Clay weekly context brief for the Nonlinear Sciences category (ISO week 2026-W38).

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. Fourier Transforms of Color Glass Condensate Multi-Wilson-Line Correlators via Filon Quadrature
   Source: nucl-th (Nuclear Theory)
   Link: https://arxiv.org/abs/2608.18589
   Calculating cross sections in the Color Glass Condensate effective theory requires Fourier transforms of multi-Wilson-line correlators from transverse coordinate space to transverse momentum space.
2. Nuclear Mass Models with Deformation Optimized and Diagnosed by Bayesian Analysis with Markov Chain Monte Carlo
   Source: nucl-ex (Nuclear Experiment)
   Link: https://arxiv.org/abs/2606.30519
   We employ a full Bayesian analysis with adaptive Metropolis-Hastings Markov chain Monte Carlo (BA-MCMC) sampling to systematically study the posterior probability distributions of the strengths of energy terms in optimized nuclear mass models of Bethe-Weizs\"{a}cker variants.
3. 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.
4. Coupled multiscale paleoclimate reconstruction with four-dimensional variational data assimilation
   Source: nlin.CD (Chaotic Dynamics)
   Link: https://arxiv.org/abs/2608.19469
   Paleoclimate archives extend climate knowledge beyond the instrumental era, registering different seasons, variables, time averages, and memory lengths.
5. Attention by Synchronization in Coupled Oscillator Networks
   Source: nlin.AO (Adaptation and Self-Organizing Systems)
   Link: https://arxiv.org/abs/2606.12059
   We address transformer attention on energy-constrained physical substrates.
6. A Lax representation, symmetries, and conservation laws for the three-dimensional Euler--Helmholtz equations
   Source: nlin.SI (Exactly Solvable and Integrable Systems)
   Link: https://arxiv.org/abs/2409.05752
   We consider the three-dimensional Euler--Helmholtz equations for an inviscid incompressible fluid.
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. Few-gluon interactions and multipole radiation in high energy nuclear collisions
   Source: nucl-th (Nuclear Theory)
   Link: https://arxiv.org/abs/2607.25017
   Broad claims have been made over years about achievement of quark-gluon plasma (QGP) formation in high-energy heavy-ion collisions based on certain phenomena anticipated for QGP formation.
9. Shape evolution of krypton isotopes calculated with axially deformed relativistic Hartree-Bogoliubov approach
   Source: nucl-ex (Nuclear Experiment)
   Link: https://arxiv.org/abs/2606.01253
   We perform a systematic study of the structure and properties of the krypton isotopic chain including both even-even and odd-$A$ nuclei based on the axially deformed relativistic Hartree-Bogoliubov approach.
10. 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.
11. Fluctuation-dissipation of the Kuramoto model on fruit-fly connectomes
   Source: nlin.CD (Chaotic Dynamics)
   Link: https://arxiv.org/abs/2503.20708
   We investigate the distance from equilibrium using the Kuramoto model via the degree of fluctuation-dissipation violation as the consequence of different levels of edge weight anisotropies.
12. Cortical information transfer reveals conserved hemispherical network dynamics across human handedness
   Source: nlin.AO (Adaptation and Self-Organizing Systems)
   Link: https://arxiv.org/abs/2609.10870
   Whether human motor and brain lateralization arises from fundamentally distinct neural architectures or emerges from conserved network dynamics remains a central question at the intersection of network science and neurobiology.
13. Symmetries of the Generalized Yang--Baxter Equations
   Source: nlin.SI (Exactly Solvable and Integrable Systems)
   Link: https://arxiv.org/abs/2606.26510
   The generalized Yang-Baxter equations are multi-site versions of the standard Yang-Baxter equation.
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. Nucleon 3D intrinsic spin structure from the weak-neutral axial-vector form factors
   Source: nucl-th (Nuclear Theory)
   Link: https://arxiv.org/abs/2512.06801
   Relativistic 3D weak-neutral axial-vector four-current and spin distributions inside a nucleon (or a general spin-$\frac{1}{2}$ hadron) including three weak-neutral axial-vector form factors are investigated for the first time.
16. Updated Hadron List for Transport Simulations of Heavy-Ion Collisions
   Source: nucl-ex (Nuclear Experiment)
   Link: https://arxiv.org/abs/2309.01737
   Hadronic transport approaches used in heavy-ion collision simulations rely on a consistent and accurate hadron list with decay channels.
17. 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.
18. Nonlinear dynamics and mechanical frequency combs with a Meissner-levitated micromagnet
   Source: nlin.CD (Chaotic Dynamics)
   Link: https://arxiv.org/abs/2609.11668
   Nonlinearities in multimode mechanical systems can give rise to rich dynamical phenomena with great potential for sensing applications and for future quantum experiments.
19. Making the Graph Laplacian Physical: Multiscale Coarse-Graining in Electrical Oscillator Networks
   Source: nlin.AO (Adaptation and Self-Organizing Systems)
   Link: https://arxiv.org/abs/2609.10386
   Spectral gaps are widely interpreted as signatures of collective organization, yet it is rarely clear whether the resulting modes correspond to physical variables or merely to convenient mathematical coordinates.
20. On monodromy of monodromy surfaces
   Source: nlin.SI (Exactly Solvable and Integrable Systems)
   Link: https://arxiv.org/abs/2608.25594
   Different instances of the Riemann-Hilbert correspondence relate initial value spaces of Painlev\'e equations to affine varieties known as monodromy surfaces, built from monodromy invariants for associated linear ODEs.
21. The N$^3$LO Twist-2 Matching of Helicity TMDs and SIDIS $q_\ast$ Spectrum
   Source: nucl-th (Nuclear Theory)
   Link: https://arxiv.org/abs/2509.01655
   We compute the twist-2 matching of transverse momentum dependent (TMD) helicity parton distribution and fragmentation functions at next-to-next-to-next-to-leading order (N$^3$LO) in QCD.
22. Laser Spectroscopy of Thulium Isotopes Near the (N=82) Shell Closure: Nuclear Moment and Charge Radius of ${}^{152\mathrm{m}}\mathrm{Tm}$
   Source: nucl-ex (Nuclear Experiment)
   Link: https://arxiv.org/abs/2607.25033
   We report on resonance ionization laser spectroscopy measurements performed on both neutron-deficient and neutron-rich thulium ($\mathrm{Tm}, Z=69$) isotopes.
23. 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.
24. Block regularisation of the logarithm central problem
   Source: nlin.CD (Chaotic Dynamics)
   Link: https://arxiv.org/abs/2302.12181
   The logarithm function is the gravitational potential in $\mathbb{R}^2$.
25. 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.
26. Anomalous current fluctuations in the stochastic XNOR hopping model
   Source: nlin.SI (Exactly Solvable and Integrable Systems)
   Link: https://arxiv.org/abs/2608.10536
   We consider fluctuations of the spin current in the stochastic XNOR process, a kinetically constrained hopping model in one spatial dimension.
27. Breakdown of the Plane-Wave Trojan Horse Analysis of the $^{12}\mathrm{C}+{}^{12}\mathrm{C}$ Fusion Reaction: Critical Role of Coulomb Distortions
   Source: nucl-th (Nuclear Theory)
   Link: https://arxiv.org/abs/2609.04498
   Recently, a new Trojan Horse Method (THM) measurement of carbon-carbon fusion was reported by Li \textit{et al.} [Phys.
28. Nuclear-physics-guided Gaussian Processes
   Source: nucl-ex (Nuclear Experiment)
   Link: https://arxiv.org/abs/2609.11714
   Gaussian Process Regression is a powerful nonparametric Bayesian method that provides both predictions and principled uncertainty estimates in closed form.
29. Speed and stability of segregated waves in a pressure-based model of heterogeneous cell populations
   Source: nlin.PS (Pattern Formation and Solitons)
   Link: https://arxiv.org/abs/2609.09043
   We consider a minimal pressure-based model of heterogeneous cell populations consisting of proliferative and non-proliferative cells with different mobilities.
30. Predicting tipping points: The many shades of non-equilibrium and catch-22s of early-warning
   Source: nlin.CD (Chaotic Dynamics)
   Link: https://arxiv.org/abs/2609.10378
   The potential of crossing climate tipping points (TP) has reached the attention of many researchers and the general public.
31. Pulse in collapse: a game dynamics experiment
   Source: nlin.AO (Adaptation and Self-Organizing Systems)
   Link: https://arxiv.org/abs/2302.09336
   The collapse process is a constitutive sub-process in the full finding Nash equilibrium process.
32. On B\"acklund transformations preserving the Darboux integrability of hyperbolic equations
   Source: nlin.SI (Exactly Solvable and Integrable Systems)
   Link: https://arxiv.org/abs/2609.06217
   This paper deals with two kinds of B\"acklund transformations for scalar hyperbolic partial differential equations.

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 451 available items for this weekly brief.