# gst: dynamics of coupled stochastic van der Pol oscillators; bifurcations, synchronization and chaos.

<< ️This (AA) work presents a comprehensive analysis of coupled stochastic van der Pol oscillators, a paradigm for understanding synchronization, bifurcations, and chaos in nonlinear systems subject to random fluctuations. The system comprises two or more oscillators with nonlinear damping, linear diffusive coupling, and additive Gaussian white noise. >>

<< ️(AA) develop a unified framework that systematically connects global bifurcations, synchronization phenomena, and chaotic dynamics within a single coherent stochastic model. (They) explore the stochastic dynamics of coupled van der Pol oscillators by seamlessly blending theoretical principles with in-depth numerical simulations. This integrated approach forms a robust framework for analysis, with essential phenomena clearly depicted in the accompanying figures. (AA) then extend this framework to a comprehensive investigation of large networks, focusing on their continuum limit, emergent pattern formation, the role of noise, and the onset of collective chaos. >>

Shenglan Yuan, Xiang Zhou. Dynamics of Coupled Stochastic van der Pol Oscillators: Bifurcations, Synchronization and Chaos.  arXiv: 2606.31445v1 [nlin.CD]. Jun 30, 2026. 

https://arxiv.org/abs/2606.31445v1

Also: chaos, noise, random, disorder & fluctuations, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, chaos, noise, randomness, disorder, fluctuations, coupled stochastic van der Pol oscillators, synchronization, bifurcations, emergent pattern formation, collective chaos.

# gst: quadruple decomposition of boundary vorticity flux.

<< ️First introduced by Lighthill in 1963 for two-dimensional flows and later generalized by Jie-Zhi Wu to three-dimensional scenarios since 1986, the boundary vorticity flux (BVF) is the cornerstone of boundary vorticity dynamics, which quantifies the vorticity source strength on a solid boundary. Recent advances in vorticity and vortex dynamics have revealed both the rigid-rotation and spin modes of vorticity from multiple perspectives. >>

<< ️In the present study, (AA) propose a novel quadruple decomposition of the BVF on a stationary solid wall, which essentially uncovers the boundary creation rates of the elementary vorticity modes for both the tangential and wall-normal BVF components, respectively. >>

<< The proposed framework is illustrated through skin-friction and surface-pressure measurements for flow over a hill model in a low-speed wind tunnel, revealing a set of intriguing BVF patterns for the first time. These theoretical results are expected to be valuable for global surface flow diagnostics when combined with experiments, as well as for understanding the formation mechanisms of near-wall coherent structures and flow-induced noise. >>

Tao Chen, Tianshu Liu. Quadruple decomposition of boundary vorticity 

flux. arXiv: 2606.28761v1 [physics.flu-dyn]. Jun 27, 2026. 

https://arxiv.org/abs/2606.28761

Also: vortex, noise, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, vortex, noise, transitions, boundary vorticity dynamics, boundary vorticity flux (BVF), skin-friction, 

surface-pressure, near-wall coherent structures, flow-induced noise. 

# life: continual learning against data poisoning attacks.

<< ️Continual learning (CL), where a model is trained on a sequence of data tasks, is increasingly being adopted across key fields such as large language models and image recognition, yet it remains highly vulnerable to data poisoning that triggers learning divergence or severe excess risk. Despite these threats, a principled theoretical foundation in CL for understanding attack and defense remains lacking. >>

<< ️In this paper, (AA) develop a theoretical framework to analyze strategic attacks and defenses in regularization-based CL, a cornerstone of recent CL theory. By framing the adversary-defender interaction as an online zero-sum game, (They) first establish a fundamental performance limit: no defense succeeds when an adversary poisons a linear proportion of tasks by injecting unbounded noise or pattern shifts in regularization-based CL. >>

<< ️(AA) then analyze two possibly defensible scenarios: infrequent attacks and bounded noise per attack. For the former regime, (They) propose a task-to-task verification mechanism to detect data poisoning and reduce cumulative bias for learning convergence. For the latter regime, (They) derive a robust defense that minimizes the model's sensitivity to poisoned features, provably accelerating the convergence rate. Extensive experiments on realistic tasks further validate our theoretical results. >>

Yiting Hu, Lingjie Duan. Theory of Continual Learning Against Data Poisoning Attacks. Proceedings of the 43rd International Conference on Machine Learning, Seoul, South Korea. PMLR 306, 2026. arXiv: 2606.29841v1 [cs.LG]. Jun 29, 2026.

https://arxiv.org/abs/2606.29841

Also: ai (artificial intell) (bot), nfulaw, noise, in https://www.inkgmr.net/kwrds.html 

Keywords: artificial intelligence (AI), bot, nfulaw, war, life, machine learning (ML), continual learning (CL), large language models (LLM), image recognition, vulnerability, data poisoning, robust defense, adversarial dynamics, adversarial manipulation, adversary-defender interaction, noise, unbounded noise. 

# gst: apropos of avalanche propagations (e.g. large cascades), sandpile models on complex networks.

<< ️(AA) investigate the sandpile model on complex networks by developing a branching-process framework that explicitly incorporates dissipation during avalanche propagation. Unlike classical branching descriptions, which assume conservative transport and locally tree-like independence, the present approach introduces grain-loss effects directly into the offspring distribution, yielding generalized generating functions for dissipative avalanche dynamics. >>

<< ️In the dissipative regime, avalanche-size distributions acquire exponential cutoffs while preserving topology-dependent scaling behavior. Numerical simulations confirm the theoretical predictions on sparse random networks and reveal systematic deviations in highly structured topologies. In particular, by using Holme-Kim clustered scale-free networks, (They) show that increasing clustering continuously lowers the avalanche exponent and enhances the probability of large cascades, demonstrating that short cycles generate strong correlations that invalidate the classical independent-branch approx imation. >>

<< ️Surprisingly, trees also exhibit substantial deviations from power-law because low edge density and the abundance of leaves constrain avalanche propagation. These results show that dissipation, clustering, and sparse connectivity fundamentally reshape avalanche size distribution of the sandpile model on networks and establish quantitative limits for branching-process descriptions of avalanche dynamics. >>

Komlan Fiagbe, Jean-François de Kemmeter, Timoteo Carletti. Sandpile Models on complex networks. arXiv: 2607.02023v1 [cond-mat.stat-mech]. Jul 2, 2026.

https://arxiv.org/abs/2607.02023

Also: network, dissipation, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, network, dissipation, sandpile, branching-process framework, avalanche propagation, grain-loss effects, dissipative avalanche dynamics, sparse random networks, clustering, sparse connectivity.

# gst: sudden expansion stability thresholds modified by lateral flows.

<< ️(AA) study the flow in a symmetric three-dimensional confined sudden expansion with lateral inflow at Reynolds number below 300 and varying lateral-to-central flow rate ratio, using experiments, linear stability analysis, weakly nonlinear theory, and direct numerical simulations. >>

<< ️Three distinct flow regimes are identified. Outside an intermediate band of lateral-to-central flow rate ratio, the flow undergoes a steady symmetry-breaking bifurcation above a critical Reynolds number, deflecting the central jet toward one side wall; weakly nonlinear analysis shows this bifurcation to be supercritical, excepting a very narrow parametric range. Within the intermediate band, no such critical Reynolds number exists and direct numerical simulations confirm that residual velocity asymmetries reflect the imposed geometric imperfections rather than intrinsic amplification. Fluctuations observed experimentally in the intermediate band of lateral-to-central flow rate ratio remain unexplained and warrant further investigation. >>

T. Salamon, R. Debuysschère, A. Chafaï, et al. Sudden expansion stability thresholds modified by lateral flows. arXiv: 2606.30269v1 [physics.flu-dyn]. Jun 29, 2026.

https://arxiv.org/abs/2606.30269

Also: particle, instability, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, particles, instability, transitions, fluctuations, criticality, bifurcations, supercritical bifurcations, geometrical defects.

# gst: delay coordinates synchronization and induces abrupt transition in excitable networks.

<< ️Neuronal communication is inherently time-delayed, due to the finite speed of signal propagation. Although often considered challenging or disruptive, such time delays can also endow neural circuits with useful capabilities. Here, (AA) show that delays in excitatory connections between excitable neurons coordinate their synchronization patterns by creating self-sustained oscillations that may be out-of-phase or in-phase. The emergence of these oscillations leads to an abrupt, explosive, transition to in-phase synchronized regimes due to small changes in connection strength or time-delay. >>

<< ️(They) describe the mechanism underlying these phenomena as an interaction between the neuron's excitable dynamics and the delay in signal transmission, explaining many aspects of how the oscillations emerge. (They) show this phenomenon in different network connectivities, neuronal models, with and without excitation, with and without noise, highlighting the generality of the mechanism. >>

Bruno R.R. Boaretto, Kalel L. Rossi, Lyle E. Muller, et al. Delay coordinates synchronization and induces abrupt transition in excitable networks. arXiv: 2606.21703v1 [q-bio.NC]. Jun 19, 2026.

https://arxiv.org/abs/2606.21703

Also: network, brain, pause, noise, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, networks, brain, pause, noise, transitions, neuronal communication, time delay, synchronization patterns, self-sustained oscillations.

# brain: apropos of persistent exploratory predisposition, chaotic pigeons are helping redefine what we know about learning.

<< ️Pigeons seem to defy a century-old psychology law about how rewards and consequences help us learn. >>

<< ️New research suggests the birds themselves avoid stability in their decision-making, instead choosing to live “at the edge of chaos.” As model species for learning and behavior, these birds are helping researchers test a century-old law about how humans and other creatures learn. >>

<< ️When learning something new, people and animals alike tend to repeat behaviors that are rewarded. First proposed by Edward Thorndike in 1898, this principle is so well established in psychology that it's become known as the law of effect. But the law implies that beyond making a behavior more frequent, rewards also make it more consistent: reducing variability in the specific way behaviors are performed over time. >>

<< ️Edward A. Wasserman and his colleagues decided to put it to the test in pigeons—a species that has been integral to the study of learning at the university’s Comparative Cognition Laboratory for more than 50 years. And the study’s results, published in the Journal of Experimental Psychology: Animal Learning and Cognition, suggest these birds experience variability as the spice of life. >>

<< ️You could argue the birds are just utterly resistant to locking into anything stable. >> Edward A. Wasserman.

<< ️this paper leaves open many questions about the [neurological] mechanisms for future scientists to explore. >> Aaron Blaisdell.

K. R. Callaway, Sarah Lewin Frasier. Chaotic pigeons are helping redefine what we know about learning. SciAm. Jun 30, 2026. 

https://www.scientificamerican.com/article/chaotic-pigeons-are-helping-redefine-what-we-know-about-learning

Wasserman E.A., Orr O.R.P., Li S. Variability, stability, and the law of effect. J. of Exp. Psychol: Animal Learning and Cognition, 52(3), 129–138. Jul 2026. 

https://psycnet.apa.org/record/2027-47688-001

Also: brain, neuro, behav, curiosity, game, Nomads, in https://www.inkgmr.net/kwrds.html 

Keywords: brain, behavior, curiosity, games, Nomads.

# aibot: critical percolation as a synthetic data model for interpretability.

<< ️Neural networks learn features that reflect the hierarchical, multi-scale structure of natural data. Synthetic datasets used to evaluate interpretability methods typically lack this structure, limiting their value as realistic toy models. >>

<< ️To close this gap, (AA) introduce a family of synthetic datasets consisting of hierarchical functions defined on critical mean-field percolation clusters embedded in a high-dimensional data space. The percolation data consists of sparse, low-dimensional fractal clusters with a power-law size distribution. Latent variables modeling a taxonomic hierarchy generate each data point's target value. >>

<< The data model is analytically tractable with known critical exponents that fix its properties without requiring hyperparameter tuning. (They) leverage a mapping between percolation clusters, random trees, and additive coalescence to propose an almost linear-time algorithm to jointly sample a random tree and its hierarchical latent decomposition, enabling data generation at arbitrary scale. >>

<< ️Using probing experiments, (AA) find that the model's ground-truth latent variables can be linearly decoded from neural network activations. Together, sparsity, self-similarity, power-law statistics, and analytical tractability make critical percolation a principled testbed for interpretability research. >>

Aryeh Brill, Tom Ingebretsen Carlson. Critical Percolation as a Synthetic Data Model for Interpretability. arXiv: 2606.20347v1 [cs.LG]. Jun 18, 2026.

https://arxiv.org/abs/2606.20347

Also: ai, artificial intell, bot, network, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, ai, artificial intell, bot, networks, neural networks, percolation, criticality, critical percolation, critical mean-field percolation clusters, interpretability research, random trees, fractals, hierarchical latent decomposition, sparsity, self-similarity, power-law statistics.

# gst: localization pattern of a mobile impurity in the disordered Kitaev chain.

<< (AA) study a mobile impurity coupled to a Kitaev chain with chemical-potential disorder and ask whether the impurity behavior distinguishes different regimes of the host system. Exact diagonalization calculations for small periodic chains shows that in the deep topological regime the impurity localizes only partially, with a smooth increase of IPR_d, whereas in the deep trivial regime it undergoes a much sharp transition to nearly single-site localization. >>

<< For open chains at strong interaction, DMRG shows edge-localized impurity density near the Kitaev sweet spot. With increasing chemical potential, the impurity weight spreads into the bulk and eventually becomes almost uniform. (They) explain the edge preference analytically from the Majorana-dimer structure: a bulk impurity rearranges two neighboring dimers, while an edge impurity affects only one. >>

<< Disorder competes with this clean edge bias and can pin the impurity in the bulk. Thus, the impurity is sensitive to the regime of the host system, although (AA) do not find a strict one-to-one correspondence between the impurity localization pattern and the host topology. Instead, the disorder-averaged behavior suggests only an indirect correlation between impurity localization and the underlying phase of the chain. >>

A.V. Sadovnikov, A.N. Rubtsov. 

Localization pattern of a mobile impurity in the disordered Kitaev chain. arXiv: 2606.21499v1 [cond-mat.str-el]. Jun 19, 2026.

https://arxiv.org/abs/2606.21499

Also: disorder, disorder & fluctuations, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, disorder, disorder & fluctuations, mobile impurity, bulk impurity, edge impurity, deep topological regime, deep trivial regime. 

# gst: uncertainty growth in stably stratified turbulence.

<< ️(AA) investigate uncertainty growth and chaotic dynamics in statistically steady, stably stratified three-dimensional turbulence. Using direct numerical simulations of the Boussinesq equations, (They) quantify the divergence of initially infinitesimal perturbations via twin simulations and decorrelator diagnostics. >>

<< ️At short times, perturbations exhibit exponential growth, allowing us to define a (largest) Lyapunov exponent. (AA) systematically examine how this exponent depends on stratification strength, quantified by the Brunt-Väisälä frequency and the Froude number, in a parameter regime relevant to oceanic flows. >>

<< (They) find that increasing stratification leads to a monotonic reduction of the Lyapunov exponent, indicating suppressed chaoticity. Despite this reduction, uncertainty growth retains the universal temporal sequence observed in homogeneous isotropic turbulence—initial decay, exponential growth, and saturation. The growth phase is characterized by self-similar decorrelator spectra, but exhibits strong anisotropy: uncertainty spreads much more slowly along the stratification direction than horizontally, with the disparity increasing with stratification strength. >>

<< ️An analysis of the decorrelator evolution equation reveals that the suppression of chaos arises primarily from strain-mediated alignment dynamics rather than direct buoyancy coupling. (AA) results provide a quantitative characterization of predictability and uncertainty growth in stratified turbulence and highlight the utility of decorrelator-based methods for anisotropic geophysical flows. >>

Mrinal Jyoti Powdel, Samriddhi Sankar Ray. Uncertainty growth in stably stratified turbulence. Phys. Rev. Fluids 11, 064615. Jun 23, 2026. 

https://journals.aps.org/prfluids/abstract/10.1103/xblr-vpl3

arXiv: 2512.05656v1 [physics.flu-dyn].

https://arxiv.org/abs/2512.05656

Also: chaos, turbulence, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, chaos, turbulence, transitions, uncertainty growth, three-dimensional turbulence, stratified turbulence, infinitesimal perturbations, stratification strength, anisotropy. 

# gst: oscillating concentrations suppress condensate coarsening.

<< ️Living cells utilize condensates to spatially concentrate molecules in response to dynamic signals. For instance, nuclear condensates respond to oscillations in transcription factor levels in the nucleoplasm, including those involved in repairing multiple DNA breaks. >>

<< ️To understand how oscillating signals affect condensates, (AA) analyze a theoretical model using numerical simulations and analytical theory. While passive dynamics would drive all molecules into a single condensate, (They) find that sufficiently fast oscillations stabilize multiple droplets, allowing control of their sizes. (They) thus reveal a new behavior of chemically active droplets, which could be exploited in synthetic applications. >>

Mathias S. Heltberg, Lukas H. Kristensen, Mogens H. Jensen, David Zwicker. Oscillating concentrations suppress condensate coarsening. arXiv: 2606.16614v1 [physics.bio-ph]. Jun 15, 2026.

https://arxiv.org/abs/2606.16614

Also: drop, droplet, droploid, self-assembly, disorder & fluctuations, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, drop, droplet, droploid, self-assembly, disorder & fluctuations, chemically active droplets, spatially concentration, nuclear condensate. 

# gst: chiral packings in cylinders are ultrasensitive to confinement deformation.

<< ️Sphere packings in circular cylinders have attracted substantial research interest, among which the discovery of chiral helical structures is the most iconic. However, recent experimental results on zebrafish do not match the known packing structures in circular cylinders. >>

<< ️To account for the inherent imperfections of biological tubes, (AA) take elliptic cylinders as the canonical deformation of circular cylinders and investigate the densest packings of hard spheres in them using simulation, theory, and experiments. Starting from the chiral structures in circular cylinders, (They) demonstrate that even a weak cross-sectional deformation can trigger entirely new phases, including ones that either eliminate global chirality or significantly complicate the chiral structures. ️This reveals the significant effect of cylindrical anisotropy. >>

<< ️The new helical phases under anisotropic confinement remain chiral and develop hierarchical periodic structures, which are difficult to obtain by simulations but are predicted by our newly developed theory for helical phases in elliptic cylinders. >> 

<< ️The theory also predicts double oscillated-chain phases without chirality, which perfectly match the simulations. (Their) work offers fresh insights into understanding packings in anisotropic cylinders, which will help researchers to design new materials and to understand many living systems. >>

Xuebin Wang, Jiahao Guo, Yao Li. Chiral Packings in Cylinders are Ultrasensitive to Confinement Deformation. arXiv: 2606.19082v1 [cond-mat.soft]. Jun 17, 2026.

https://arxiv.org/abs/2606.19082

Also: chiral, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, chirality, transitions, packings, chiral helical structures, elliptic cylinders, cylindrical anisotropy, double oscillated-chain phases. 

# gst: rotation sets and topological entropy for random circle endomorphisms.

<< ️(AA) study the topological dynamics of random circle endomorphisms of degree one over an ergodic measure-preserving dynamical system. Under an integrability assumption, (They) prove that the random rotation set is almost surely the compact interval whose endpoints are the mean random rotation numbers of the associated lower and upper random maps. (They) also show that the natural orbitwise versions of the random rotation set agree almost surely, and on the same full-measure set, every value in this interval is realised as the asymptotic average displacement along an individual orbit. >>

<< ️In addition, every closed subinterval of the random rotation set is realised, on a full-measure set, as the set of accumulation values of the displacement averages along a single orbit. ️Finally, (AA) prove that a positive length of the random rotation set implies a positive random topological entropy, in contrast to random monotone maps, which have zero random topological entropy. (They) illustrate the theory by computing the random rotation set and random topological entropy for a piecewise linear example. >>

Zixu Li, Simon Lloyd, Sergio Romaña. Rotation Sets and Topological Entropy for Random Circle Endomorphisms. arXiv: 2606.16498v1 [math.DS]. Jun 15, 2026.

https://arxiv.org/abs/2606.16498

Keywords: gst, randomness, random rotations, entropy.

# gst: on the geometry of spreading puddles.

<< ️(AA) develop a geometric model for the spreading of shallow, viscous puddles of arbitrary shape, building on the recent 'capillary current' model for axisymmetric droplets. In short, (They) assume that a spreading puddle remains close to instantaneous mechanical equilibrium as it spreads, with hydrostatic pressure balanced by surface curvature. In turn, its contact line advances so as to maximize the rate of energy loss subject to viscous dissipation. >>

<< ️The resulting system yields a natural geometric evolution equation for both the two-dimensional footprint and the three-dimensional depth profile of a spreading puddle. In appropriate limits, it recovers the classical spreading laws for axisymmetric droplets, a local version of the Hoffman-Voinov-Tanner law for small non-axisymmetric puddles, and a nonlocal Hele-Shaw-like description for large, relatively regular puddles. >>

David Darrow. On the Geometry of Spreading Puddles. arXiv: 2606.13893v1 [physics.flu-dyn]. Jun 11, 2026.

https://arxiv.org/abs/2606.13893

Also: drop, droplet, droploid, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, drops, droplets, droploids, spreading puddle, axisymmetric droplets, surface curvature, viscous dissipation.

# gst: dissipation-coherence tradeoff for stochastic oscillations.

<< ️Autonomous noisy oscillations in biochemical and mesoscopic systems require nonequilibrium driving and therefore dissipation. A striking conjecture by Oberreiter, Barato, and Seifert (OBS) proposes a universal lower bound on the entropy produced per oscillation period in terms of the coherence number of the slowest oscillatory mode (L. Oberreiter et al. [Phys. Rev. E 106, 014106 (2022)]). >>

<< ️Here (AA) derive a weaker but rigorous lower bound that preserves the OBS structure while introducing a mode-uniformity factor that quantifies how evenly the oscillatory eigenmode is distributed across states in the steady-state inner product. The result makes explicit that an eigenvalue-only prefactor can fail when the dominant oscillatory mode is localized. >>

<< ️(They) also outline a proof-of-principle route for estimating this factor from low-dimensional data under single-mode dominance and sufficiently informative measurements, and derive an eigenvector-free corollary using only the smallest stationary probability. >>

<< ️Translation-invariant Markov jump processes on a ring provide a symmetry-protected class with 𝜂=1, so the refinement reduces to the OBS form; the drift-diffusion limit on a circle saturates the bound. >>

Jie Gu. Dissipation-coherence tradeoff for stochastic oscillations. Phys. Rev. E 113, 064130.  Jun 15, 2026.

https://journals.aps.org/pre/abstract/10.1103/zxw1-zdb7

arXiv: 2606.05498v1 [cond-mat.stat-mech]. Jun 3, 2026.

https://arxiv.org/abs/2606.05498

Also: noise, disorder, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, noise, disorder, dissipation, entropy, stochasticity, stochastic processes, autonomous noisy oscillations, stochastic oscillations, disorder-induced localization, time series analysis, transitions.

# life: apropos of singular, bizarre, un.expected convergences, here an asymptotic, extreme, double 'quasistochastic tit-for-tat' exploit (within the same time window).

(A1)

<< “There were no moments of friction or disagreement,” Italian Prime Minister Giorgia Meloni said at a press conference Wednesday. “I found that, overall, there was a desire to work together, and that’s not something to be taken for granted.” >>. 

Myah Ward, Clea Caulcutt, Giorgio Leali. Trump clears low bar for G7 summit in France. Jun 17, 2026.

https://www.politico.com/news/2026/06/17/trump-and-allies-keep-the-peace-at-the-g7-summit-after-months-of-tumult-00966117

(A2)

<< However, Trump has since given a phone interview with Italy's La7 TV channel in which he alleged: "She begged me to take a photo with her; I felt sorry for her." >>. 

Paul Kirby, Europe digital editor, Davide Ghiglione, Rome, James Landale, Diplomatic correspondent. Italy's Meloni says Trump 'made up' story that she 'begged' him for photo at G7. BBC. Jun 19, 2026. 

https://www.bbc.com/news/articles/c20y1ygn707o

(B) 

<< Donald Trump arrived in France yesterday for this morning’s G7

summit and promptly confirmed America’s capitulation to Iran. >>

Tom Nichols. Trump Does Not Understand the War He Lost. The Atlantic Daily. Jun 16, 2026.

https://www.theatlantic.com/newsletters/2026/06/trump-g7-comments-misunderstsand-middle-east/687569/

(A&B)

<< qui i due estremi: era modicamente non cooperatore e ha ricevuto come reazione una "bastonata"; era assolutamente ostile e ha ricevuto la classica "pacca sulla spalla" ... >>

Donald, what he can do (with less than four lines ...). FonT. May 23, 2016.

https://flashontrack.blogspot.com/2016/05/p-usa-potus-race-donald-what-he-can-do.html 

FonT

Ultimately, here too one could hypothesize another case of historic, singular checkmate of 'one against all'. Anzicheforse?

Also: Mr. Donald, tit-for-tat, game, dance, in https://www.inkgmr.net/kwrds.html

Also: here's another checkmate (FonT. Dec 4, 2024)

https://flashontrack.blogspot.com/2024/12/life-apropos-of-saliva-healers-herd.html 

Keywords: Mr. Donald, tit-for-tat, game, dance 

# gst: on maximal delay of stability loss for dynamical bifurcations.

<< ️(AA) consider a dynamical bifurcation caused by a slow passage through a static bifurcation point: in a system depending on a parameter, the parameter changes slowly in time and passes through the critical value corresponding to the loss of stability of an equilibrium via a Poincaré--Andronov--Hopf bifurcation in the frozen system. >>

<< ️If the system is analytic, then the loss of stability is inevitably delayed: phase points attracted to the equilibrium in the stability region remain near the equilibrium for a long time after entering the instability region, so that the parameter changes by an amount of order ~1 independently of how slow the variation of the parameter is. Remarkably, there exists a maximal delay: all phase points attracted to the stable equilibrium before a certain threshold value of the parameter leave a neighbourhood of the unstable equilibrium almost simultaneously near another threshold value of the parameter, known as a buffer point. >>

<< ️A delay of stability loss beyond the buffer point is impossible unless the initial data have a very special form. (AA) assume that, although the equilibrium is non-degenerate for real values of the parameter, one of its eigenvalues vanishes generically for some complex value of the parameter (a complex analogue of a saddle-node bifurcation), and that this complex singularity is, in a suitable sense, the closest one to the real Poincaré--Andronov--Hopf bifurcation point. >>

<< ️(AA) show that the value of maximal delay is determined by this complex singularity: the threshold values defining the maximal delay are the intersection points of the Stokes lines associated with this singularity and the real axis. (They) study these phenomena in the framework of slow--fast dynamical systems. >>

Anatoly Neishtadt. On Maximal Delay of Stability Loss for Dynamical 

Bifurcations. arXiv: 2606.07662v1 [math.DS]. Jun 3, 2026.

https://arxiv.org/abs/2606.07662

Also: instability, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, instability, transitions, dynamical bifurcation, bifurcation point, loss of stability, delay, maximal delay, buffer point, saddle-node bifurcation, complex singularity, slow--fast dynamical systems.

# aibot: parasitic masquerade; societal scale human-machine interaction.

<< This (AA) work extends recent developments in studying human--machine interaction by scaling from individual game-theoretic models to a societal-level model. (They) adopt a Graphon Mean-Field Game (GMFG) that models the interaction among four groups of internally-homogeneous but externally-heterogeneous agents in a shared environment. >>

<< (AA) results show that parasitism can masquerade as productive learning, with knowledge distribution and actions appearing healthy while being driven by machine coupling rather than independent investigation. To detect this, (They) measure the direction of information flow and belief entropy of the environment, revealing that human to machine channel dominates across all scenarios, with the asymmetry intensifying under parasitism. >>

<< (They) further demonstrate that the system exhibits coexisting mutualistic and parasitic equilibria, where environmental noise can induce a tipping point that shifts agents past the cognitive cost barrier. These emergent phenomena are not designed into any individual agent but arise from the collective interaction structure, underscoring the need to study the sociology of humans and machines holistically as a complex system. >>

Jiejun Hu-Bolz, James Stovold. Parasitic Masquerade: Societal Scale Human-Machine Interaction. arXiv: 2606.17925v1 [cs.GT]. Jun 16, 2026.

https://arxiv.org/abs/2606.17925

Also: ai, bot, artificial intelligence, analogy, noise, in https://www.inkgmr.net/kwrds.html

Keywords: ai, aibot, artificial intelligence, human--machine interaction, Graphon Mean-Field Game (GMFG), parasitism, masking, masquerade as productive learning, mutualistic and parasitic equilibria, environmental noise, sociology of humans and machines.

# gst: collective drift and pinning in active rotator networks with Kuramoto coupling and mixed-sign feedback disorder.

<< ️Active rotator models provide a minimal phase description of excitable and oscillatory systems, and have long been used to study mutual entrainment, synchronization, and collective transitions. >>

<< ️Here, (AA) investigate fully connected active rotator networks with Kuramoto coupling, where a common intrinsic drive competes with local feedback amplitudes drawn from a zero-mean Gaussian distribution. This produces a competition between local pinning and collective phase alignment. >>

<< ️Using mean absolute late-time drift and the fractions of positive and negative drifting oscillators, (They) construct numerical regime maps in the feedback-disorder-coupling plane. At weak coupling, increasing the feedback disorder strength suppresses drift, while stronger coupling can restore positive late-time drift when feedback disorder is not too strong. (They) interpret these regimes using analytical limits for the uncoupled and coherent strong-coupling cases. >>

<< ️(They) also examine finite-size effects and zero-mean distributed intrinsic frequencies. Together, these results show that mixed-sign local feedback alone can reshape the balance between pinning and drifting in coupled active rotator networks, even when the intrinsic drive is homogeneous. >>

Arpan Dey. Collective drift and pinning in active rotator networks with Kuramoto coupling and mixed-sign feedback 

disorder. arXiv: 2606.10032v1 [nlin.AO]. Jun 8, 2026.

https://arxiv.org/abs/2606.10032

Also: networks, disorder, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, networks, disorder, transitions, active rotator networks, excitable- oscillatory- systems, Kuramoto coupling, local feedbacks, feedback disorder.

# gst: randomised mixed labyrinth fractals.

<< ️In this (AA) paper, the class of randomised mixed labyrinth fractals is introduced. It is a class of finitely ramified Sierpinski carpets that generalize mixed labyrinth fractals. >>

<< ️The structures are generated by randomly selected labyrinth patterns with fixed selection probabilities at each iteration level, offering a flexible framework to study fractal topology, arc dimensions, and shortest path properties. Here, the focus lies on analysing how the randomised mixing of patterns - specifically their shape, symmetry, and path geometry - effects arc dimensions, path lengths, and isotropy restoration. >> 

<< ️The (AA) study reveals that isotropy, previously shown for self-similar fractals, extends to the randomised mixed class. Various scaling behaviours of shortest path dimensions with respect to the mixing probability are identified, including linear and nonlinear monotonic trends, as well as transitions with maxima. The approximated path matrix is proposed as an efficient alternative to extensive iterative simulations, reliably reproducing statistical results. >>

<< ️The findings highlight the relevance of pattern properties in determining fractal structures and dynamics and suggest applications in physical systems such as diffusion, signal processing, and antenna design. >>

Janett Prehl, Ligia Loretta Cirstea, Daniel Dick. Randomised mixed labyrinth 

fractals. arXiv: 2606.07241v1 [cond-mat.dis-nn]. Jun 5, 2026.

https://arxiv.org/abs/2606.07241

Also: random, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, randomness, transitions, fractals, fractal topology, labyrinth fractals, Sierpinski carpets, randomly labyrinth patterns.

# game: apropos of “tit-for-tat” approach, the evolution of lying in a spatially-explicit prisoner's dilemma model.

<< ️(AA) present the results from a spatial model of the prisoner’s dilemma, played on a toroidal lattice. Each individual has a default strategy of either cooperating (C) or defecting (D). Two strategies were tested, including “tit-for-tat” (TFT), in which individuals play their opponent’s last play, or simply playing their default play. Each individual also has a probability of telling the truth (0 ≤ P_(truth) ≤ 1) about their last play. >>

<< ️This parameter, which can evolve over time, allows individuals to be, for instance, a defector but present as a cooperator regarding their last play. >>

<< ️This leads to interesting dynamics where mixed populations of defectors and cooperators with P_(truth) ≥ 0.75 move toward populations of truth-telling cooperators. >>

<< ️Likewise, mixed populations with P_(truth) < 0.7 become populations of lying defectors. >>

<< ️Both such populations are stable because they each have higher average scores than populations with intermediate values of P_(truth). Applications of this model are discussed with regards to both humans and animals. >> 

Gregg Hartvigsen. The Evolution of Lying in a Spatially-Explicit Prisoner's Dilemma Model. arXiv: 2602.02587v1 [physics.soc-ph]. Jan 31, 2026.

https://arxiv.org/abs/2602.02587

Also: tit-for-tat, game, in https://www.inkgmr.net/kwrds.html 

Keywords: game, tit-for-tat, prisoner's dilemma, toroidal lattice, cooperating- defecting- strategies, truth-telling cooperators, lying defectors.

# behav: decomposition of anomalous diffusion in two-state random walks.

<< ️Two-state stochastic models, where motion alternates between distinct dynamical modes, are widely observed in complex systems. Here (AA) study the Two-State Random Walk (TSRW), which switches between a continuous-time random walk (CTRW) rest state and a standard Lévy walk (LW) motion state, each with power-law distributed sojourn times. >>

<< ️Using anomalous diffusion decomposition, (They) show that TSRWs exhibit a generic coexistence of Joseph (correlation), Noah (heavy-tailed increments), and Moses (aging) effects. >>

<< ️Strikingly, although classical Lévy walks alone possess only the Joseph effect, both Noah and Moses effects emerge in TSRWs solely due to stochastic switching with the CTRW phase. >>

<< ️(Their) results demonstrate that coupling between dynamical states can fundamentally reshape the mechanisms driving anomalous diffusion, offering a minimal yet powerful framework for transport in heterogeneous and intermittently switching environments. >>

Abhijit Bera, Kevin. E. Bassler. Decomposition of Anomalous Diffusion in two-state random walks. arXiv: 2606.00149v2 [nlin.AO]. Jun 7, 2026.

https://arxiv.org/abs/2606.00149

Also: behav, random, walk, walking, in https://www.inkgmr.net/kwrds.html 

Keywords: behavior, randomness, walk, walking, two-state stochastic behavior, two-state random walk, stochastic switching, Lévy walk motion, Joseph Noah Moses effects, anomalous diffusion, heterogeneous and intermittently switching environments. 

# gst: localization of active particles on random arrays of parallel filaments.

<< ️Quenched disorder in the environment can fundamentally alter transport dynamics in both active and passive systems. (AA) explore how disordered arrays of filaments govern the distribution of intermittently moving particles which switch between diffusive and processive transport. >>

<<️ Motivated by the mixed-polarity arrangements of parallel microtubules observed in mammalian dendrites, (They) show that such arrays tend to result in localization of particles at regions of convergent filament orientation. In the rapid attachment-detachment limit, the disordered system can be described by a noisy one-dimensional effective energy landscape, whose structure is approximated by a random walk. >>

<< ️The depth and width of wells on this landscape are expressed as a function of the transport kinetics and system geometry. Localization is shown to be strongest at intermediate run-lengths, where biased transport persists long enough to sense the quenched filament polarity but not so long as to facilitate escape from local traps. >>

<< ️These (AA) results demonstrate robust localization of particles moving on random filament networks, highlighting the emergent spatial organization that arises from an interplay of active transport and quenched disorder. >>

Owen Santoso, Elena Koslover. Localization of Active Particles on Random Arrays of Parallel Filaments. arXiv: 2606.00286v1 [cond-mat.dis-nn]. May 29, 2026.

https://arxiv.org/abs/2606.00286

Also: noise, disorder, disorder & fluctuations, random, intermittency, escape, particle, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, noise, disorder, disorder & fluctuations, randomness, intermittency, escape, particles, quenched disorder, transport dynamics, diffusive and processive transport, arrays of filaments, random walk, random filament networks, escape from local traps.

# gst: hierarchical crack patterns; identification of crack generations.

<< ️Hierarchical crack patterns of various origins are ubiquitous in the world around us. (AA) reduce the problem of classifying crack generations in an image of a part of the entire hierarchical crack pattern to the well-known topological sorting of a directed acyclic graph. The classification demonstrates robustness to reasonable shifts in the pattern image boundaries. >>

Yuri Yu. Tarasevich, Andrei S. Burmistrov, Andrei V. Eserkepov. Hierarchical crack patterns: Identification of crack generations. arXiv: 2606.03473v1 [cond-mat.dis-nn]. Jun 2, 2026.

https://arxiv.org/abs/2606.03473

Also: crack, fracture, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, crack, fracture, fragment of hierarchical crack pattern, topological sorting, root cracks, network 

fragment, hierarchical network structure.

# gst: percolation criticality of amorphous-amorphous transitions (in compressed glasses).

<< ️The low-to-high-density transition in compressed silica glass is investigated using percolation theory. Large-scale molecular dynamics simulations of SiO glasses, (..) were carried out (by AA) to investigate the emergence of structural motifs and their growth to system-spanning length scales under compression. >>

<< ️Taken together, these results underline the consistency between the bonded and non-bonded approaches. Native tetrahedral clusters, (..) collapse according to a process close to the random percolation model. >>

<< ️For all other percolation transitions, i.e. involving clusters with higher coordination number and connectivity, the deviation of the exponents instead suggests a different universality class. It can be argued that for these structures, the transition occurs in a medium where the percolating cluster is surrounded by an infinite cluster of lower coordination and connectivity, alongside emerging clusters with higher coordination and connectivity, resulting in topological, and hence elastic, heterogeneities. This behavior recalls topological constraint theory, also known as percolation rigidity, that arises from a flexible to a rigid network as local connectivity changes >>.

Julien Perradin, Simona Ispas, Ricardo V. Paredes, et al. Percolation Criticality of Amorphous-Amorphous Transitions in Compressed Glasses. arXiv: 2606.04748v1 [cond-mat.dis-nn]. Jun 3, 2026.

https://arxiv.org/abs/2606.04748

Also: random, fluctuations, collapse, transition,  in https://www.inkgmr.net/kwrds.html 

Keywords: gst, randomness, fluctuations, collapse, transitions, percolation theory, random percolation, rigidity percolation, critical percolation, bonded and non-bonded approaches, topological constraint theory, amorphous structures, crystalline polymorphs, origin of plasticity.

# gst: effective synchronization amid noise-induced chaos.

<< ️Two remote agents with synchronized clocks may use them to act in concert and communicate. This necessitates some means of creating and maintaining synchrony. One method, not requiring any direct interaction between the agents, is to expose them to a common, environmental, stochastic forcing. This “noise-induced synchronization” occurs only under sufficiently mild forcing; stronger forcing disrupts synchronization. >>

<< ️(AA) investigate the regime of strong noise, where the clocks' relative phases evolve chaotically. Using a simple realization of disruptive noise, (They) demonstrate effective synchronization. First, although the relative phases of the two clocks varied erratically, (They) confirm that they became statistically independent of initial conditions and hence equivalent after a well-defined timescale. Second, (They) show that an agent can estimate an effective phase that closely agrees with the other's phase. Thus, synchronization is practically attainable beyond the regime of conventional noise-induced synchronization. >>

Benjamin Sorkin, Thomas A. Witten. Effective synchronization amid noise-induced chaos. Phys. Rev. E 113, 054215. May 19, 2026.

https://journals.aps.org/pre/abstract/10.1103/rqgs-99d9

arXiv: 2505.08942v3 [cond-mat.stat-mech]. Feb 22, 2026.

https://arxiv.org/abs/2505.08942

Also: noise, chaos, transition,  in https://www.inkgmr.net/kwrds.html 

Keywords: gst, noise, chaos, transitions, noise-induced transitions, noise-induced synchronization, noise-induced chaos, synchronization transition, kick, kicked trajectory.

# gst: superflows around corners.

<< ️(AA) investigate analytically and numerically the dynamics of a two-dimensional superflow governed by the Gross-Pitaevskii equation passing over finite-size rectangular obstacles: an impenetrable wall and an impenetrable rectangular well. >>

<< ️Extending classical studies of vortex nucleation around smooth obstacles, (They) focus on the role of sharp corners in determining the onset of vortex nucleation. Using a combination of analytical techniques based on the Schwarz-Christoffel methods for potential flow and on numerical simulations, (They) show that local velocity amplification near sharp corners crucially controls the critical flow velocity for vortex nucleation. For both wall and well configurations, (They) identify analytically and theoretically the critical velocities as a function of the obstacle width and its height or depth, finding excellent agreement between the theory and numerical simulations. >>

<< ️(Their) results provide a simple  framework for understanding superflow stability past finite-size obstacles with sharp features, and they are directly relevant to experimentally realizable configurations in atomic Bose-Einstein condensates and related superfluid systems. >>

Thomas Frisch, Christophe Josserand, Sergio Rica. Superflows around corners. Phys. Rev. Fluids 11, 054703. May 20, 2026.

https://journals.aps.org/prfluids/abstract/10.1103/77hn-2hqf

arXiv:2602.18876v1 [cond-mat.quant-gas]. Feb 21, 2026.

https://arxiv.org/abs/2602.18876

Also: vortex, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, vortex, vortex nucleation, two-dimensional superflow. 

# gst: describing a universal critical behavior in a transition from order to chaos.

<< ️(AA) present a comprehensive discussion of a transition from integrability to nonintegrability in an oval billiard with a static boundary. This transition is controlled by a deformation parameter 𝜀, which modifies the boundary shape from circular, corresponding to 𝜀=0 and an integrable dynamics, to oval for 𝜀≠0, where nonintegrability emerges. >>

<< ️The deformation of the circular billiard gives rise to a chaotic layer that develops along a well-defined stripe in phase space. By introducing a set of transformations that isolate this chaotic stripe, (They) characterize the diffusive spreading of ensembles of trajectories and identify an observable, 𝜔_(rms,sat), which plays the role of an order parameter for the transition. >>

<< For small deformations, the saturation value of the diffusion obeys the scaling law 𝜔_(rms,sat)∝𝜀^(˜𝛼), with a critical exponent ˜𝛼=0.507⁢(2), vanishing continuously as 𝜀→0. The associated susceptibility, 𝜒=𝑑⁢𝜔_(rms,sat)/𝑑⁢𝜀, diverges in the same limit, signaling the presence of critical behavior analogous to that observed in second-order (continuous) phase transitions in statistical mechanics. >>

Edson D. Leonel, Mayla A. M. de Almeida, Juan Pedro Tarigo, et al. Describing a universal critical behavior in a transition from order to chaos. Phys. Rev. E 113, 054220. May 28, 2026.

https://journals.aps.org/pre/abstract/10.1103/7231-j7zv

arXiv: 2602.17810v1 [nlin.CD]. Feb 19, 2026.

https://arxiv.org/abs/2602.17810

Also: billiard, transition, order, disorder, chaos, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, billiard, oval billiard, transitions, order, disorder, elementary excitations, small deformations, topological defects, criticality, chaotic stripes, chaos.

# gst: orbital instability and spanwise vortex structure of unstable periodic orbits in large-eddy simulations of plane Couette flow.

<< ️(AA) perform an unstable periodic orbit (UPO) analysis of moderately developed Couette turbulence with large-eddy simulations (LES) using a static eddy viscosity model. >>

<< ️(They) find that spanwise vortices, stretched between streamwise rolls, approach the walls, over which new spanwise vortices are generated. The stretching of these vortices is driven by strong shear layers induced by the streamwise rolls. This vortex-generation mechanism, as revealed by the LES UPOs, is a significant dynamical process in LES turbulence at high Reynolds numbers. >>

<< ️By computing local Lyapunov exponents, which quantify the least stable perturbation growth rates along the UPOs, (They) show that the stretching process amplifies their growth. The corresponding Lyapunov vectors highlight the instability of prominent shear layers through which the stretched spanwise vortices emerge between the rolls. >>

<< ️(Their) results suggest that high-strain-rate structures in developed turbulence play a central role in shaping the geometrical structure of turbulent orbits in phase space. >>

Eiichi Sasaki, Javier Jiménez, Genta Kawahara. Orbital instability and spanwise vortex structure of unstable periodic orbits in large-eddy simulations of plane Couette flow. Phys. Rev. Fluids 11, 054603. May 14, 2026.

https://journals.aps.org/prfluids/abstract/10.1103/mtw2-29r3

Also: instability, turbulence, vortex, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, instability, turbulence, vortex, spanwise vortices, eddy viscosity model, unstable periodic orbit (UPO), streamwise rolls, stretching process.

# gst: apropos of interfacial contact events, bounce or coalescence, a physical learning frame.

<< ️In this study, (AA) develop an interface-contact simulation framework based on physical criteria and machine-learning-assisted classification to describe coalescence and bouncing within a unified formulation. The framework realizes interfacial coalescence and bouncing through the fusion and generation of multiple volume-of-fluid fields. When adjacent interfaces are predicted to coalesce, multiple VOF fields are collapsed into a single VOF field. When approaching interfaces are predicted to bounce, a single VOF field is regenerated into multiple VOF fields, allowing the interfaces to continue evolving independently. >>

<< With this treatment, the difficulties associated with topological transition, regime-map identification, increasing computational demand, and stochastic behavior during interfacial approach are separated from the interface-tracking procedure. These decisions are instead assigned to a physics-guided machine-learning model with strong adaptability. This strategy avoids the direct resolution of an ultrathin gas film and reduces the dependence on empirical molecular-force parameters. >>

<< ️Simulations of droplet--droplet collisions show that the proposed framework can reproduce both coalescence and bouncing over different impact conditions. By further introducing a drainage-time criterion, the framework is extended to the simulation of droplet impact on a liquid surface. For this problem, the numerical results agree well with both previous experimental observations and the present experiments. >>

<< ️Moreover, the framework captures the complete sequence of bouncing followed by subsequent coalescence within a single simulation, These (AA) results demonstrate that the proposed framework has strong adaptability for interfacial contact problems and provides a unified modeling route for droplet coalescence, bouncing. >>

J.H. Xu, Z.L. Wang. Bounce or coalescence: a physical learning frame. arXiv: 2605.15844v1 [physics.flu-dyn]. May 15, 2026. 

https://arxiv.org/abs/2605.15844

Also: drop, droplet, droploid, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, drops, droplets, droploids, coalescence, bouncing, volume-of-fluid (VOF) field, transitions, topological transitions, stochasticity, droplet--droplet collisions, interfacial contact events, 

# gst: multi-cluster chimeras in phase oscillators with repulsive nonlocal coupling.

<< ️Local repulsive coupling tend to a desynchronize ensembles of globally coupled oscillators, but when the repulsive coupling is nonlocal, multi-cluster chimeras can result. In this case, several groups of synchronized oscillators (the so-called clusters) are formed, and these coexist with a set of desynchronized oscillators. >>

<< ️For phase oscillators on a ring with nonlocal piecewise linear repulsive coupling that also involves a phase lag, (AA) find that in the multi-cluster chimera state the synchronized clusters are either antiphase or in splay with respect to each other, namely the n consecutive synchronized clusters differ in phase by 2π/n. >>

<< ️This is in contrast to multi-cluster chimeras that are formed with nonlocal attractive coupling. The synchronized solutions are studied numerically as well as analytically and by analysing their stability, (They) identify the parameter regions where these can be observed. (Their) numerical results are validated by dimensional reduction using the Ott-Antonsen analysis. >>

Ayushi Saxena, Sangeeta Rani Ujjwal, Ram Ramaswamy. Multi-cluster chimeras in phase oscillators with repulsive nonlocal coupling. arXiv: 2605.15628v1 [nlin.AO]. May 15, 2026.

https://arxiv.org/abs/2605.15628

Also: chimera, stability, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, chimera, stability, coupled oscillators, repulsive coupling, multi-cluster chimeras. 

# gst: formation of mechanical rogue waves.

<< ️Rogue waves, characterized by their abrupt and extreme localization in space and time, have evolved from maritime folklore to subjects of intense study across diverse fields, from hydrodynamics and nonlinear optics to plasmas and condensed matter physics. In mechanical systems, however, experimental realization remains elusive despite theoretical and numerical predictions. This gap stems from the stringent requirements for controllable nonlinearity, the high-fidelity initialization of the system, and the necessity to overcome inherent energy dissipation. >>

<< ️Here, (AA) report the experimental formation of mechanical rogue waves in a precisely engineered one-dimensional metamaterial lattice with tailored nonlinearity and minimal dissipative losses. Using a precision electromagnetic release system, (They) prescribe initial strain profiles that trigger a transition from dispersive decay to extreme wave focusing. >>

<< ️(Their) parametric analysis reveals that the emergence of these extreme events is strictly contingent upon a synergy between high nonlinearity and a broad spatial energy reservoir within the initial seed. Crucially, neither factor alone is sufficient to overcome dispersion and trigger the observed focusing. >> 

<< ️These findings establish a robust platform for studying transient nonlinear wave focusing phenomena in mechanical systems and offer insights for harnessing extreme wave localization for applications such as energy harvesting, waveguiding, and mechanical signal processing. >>

Yasuhiro Miyazawa, Christopher Chong, Panayotis G. Kevrekidis, et al. Formation of mechanical rogue waves. arXiv: 2605.18518v1 [nlin.PS]. May 18, 2026.

https://arxiv.org/abs/2605.18518

Also: waves, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, waves, rogue waves, mechanical rogue waves, transitions.

# gst: spin-hair induced chaos of spinning test particles in rotating hairy black holes.

<< ️(AA) investigate the finite-time instability of massive spinning test particles around a rotating hairy black hole generated through gravitational decoupling. (They) show that spin–curvature coupling and the hairy geometry can shift the evolved orbit away from the requested seed parameters, making the empirical orbital map essential for interpreting the dynamics. >>

<< Small-spin and geodesic trajectories remain close to regular behavior, whereas large-spin trajectories show stronger finite-time growth. A scan of the (S,β) plane shows that the instability does not grow monotonically, but appears in localized regions where the particle spin and the radial profile of the hair act cooperatively. Thus, the hairy background does not simply rescale the Kerr result; it reorganizes the strong-field phase-space region sampled by spinning particles. >>

Surojit Dalui, Xian-Hui Ge. Spin-Hair Induced Chaos of Spinning Test Particles in Rotating Hairy Black Holes. arXiv: 2605.19673v1 [gr-qc]. May 19, 2026.

https://arxiv.org/abs/2605.19673

Also: black hole, instability, particle, chaos, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, black hole, instability, particle, chaos, rotating hairy black hole.

# gst: free-surface deformations induced by three-dimensional turbulence.

<< ️(AA) report the experimental characterization of free-surface deformations generated by three-dimensional homogeneous and isotropic turbulence. Using Fourier transform profilometry in a jet-forced turbulent tank, (They) perform spatiotemporal measurements of the surface elevation field over a wide range of turbulence intensities. >>

<< ️The standard deviation of surface deformations scales linearly with subsurface velocity fluctuations. The spectra of surface deformations highlight the coexistence of two mechanisms: transient coherent structures (e.g., upwelling) contributing to the low-frequency, large-scale spectral components, and a passive response to subsurface turbulent pressure fluctuations responsible for the power-law spectral scaling. The wavenumber and frequency spectra of surface deformations exhibit similar power-law exponents (−2.5), suggesting the advection of turbulent structures at the free surface. >> 

<< ️(They) develop a linear response model based on the transfer function from the free surface to turbulent pressure fluctuations, incorporating wave-turbulent damping. The model successfully predicts the main features of the turbulent surface: spatiotemporal spectrum shape, similar spectrum power-law exponents (−7/3), and dominance of passive response over wave generation. These findings provide new insights into free-surface turbulence in regimes where turbulent velocities remain below the surface-breaking threshold. >>

Michaël Berhanu, Eric Falcon. Free-surface deformations induced by three-dimensional turbulence. arXiv: 2605.13654v1 [physics.flu-dyn]. May 13, 2026.

https://arxiv.org/abs/2605.13654

Also: fluctuations, waves, turbulence, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, free-surface turbulence, free-surface deformations, subsurface velocity fluctuations, wave-turbulent damping, surface-breaking threshold.

# gst: apropos of control by noise, diffusive transport from spatially correlated random phase kicks.

<< ️(AA) study the dynamics of a single-particle wave packet on a one-dimensional lattice subject to periodic random phase kicks with finite spatial correlation length. This stroboscopic setting provides a controllable model of dephasing in driven quantum systems. >>

<< ️Using a momentum-space formulation, (They) show that the evolution is governed by an accumulated phase whose structure determines the spreading of the wave packet. (They) find that the phase kicks strongly suppress ballistic transport and induce diffusion at long times. (They) derive an explicit analytical expression for the diffusion coefficient as a function of the correlation length, in excellent agreement with numerical simulations. >>

<< (Their) results uncover a simple mechanism by which spatially correlated phase noise controls quantum transport, and provide a quantitatively testable prediction for diffusion in periodically driven lattice systems. Possible experimental realizations in cold-atom platforms are discussed. >>

Pei Wang. Diffusive transport from spatially correlated random phase kicks. arXiv: 2605.06701v1 [cond-mat.mes-hall]. May 5, 2026.

https://arxiv.org/abs/2605.06701

Also: particle, waves, random, noise, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, particle, waves, randomness, noise, single-particle wave packet, periodic random phase kicks, spatially correlated phase noise, quantum transport.

# music: rhythm as an ordered phase of sound; how musical meter emerges in a statistical mechanical model.

<< ️(AA) develop a model of musical rhythm and meter based on optimizing the trade-off between human psychological preferences for perceiving repeated patterns in time with a desire for variety and complexity. >>

<< ️By mapping these competing preferences onto analogous quantities in statistical physics, (They) define an effective free energy which is minimized in the grand canonical ensemble. Using a mean field approximation, (They) observe phase transitions in the model from disordered events in time to orderings that closely reproduce those seen in music. >>

<< ️(They) then compare the range of rhythmic characteristics predicted by the model to a data set drawn from compositions by Johann Sebastian Bach, finding generally good quantitative agreement. The results provide a lens through which to study musical rhythm and a method for generatively producing rhythms. >>

Robert St. Clair, Jesse Berezovsky. Rhythm as an ordered phase of sound: How musical meter emerges in a statistical mechanical model. Phys. Rev. E 113, 054116. May 11, 2026.

https://journals.aps.org/pre/abstract/10.1103/kjfs-v245

arXiv: 2604.07476v1 [cond-mat.stat-mech]. Apr 8,2026.

https://arxiv.org/abs/2604.07476

Also: music, sound, jazz, brain, in https://www.inkgmr.net/kwrds.html 

Keywords: music, sound, jazz, brain, musical rhythms, perceiving repeated patterns, desire for variety and complexity, phase transitions, disordered events, J.S. Bach.

# gst: from chaos to synchrony in recurrent excitatory-inhibitory networks with target-specific inhibition.

<< ️Biological neural networks can operate in qualitatively distinct dynamical regimes, and transitions between these regimes are thought to underlie changes in computation and behavior. The seminal work of Sompolinsky, Crisanti, and Sommers (SCS) showed that random recurrent networks undergo a transition from quiescence to asynchronous chaos, establishing a paradigmatic link between random connectivity, dynamical instability, and internally generated fluctuations in neural circuits. >>

<< ️Here, (AA) extend this framework to two-population firing-rate networks with segregated excitatory and inhibitory neurons and target-specific inhibitory couplings that break excitation--inhibition balance. Using dynamical mean-field theory, (They) derive self-consistent equations for the macroscopic mean activities and autocorrelations, together with stability criteria distinguishing mean-driven and fluctuation-driven instabilities. (They) show that target-specific inhibition organizes the phase diagram into three qualitative classes: inhibition-dominated or strictly balanced networks display only quiescent activity and asynchronous chaos; excitation-dominated networks display persistent activity together with either synchronous chaos with non-vanishing mean activity or coherent oscillations, depending on the stability-matrix eigenvalues. >>

<< Crucially, coherent oscillations do not coexist with chaotic fluctuations around the periodic mean trajectory; rather, their onset suppresses the chaotic component, reminiscent of input-induced suppression of chaos. These results generalize SCS theory to recurrent networks with explicit excitatory--inhibitory structure and identify target-specific inhibition as a key control parameter for large-scale neural dynamics. >>

Carles Martorell, Rubén Calvo, Alessia Annibale, et al. From Chaos to Synchrony in Recurrent Excitatory-Inhibitory Networks with Target-Specific Inhibition. arXiv: 2605.14916v1 [cond-mat.dis-nn]. May 14, 2026.

https://arxiv.org/abs/2605.14916

Also: network, fluctuations, instability, transition, chaos, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, networks, fluctuations, instability, transitions, chaos, biological neural networks, random recurrent networks, asynchronous chaos, excitation--inhibition balance, target-specific inhibition.

# gst: rigorous ultimate scaling in rapidly rotating steady convection.

<< ️Rapidly rotating Rayleigh-Bénard convection admits a class of exact steady single-mode solutions describing high-amplitude convection cells. Using a matched asymptotic analysis in the high-Rayleigh-number limit, (AA) obtain a rigorous characterization of their bulk and boundary-layer structure, yielding explicit scaling laws for the Nusselt and Reynolds numbers, including their dependence on the horizontal wavenumber. >>

<< (They) show that, for suitable wavenumbers, these solutions attain the diffusivity-free ultimate scalings frequently assumed for geophysical and astrophysical convection, with additional enhancing logarithmic corrections. This reveals a specific mechanism through which rapidly rotating convection can approach ultimate heat transport via coherent columnar structures with well-defined horizontal scales. >>

Gabriel Hadjerci, Shingo Motoki, Genta Kawahara. Rigorous ultimate scaling in rapidly rotating steady convection. arXiv: 2605.05574v1 [physics.flu-dyn]. May 7, 2026.

https://arxiv.org/abs/2605.05574

Also: waves, vortex, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, waves, vortex, convection, convection cells, Rayleigh-Bénard convection, bulk and boundary-layer structure, rotation, rotating convection.

# gst: delay-induced chimera transitions via mode selection in a multiplex FitzHugh Nagumo network.

<< ️(AA) investigate delay-induced collective dynamics in a two-layer multiplex FitzHugh Nagumo network with nonlocal intra layer coupling and delayed inter layer interactions. While delay effects are often treated as secondary, (They) show that deterministic inter-layer delay alone can act as a control mechanism for spatial coherence. >>

<< ️Through systematic numerical simulations, (They) observe a clear transition as the delay parameter increases: fragmented incoherence evolves into chimera-like partial coherence, and eventually into a coherent traveling-wave state. This transition is consistently captured by spatial snapshots, space-time plots, and mean phase velocity profiles. >>

<< ️To explain this behavior, (They) analyze the stability of spatial Fourier modes and show that the delay term introduces a mode-dependent exponential factor in the characteristic equation. This term induces non-monotonic changes in modal stability, effectively acting as a mode-selection mechanism: intermediate delays selectively destabilize a subset of modes, producing chimera-like coexistence, while larger delays suppress incoherent modes and restore global coherence. >>

<< ️(Their) results demonstrate that inter-layer delay provides a simple and robust mechanism for controlling pattern formation in multiplex excitable networks, offering new insight into delay driven synchronization phenomena. >>

Hui Wu. Delay-induced chimera transitions via mode selection in a multiplex FitzHugh Nagumo network. arXiv: 2605.04430v1 [physics.bio-ph]. May 6, 2026.

https://arxiv.org/abs/2605.04430

Also: chimera, network, transition, waves, pause, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, chimera, networks, transitions, waves, pause, delay, inter-layer delay, delay-induced collective dynamics, two-layer multiplex excitable network.