# gst: spatially heterogeneous noise restructures flocking into geometry-locked and vortex states.

<< ️Spatially heterogeneous environments continually challenge the ability of active matter to sustain coherent collective motion. Understanding how collective motion remains robust under changing environments is central to both the functioning of biological systems and the design of smart active matter. >>

<< ️Here, (AA) extend the Vicsek model to include a circular non-noisy region surrounded by a noisy environment - a configuration in which the noise difference sets up a contrast in local directional order between the two regions. (They) find that, as the surrounding noise is increased, the system passes through three distinct dynamical regimes: (i) conventional global flocking at low noise; (ii) geometry-locked motion, aligned with simulation boundaries, at intermediate noise; and (iii) vortical motion within the non-noisy region at high noise. >>

<< Extending the environment to multiple non-noisy regions, (AA) find that the geometry-locked regime can develop a directional coupling, while the vortex mode leads to antiferromagnetic order between the regions. Taken together, (Their) results demonstrate that the spatial modulation of order and disorder offers a powerful and generic strategy for steering active matter, aligning with recent experimental observations of active particles in patterned landscapes. >>

Ankush Semwal, Mahak Poonia, Pintu Patra. Spatially heterogeneous noise restructures flocking into geometry-locked and vortex states. arXiv: 2607.05870v1 [cond-mat.soft]. Jul 7, 2026.

https://arxiv.org/abs/2607.05870

Also: particle, noise, vortex, order, disorder, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, particle, noise, vortex, order, disorder, active matter, steering active matter, coherent collective motion, noisy environment, vortical motion, geometry-locked regime. 

# life: apropos of bifurcations from stable consensus to periodic multiconsensus, consensus-breaking global Hopf bifurcation in memory-based Multi-Agent Systems.

<< ️This (AA) dissertation provides the first systematic study of symmetric consensus-breaking bifurcation to periodic multiconsensus in multi-agent systems. It analyzes this for three classes of multi-agent systems based on three different types of memory, whose closed-loop dynamics equations form delay differential equations of retarded type, neutral type, and pseudoneutral type - a subclassification of retarded type equations introduced in this dissertation which bridges retarded and neutral type delay equations. >>

<< ️Equivariant twisted degree is used to analyze the symmetric global Hopf bifurcation problem in these systems, i.e. bifurcation from a stable consensus to periodic multiconsensus. This shows how the effects of memory allow self-organizing agents to move beyond mere stationary consensus. Theoretical results for the global Hopf bifurcation and symmetric classification of periodic multiconsensus solutions across all three systems are provided, and numerical results are conducted to both validate and enhance the theoretical predictions by providing stability information on the branches which is not obtainable by the degree alone. >>

<< These principles are demonstrated in three real-world applications: one involving the control of formations of UAVs (Unmanned Aerial Vehicles), allowing them to maintain their overall spatial relationships while dancing in complex selectable oscillations; and two more in networked asset markets featuring different traders with different memory-based strategies, showing how similar mechanisms can be responsible for economic cycles of bubbles and crashes. >>

<< Finally, (AA) also numerically investigate resonant double Hopf bifurcations in the neutral delay system, showing strong evidence of a breakdown to chaos via the Ruelle-Takens-Newhouse scenario and the existence of riddled basins. >>

Casey Maikalani Crane. Consensus-Breaking Global Hopf Bifurcation in Memory-Based Multi-Agent Systems. Dissertation. The University of Texas at Dallas. Aug 2026. Supervising Professor: Wieslaw Krawcewicz, Chair.  arXiv: 2607.02388v1 [math.DS]. Jul 2, 2026.

https://arxiv.org/abs/2607.02388

Also: network, swarm, bubble, crack, chaos, transition, dance, in https://www.inkgmr.net/kwrds.html 

Keywords: life, gst, networks, swarm, bubbles, crack, chaos, transitions, dance, multi-agent systems, symmetric consensus-breaking bifurcation, stable consensus, periodic multiconsensus, symmetric global Hopf bifurcation, self-organizing agents, economic cycles of bubbles and crashes, riddled basins. 

# gst: hyperuniform systems are maximally irreversible.

<< ️Hyperuniform systems, defined by the anomalous suppression of large-scale density fluctuations, are a paradigm of non-equilibrium self-assembly. While mechanisms underlying the self-assembly of hyperuniform states have been widely studied, the energetics of this process remain unexplored. This raises a fundamental question: what is the energetic cost of self-assembling a hyperuniform system? >>

<< ️Here, (AA) address this question across several noisy particle systems drawn from soft matter and machine learning, in which hyperuniformity can be induced by tuning noise correlations. Despite their distinct microscopic dynamics, (They) uncover a universal behavior across all systems: hyperuniform states are maximally irreversible, as quantified by the entropy production rate. >>

<< ️Further, (AA) develop a path integral formulation of the entropy production rate directly from the microscopic dynamics, which explains (Their) observations. (AA) work establishes a direct link between emergent long-range structure and time irreversibility and opens a new avenue of probing the energetic cost of hyperuniform self-assembly, ubiquitous across physics, biology, and materials science. >>

Mathias Casiulis, Satyam Anand, Stefano Martiniani. Hyperuniform systems are maximally irreversible.  arXiv: 2607.07411v1 [cond-mat.soft]. Jul 8, 2026.

https://arxiv.org/abs/2607.07411

Also: particle, disorder & fluctuations, self-assembly, noise, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, particles, fluctuations, self-assembly, noise, transitions, tuning noise correlations, entropy production rate, long-range structure.

# life: apropos of anomalous (meta)mechanical responses, from active to odd to smart matter.

<< ️The study of active matter has reshaped our understanding of collective states of matter far from equilibrium by proving that energy pumped into the microscopic scale leads to order on the macroscopic scale, collective motion, and anomalous mechanical responses. >>

<< More recently, the discovery of odd elasticity and nonreciprocal mechanical couplings has extended these ideas to solid-like active systems, revealing materials with nonconservative elastic response. >>

<< ️Simultaneously, innovative developments in swarm robotics, programmable metamaterials, and learning algorithms have led to the emergence of a new frontier in which collective behavior and mechanical response are no longer fixed by design, but adapted, optimized, and learned toward functional goals. >>

<< ️This perspective proposes a unifying trajectory, from active to odd to smart matter, organized along two intertwined axes: the traditional gas-liquid-solid progression of condensed matter, and the more recent paradigm shift from spontaneous collective dynamics to task-driven functionality. >> 

<< ️(AA) try to highlight emerging principles, conceptual shifts, and open challenges that come along this trajectory, and argue that learning may play the role of a specific form of emergence, which could advantageously replace the more traditional view of control, at least in the realm of physics. >>

Olivier Dauchot. From active to odd to smart matter. Phys. Rev. E 114, 011001. Jul 8, 2026.

https://journals.aps.org/pre/abstract/10.1103/tzyr-t47w

arXiv: 2607.06051v1 [cond-mat.soft]. Jul 7, 2026.

https://arxiv.org/abs/2607.06051

Also: 'a sciogliere nella metaciotola l' eccessivo rigido neurodistico ...', in: Voli in codice quasistocastico. Notes (quasistochastic poetry). Dec 09, 2004.

https://inkpi.blogspot.com/2004/12/1798-voli-in-codice-quasistocastico.html

Also: Anagrammanti neurali. Notes (quasistochastic poetry). Sep 09, 2006.

https://inkpi.blogspot.com/2006/09/2056-anagrammanti-neurali.html

Also: self-assembly, elastic, disorder, swarm, swarmalators, ai (artificial intell) (bot), brain, game, in https://www.inkgmr.net/kwrds.html 

Keywords: life, self-assembly, elasticity, disorder, swarm, swarmalators, ai,  artificial intelligence, bot, brain, games, active matter, collective states, anomalous responses, odd elasticity, nonreciprocal couplings, nonconservative elastic response, spontaneous collective dynamics, task-driven functionality, learning as a specific form of emergence, learning & adaptation without a brain.

# gst: riding the wave; polymers in time-dependent nonequilibrium baths.

<< Directed transport is a characteristic feature of numerous biological systems in response to signals such as nutrient and chemical gradients. These signals often depend on time owing to the high complexity of interactions in these systems. >>

<< In this study, (AA) focus on the steady-state behavior of polymeric systems responding to such time-dependent signals. (They) model them as ideal Rouse polymers submerged in a nonequilibrium bath, which is described by a spatially and temporally varying self-propulsion wave field. Through a coarse-graining analysis, (They) show that these polymers display rich emergent response to the temporal stimuli as a function of their length and topology. >>

<< In particular, long polymers and structures with ring and star topologies ride the wave, displaying a positive drift in the direction of the wave, whereas shorter polymers and fully connected structures drift against the wave signal. (They) confirm these analytical predictions with robust numerical simulations, showing that the response of polymeric systems to temporal stimuli can be controlled by the topology or the length of the polymer. >>

Bhavesh Valecha, Jens-Uwe Sommer, Abhinav Sharma. Riding the wave: Polymers in time-dependent nonequilibrium baths. Phys. Rev. E 114, 015408. Jul 9, 2026.

https://journals.aps.org/pre/abstract/10.1103/9z9n-9p57

arXiv: 2603.02777v1 [cond-mat.soft]. Mar 3, 2026.

https://arxiv.org/abs/2603.02777

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

Keywords: gst, waves, polymers, topology, directed transport, steady-state behavior, self-propulsion wave field. 

# 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.