic forces). Furthermore, we establish that the higher-order spatial derivatives inherent to these multi-spin interactions provide an intrinsic energetic barrier that bypasses Derrick's Theorem, stabilizing 2D topological solitons without the strict need for Dzyaloshinskii-Moriya Interaction (DMI).
Noah Palmer, Heather L. Cihak, Daniele Avitabile, Zachary P. Kilpatrick
Apr 11, 2026·q-bio.NC·PDF Persistent neural activity underlying working memory requires sustained synaptic transmission, yet the metabolic and neurotransmitter support provided by astrocyte networks is largely absent from spatially extended neural circuit models. We introduce a coupled astrocyte-neural field model in which synaptic efficacy is regulated by depletion and recovery of a conserved resource pool recycled and spatially redistributed through diffusively coupled astrocytes. We obtain explicit stationary bump profiles and self-consistency conditions for bump width and amplitude on a canonical ring architecture. Linearizing about these solutions while carefully accounting for perturbations at bump boundaries, we analyze the resulting spectral problem governing stability. Our analysis, supported by numerical simulations and low-dimensional Fourier truncations, reveals a two-stage stabilization mechanism: astrocytic diffusion smooths resource asymmetries created by small bump displacements, and synaptic replenishment transfers this smoothing back to the synaptic pool. Together, sufficiently strong diffusion and replenishment suppress drift instabilities and enlarge the parameter regime in which stationary bumps persist.
M. Ahumada, J. F. Marín
We demonstrate a thermodynamic engine whose working substance is a sine-Gordon soliton in a heterogeneous current-driven Josephson junction. We show that solitons can act as thermodynamic working substances whose internal spectral structure enables energy conversion beyond conventional few-level engines. By dynamically deforming the soliton using a controllable dipole current, the internal bound-state spectrum of the soliton can be engineered in time, enabling a finite-time Carnot-like cycle based on spectral control, in close analogy with quantum heat engines. Mapping the instantaneous nonlinear field configuration to an effective Schrödinger operator, we reveal how bound states appear, approach the continuum threshold, and disappear during the cycle. Comparing three thermodynamic descriptions (full nonlinear field dynamics, a coarse-grained mesoscopic model, and a two-level spectral model), we show that few-level descriptions systematically underestimate the engine performance. The enhanced efficiency arises from the extended nature of the soliton, whose internal spectral degrees of freedom provide additional energy storage and transfer channels. Our results reveal a general thermodynamic principle: extended nonlinear excitations with particle-like behavior can serve as tunable working media, whose internal spectral degrees of freedom provide additional reversible channels for energy storage and transfer beyond those of few-level systems.
Bastian Hilder, Jonas Jansen
We rigorously prove the bifurcation of slow-moving pattern interfaces with general direction in a two-dimensional Swift-Hohenberg-type model close to a Turing instability for a large class of nonlinearities. These interfaces describe the invasion of stripe and hexagonal patterns into the spatially homogeneous state and model a possible mechanism for pattern formation, as observed in a wide range of real-world applications. For this, we develop a rigorous framework to establish the existence of such solutions using spatial dynamics and non-standard centre manifold theory. Our approach exploits geometric and algebraic structures generic to $\mathrm{O}(2)$-symmetric pattern-forming systems near a Turing instability, and addresses fundamental technical challenges due to a non-uniform spectral gap around the imaginary axis, quadratic resonances induced by the hexagonal structure, and the high-dimensional phase space of the reduced equations.
Sara Ameli
Accurate segmentation of surgical instruments in robotic-assisted surgery is critical for enabling context-aware computer-assisted interventions, such as tool tracking, workflow analysis, and autonomous decision-making. In this study, we benchmark five deep learning architectures-UNet, UNet, DeepLabV3, Attention UNet, and SegFormer on the SAR-RARP50 dataset for multi-class semantic segmentation of surgical instruments in real-world radical prostatectomy videos. The models are trained with a compound loss function combining Cross Entropy and Dice loss to address class imbalance and capture fine object boundaries. Our experiments reveal that while convolutional models such as UNet and Attention UNet provide strong baseline performance, DeepLabV3 achieves results comparable to SegFormer, demonstrating the effectiveness of atrous convolution and multi-scale context aggregation in capturing complex surgical scenes. Transformer-based architectures like SegFormer further enhance global contextual understanding, leading to improved generalization across varying instrument appearances and surgical conditions. This work provides a comprehensive comparison and practical insights for selecting segmentation models in surgical AI applications, highlighting the trade-offs between convolutional and transformer-based approaches.
Sathyanarayanan Chandramouli, Patrick Sprenger, Mark A. Hoefer
Stationary solutions asymptoting to nonlinear plane waves of the nonlinear Schrödinger equation with a PT-symmetric, complex linear potential are characterized. The potential includes both a spatially varying gain-loss profile and a repulsive real part, generated by a Wadati potential function,that support the existence of homoclinic and heteroclinic solutions that asymptote to the same or different, respectively, nonlinear plane waves in the far field. Asymptotic analysis and numerical simulations are used to examine solution existence, bifurcations, and structure. Such solutions play an important role in resonant nonlinear wave generation of dispersive media with localized gain and loss.
Yoshiyuki Y. Yamaguchi, Julien Barré
The Comment criticizes the bifurcation analysis performed in the original paper on a Vlasov equation. This criticism can be traced back to a discrepancy in the definition of the paramagnetic phase. Apart from this discrepancy, there is no conflict between the Comment and the original paper.