# gst: spatial self-organization driven by temporal noise.

<< ️The counterintuitive emergence of order from noise is a central phenomenon in science, ranging from pattern formation and synchronization to order-by-disorder in frustrated systems. While large-scale spatial self-organization induced by local spatial noise is well studied, whether temporal noise can also drive such organization remains an open question. >>

<< ️Here, by studying interacting particle systems, (AA) show that temporally correlated noise can lead to a self-organized state with suppressed long-range density fluctuations, or hyperuniformity. Further, (They) develop a fluctuating hydrodynamic theory that quantitatively explains the origin of this phenomenon. >>

<< ️Finally, by casting the dynamics as a stochastic optimization problem, (They) show that temporal correlations lead to better solutions, akin to perturbed gradient descent in neural networks -- where noise is injected during training to escape poor minima. This reveals a striking correspondence between perturbed gradient descent dynamics on the energy landscapes of particle systems and the loss landscapes of neural networks. >>

Satyam Anand, Guanming Zhang, Stefano Martiniani. Spatial self-organization driven by temporal noise. arXiv: 2601.23098v1 [cond-mat.soft]. Jan 30, 2026.

https://arxiv.org/abs/2601.23098

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

Keywords: gst, self-assembly, noise, order, disorder, disorder & fluctuations, particles, networks, neural networks, spatial noise, temporal noise, noise-driven self-organization.

# phys: probing quantum mechanics with nanoparticle matter-wave interferometry.

<< ️The quantum superposition principle is a fundamental concept of physics and the basis of numerous quantum technologies. Yet, it is still often regarded counterintuitive because we do not observe its key features on the macroscopic scales of our daily lives. It is, therefore, interesting to ask how quantum properties persist or change as we increase the size and complexity of objects. >>

<< ️A model test for this question can be realized by matter-wave interferometry, in which the motion of individual massive particles becomes delocalized and needs to be described by a wave function that spans regions far larger than the particle itself. Over the years, this has been explored with a series of objects of increasing mass and complexity and a growing community aims at pushing this to ever larger limits. >>

<< ️Here (AA) present an experimental platform that extends matter-wave interference to large metal clusters, a qualitatively new material class for quantum experiments. (They) specifically demonstrate quantum interference of sodium nanoparticles, which can each contain more than 7,000 atoms at masses greater than 170,000 Da. They propagate in a Schrödinger cat state with a macroscopicity of μ = 15.5, surpassing previous experiments by an order of magnitude. >>

Sebastian Pedalino, Bruno E. Ramírez-Galindo, Richard Ferstl, et al. Probing quantum mechanics with nanoparticle matter-wave interferometry. Nature 649, 866–870. Jan 21, 2026.

https://www.nature.com/articles/s41586-025-09917-9

Also: keyword 'quantum' in FonT

https://flashontrack.blogspot.com/search?q=quantum

Keywords: particles, quantum mechanics, quantum superposition.

# gst: rising bubbles draw surface patterns.

<< ️Small bubbles rising in a chain can self-organize into regular patterns upon reaching a liquid's free surface. This phenomenon is investigated (by AA) through direct numerical simulations. By varying the bubble release period, distinct branching patterns characterized by different numbers of arms are observed. These macroscopic patterns are found to stem from localized interactions between the bubbles, the free surface, and the surrounding liquid flow. >>

<< A heuristic model is proposed that quantitatively relates the number of arms to the bubble release period and predicts the probability of observing specific arm counts. This (AA) study provides insights into broader nonlinear pattern formation and self-organization phenomena. >>

Dabao Li, Lang Qin, Zhigang Zuo, et al. Rising bubbles draw surface patterns: A numerical study. Phys. Rev. Fluids 11, 023602. Feb 6, 2026.

https://journals.aps.org/prfluids/abstract/10.1103/bd6d-fwmn

arXiv: 2509.01315v2 [physics.flu-dyn]. Jan 27, 2026.

https://arxiv.org/abs/2509.01315

Also: bubble, self-assembly, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, bubble, self-assembly, branching patterns.

# gst: fractals in rate-induced tipping.

<< ️When parameters of a dynamical system change sufficiently fast, critical transitions can take place even in the absence of bifurcations. This phenomenon is known as rate-induced tipping and has been reported in a variety of systems, from simple ordinary differential equations and maps to mathematical models in climate sciences and ecology. In most examples, the transition happens at a critical rate of parameter change, a rate-induced tipping point, and is associated with a simple unstable orbit (edge state). >>

<< ️In this work, (AA) show how this simple picture changes when non-attracting fractal sets exist in the autonomous system, a ubiquitous situation in non-linear dynamics. (They) show that these fractals in phase space induce fractals in parameter space, which control the rates and parameter changes that result in tipping. (They) explain how such rate-induced fractals appear and how the fractal dimensions of the different sets are related to each other. >>

<< ️(AA) illustrate (Their) general theory in three paradigmatic systems: a piecewise linear one-dimensional map, the two-dimensional Hénon map, and a forced pendulum. >>

Jason Qianchuan Wang, Yi Zheng, Eduardo G. Altmann. Fractals in rate-induced tipping. arXiv: 2601.16373v1 [nlin.CD]. Jan 23, 2026.

https://arxiv.org/abs/2601.16373

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

Keywords: gst, transitions, pendulum, forced pendulum, fractals, absence of bifurcations, rate-induced tipping, criticality.

# gst: directionality and node heterogeneity reshape criticality in hypergraph percolation.

<< Directed and heterogeneous hypergraphs capture directional higher-order interactions with intrinsically asymmetric functional dependencies among nodes. As a result, damage to certain nodes can suppress entire hyperedges, whereas failure of others only weakens interactions. Metabolic reaction networks offer an intuitive example of such asymmetric dependencies. >>

<< Here (AA) develop a message-passing and statistical mechanics framework for percolation in directed hypergraphs that explicitly incorporates directionality and node heterogeneity. Remarkably, (They)  show that these hypergraph features have a fundamental effect on the critical properties of hypergraph percolation, reshaping criticality in a way that depends on network structure. >>

<< Specifically, (AA) derive anomalous critical exponents that depend on whether node or hyperedge percolation is considered in maximally correlated, heavy-tailed regimes. These theoretical predictions are validated on synthetic hypergraph models and on a real directed metabolic network, opening new perspectives for the characterization of the robustness and resilience of real-world directed, heterogeneous higher-order networks. >>

Yunxue Sun, Xueming Liu, Ginestra Bianconi. Directionality and node heterogeneity reshape criticality in hypergraph percolation. arXiv: 2601.20726v1 [cond-mat.dis-nn]. Jan 28, 2026.

https://arxiv.org/abs/2601.20726

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

Keywords: gst, networks, transitions, criticality, hypergraph, percolation, anchor nodes.

# gst: anisotropic active Brownian particle in two dimensions under stochastic resetting.

<< ️(AA) study the dynamical behavior of an anisotropic active Brownian particle subjected to various stochastic resetting protocols in two dimensions. The motion of shape-asymmetric active Brownian particles in two dimensions leads to anisotropic diffusion at short times, whereas rotational diffusion causes the transport to become isotropic at longer times. >>

<< ️(They) have considered three different resetting protocols: (1) complete resetting, when both position and orientation are reset to their initial states, (2) only the position is reset to its initial state, and (3) only orientation is reset to its initial state. >>

<< ️(They) reveal that orientational resetting sustains anisotropy even at late times. When both the spatial position and orientation are subject to resetting, a complex position probability distribution forms in the steady state. This distribution is shaped by factors such as the initial orientation angle, the anisotropy of the particle, and the resetting rate. >>

<< ️When only the translational degrees of freedom are reset, while the particle's orientation evolves naturally, the steady state no longer depends on particle asymmetry. In contrast, if only the orientation is reset, the long-term probability distribution becomes Gaussian, using an effective diffusion tensor—containing nondiagonal elements—defined by the resetting rate. More broadly, the interaction between translational and rotational dynamics, in combination with stochastic resetting, produces distinct behaviors at late times that are absent in symmetric particles. >>

<< ️Given recent progress in experimental resetting techniques, these (AA) results could be highly useful for controlling asymmetric active colloids, such as in self-assembly applications. >>

Anirban Ghosh, Sudipta Mandal, Subhasish Chaki. Anisotropic active Brownian particle in two dimensions under stochastic resetting. Phys. Rev. E 113, 014142. Jan 29, 2026.

https://journals.aps.org/pre/abstract/10.1103/11f6-srsx

arXiv: 2501.05149v2 [cond-mat.stat-mech]. Nov 25, 2025. 

https://arxiv.org/abs/2501.05149

Also: particle, self-assembly, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, particle, self-assembly, stochastic resetting.

# gst: nonlocal Kramers-Moyal formulas and data-driven discovery of stochastic dynamical systems with multiplicative Lévy noise.

<< ️Traditional data-driven methods, effective for deterministic systems or stochastic differential equations (SDEs) with Gaussian noise, fail to handle the discontinuous sample paths and heavy-tailed fluctuations characteristic of Lévy processes, particularly when the noise is state-dependent. >>

<< ️To bridge this gap, (AA) establish nonlocal Kramers-Moyal formulas, rigorously generalizing the classical Kramers-Moyal relations to SDEs with multiplicative Lévy noise. These formulas provide a direct link between short-time transition probability densities (or sample path statistics) and the underlying SDE coefficients: the drift vector, diffusion matrix, Lévy jump measure kernel, and Lévy noise intensity functions. >>

<< This (AA) work provides a principled and practical toolbox for discovering interpretable SDE models governing complex systems influenced by discontinuous, heavy-tailed, state-dependent fluctuations, with broad applicability in climate science, neuroscience, epidemiology, finance, and biological physics. >>

Yang Li, Jinqiao Duan. Nonlocal Kramers-Moyal formulas and data-driven discovery of stochastic dynamical systems with multiplicative Lévy noise. arXiv: 2601.19223v1 [math.DS]. Jan 27, 2026.

https://arxiv.org/abs/2601.19223

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

Keywords: gst, noise, randomness, transitions, fluctuations.