Clay weekly context brief for the Nonlinear Sciences category (ISO week 2026-W40). 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. Chiral anomaly and nucleon spin decomposition in the chiral quark soliton model Source: nucl-th (Nuclear Theory) Link: https://arxiv.org/abs/2609.25867 We investigate how the chiral anomaly influences the decomposition of nucleon spin between quark spin and orbital motion. 2. Femtoscopy Measurement with S$\pi$RIT TPC in Radioactive BeamHeavy-ion Collisions Source: nucl-ex (Nuclear Experiment) Link: https://arxiv.org/abs/2607.24815 Femtoscopy is a powerful tool for exploring the dynamic emitting structure in heavy-ion collisions, while radioactive beam heavy-ion collisions enable the investigation of nuclear matter under extreme isospin conditions. 3. Tsunami Solitons Emerging from Superconducting Gap Source: nlin.SI (Exactly Solvable and Integrable Systems) Link: https://arxiv.org/abs/2508.18311 We propose a classical integrable system exhibiting tsunami-like solitons with a rocky-desert-like disordered stationary background. 4. When is logistic error growth a spectral reduction? Source: nlin.CD (Chaotic Dynamics) Link: https://arxiv.org/abs/2608.26492 Forecast-error growth has been studied through complementary approaches: scalar models describe the evolution of bulk error, whereas spectral theories follow decorrelation and error transfer across scales. 5. A nonlinear theory for chemotactic fronts of mixed populations Source: nlin.AO (Adaptation and Self-Organizing Systems) Link: https://arxiv.org/abs/2606.17891 Collective migration of heterogeneous cell populations is central to many biological and physiological processes, including development and immune response. 6. Quantum inversion of the vacuum hierarchy and multi-kink unbinding in the non-degenerate double sine-Gordon model Source: nlin.PS (Pattern Formation and Solitons) Link: https://arxiv.org/abs/2609.24861 We study the quantum corrections to the vacuum energies and to the binding of the multi-kinks of the non-degenerate double sine-Gordon model. 7. Diagonal Bases and Diagonal Periods of Elementary Cellular Automata Source: nlin.CG (Cellular Automata and Lattice Gases) Link: https://arxiv.org/abs/2609.25078 Which cellular-automaton diagonal families form bases in every finite window? 8. Exploring interference between $P_{c \bar c}$ resonances and background in the pion-induced reaction Source: nucl-th (Nuclear Theory) Link: https://arxiv.org/abs/2609.23300 We present a phenomenological study of the near-threshold $\pi^- p \to J/\psi n$ reaction, focusing on the interference effects between the $s-$channel $P_{c \bar c}$ resonances and non-resonance background. 9. Pairing correlations, orientations and quantum fluctuations in one- and two-nucleon transfer reactions at sub-barrier energies Source: nucl-ex (Nuclear Experiment) Link: https://arxiv.org/abs/2601.13667 This work investigates one- and two-neutron transfer in the $^{96}\text{Zr} + {}^{40}\text{Ca}$ reaction at sub-barrier energies using a microscopic framework based on time-dependent covariant density functional theory (TD-CDFT). 10. On singular solitons of the KP equation and the Go-diagrams Source: nlin.SI (Exactly Solvable and Integrable Systems) Link: https://arxiv.org/abs/2606.04663 It has been proven that real and regular soliton solutions of the KP equation are classified in terms of the totally nonnegative Grassmannian. 11. Orbital Error Dynamics: Self-Organized Criticality, Ephemeral Parameter Resonance, and Non-Linear Biological Ontologies in Zero-Storage Neural Synthesis Source: nlin.CD (Chaotic Dynamics) Link: https://arxiv.org/abs/2609.30115 Modern deep neural networks treat parameters as static floating-point matrices stored in physical memory, incurring Von Neumann memory bottlenecks and representation collapse. 12. Preferential Attachment with Local Flexibility Source: nlin.AO (Adaptation and Self-Organizing Systems) Link: https://arxiv.org/abs/2512.22542 From the formation of social ties to the budding quantum internet, growing networks often exhibit local flexibility upon new nodes attaching to an existing network. 13. Shift-register synchronization of dual-wavelength pulse trains in resonators with quadratic nonlinearity Source: nlin.PS (Pattern Formation and Solitons) Link: https://arxiv.org/abs/2609.27655 Self-organization of nonlinear waves underpins phenomena ranging from hydrodynamic pattern formation to optical frequency-comb generation. 14. Dimension-dependent continuum limits in tissue mechanics Source: nlin.CG (Cellular Automata and Lattice Gases) Link: https://arxiv.org/abs/2607.07000 Continuum descriptions of epithelial tissue mechanics can replace expensive individual-based simulations with tractable macroscopic models, yet the link between cell-scale forces and tissue-scale transport remains poorly understood. 15. Extraction of the pion-nucleon coupling constant using the effective-range expansion with the left-hand cut Source: nucl-th (Nuclear Theory) Link: https://arxiv.org/abs/2602.03115 We apply the generalized effective-range expansion of Phys. 16. Large amplification of the isospin-dependence of proton emitting source size in nuclear collisions induced by radioactive ion beams: A signal of n-p correlation Source: nucl-ex (Nuclear Experiment) Link: https://arxiv.org/abs/2604.25107 We report proton-proton correlation function measurements in central $^{132}$Sn+$^{124}$Sn and $^{108}$Sn+$^{112}$Sn collisions at 270 MeV/nucleon. 17. Large-space and Large-time Asymptotics for the Focusing Nonlinear Schr\"{o}dinger Soliton Gas Source: nlin.SI (Exactly Solvable and Integrable Systems) Link: https://arxiv.org/abs/2605.21091 We investigate the large-space and large-time asymptotic behavior of a soliton gas for the focusing nonlinear Schr\"odinger equation. 18. Conditional preservation of chimera states under equitable network coarse-graining Source: nlin.CD (Chaotic Dynamics) Link: https://arxiv.org/abs/2609.28733 Chimera states, characterized by the coexistence of coherent and incoherent dynamics in networks of coupled oscillators, are among the most intriguing collective phenomena in nonlinear systems and are strongly shaped by the underlying topology and initial conditions. 19. From Periodicity to Chaos - Stabilization, Bifurcation, and Synchronization of the Van der Pol Oscillator Source: nlin.AO (Adaptation and Self-Organizing Systems) Link: https://arxiv.org/abs/2309.07010 This work investigates the dynamics of the van der Pol oscillator, a well-known dynamical model used to represent many naturally occurring phenomena, under both unforced and externally forced conditions, with a focus on its stability characteristics and bifurcation behavior. 20. Computation of Turing bifurcation normal form for n-component reaction-diffusion systems Source: nlin.PS (Pattern Formation and Solitons) Link: https://arxiv.org/abs/2609.28039 General expressions are derived for the amplitude equation valid at a Turing bifurcation of a system of reaction-diffusion equations in one spatial dimension, with an arbitrary number of components. 21. 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. 22. Strangeness Production in Heavy-Ion Collisions: Color Ropes or Hydrodynamic Evolution? Source: nucl-th (Nuclear Theory) Link: https://arxiv.org/abs/2609.28070 We investigate strangeness production and transverse dynamics in heavy-ion collisions at $\sqrt{s_{\mathrm{NN}}}\approx 2.5-20~\mathrm{GeV}$ using the transport approach SMASH (Simulating Many Accelerated Strongly-interacting Hadrons), its extension with rope hadronization, and the SMASH+vHLLE hybrid approach. 23. Observation of flow vector fluctuations in p$-$Pb collisions at $\mathbf{\sqrt{\textit{s}_{_{\bf NN}}}}=$ 5.02 TeV Source: nucl-ex (Nuclear Experiment) Link: https://arxiv.org/abs/2602.10645 Measurements of transverse momentum ($p_{\rm T}$) and pseudorapidity ($\eta$) dependent flow vector fluctuations in p$-$Pb collisions at $\sqrt{s_{_{\rm NN}}} = 5.02$ TeV at the CERN Large Hadron Collider are presented. 24. Hard to soft edge transition for the Muttalib-Borodin ensembles with integer parameter $\theta$ Source: nlin.SI (Exactly Solvable and Integrable Systems) Link: https://arxiv.org/abs/2501.16746 We find the universal limiting correlation kernels of the Muttalib-Borodin (MB) ensembles with integer parameter $\theta \geq 2$ at $0$ in the transitive regime between the hard edge regime and the soft edge regime. 25. Benchmarking Proton Tunneling Splittings with a Wavefunction-Based Double-Well Model: Application to the Formic Acid Dimer Source: nlin.CD (Chaotic Dynamics) Link: https://arxiv.org/abs/2511.01903 Proton tunneling across hydrogen bonds is a fundamental quantum effect with implications for spectroscopy, catalysis, and biomolecular stability. 26. Fluctuation--Response Relation in Finite-Size Noisy Coupled Phase Oscillators Source: nlin.AO (Adaptation and Self-Organizing Systems) Link: https://arxiv.org/abs/2609.28834 Fluctuation--response relations (FRRs) provide a fundamental relation between spontaneous fluctuations and the linear response to external perturbations, yet their validity in non-equilibrium systems remains an open problem. 27. Amplitude equations for wave bifurcations in reaction-diffusion systems Source: nlin.PS (Pattern Formation and Solitons) Link: https://arxiv.org/abs/2609.28037 A wave bifurcation is the counterpart to a Turing instability in reaction-diffusion systems, but where the critical wavenumber corresponds to a pure imaginary pair rather than a zero temporal eigenvalue. 28. 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. 29. Imprints of the nuclear liquid-gas phase transition on net-baryon number fluctuations Source: nucl-th (Nuclear Theory) Link: https://arxiv.org/abs/2609.17328 We investigate net-baryon number fluctuations in the high-density, low-temperature region of the QCD phase diagram using the parity-doublet model (PDM) under the mean-field approximation. 30. Space-time evolution of particle emission in p$-$Pb collisions at $\mathbf{\sqrt{s_{\rm NN}}=~5.02}$ TeV with 3D kaon femtoscopy Source: nucl-ex (Nuclear Experiment) Link: https://arxiv.org/abs/2601.15081 The measurement of three-dimensional femtoscopic correlations between identical charged kaons (K$^\pm$K$^\pm$) produced in p$-$Pb collisions at center-of-mass energy per nucleon pair $\sqrt{s{_{\rm NN}}} = 5.02$ TeV with ALICE at the LHC is presented for the first time. 31. The Nakamura Conjecture Revisited: Toda Molecules and Stationary Axisymmetric Gravity Source: nlin.SI (Exactly Solvable and Integrable Systems) Link: https://arxiv.org/abs/2609.16414 We revisit the Nakamura conjecture, which relates the Tomimatsu-Sato solutions of stationary axisymmetric gravity to finite Toda molecules. 32. Effects of the Internal Transport Barrier in the plasma confinement with Resonant Magnetic Perturbations Source: nlin.CD (Chaotic Dynamics) Link: https://arxiv.org/abs/2609.27164 In the pursuit of steady-state fusion energy, Advanced Tokamak regimes rely on Internal Transport Barriers (ITBs) with reversed magnetic shear. 33. Bifurcation and Multistability in a Collective-Risk Public Goods Game with Quorum-Activated Protection Source: nlin.AO (Adaptation and Self-Organizing Systems) Link: https://arxiv.org/abs/2609.28132 The danger of collective risk in a public goods game could provide an effective escape route from the tragedy of the commons. 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 33 of 466 available items for this weekly brief.