Clay weekly context brief for the Nonlinear Sciences category (ISO week 2026-W30).

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. Bayesian Basin Tracking: Efficient Global Continuation of Multistable Dynamical Systems
   Source: nlin.CD (Chaotic Dynamics)
   Link: https://arxiv.org/abs/2607.14762
   Mapping the global phase space of high-dimensional multistable dynamical systems is computationally prohibitive because conventional approaches require extensive numerical integration.
2. 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.
3. Bayesian Inference for Extracting Barrier Distributions from Fusion Excitation Functions
   Source: nucl-ex (Nuclear Experiment)
   Link: https://arxiv.org/abs/2607.14422
   Barrier distributions encode rich information about the structure and dynamics of fusing nuclei, but extracting them from experimental fusion cross sections requires an estimate of the fusion excitation function's second derivative.
4. Lie Meets Network Dynamics: Exact Macroscopic Reductions (Finite Systems)
   Source: nlin.AO (Adaptation and Self-Organizing Systems)
   Link: https://arxiv.org/abs/2607.12210
   We establish a unified framework for exact dimensional reductions in network dynamical systems using Lie-Scheffers theory.
5. Octupole deformation in even-even Ra isotopes from covariant density functional theory with localized exchange terms in a three-dimensional lattice space
   Source: nucl-th (Nuclear Theory)
   Link: https://arxiv.org/abs/2607.12633
   The covariant density functional theory in a three-dimensional lattice space is extended to the PCF-PK1 functional with localized exchange terms and is employed to study the nuclear shape evolution of even-even Ra isotopes.
6. Microscopic Variability Alters Macroscopic Rotation Speed in Stochastic Spiral Waves
   Source: nlin.PS (Pattern Formation and Solitons)
   Link: https://arxiv.org/abs/2511.21710
   We present a general theory for noise-induced corrections to the angular velocity of spiral waves.
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. Infectious Disease Induces Emergent Oscillations, Extinction and Changes in Community Persistence in a Food Chain
   Source: nlin.CD (Chaotic Dynamics)
   Link: https://arxiv.org/abs/2607.14360
   Food webs have been extensively studied from both ecological and mathematical aspects.
9. Riemann-Hilbert problem and long-time asymptotics of the Yajima-Oikawa equation
   Source: nlin.SI (Exactly Solvable and Integrable Systems)
   Link: https://arxiv.org/abs/2507.15645
   The Yajima-Oikawa equation is an integrable long wave-short wave resonance interaction model arising as a deformation of the Zakharov system for Langmuir waves coupled to ion-acoustic waves.
10. Impact of tensor-rank components of chiral three-nucleon forces on the single-particle structure of calcium isotopes
   Source: nucl-ex (Nuclear Experiment)
   Link: https://arxiv.org/abs/2607.14458
   Background: Chiral three-nucleon forces (3NFs) play a key role in the microscopic description of nuclear shell evolution.
11. Structured Fluctuations and the Information Dynamics of Self-Maintenance in Growing Neural Cellular Automata
   Source: nlin.AO (Adaptation and Self-Organizing Systems)
   Link: https://arxiv.org/abs/2607.12403
   Growing Neural Cellular Automata (GNCA) are capable of robust self-maintenance and self-repair, yet the internal dynamical mechanisms that support these capabilities remain poorly understood.
12. Harmonic-dependent geometry-to-flow transfer in AMPT Ru+Ru and Zr+Zr isobar collisions
   Source: nucl-th (Nuclear Theory)
   Link: https://arxiv.org/abs/2607.12660
   We present a fixed-$N_{\rm part}$ study of geometry-to-flow transfer in string-melting AMPT simulations of $^{96}{\rm Ru}+^{96}{\rm Ru}$ and $^{96}{\rm Zr}+^{96}{\rm Zr}$ collisions at $\sqrt{s_{NN}}=200$ GeV.
13. Resonance phenomena in vortex-antivortex collisions
   Source: nlin.PS (Pattern Formation and Solitons)
   Link: https://arxiv.org/abs/2510.17964
   In this work, we provide a full map of scattering scenarios between a Nielsen-Olesen vortex and antivortex.
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. Inferring Non-Normal Amplification Geometry from Multivariate Time Series
   Source: nlin.CD (Chaotic Dynamics)
   Link: https://arxiv.org/abs/2607.14786
   Across hydrodynamics, ecology, neuroscience, network dynamics, non-Hermitian physics, and socio-economic systems, asymptotically stable dynamics can exhibit large transient amplifications that are invisible to eigenvalue-based analyses.
16. On the discrete Painlev\'e equivalence problem, non-conjugate translations and nodal curves
   Source: nlin.SI (Exactly Solvable and Integrable Systems)
   Link: https://arxiv.org/abs/2604.13782
   We consider several examples of nonautonomous systems of difference equations coming from semi-classical orthogonal polynomials via recurrence coefficients and ladder operators, with respect to various generalisations of Laguerre and Meixner weights.
17. Node-locked phase of annual modulations from the gravitational chiral anomaly in the solar Kerr field
   Source: nucl-ex (Nuclear Experiment)
   Link: https://arxiv.org/abs/2607.07912
   The leading parity-odd mass--spin curvature invariant of the solar exterior, $P_{\odot}\equiv{}^{*}\!R\,R\simeq 288\,G^{2}M_{\odot}^{2}a_{\odot}\cos\theta/c^{4}r^{7}$, changes sign when the Earth crosses the solar equatorial plane and acts as the geometric source of the gravitational chiral anomaly.
18. Higher-order interactions for controlling time-delayed Kuramoto model
   Source: nlin.AO (Adaptation and Self-Organizing Systems)
   Link: https://arxiv.org/abs/2607.10759
   We propose a framework for controlling the collective dynamics of the time-delayed Kuramoto model based on a delay-free, higher-order approximation of the delayed interactions.
19. Role of the pre-equilibrium particle emission in the $^{249-251}$No production in the $^{204}$Pb($^{48}$Ca, xn)$^{252-x}$No reaction
   Source: nucl-th (Nuclear Theory)
   Link: https://arxiv.org/abs/2607.12677
   Experimental data on the production of the $^{250}$No isotope in an isomeric state in the $^{204}$Pb($^{48}$Ca, 2n)$^{250}$No reaction at $^{48}$Ca energies from 200 to 240 MeV are analyzed within a unified approach based on the Hauser-Feshbach model and Griffin's exciton model for the description of nuclear reactions, assuming one pre-equilibrium particle emission.
20. Stabilization of two-dimensional optical continuous-wave states by a potential trough
   Source: nlin.PS (Pattern Formation and Solitons)
   Link: https://arxiv.org/abs/2607.09607
   We consider quasi-one-dimensional (Q1D) continuous waves (CWs) in the two-dimensional (2D) optical system with the cubic-quintic nonlinearity and a Q1D potential trough.
21. Recurrence and anti-recurrence patterns reveal an antiperiodic fingerprint that survives into chaos in the Duffing--Holmes oscillator
   Source: nlin.CD (Chaotic Dynamics)
   Link: https://arxiv.org/abs/2607.05323
   The periodically forced Duffing--Holmes oscillator possesses a discrete symmetry under sign reversal of the coordinate combined with a half-period shift of the drive.
22. Pole Dynamics, Linearization, and Perturbations of the Satsuma--Mimura Equation
   Source: nlin.SI (Exactly Solvable and Integrable Systems)
   Link: https://arxiv.org/abs/2606.16789
   This paper investigates the pole dynamics and perturbation theory of algebraic soliton solutions associated with the Satsuma--Mimura (SM) equation.
23. Ab initio calculations of two-neutrino and neutrinoless double-$\boldsymbol{\beta}$ decay of $^{48}$Ca and related Gamow-Teller strength distributions
   Source: nucl-ex (Nuclear Experiment)
   Link: https://arxiv.org/abs/2607.11733
   We present ab initio calculations of two-neutrino double-beta ($2\nu\beta\beta$) decay of $^{48}$Ca and the related Gamow-Teller (GT) strength functions in $^{48}$Sc using the valence-space in-medium similarity renormalization group (VS-IMSRG) with nuclear interactions and electroweak currents based on chiral effective field theory.
24. Revisiting the non-equilibrium phase transitions of the continuous-trait Axelrod model
   Source: nlin.AO (Adaptation and Self-Organizing Systems)
   Link: https://arxiv.org/abs/2607.10381
   We investigate the non-equilibrium phase transitions of the continuous-trait Axelrod model, an agent-based framework where individual culture is represented by a vector of $F$ continuous features confined to the interval $(0,1)$.
25. Three-dimensional, boost-invariant formalism for systems of relativistically moving constituents
   Source: nucl-th (Nuclear Theory)
   Link: https://arxiv.org/abs/2607.12869
   Light front quantum mechanics in three dimensions can be used to construct boost-invariant wave functions for the internal structure of relativistic systems.
26. Superheavy dark-bright soliton as a signature of spatial symmetry breaking transition in harmonically trapped Bose mixtures
   Source: nlin.PS (Pattern Formation and Solitons)
   Link: https://arxiv.org/abs/2607.09064
   We investigate the dynamics of a dark-bright soliton in harmonically trapped two-component Bose-Einstein condensates and reveal an interesting spontaneous spatial symmetry breaking driven by nonlinear interactions.
27. Quantum many-body mixed phase space revealed by hybrid feedback control
   Source: nlin.CD (Chaotic Dynamics)
   Link: https://arxiv.org/abs/2607.14223
   Understanding how complex systems transition between order and chaos is a central challenge of nonequilibrium physics.
28. Discrete Gerdjikov-Ivanov models and their higher-order counterparts from the Cauchy matrix scheme
   Source: nlin.SI (Exactly Solvable and Integrable Systems)
   Link: https://arxiv.org/abs/2607.09333
   The Gerdjikov-Ivanov (GI) equation is an important model in the derivative nonlinear Schrodinger system, yet its fully discrete integrable analogues remain unexplored.
29. High-precision measurement of the kaonic hydrogen 1s level shift and width with SIDDHARTA-2
   Source: nucl-ex (Nuclear Experiment)
   Link: https://arxiv.org/abs/2607.13952
   Kaonic atoms provide a unique experimental probe of strong interaction in the low-energy regime.
30. Coherence as Thermodynamic Organization: Toward a Non-Equilibrium Turbulence Theory
   Source: nlin.AO (Adaptation and Self-Organizing Systems)
   Link: https://arxiv.org/abs/2607.11817
   Since the foundational studies in the late nineteenth century, fluid turbulence has stood as a profound, unsolved challenge in classical 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 30 of 341 available items for this weekly brief.