Clay weekly context brief for the Nonlinear Sciences category (ISO week 2026-W39).

Clay tracks publications from the Nonlinear Sciences feed list. Below are recent items from this category, each with its source and a short description of what the publication covers when one is available in the source feed.

Recent publications:
1. Wake interactions drive synchronized vortex merging in a hovering quadcopter
   Source: nlin.AO (Adaptation and Self-Organizing Systems)
   Link: https://arxiv.org/abs/2609.19507
   The most energetic coherent structure of a hovering full-scale quadcopter is associated with a self-organizing process in which the individual rotor vortices synchronize their frequencies while undergoing merging events, yielding a globally correlated structure.
2. Binning-Independent Bayesian Analysis of Time-Dependent Perturbed Angular Distribution data
   Source: nucl-ex (Nuclear Experiment)
   Link: https://arxiv.org/abs/2609.19227
   We propose a new approach for analyzing Time-Dependent Perturbed Angular Distribution data.
3. Long-Lived False-vacuum-Trapped Self-Bound Neutron-rich Droplets
   Source: nucl-th (Nuclear Theory)
   Link: https://arxiv.org/abs/2609.19433
   We propose a novel class of anomalous nuclear matter: self-bound, neutron-rich droplets trapped in false vacuum associated with the nuclear liquid-gas phase transition in heavy-ion collisions.
4. Provable quantum thermalization without statistical averages
   Source: nlin.CD (Chaotic Dynamics)
   Link: https://arxiv.org/abs/2604.02417
   We develop a rigorous system-agnostic method to predict quantum thermalization in an overwhelming fraction of accessible pure states in a many-body system, entirely in terms of certain out-of-time-ordered correlators of few-body observables.
5. Deformations of (2+1)-dimensional integrable systems and isotropic and anisotropic Harry Dym variants
   Source: nlin.SI (Exactly Solvable and Integrable Systems)
   Link: https://arxiv.org/abs/2608.01293
   The deformation algorithm based on conservation laws can lift (1+1)-dimensional integrable systems to higher-dimensional counterparts while preserving Lax integrability, yet its generalization to (2+1)-dimensional models has remained an open problem.
6. Trees that can be grown in "too many" ways: Bouch's construction and a bound for every size
   Source: nlin.PS (Pattern Formation and Solitons)
   Link: https://arxiv.org/abs/2412.16912
   We show that, for every positive integer $L$, there is a rooted tree on the square lattice that can be grown in at least $L!/C^L$ distinct ways, where $L$ denotes the number of bonds and $C>1$ is a constant independent of $L$.
7. Collision-based logic in Lenia and its composition boundary
   Source: nlin.CG (Cellular Automata and Lattice Gases)
   Link: https://arxiv.org/abs/2609.01348
   Continuous cellular automata such as Lenia spontaneously produce lifelike, self-propelling patterns, including the Orbium glider, which travels in a straight line while pulsing through a fixed breathing cycle.
8. The dynamics of early transoceanic voyages: A resource-coupled model of crew health and survival
   Source: nlin.AO (Adaptation and Self-Organizing Systems)
   Link: https://arxiv.org/abs/2609.20430
   The great transoceanic voyages of the Age of Discovery imposed severe human costs on their crews.
9. Three-State Mixing as a Phenomenological Framework for Multiple Shape Coexistence
   Source: nucl-ex (Nuclear Experiment)
   Link: https://arxiv.org/abs/2609.19300
   Shape coexistence represents one of the most striking manifestations of competing collective and single-particle degrees of freedom in atomic nuclei.
10. Interpretable hybrid nuclear mass prediction based on term-by-term model discrepancies
   Source: nucl-th (Nuclear Theory)
   Link: https://arxiv.org/abs/2609.19578
   Various theoretical mass models have consistently achieved impressive accuracy in reproducing experimental masses.
11. Experimental detection of energy transfer into the antiphase mode in a branched double pendulum
   Source: nlin.CD (Chaotic Dynamics)
   Link: https://arxiv.org/abs/2609.20688
   Multiple pendulum with branching is proposed as a convenient platform to study energy transfer between different modes.
12. Lax Pairs: Integrable, Less Integrable and Nonintegrable Systems
   Source: nlin.SI (Exactly Solvable and Integrable Systems)
   Link: https://arxiv.org/abs/2603.09224
   Completely integrable finite dimensional Hamiltonian systems are well understood thanks to the work of Liouville and Arnold.
13. Polychromatic Localized Waves with Complex Frequencies in Nonlinear Maxwell Equations with Material Dispersion
   Source: nlin.PS (Pattern Formation and Solitons)
   Link: https://arxiv.org/abs/2511.21467
   We study the existence of polychromatic solutions of cubically nonlinear Maxwell equations in the whole space and with dispersive media, i.e., with a time delayed polarization.
14. Squeezing codes: robust fluctuation-stabilized memories
   Source: nlin.CG (Cellular Automata and Lattice Gases)
   Link: https://arxiv.org/abs/2509.20730
   We introduce families of classical stochastic dynamics in two and higher dimensions which stabilize order in the absence of any symmetry.
15. Fragmentation and Cluster Prediction in One-Dimensional Finite-Range Normalized Alignment Dynamics
   Source: nlin.AO (Adaptation and Self-Organizing Systems)
   Link: https://arxiv.org/abs/2609.07992
   State-dependent networks couple relaxation to the motion that changes the interaction topology.
16. Gaussian characterization of two-neutron halo nuclei
   Source: nucl-ex (Nuclear Experiment)
   Link: https://arxiv.org/abs/2609.19997
   The halo nucleon-core system is, by definition, a shallow state nucleus.
17. Bayesian calibration of a regional optical potential and uncertainty-quantified predictions for compound nucleus reactions
   Source: nucl-th (Nuclear Theory)
   Link: https://arxiv.org/abs/2609.20120
   Uncertainty-quantified global optical potential parameterizations are useful for making systematic studies across the nuclear chart and making predictions away from stability.
18. Quantum Chaos Diagnostics for non-Hermitian Systems from Bi-Lanczos Krylov Dynamics
   Source: nlin.CD (Chaotic Dynamics)
   Link: https://arxiv.org/abs/2508.13956
   In Hermitian systems, Krylov complexity has emerged as a powerful diagnostic of quantum dynamics, capable of distinguishing chaotic from integrable phases, in agreement with established probes such as spectral statistics and out-of-time-order correlators.
19. Machine Learning of Nonlinear Waves: Data-Driven Methods for Computer-Assisted Discovery of Equations, Symmetries, Conservation Laws, and Integrability
   Source: nlin.SI (Exactly Solvable and Integrable Systems)
   Link: https://arxiv.org/abs/2510.15069
   The purpose of this article is to provide a perspective---admittedly, a rather subjective one---of recent developments at the interface of machine learning (ML)/data-driven methods and nonlinear wave studies.
20. Long interfacial internal waves with currents: current profiles with quadratic depth-dependence
   Source: nlin.PS (Pattern Formation and Solitons)
   Link: https://arxiv.org/abs/2609.10820
   Internal waves often propagate in the presence of currents.
21. Inferring Coupling Strength from the Kuramoto Order Parameter
   Source: nlin.AO (Adaptation and Self-Organizing Systems)
   Link: https://arxiv.org/abs/2607.28046
   Accurately estimating the coupling strength in oscillator networks from macroscopic observations is essential for predicting synchronization transitions.
22. A comprehensive theory framework for perturbative calculations of $\delta_C$ in superallowed beta decays
   Source: nucl-ex (Nuclear Experiment)
   Link: https://arxiv.org/abs/2609.20448
   The present high precision determination of $|V_{ud}|$ from superallowed beta decays of $J^P=0^+$, $T=1$ nuclei is largely built on top of the ``standard'' calculation of the isospin breaking correction $\delta_C$ to the Fermi matrix element, which assumes the splitting $\delta_C=\delta_{C1}+\delta_{C2}$, where $\delta_{C1}$ and $\delta_{C2}$ represent the ``isospin mixing'' correction and the ``radial mismatch'' correction, respectively.
23. Probing Forward-Backward Multiplicity Correlations and Fluctuations Using the Strongly Intensive Observable $\Sigma$ in Pb-Pb Collisions at SPS Energies with
   Source: nucl-th (Nuclear Theory)
   Link: https://arxiv.org/abs/2609.20246
   The strongly intensive observable $\Sigma$, constructed from charged-pion multiplicities in separated forward (F) and backward (B) pseudorapidity intervals $\Delta\eta$, is studied within the UrQMD transport model for Pb--Pb collisions at SPS energies.
24. Quantum Chaos and Spread of States in Krylov Subspace: A Topical Review
   Source: nlin.CD (Chaotic Dynamics)
   Link: https://arxiv.org/abs/2608.26825
   Krylov state complexity, or spread complexity, has emerged as a sharp and versatile diagnostic of quantum chaos, information spreading, and many-body dynamics.
25. On the geometry of WDVV equations and their Hamiltonian formalism in arbitrary dimension
   Source: nlin.SI (Exactly Solvable and Integrable Systems)
   Link: https://arxiv.org/abs/2509.13757
   It is known that in low dimensions WDVV equations can be rewritten as commuting quasilinear bi-Hamiltonian systems.
26. Stable vortex soliton arrays in disclination-fractal systems
   Source: nlin.PS (Pattern Formation and Solitons)
   Link: https://arxiv.org/abs/2609.09825
   Vortex light fields carry orbital angular momentum and have attracted significant attention because of their wide applications in light field manipulations, optical communications, and quantum information processing.
27. Synchronization with Annealed Disorder and Higher-Harmonic Interactions in Arbitrary Dimensions: When Two Dimensions Are Special
   Source: nlin.AO (Adaptation and Self-Organizing Systems)
   Link: https://arxiv.org/abs/2601.10646
   The impact of disorder on collective phenomena depends crucially on whether it is quenched or annealed.
28. Measurements of $\gamma_v p \to \pi^+ \pi^- p'$ Cross Sections with the CLAS Detector for $Q^{2}$ from 2.0--5.0~GeV$^{2}$ and $W$ from 1.400--2.125~GeV
   Source: nucl-ex (Nuclear Experiment)
   Link: https://arxiv.org/abs/2607.06793
   Observables in the electroproduction of the $\pi^+\pi^-p$ reaction channel off the proton that are sensitive to the polarization of the virtual photon are presented for the first time in addition to the extraction of the nine single-differential and fully integrated cross sections within the kinematics area of 2.
29. Parametric Neural Quantum States for Nuclear Physics
   Source: nucl-th (Nuclear Theory)
   Link: https://arxiv.org/abs/2609.20799
   We introduce a new approach, based on neural quantum states (NQSs), to rapidly compute nuclear observables when couplings in nuclear Hamiltonians are varied.
30. Local relaxation and scale-dependent alignment in compressible, magnetized turbulence
   Source: nlin.CD (Chaotic Dynamics)
   Link: https://arxiv.org/abs/2504.15538
   Driven net- and no-net-flux MHD turbulence simulations up to $10,\!368^3$ reveal sign-mixed velocity--magnetic, velocity--vorticity, and magnetic--current aligned patches below the energy equipartition scale.
31. On the commuting charges and the Bethe ansatz for the quantised Kadomtsev-Petviashvili equation
   Source: nlin.SI (Exactly Solvable and Integrable Systems)
   Link: https://arxiv.org/abs/2609.15316
   We study the quantised version of the Kadomtsev-Petviashvili equation in the formulation proposed in [4].
32. Optical creation of dark-bright soliton lattices in one-dimensional multicomponent Bose-Einstein condensates
   Source: nlin.PS (Pattern Formation and Solitons)
   Link: https://arxiv.org/abs/2603.28876
   We present a widely accessible and experimentally realizable technique for the controlled creation of dark-bright solitons and soliton lattices in one-dimensional atomic Bose-Einstein condensates.

Sources in this brief: nlin.AO (Adaptation and Self-Organizing Systems); nlin.CD (Chaotic Dynamics); nlin.CG (Cellular Automata and Lattice Gases); nlin.PS (Pattern Formation and Solitons); nlin.SI (Exactly Solvable and Integrable Systems); nucl-ex (Nuclear Experiment); nucl-th (Nuclear Theory).
Selected 32 of 474 available items for this weekly brief.