Clay weekly context brief for the Nonlinear Sciences category (ISO week 2026-W32).

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. Continuous Game of Life: cell emergence and self-organization at the edge of growth
   Source: nlin.AO (Adaptation and Self-Organizing Systems)
   Link: https://arxiv.org/abs/2607.27402
   Conway's Game of Life shows that simple rules can generate a rich diversity of emerging structures.
2. Nonlinear Fourier spectral signatures of rogue waves observed in Bose-Einstein condensates
   Source: nlin.PS (Pattern Formation and Solitons)
   Link: https://arxiv.org/abs/2607.27734
   Modulation instability provides an important framework for understanding rogue wave (RW) formation on continuous backgrounds.
3. $^{15}$C inelastic $1/2^+ \rightarrow 5/2^+$ excitation: A single-particle versus a collective process
   Source: nucl-ex (Nuclear Experiment)
   Link: https://arxiv.org/abs/2607.23291
   Background: The excitation of one-neutron halo nucleus $^{15}$C from the $1/2^+$ ground state to the $5/2^+$ first excited state was measured at Argonne National Laboratory by impinging $^{15}$C on a deuterated target at $7.1 A$ MeV.
4. The real butterfly effect: from the pop culture to mathematics and physics
   Source: nlin.CD (Chaotic Dynamics)
   Link: https://arxiv.org/abs/2607.24715
   The "butterfly effect", introduced over half a century ago by Edward Lorenz, has shifted from a cornerstone of dynamical systems to a popular metaphor, yet its true physical manifestation in fully developed turbulence spans a spectrum of phenomena from standard chaotic sensitivity to the recently established concept of Eulerian spontaneous stochasticity.
5. Single-particle structure of the semi-magic nucleus ${}^{90}$Zr from a nonlocal dispersive optical model
   Source: nucl-th (Nuclear Theory)
   Link: https://arxiv.org/abs/2607.21875
   A nonlocal dispersive-optical-model (DOM) analysis has been carried out for neutrons and protons in the semi-magic nucleus $^{90}$Zr.
6. Integrable Volterra hierarchies over nonabelian algebras
   Source: nlin.SI (Exactly Solvable and Integrable Systems)
   Link: https://arxiv.org/abs/2607.17868
   Known integrable systems with noncommutative dependent variables are typically formulated over free associative algebras, quantum algebras, or Grassmann algebras.
7. PyTorchFire: A GPU-Accelerated Wildfire Simulator with Differentiable Cellular Automata
   Source: nlin.CG (Cellular Automata and Lattice Gases)
   Link: https://arxiv.org/abs/2502.18738
   Accurate and rapid prediction of wildfire trends is crucial for effective management and mitigation.
8. Targeted Quarantine Strategies Mitigate SIS-model Cyber Epidemics on Complex Networks
   Source: nlin.AO (Adaptation and Self-Organizing Systems)
   Link: https://arxiv.org/abs/2607.27624
   The rapid expansion of highly connected and heterogeneous digital infrastructures has fundamentally altered the dynamics of cyber epidemics, making it increasingly important to understand how malware propagates under realistic structural and policy conditions.
9. Wave patterns in two-dimensional networks of non-locally coupled oscillators with phase delay
   Source: nlin.PS (Pattern Formation and Solitons)
   Link: https://arxiv.org/abs/2607.27791
   We studied the wave patterns in non-locally, repulsively coupled oscillators on a 2D lattice.
10. Ab initio lattice calculation of nuclear magnetic dipole moments with systematic error quantifications
   Source: nucl-ex (Nuclear Experiment)
   Link: https://arxiv.org/abs/2607.25464
   Nuclear magnetic moments are sensitive probes of nuclear structure.
11. Photonic reservoir computing with complex networks
   Source: nlin.CD (Chaotic Dynamics)
   Link: https://arxiv.org/abs/2607.23285
   Photonic reservoir computing has attracted increasing attention as a fast and low-cost approach for time-series prediction.
12. Phaseless auxiliary-field quantum Monte Carlo in the Hartree-Fock-Bogoliubov manifold
   Source: nucl-th (Nuclear Theory)
   Link: https://arxiv.org/abs/2607.21929
   We formulate and implement the phaseless auxiliary-field quantum Monte Carlo (AFQMC) method in the Hartree-Fock-Bogoliubov (HFB) manifold for systems with strong pairing correlations.
13. Real-Spectrum Darboux Limits at Multiple Spatial Roots of the Coupled Fokas-Lenells System
   Source: nlin.SI (Exactly Solvable and Integrable Systems)
   Link: https://arxiv.org/abs/2607.17955
   We investigate Darboux constructions generated by multiple spatial roots of the coupled Fokas-Lenells system on a plane-wave background.
14. It's Much Easier for Neural Networks to learn Game of Life Dynamics with the Right Activation Function: Polynomial Kolmogorov-Arnold Networks
   Source: nlin.CG (Cellular Automata and Lattice Gases)
   Link: https://arxiv.org/abs/2606.23587
   Previous work has found a gap between the scale of neural networks that reliably learn Conway's Game of Life, and minimal networks capable of representing the classic cellular automaton with hard-coded parameter values.
15. 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.
16. Nondegenerate bright solitons and their interactions in the generalized coupled nonlinear Schroedinger system
   Source: nlin.PS (Pattern Formation and Solitons)
   Link: https://arxiv.org/abs/2607.28197
   It is known that the generalized coupled nonlinear Schroedinger (GCNLS) equations can be reduced to the basic vector nonlinear Schroedinger models through various symmetry reductions.
17. Impacts of hexadecapole correlations in actinide nuclei
   Source: nucl-ex (Nuclear Experiment)
   Link: https://arxiv.org/abs/2607.26499
   The impact of hexadecapole correlations on the low-energy spectroscopic properties of Th, U, and Pu nuclei, within the mass range $232 \le A \le 240$, is studied systematically using the mapped $sdg$-IBM model.
18. Approximate reservoir computing with a semiconductor laser for reducing energy consumption
   Source: nlin.CD (Chaotic Dynamics)
   Link: https://arxiv.org/abs/2607.23288
   Photonic reservoir computing is a promising physical machine-learning technique for predicting time-series data.
19. Nuclear incompressibility and fourth moment of the nuclear density in Skyrme functionals
   Source: nucl-th (Nuclear Theory)
   Link: https://arxiv.org/abs/2607.22003
   Recent experimental advances could soon allow the accurate extraction of not only the root-mean-square radius but also the fourth radial moment of the nuclear electric charge density distribution.
20. Symplectic mechanics of relativistic spinning compact bodies. III. quadratic-in-spin integrability in Type-D Einstein spacetimes: persistence and breakdown
   Source: nlin.SI (Exactly Solvable and Integrable Systems)
   Link: https://arxiv.org/abs/2601.06416
   We investigate the integrability of spinning compact body dynamics at quadratic order in spin in four-dimensional Einstein spacetimes admitting a non-degenerate Killing--Yano tensor.
21. Inferring Coupling Strengths in Synchronized Oscillators
   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 alone is essential for predicting synchronization transitions.
22. 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.
23. The CROSS experiment: detector construction, background projection, and sensitivity to $^{100}$Mo $0\nu2\beta$ decay
   Source: nucl-ex (Nuclear Experiment)
   Link: https://arxiv.org/abs/2607.26732
   The CROSS experiment to search for neutrinoless double-beta ($0\nu2\beta$) decay in $^{100}$Mo with the help of an array of scintillating cryogenic calorimeters, containing 4.9 kg of $^{100}$Mo, has been ongoing in a low-background setup at the Canfranc underground laboratory (Spain) since mid-November 2025.
24. Physics-Informed Neural Networks for Discovering Periodic Orbits in the Gravitational Three-Body Problem
   Source: nlin.CD (Chaotic Dynamics)
   Link: https://arxiv.org/abs/2607.23501
   Locating periodic solutions of chaotic dynamical systems normally requires an initial guess close enough to the target orbit for numerical continuation or gradient-based search to converge.
25. Momentum anisotropy from Resistive Magnetohydrodynamics
   Source: nucl-th (Nuclear Theory)
   Link: https://arxiv.org/abs/2607.21879
   We derive relativistic resistive magnetohydrodynamics framework for a two-component ultrarelativistic plasma of massless, oppositely charged particles directly from the Boltzmann-Vlasov equation using the 14-moment approximation.
26. Deriving the $\text{AdS}_3\times\text{S}^3\times \text{T}^4$ Quantum Spectral Curve I: Y-system and discontinuity relations
   Source: nlin.SI (Exactly Solvable and Integrable Systems)
   Link: https://arxiv.org/abs/2607.13673
   The mirror Thermodynamic Bethe Ansatz (TBA) describes the spectrum of $\text{AdS}_3\times\text{S}^3\times \text{T}^4$ superstrings supported by a mixture of Ramond-Ramond (RR) and Neveu-Schwarz-Neveu-Schwarz (NSNS) flux.
27. From Exponential to Gaussian Tails: Fractal Wavefront Scaling and the $\kappa$-Weibull Distribution at Phase Transitions
   Source: nlin.AO (Adaptation and Self-Organizing Systems)
   Link: https://arxiv.org/abs/2607.28172
   The paper examines the features of critical evolution in an active medium modeled by a cellular automaton.
28. Phase transitions and microphases in elastomers. I. Emergence of stable domains
   Source: nlin.PS (Pattern Formation and Solitons)
   Link: https://arxiv.org/abs/2607.27516
   Elasticity often plays a key role in regulating phase separation in physical systems.
29. Critical net-proton number fluctuations with hydrodynamics
   Source: nucl-ex (Nuclear Experiment)
   Link: https://arxiv.org/abs/2607.26912
   We compute the net-proton number fluctuations and their ratios $C_2/C_1$, $C_3/C_2$ and $C_4/C_2$ on the hydrodynamic freeze-out hypersurface of particlization at nine collision energies, $\sqrt{s_{\mathrm{NN}}}=7.
30. An angular-momentum preserving dissipative model for the point-mass N -body problem
   Source: nlin.CD (Chaotic Dynamics)
   Link: https://arxiv.org/abs/2603.12452
   A simple mathematical model emulating energy dissipation due to tidal effects is proposed.
31. First Measurement of the $K^-$ Escape Cross Section in the ${}^{12}{\rm C}(K^{-},p)$ Reaction
   Source: nucl-th (Nuclear Theory)
   Link: https://arxiv.org/abs/2606.18398
   We investigated the $\bar{K}$-nucleus interaction through the simultaneous measurement of the inclusive $^{12}{\rm C}(K^-, p)$ and exclusive $K^-$-escape $^{12}{\rm C}(K^-, p K^-_{esc})$ reactions at $1.8$ GeV/$c$ at J-PARC.
32. Discrete-time maximally superintegrable systems and deformed symmetry algebras: the Calogero-Moser case
   Source: nlin.SI (Exactly Solvable and Integrable Systems)
   Link: https://arxiv.org/abs/2601.10625
   We determine the complete structure of the symmetry algebras associated with the N-body Calogero-Moser system and its maximally superintegrable discretization.

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 480 available items for this weekly brief.