Clay weekly context brief for the Nonlinear Sciences category (ISO week 2026-W43).

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. Letter of Intent for Alpha Knockout from Nuclei in Hard Exclusive Processes with ALERT
   Source: nucl-ex (Nuclear Experiment)
   Link: https://arxiv.org/abs/2610.16218
   We propose to measure hard exclusive $\alpha$-knockout reactions from the light $\alpha$-conjugate nuclei $^{12}$C, $^{16}$O, and $^{20}$Ne using electron scattering.
2. Effective shear viscosity from the friction term in relativistic multi-fluid hydrodynamics
   Source: nucl-th (Nuclear Theory)
   Link: https://arxiv.org/abs/2610.20872
   Within a three-fluid description of heavy-ion collisions, we investigate how nuclear friction can be used to model shear stress.
3. Collision Dynamics of False-Vacuum Oscillons
   Source: nlin.PS (Pattern Formation and Solitons)
   Link: https://arxiv.org/abs/2605.12633
   We study the collision dynamics of localized oscillons in two classes of $(1+1)$-dimensional scalar field theories with metastable false vacua, a normal class with a positive quartic self-interaction term and an inverted class with a negative quartic term.
4. Resonant interactions in the $\alpha$-FPUT lattice with site-dependent coefficients
   Source: nlin.CD (Chaotic Dynamics)
   Link: https://arxiv.org/abs/2605.24268
   The wave turbulence framework has proven to be an effective tool for analyzing certain features of nonlinear energy transfer in one-dimensional nonlinear chains.
5. A vectorial Darboux transformation for integrable matrix versions of the Fokas-Lenells equation
   Source: nlin.SI (Exactly Solvable and Integrable Systems)
   Link: https://arxiv.org/abs/2508.17534
   Using bidifferential calculus, we derive a vectorial binary Darboux transformation for an integrable matrix version of the first negative flow of the Kaup-Newell hierarchy.
6. Idempotence criteria for lazy cellular automata
   Source: nlin.CG (Cellular Automata and Lattice Gases)
   Link: https://arxiv.org/abs/2610.11811
   A lazy cellular automaton $\tau:A^G\to A^G$ is determined by a finite neighborhood $S\subseteq G$ containing the group identity $e$, a pattern $p\in A^S$, and a writing symbol $a\in A\setminus\{p(e)\}$: its local rule is equal to the projection to $e$ except when it reads the pattern $p$, in which case it writes $a$.
7. Breathing chimera states from purely triadic interactions
   Source: nlin.AO (Adaptation and Self-Organizing Systems)
   Link: https://arxiv.org/abs/2607.28017
   Chimera states, characterized by the coexistence of synchronized and desynchronized dynamics in identical oscillators, are typically studied in systems with pairwise interactions.
8. Radiative corrections to the parity-violating spin asymmetry
   Source: nucl-ex (Nuclear Experiment)
   Link: https://arxiv.org/abs/2507.15380
   The parity-violating spin asymmetry Apv for elastic electron scattering from spin-zero nuclei, together with its QED corrections, is evaluated non-perturbatively within the phase-shift analysis.
9. Algebraic coefficients of fractional parentage for three particles in the oscillator Jacobi basis
   Source: nucl-th (Nuclear Theory)
   Link: https://arxiv.org/abs/2610.21385
   We present a closed-form construction of the orbital coefficients of fractional parentage (CFP) of three identical particles in the translationally invariant harmonic oscillator (HO) Jacobi basis.
10. Minimum nonlinearity for pattern-forming Turing instability in a mathematical autocatalytic model
   Source: nlin.PS (Pattern Formation and Solitons)
   Link: https://arxiv.org/abs/2412.13783
   Pattern formation is ubiquitous in nature and the mechanism widely-accepted to underlay them is based on the Turing instability, predicted by Alan Turing decades ago.
11. Is Flow Matching Just Trajectory Replay for Sequential Data?
   Source: nlin.CD (Chaotic Dynamics)
   Link: https://arxiv.org/abs/2602.08318
   Flow matching (FM) is increasingly used in scientific domains for time series generation and forecasting, where data often arise from underlying dynamical systems.
12. Topological recursion for spin enumeration of hypermaps
   Source: nlin.SI (Exactly Solvable and Integrable Systems)
   Link: https://arxiv.org/abs/2610.20464
   We establish topological recursion for the spin enumeration of hypermaps, or, in the dual language, spin dessins d'enfants.
13. Frobenius Revivals in Laplacian Cellular Automata: Replication, Entropy, and Information Recovery
   Source: nlin.CG (Cellular Automata and Lattice Gases)
   Link: https://arxiv.org/abs/2511.17389
   We investigate Frobenius revivals in prime-modulus Laplacian cellular automata.
14. Network Reconstruction in Consensus Algorithms with Hidden Agents
   Source: nlin.AO (Adaptation and Self-Organizing Systems)
   Link: https://arxiv.org/abs/2604.05709
   Reconstructing the parameters that encode the influence between model variables based on time-series measurements represents an outstanding question in the theory of complex network-coupled systems.
15. State-resolved quantum-information fingerprints of partial dynamical symmetry in the interacting boson model
   Source: nucl-ex (Nuclear Experiment)
   Link: https://arxiv.org/abs/2608.04486
   Partial dynamical symmetry (PDS) is an algebraic structure in which a symmetry is neither exact nor fully broken: a subset of eigenstates keeps good quantum numbers and stays solvable while the rest mix.
16. $^6$He structure from semiclassical 3D models based on $\textit{ab initio}$ spatial correlations
   Source: nucl-th (Nuclear Theory)
   Link: https://arxiv.org/abs/2610.22365
   We construct semiclassical 3D models based on $\textit{ab initio}$ no-core shell model calculated two-body spatial correlations, which represent the preferred spatial configuration of nucleons for the ground state of $^6$He.
17. Cone Invariance and Homoclinic Standing Waves for Cooperative Finite-Range DNLS Equations
   Source: nlin.PS (Pattern Formation and Solitons)
   Link: https://arxiv.org/abs/2610.22166
   We develop a constrained-power variational framework for positive homoclinic standing waves in one-dimensional discrete nonlinear Schr\"odinger equations with cooperative finite-range interactions.
18. When is a System Discoverable from Data? Discovery Requires Chaos
   Source: nlin.CD (Chaotic Dynamics)
   Link: https://arxiv.org/abs/2511.08860
   The deep learning revolution has enabled major AI advances in physical sciences, particularly in discovering dynamical systems from observational data.
19. Quantized six-vertex realizations of frustration graphs
   Source: nlin.SI (Exactly Solvable and Integrable Systems)
   Link: https://arxiv.org/abs/2610.20166
   A recent graph-theoretic criterion for a Hamiltonian to exhibit a free-parafermion spectrum is that its frustration graph be an indifference graph.
20. When do lazy and invertible cellular automata generate all cellular automata?
   Source: nlin.CG (Cellular Automata and Lattice Gases)
   Link: https://arxiv.org/abs/2610.18480
   Let $G$ be a group and let $A$ be a set with at least two elements.
21. Interaction order controls stochastic-resonance enhancement and redistribution in delayed multiplex neural networks
   Source: nlin.AO (Adaptation and Self-Organizing Systems)
   Link: https://arxiv.org/abs/2608.15421
   We investigate stochastic resonance in a hierarchy of delayed excitable systems, from a single FitzHugh--Nagumo neuron to single-layer and duplex networks with autaptic, pairwise, triadic higher-order, and interlayer interactions.
22. Pion emission source shape in UrQMD Au + Au collisions at STAR energies
   Source: nucl-ex (Nuclear Experiment)
   Link: https://arxiv.org/abs/2605.15717
   Femtoscopic measurements of two-pion Bose--Einstein correlations have established that particle-emitting sources in heavy-ion collisions are well described by L\'evy $\alpha$-stable distributions, motivating systematic studies across a wide range of collision energies.
23. Inclusive breakup of three-body projectiles: A unified four-body framework for pair-detection and single-particle observables
   Source: nucl-th (Nuclear Theory)
   Link: https://arxiv.org/abs/2605.03342
   Inclusive breakup measurements detect only part of a projectile while the remaining fragments interact with the target.
24. Real-time identification of the onset of financial rogue waves
   Source: nlin.PS (Pattern Formation and Solitons)
   Link: https://arxiv.org/abs/2606.31475
   Extreme events in financial systems, often captured by indicators such as volatility, remain difficult to identify close to their onset.
25. Intrinsic instantaneous coarse-to-fine recoverability in multiscale chaos: The Lorenz-96 system
   Source: nlin.CD (Chaotic Dynamics)
   Link: https://arxiv.org/abs/2607.08323
   In multiscale chaotic systems, a central question for closure is how much of an unresolved fine-scale target can be inferred from a simultaneous coarse observation.
26. The WKB Riemann-Hilbert Problem for the Painlev\'e I System
   Source: nlin.SI (Exactly Solvable and Integrable Systems)
   Link: https://arxiv.org/abs/2610.20123
   In this paper, we solve the direct monodromy problem for the Borel-summed $0$-parameter solution of Painlev\'e~I.
27. Geometry-Controlled Initial-Density Dependence in Branching-Merging Exclusion Processes
   Source: nlin.CG (Cellular Automata and Lattice Gases)
   Link: https://arxiv.org/abs/2610.15333
   We study geometry-controlled, initial-density-dependent stationary states in exclusion processes with branching-merging structures.
28. Overcoming unfairness via repeated interactions in mini-ultimatum game
   Source: nlin.AO (Adaptation and Self-Organizing Systems)
   Link: https://arxiv.org/abs/2604.03625
   Repeated interactions are ubiquitous and known to promote social behaviour.
29. Experimental Review on Bulk Properties and Light/Strange Hadron Production in Heavy-Ion Collisions
   Source: nucl-ex (Nuclear Experiment)
   Link: https://arxiv.org/abs/2607.11640
   This proceedings article reviews recent experimental results on bulk properties and light/strange hadron production in heavy-ion collisions, presented at the Strangeness in Quark Matter 2026 conference.
30. Representation dependence of the neutron-proton kinetic energy in adiabatic deuteron stripping
   Source: nucl-th (Nuclear Theory)
   Link: https://arxiv.org/abs/2610.16472
   Deuteron stripping reactions such as (d,p) are a main tool for studying the single-particle structure of nuclei, and they are usually analyzed with the adiabatic distorted-wave approximation (ADWA).
31. Neuromorphic Computing Based on Parametrically-Driven Oscillators and Frequency Combs
   Source: nlin.PS (Pattern Formation and Solitons)
   Link: https://arxiv.org/abs/2604.21861
   Parametrically driven oscillators exhibit distinct dynamical regimes that strongly influence their computational capability as physical reservoirs.
32. The Physics Is the Network: Fast, Training-Free Neural Emulation
   Source: nlin.CD (Chaotic Dynamics)
   Link: https://arxiv.org/abs/2610.20525
   Neural emulation need not require learning a substitute for known physics.

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 426 available items for this weekly brief.