Clay weekly context brief for the Nonlinear Sciences category (ISO week 2026-W35).

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. The structure of networks that evolve under a combination of growth, via node addition and random attachment, and contraction, via random node deletion
   Source: nlin.AO (Adaptation and Self-Organizing Systems)
   Link: https://arxiv.org/abs/2209.10027
   We present analytical results for the emerging structure of networks that evolve via a combination of growth (by node addition and random attachment) and contraction (by random node deletion).
2. Intermittent Flocking and Fractal Collective Order Induced by Time-Varying Delays
   Source: nlin.CD (Chaotic Dynamics)
   Link: https://arxiv.org/abs/2608.19887
   Time-varying interaction delays are ubiquitous in active matter, yet their collective effects remain largely unexplored.
3. Nonlinear tunnel oscillations of light in spherical Bragg resonators
   Source: nlin.PS (Pattern Formation and Solitons)
   Link: https://arxiv.org/abs/2608.19731
   A weakly nonlinear regime of radial tunneling is theoretically considered for a light wave in a spherical dielectric Bragg resonator containing a set of ``shell'' eigenmodes (both TE and TM) with different azimuthal numbers $l\geq 1$, which are concentrated near a defect of the Bragg structure, several layers away from the origin.
4. Size and Distance Scales in the Nucleon and in Dense Baryonic Matter
   Source: nucl-th (Nuclear Theory)
   Link: https://arxiv.org/abs/2608.19792
   This memorial tribute to Mannque Rho follows a line of thoughts and ideas that he continuously inspired and shaped over many decades: from the two-scales picture of low-energy nucleon structure to dense and cold baryonic matter as it is realized in the cores of neutron stars.
5. Determination of Tritium Content in D2 Gas and Heavy Water
   Source: nucl-ex (Nuclear Experiment)
   Link: https://arxiv.org/abs/2608.17059
   A simple experimental method for the determination of tritium concentration in natural hydrogen and deuterium gas down to the femtomole level is described.
6. Poisson structures for a similarity reduction of the Drinfeld-Sokolov hierarchy of type $A$
   Source: nlin.SI (Exactly Solvable and Integrable Systems)
   Link: https://arxiv.org/abs/2608.15484
   In this article we consider the Drinfeld-Sokolov hierarchy of type $A$ and its similarity reduction.
7. The effect of preferential node deletion on the structure of networks that evolve via preferential attachment
   Source: nlin.AO (Adaptation and Self-Organizing Systems)
   Link: https://arxiv.org/abs/2505.16574
   We present analytical results for the effect of preferential node deletion on the structure of networks that evolve via node addition and preferential attachment.
8. Coherent states in quantum billiards constructed in the basis of the continued eigenfunctions
   Source: nlin.CD (Chaotic Dynamics)
   Link: https://arxiv.org/abs/2608.20302
   In the article a new approach to construction of generalized coherent states in quantum billiards is proposed.
9. A resonance in phonons scattering off a kink in the absence of a Peierls-Nabarro potential
   Source: nlin.PS (Pattern Formation and Solitons)
   Link: https://arxiv.org/abs/2607.01450
   We investigate the interaction of small-amplitude waves called phonons, with an initially static kink in an exceptional discretization of the $\phi^4$ model that is free of the Peierls-Nabarro potential.
10. Relativistic Effects in Femtoscopy and Deuteron Formation
   Source: nucl-th (Nuclear Theory)
   Link: https://arxiv.org/abs/2603.00354
   For a long time studies of femtoscopic correlations have provided information about space-time characteristics of particle sources in high-energy collisions.
11. Revised $^{45}$V($p,\gamma$)$^{46}$Cr reaction rate and its impact on the production of $^{44}$Ti in core-collapse supernovae
   Source: nucl-ex (Nuclear Experiment)
   Link: https://arxiv.org/abs/2608.17757
   The thermonuclear $^{45}$V($p,\gamma$)$^{46}$Cr reaction is the primary leakage pathway from the $^{44}$Ti--$^{45}$V quasi-equilibrium cluster during $\alpha$-rich freeze-out in core-collapse supernovae (CCSN), governing the final abundance of the $\gamma$-ray-emitting isotope $^{44}$Ti.
12. Matrix product operator representations for the local conserved quantities of the spin-$1/2$ XYZ chain
   Source: nlin.SI (Exactly Solvable and Integrable Systems)
   Link: https://arxiv.org/abs/2601.09245
   We present explicit matrix product operator (MPO) representations for the local conserved quantities of the spin-$1/2$ XYZ chain.
13. Collective dynamics of higher-order Vicsek model emerging from local conformity interactions
   Source: nlin.AO (Adaptation and Self-Organizing Systems)
   Link: https://arxiv.org/abs/2512.19318
   The Vicsek model is the paradigmatic framework for collective motion in systems of self-propelled particles.
14. 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.
15. Vector Akhmediev Breathers and State Transitions in the Degenerate and Nondegenerate Regimes for the Coupled Sasa-Satsuma System
   Source: nlin.PS (Pattern Formation and Solitons)
   Link: https://arxiv.org/abs/2608.17104
   We investigate vector Akhmediev breathers (ABs) in the degenerate and nondegenerate regimes for the coupled Sasa-Satsuma system describing two coupled ultrashort optical pulse envelopes.
16. The renormalization of the shell-model neutrinoless double-beta decay operator starting from effective field theory (I)
   Source: nucl-th (Nuclear Theory)
   Link: https://arxiv.org/abs/2606.25486
   In this work, we approach for the first time the task to perform a shell-model calculation of the matrix element for the neutrinoless double-beta decay, within a fully-consistent framework where the expressions of the nuclear Hamiltonian and of the decay operators have been derived through chiral perturbation theory.
17. Symbolic Regression for Interpretable Emulation of Proton Collective Flow in Intermediate-Energy Heavy-Ion Collisions
   Source: nucl-ex (Nuclear Experiment)
   Link: https://arxiv.org/abs/2608.17828
   Symbolic regression provides an interpretable machine-learning approach for constructing explicit analytic relations between physical inputs and observables.
18. New 5th-order Schwarzian evolution equations and their higher-order symmetries
   Source: nlin.SI (Exactly Solvable and Integrable Systems)
   Link: https://arxiv.org/abs/2608.16496
   We report new quasilinear and fully-nonlinear 5th-order Schwarzian evolution equations.
19. A robust method to identify chimera states
   Source: nlin.AO (Adaptation and Self-Organizing Systems)
   Link: https://arxiv.org/abs/2603.22026
   Chimera states are one of the most intriguing phenomena in nonlinear dynamics, characterized by the coexistence of coherent and incoherent behavior in systems of coupled identical oscillators.
20. Learning-Performance Evaluation of a Physical Reservoir Based on a Vortex Spin-Torque Oscillator with a Modified Free Layer
   Source: nlin.CD (Chaotic Dynamics)
   Link: https://arxiv.org/abs/2603.01351
   In this study, we numerically evaluate the learning performance of a vortex spin-torque oscillator (VSTO) with a modified free layer, called a modified VSTO (m-VSTO), in which an additional layer (AL) of smaller radius is stacked on the free layer, for physical reservoir computing.
21. Variable-mass sine-Gordon with point defects: integrability, soliton transmission, and quasi-conservation
   Source: nlin.PS (Pattern Formation and Solitons)
   Link: https://arxiv.org/abs/2608.17211
   We study integrable variable-mass sine-Gordon model (vmSG) with point defects.
22. Correspondence between hydrodynamic frames, transport coefficients, and hydrodynamic modes in relativistic fluids
   Source: nucl-th (Nuclear Theory)
   Link: https://arxiv.org/abs/2608.20324
   The choice of hydrodynamic frame directly influences the numerical values of transport coefficients in relativistic dissipative hydrodynamics.
23. Energy spectra of light charged particles emitted following muon nuclear capture on $^\mathrm{nat}$Si
   Source: nucl-ex (Nuclear Experiment)
   Link: https://arxiv.org/abs/2601.09106
   Background: Charged-particle emission following muon nuclear capture (muNC) probes the de-excitation dynamics of highly excited nuclei, particularly the interplay between preequilibrium and evaporation processes.
24. New Instantons for Matrix Models
   Source: nlin.SI (Exactly Solvable and Integrable Systems)
   Link: https://arxiv.org/abs/2210.13479
   The complete, nonperturbative content of random matrix models is described by resurgent-transseries -- general solutions to their corresponding string-equations.
25. Ising-machine-like Driving Condition Restrictions in SSBM and Additional Pseudo-annealing- Driving Method for SSBM that Achieves Best Cut Value Search -
   Source: nlin.AO (Adaptation and Self-Organizing Systems)
   Link: https://arxiv.org/abs/2608.12545
   In our previous paper, we described the proposal and validation of a new physical implementation-type simulator (spontaneous symmetry breaking machine (SSBM)) for a combinatorial optimization problem that utilizes a phenomenon dual to the model in which a pseudo-spin many-body system is created by spontaneous symmetry breaking.
26. Activated switching between coexisting limit cycles
   Source: nlin.CD (Chaotic Dynamics)
   Link: https://arxiv.org/abs/2608.19060
   Noise-activated switching between coexisting stable states is a fundamental mechanism underlying stochastic dynamics in systems ranging from chemical reactions to neural networks.
27. Pure-Quartic Optical Shock Waves
   Source: nlin.PS (Pattern Formation and Solitons)
   Link: https://arxiv.org/abs/2608.16300
   In this paper, we study the emergence and dynamics of pure-quartic optical dispersive shock waves governed by the nonlinear Schr\"odinger (NLS) equation with self-defocusing Kerr nonlinearity and fourth-order dispersion.
28. Heavy quark transport in quark-gluon plasma beyond the non-relativistic limit
   Source: nucl-th (Nuclear Theory)
   Link: https://arxiv.org/abs/2608.19313
   The dynamics of heavy quarks in quark-gluon plasma (QGP) formed in heavy ion collisions provide a unique window to characterize its properties.
29. Maris polarization in the ($p,pd$) reaction
   Source: nucl-ex (Nuclear Experiment)
   Link: https://arxiv.org/abs/2511.16899
   Proton-induced knockout reactions at intermediate energies provide a clean probe for nuclear clusters.
30. Integrability from a single conservation law in quantum spin chains
   Source: nlin.SI (Exactly Solvable and Integrable Systems)
   Link: https://arxiv.org/abs/2508.20713
   We prove that, for translationally invariant quantum spin chains with finite-range interactions, the existence of a specific conservation law implies the presence of infinitely many local conserved quantities, i.e., integrability.
31. A theory of spatial early warning signals for tipping points on complex networks
   Source: nlin.AO (Adaptation and Self-Organizing Systems)
   Link: https://arxiv.org/abs/2608.15476
   Spatial early warning signals (EWSs) seek evidence of an approaching tipping point from a single snapshot of many interacting elements.
32. When More Data Become Less Informative: Finite-Precision Periodicization and Collapse of Forecast-Error Lyapunov Estimates
   Source: nlin.CD (Chaotic Dynamics)
   Link: https://arxiv.org/abs/2608.16120
   Largest Lyapunov exponents (LLEs) quantify exponential sensitivity, but data-driven estimates are often obtained from finite-precision trajectories.
33. Novel lump solutions of the modified Kadomtsev-Petviashvili-I equation
   Source: nlin.PS (Pattern Formation and Solitons)
   Link: https://arxiv.org/abs/2608.16296
   We construct novel higher-order lump solutions of the modified Kadomtsev-Petviashvili-I (mKP-I) equation by applying the generalized long-wave limit method with spectral perturbations.

Sources in this brief: nlin.AO (Adaptation and Self-Organizing Systems); nlin.CD (Chaotic Dynamics); nlin.PS (Pattern Formation and Solitons); nlin.SI (Exactly Solvable and Integrable Systems); nucl-ex (Nuclear Experiment); nucl-th (Nuclear Theory).
Selected 33 of 479 available items for this weekly brief.