Clay weekly context brief for the Nonlinear Sciences category (ISO week 2026-W34).

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. Phase-space organization of the elastic pendulum: chaotic fraction, energy exchanges, and the order-chaos-order transition
   Source: nlin.CD (Chaotic Dynamics)
   Link: https://arxiv.org/abs/2604.01503
   We study the phase-space organization of the planar elastic pendulum as a function of its two dimensionless control parameters: the reduced energy $R$ and the squared frequency ratio $\mu$.
2. Exploring the unknown territory of Dromions of (2+1) dimensional Generalized Nonlinear Schrodinger Equation
   Source: nlin.PS (Pattern Formation and Solitons)
   Link: https://arxiv.org/abs/2608.13011
   In this paper, we travel through an unknown territory of dromions, to unearth and show the new properties/attributes of dromions which have never been brought to the fore since they were first discovered by Boiti etal [1].
3. Parametric Matrix Models for Emulation in Nuclear and Many-Body Physics
   Source: nucl-th (Nuclear Theory)
   Link: https://arxiv.org/abs/2608.12837
   Progress in nuclear and many-body physics today is predicated on the ability to solve large-scale, strongly correlated quantum many-body problems.
4. Extraction of baryon number susceptibilities at finite density from heavy-ion collisions
   Source: nucl-ex (Nuclear Experiment)
   Link: https://arxiv.org/abs/2608.10238
   We present, to our knowledge, the first Bayesian extraction of baryon number susceptibilities of QCD matter at finite baryon density from heavy-ion collision data on proton number cumulants.
5. Extreme vulnerability to intruder attacks destabilizes network dynamics
   Source: nlin.AO (Adaptation and Self-Organizing Systems)
   Link: https://arxiv.org/abs/2502.08552
   Consensus, synchronization, formation control, and power grid balance are examples of desirable dynamical states that arise in networks.
6. 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.
7. Integral of an alpha unpredictable function
   Source: nlin.CD (Chaotic Dynamics)
   Link: https://arxiv.org/abs/2608.09809
   The present paper is devoted to the study of integral properties of alpha unpredictable functions.
8. Geometry-induced pulse dynamics in a bulk-surface reaction-diffusion system for cell polarization
   Source: nlin.PS (Pattern Formation and Solitons)
   Link: https://arxiv.org/abs/2605.10006
   This paper studies a bulk--surface reaction--diffusion system for cell polarization in two-dimensional domains.
9. Ab Initio Study of $^7$Li with Coupled Mass Partitions
   Source: nucl-th (Nuclear Theory)
   Link: https://arxiv.org/abs/2508.04879
   Background: Lithium is of broad interest in nuclear astrophysics, fusion energy research, and nuclear technology.
10. Probing vorticity and fluctuations in a rotating hadron resonance gas at LHC energy
   Source: nucl-ex (Nuclear Experiment)
   Link: https://arxiv.org/abs/2608.10561
   A large vorticity produced in non-central ultra-relativistic heavy-ion collisions induces an effective chemical potential in both partonic and hadronic matter, thereby influencing the quark-hadron transition and its associated properties.
11. Stochastic Models of Neuronal Growth
   Source: nlin.AO (Adaptation and Self-Organizing Systems)
   Link: https://arxiv.org/abs/2205.10723
   Neuronal circuits arise as axons and dendrites extend, navigate, and connect to target cells.
12. 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.
13. Topological spectral form factor reveals emergent non-Hermitian single-particle $\mathcal{PT}$ transitions from many-body quantum chaos
   Source: nlin.CD (Chaotic Dynamics)
   Link: https://arxiv.org/abs/2606.19331
   In equilibrium, topological defect insertions in quantum and classical partition functions provide non-perturbative probes of phase transitions beyond local observables.
14. Rogue Wave Statistics from a Sparse Coherent Structure Decomposition
   Source: nlin.PS (Pattern Formation and Solitons)
   Link: https://arxiv.org/abs/2608.09584
   While conventional rogue wave statistical models rely on linear or weakly nonlinear descriptions of random seas, we demonstrate experimentally that moderately or strongly nonlinear wave fields can be represented by sparse ensembles of coherent soliton-like packets.
15. Solution to the uncertainty problem of nuclear matrix element for neutrinoless double-$\beta$ decay
   Source: nucl-th (Nuclear Theory)
   Link: https://arxiv.org/abs/2509.16605
   The neutrinoless double-$\beta$ decay ($0\nu\beta\beta$) of nuclei is one of the major research subjects of neutrino physics nowadays because of its influence on particle physics and astrophysics.
16. Longitudinal structure of the quark-gluon plasma from differently shaped nuclei
   Source: nucl-ex (Nuclear Experiment)
   Link: https://arxiv.org/abs/2405.08749
   Ultrarelativistic collisions of atomic nuclei produce the quark--gluon plasma (QGP), an extremely hot, dense state of matter.
17. Determining Critical Temperature Differences of Low-Temperature-Differential Stirling Engines: Nonlinear Dynamics Approach
   Source: nlin.AO (Adaptation and Self-Organizing Systems)
   Link: https://arxiv.org/abs/2607.26539
   While the low-temperature-differential (LTD) Stirling engines are innovative engines that can operate with low temperature differentials in our daily life, the problem of determining the critical temperature differences below which the engine ceases to rotate remains unexplored.
18. Blowup relations and $q$-Painlev\'e VI
   Source: nlin.SI (Exactly Solvable and Integrable Systems)
   Link: https://arxiv.org/abs/2509.10938
   We propose and study blowup relations obeyed by the partition functions of $5d$ $\mathcal{N}=1$ (quiver) SYM theories with $SU(2)$ gauge group and four flavours.
19. State Diagnostics of Complexity in Open Quantum Systems
   Source: nlin.CD (Chaotic Dynamics)
   Link: https://arxiv.org/abs/2608.09705
   We study the emergence of complexity in finite-size quantum systems as their dynamics transition from closed and coherent evolution to interacting and effectively open behavior.
20. Dynamical behavior of diffusively coupled scalar differential equations as Wentzell boundary conditions
   Source: nlin.PS (Pattern Formation and Solitons)
   Link: https://arxiv.org/abs/2608.08537
   Two identical scalar dynamical systems coupled through a scalar diffusion equation are studied herein, with respect to bifurcations from a symmetric steady-state to symmetric and asymmetric steady-states and to in-phase and anti-phase oscillations.
21. Resonating group method for baryon-baryon interactions with unequal oscillator frequencies and its application to the $N\Delta$ system in a chiral quark model
   Source: nucl-th (Nuclear Theory)
   Link: https://arxiv.org/abs/2602.12148
   The resonating group method (RGM) is widely used to investigate baryon-baryon interactions at the quark level, typically under the assumption that the two baryons involved share an identical harmonic-oscillator frequency.
22. Profile-Likelihood and Baseline-Sensitivity Diagnostics for Digitized Radiation-Sensor Decay Datasets
   Source: nucl-ex (Nuclear Experiment)
   Link: https://arxiv.org/abs/2607.13118
   Accurate interpretation of radiation-sensor decay data is important for environmental monitoring, site remediation, radiation metrology, detector quality assurance, and nuclear data evaluation.
23. Wavy synchronization in locomotion of train millipedes
   Source: nlin.AO (Adaptation and Self-Organizing Systems)
   Link: https://arxiv.org/abs/2504.04173
   The sophisticated control of many legs by millipedes and centipedes establish well-organized temporal structures such as wavy synchronization in their gate patterns.
24. Generalized Integrable Boundary States in XXZ and XYZ Spin Chains
   Source: nlin.SI (Exactly Solvable and Integrable Systems)
   Link: https://arxiv.org/abs/2601.16605
   We investigate integrable boundary states in the anisotropic Heisenberg chain under periodic or twisted boundary conditions, for both even and odd system lengths.
25. Spread of Entanglement in Generalized Kicked Ising Chain
   Source: nlin.CD (Chaotic Dynamics)
   Link: https://arxiv.org/abs/2608.09695
   We investigate the dynamics of entanglement in a generalized version of the kicked Ising chain, extending the model from the standard qubit case (local dimension $q=2$) to higher local dimensions ($q > 2$).
26. Degenerate four-wave mixing in a CPT-symmetric coupler with intermodal dispersion
   Source: nlin.PS (Pattern Formation and Solitons)
   Link: https://arxiv.org/abs/2608.08628
   Four-wave mixing provides a simple setting in which dispersion, nonlinearity, and non-Hermiticity compete to select resonant energy-transfer channels.
27. An Analysis on the Parton Distribution Functions of Heavy Mesons
   Source: nucl-th (Nuclear Theory)
   Link: https://arxiv.org/abs/2605.17389
   In this work, we investigate the constituent parton distribution functions (PDFs) of the kaon and heavy pseudoscalar mesons within the light-cone quark model.
28. Tensor analyzing power $T_{20}$ in the reaction $\gamma \vec{d}\to pn$ at photon energies 350-680 MeV
   Source: nucl-ex (Nuclear Experiment)
   Link: https://arxiv.org/abs/2608.09169
   We present measurements of the tensor analyzing power $T_{20}$ in the reaction $\gamma {d}\to pn$ at photon energies $E_\gamma = 350$-$680$~MeV.
29. Exact Low-Dimensional Reduction Theory for Populations of Stuart--Landau Oscillators
   Source: nlin.AO (Adaptation and Self-Organizing Systems)
   Link: https://arxiv.org/abs/2608.04000
   This paper develops an exact low-dimensional reduction theory for populations of Stuart-Landau oscillators.
30. Scalene Yang--Baxter triples as a source of hidden symmetries beyond the ordinary Yang--Baxter equation
   Source: nlin.SI (Exactly Solvable and Integrable Systems)
   Link: https://arxiv.org/abs/2608.09081
   We study a nearest-neighbor non-Hermitian spin chain obtained from one member of an exact non-braided scalene Yang--Baxter triple.
31. Learning a quantitative criterion for distinguishing chaos from noise
   Source: nlin.CD (Chaotic Dynamics)
   Link: https://arxiv.org/abs/2608.07109
   Distinguishing chaos from noise using time-series data is fundamentally challenging because both exhibit irregular fluctuations and share many statistical and dynamical characteristics.
32. Rogue-wave and lump patterns associated with the third Painlev\'{e} equation
   Source: nlin.PS (Pattern Formation and Solitons)
   Link: https://arxiv.org/abs/2604.23275
   We report rogue-wave and lump patterns associated with Umemura polynomials, which arise in rational solutions of the third Painlev\'{e} equation.
33. Analysis of Fully-Heavy and Hidden-Heavy Tetraquarks in Anisotropic Plasma Using the Generalized Fractional Derivatives
   Source: nucl-th (Nuclear Theory)
   Link: https://arxiv.org/abs/2606.23732
   Investigating the spectroscopy and thermal stability of exotic multiquark states provides crucial insights into the fundamental confinement mechanisms of quantum chromodynamics (QCD) under extreme regimes.
34. Alpha Particle Induced Collision Cascade Fusion
   Source: nucl-ex (Nuclear Experiment)
   Link: https://arxiv.org/abs/2608.09831
   We report experimental and computational investigations of a collision-cascade mechanism to induce deuterium-deuterium (D-D) fusion.

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 34 of 485 available items for this weekly brief.